Permanent Magnet Brushless Dc Motor Drives And Controls 1118188330 [626534]

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Permanent Magnet Brushless Dc Motor Drives And Controls 1118188330 [626534]

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PERMANENT MAGNET
BRUSHLESS DC MOTORDRIVES AND CONTROLS

PERMANENT MAGNET
BRUSHLESS DC MOTORDRIVES AND CONTROLS
Chang-liang Xia
Tianjin University, P.R. China
John Wile y & Sons Sin gapore Pte. Ltd.

This edition ﬁrst published 2012
/C2112012 Science Press. All rights reserved.
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MATLAB /C210is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not
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Library of Congress Cataloging-in-Publication DataXia, Chang-liang.
Permanent magnet brushless DC motor drives and controls / Chang-liang Xia.
p. cm.
Includes bibliographical references and index.
ISBN 978-1-118-18833-0 (cloth)
1. Electric motors, Direct current. 2. Permanent magnet motors. 3. Electric motors, Brushless. I. Title.
TK2681.X53 2012
621.46–dc23
2012000619
Set in 10/12 pt Times by Thomson Digital, Noida, India

Contents
About the Author xi
Preface xiii
List of Nomenclature xv
1 Introduction 1
1.1 History of BLDC Motors 11.2 Applications for BLDC Motors 3
1.2.1 Automotive BLDC Motor 4
1.2.2 BLDC Motor in Aerospace 5
1.2.3 BLDC Motor in Household Appliances 6
1.2.4 BLDC Motor in Of ﬁce Automation 7
1.2.5 BLDC Motor in Other Industries 8
1.3 Advances in BLDC Motor Drives 8
1.3.1 Position-Sensorless Control 9
1.3.2 Torque-Ripple Reduction 10
1.3.3 Hardware Implementation 12
1.4 Future of BLDC Motor Drives 15
1.4.1 Impacts of Power Electronics and Microprocessors on
BLDC Motor 15
1.4.2 Permanent Magnet and Design Considerations 17
1.4.3 New Types of BLDC Motor 18
1.4.4 Applications of Advanced Control Strategies 20
1.5 Other Kinds of PM Motors 20Questions 21
References 21
2 Mathematical Model and Characteristics Analysis of
the BLDC Motor 25
2.1 Structure and Drive Modes 25
2.1.1 Basic Structure 25
2.1.2 General Design Method 28
2.1.3 Drive Modes 28
2.2 Mathematical Model 33

2.2.1 Differential Equations 33
2.2.2 Transfer Functions 40
2.2.3 State-Space Equations 45
2.3 Characteristics Analysis 47
2.3.1 Starting Characteristics 47
2.3.2 Steady-State Operation 48
2.3.3 Dynamic Characteristics 52
2.3.4 Load Matching 56
2.3.5 Commutation Transients 58
Questions 62
References 62
3 Simulation for BLDC Motor Drives 63
3.1 S-Function Simulation 633.2 Graphical Simulation 69
3.2.1 Simulation of Double Closed-Loop Speed-Control System 72
3.2.2 Advanced Conduction of Phase Current for
BLDC Motor Control 76
Questions 82
References 82
4 Speed Control for BLDC Motor Drives 83
4.1 Introduction 83
4.1.1 PID Control Principle 83
4.1.2 Antiwindup Controller 86
4.1.3 Intelligent Controller 88
4.1.4 Representations of Uncertainty 89
4.2 Advanced Speed Control for BLDC Motor Drives 90
4.2.1 Fuzzy Control 90
4.2.2 Neural-Network Control 94
4.2.3 Genetic Algorithm Optimization Control 102
4.2.4 Sliding-Mode Variable Structure Control 107
4.2.5 Grey Control 113
4.2.6 Other Intelligent Control Strategies 117
4.3 Inﬂuences of Machine Parameters on Dynamic Response
and Speed Range 119
4.3.1 Armature Resistance 119
4.3.2 Armature Inductance 120
4.3.3 Rotor Inertia 122
4.4 Practical Issues on Implementation 123
4.4.1 Type of Power Switches and Circuit Forms 123
4.4.2 Detection of Rotor Position 123
4.4.3 Braking Circuit and Protection Circuit 123
4.4.4 Antidisturbance Measures of Software and Hardware 124
Questions 124
References 124vi Contents

5 Analysis and Reduction of Torque Ripple 127
5.1 Cogging Torque-Ripple-Minimization Techniques Analysis 127
5.1.1 Skewing Slots and Magnets 129
5.1.2 Embedding Magnetic Slot Wedges 130
5.1.3 Auxiliary Slots and Teeth 130
5.1.4 Fractional Number of Slots Per Pole 130
5.2 Torque-Ripple Reduction with Time-Sharing Commutation Strategy 131
5.2.1 Time-Sharing Commutation Strategy 131
5.2.2 Analysis of Time-Sharing Commutation Strategy 140
5.2.3 Optimal Time-Sharing Commutation 144
5.3 Torque-Ripple Reduction with Active Disturbance Rejection Control 146
5.3.1 Principles of ADRC 146
5.3.2 ADRC Controller Design 147
5.3.3 Experimental Results 150
5.4 Torque-Ripple Reduction with BP Neutral Network 152
5.4.1 BP Neural Network 152
5.4.2 Self-Tuning Regulator 155
5.4.3 Experimental Results 155
5.5 Motor Optimization and Torque-Ripple Minimization with Fuzzy Niche
Genetic Algorithm 1575.5.1 Platform-Width Calculation of Back-EMF Waveform 158
5.5.2 Fuzzy Niche Genetic Algorithm 161
5.5.3 Optimization Design of BLDC Motors 163
Questions 165
References 165
6 Sensorless Control for BLDC Motor Drives 167
6.1 Principle of Sensorless Position Detection 167
6.1.1 Back-EMF-Based Method 168
6.1.2 Flux-Linkage-Based Method 178
6.1.3 Inductance-Based Method 179
6.1.4 Intelligence-Based Method 180
6.2 Sensorless Control Strategy 181
6.2.1 Sensorless Control Based on Disturbance Observer 181
6.2.2 Sensorless Control Based on a Kalman Filter 187
6.2.3 Sensorless Control Based on Sliding-Mode Observer 191
6.2.4 Position-Sensorless Control Using Wavelet Neural Network (WNN) 196
6.3 Starting Process for Sensorless Control 200
6.3.1 Determination of Initial Rotor Position at Standstill 200
6.3.2 Starting Methods for Sensorless Control 201
Questions 206
References 206
7 Realization of BLDC Motor Drives 209
7.1 Main Circuit 209
7.2 Driving Circuit 212Contents vii

7.2.1 MOSFET Driving Circuit 212
7.2.2 IGBT Driving Circuit 215
7.2.3 Intelligent Power Module (IPM) 215
7.3 Rotor-Position Sensor Circuit 2167.4 Microprocessor Control Circuit 218
7.4.1 Introduction 218
7.4.2 MCU Control Circuit 220
7.4.3 DSP Control Circuit 223
7.5 Protecting Circuit 224
7.5.1 Overvoltage Protection 224
7.5.2 Overcurrent Protection 229
7.5.3 Logic Protection 229
7.5.4 Other Protection Circuits 230
7.6 Sensorless Control Circuits 232
7.6.1 Voltage Detection 232
7.6.2 Filtering and Phase Shifting 234
7.6.3 Current Detection 236
7.7 ASIC for BLDC Motor Drives 238
7.7.1 MC33033 238
7.7.2 TB6537P 240
7.8 Software Design 246
7.8.1 BLDC Motor Driving with Position Sensor 246
7.8.2 BLDC Motor Driving Without Position Sensor 247
7.8.3 Reliability 248
7.9 EMC Design 250
7.9.1 EMC Design of High-Voltage Part 250
7.9.2 EMC Design of Low-Voltage Part 251
Questions 253
References 253
8 Applications of BLDC Motor Drives 255
8.1 Elevator-Door Control System 255
8.1.1 Introduction 255
8.1.2 Hardware Design 259
8.1.3 Software Design 261
8.2 Elevator Traction Machine System 265
8.2.1 Introduction 265
8.2.2 Characteristics of a BLDC Motor Gearless Elevator
Traction Machine 266
8.2.3 The Technical Requirements of the Elevator Traction
Machine 267
8.2.4 Hardware Design 268
8.2.5 Software Design 269
8.3 Inverter Air Conditioner 270
8.3.1 Control Function of Indoor Controller 271
8.3.2 Control Function of Outdoor Controller 271viii Contents

8.4 Electric Vehicles 272
8.4.1 Pure Electric Vehicles 272
8.4.2 Hybrid Electric Vehicles 273
8.5 Electric Bicycles 274
8.6 Others 275
8.6.1 The Applications in the Fan and Pump 275
8.6.2 The Application in the Washing Machine 276
8.6.3 The Application in Medical Instrumentation 277
Questions 277
References 277
Index 279Contents ix

About the Author
Chang-liang Xia was born in Tianjin, China, in 1968. He received his B.S.
degree from Tianjin University, China, in 1990, and his M.S. and Ph.D.degrees from Zhejiang University, China, in 1993 and 1995 respectively,all in electrical engineering.
He is currently a Professor in the School of Electrical Engineering and
Automation, Tianjin University. In 2008, he became “Yangtze Fund
Scholar” Distinguished Professor and is currently supported by the
National Science Fund for Distinguished Young Scholars.
His research interests include wind power generation system and intelligent control, motor
control and power electronics, novel electric machine and intelligent control, and electricalenergy saving control technology. He has published more than 180 papers in these areas.In addition, he has presided over more than 40 scientiﬁc research projects as the primeprincipal of the project. As the ﬁrst inventor, he holds 13 authorized national invention patentsof P. R. C.
In 2011, Prof. Xia was awarded the Second Prize of National Science and Technology
Advancement (Rank First) for his work “Study and Application of High-efﬁciency MachineSystem Optimal Design under Complicated Constrains.” He was also awarded the First Prizeof Science and Technology Advancement from Tianjin Province (Rank First) twice, in 2005and 2008, respectively. In addition, he has awarded the First Prize of Science and TechnologyAdvancement from the National Ministry of Education (Rank First) in 2009.
Prof. Xia is a member of China Electrotechnical Society (CES). He is an editorial member
of Transactions of China Electrotechnical Society, and the Advanced Technology of Electrical
Engineering and Energy as well. He is also a deputy committee director in Electric Control
System and Equipment Committee of CES, Electrical Automation Committee of ChineseAssociation of Automation, and Sub-committee on Electrical Machinery and ElectricalAppliances of the China Machinery Industry Federation. In addition, he is the Vice Chairmanof the Tianjin Society of Electrical Engineering.

Preface
In the past ﬁve years, the permanent magnet brushless motor market has grown much faster
than the other small-motor markets. Thus, it is essential for electrical and electromechanicalresearchers to stay up-to-date on the latest developments in modern electrical motors anddrives, including their control, simulation and hardware implementation.
I have been engaged in the design, modeling, control and application of BLDC motors
for more than 15 years. In this ﬁeld, I have published more than 50 papers in refereed journals and
conferences. I have also been an instructor for 6 PhD students and 15 Master’s students who havebeen researching on this subject. This book is an integration of many achievements from thecorresponding projects supported by the National Natural Science Foundation of China, Ministryof Education of P. R. C, and the Tianjin Municipal Science and Technology Commission.
Thus, this book is an academic book based on the above research work of the BLDC motor
drives over more than a decade. It includes many advances on the control of BLDCmotor drives, such as intelligent control, sensorless control, torque ripple reduction, hardware
implementation, and so on. Some materials of this book have been used in Tianjin University
for the Masters course – “Electrical Motor Drives and Power Electronics” since 2002. In 2009,most of these materials were published in a Chinese book by Science Press, which was entitledBrushless DC Motor Control Systems . It has been used as a textbook for the graduate course –
“Intelligent Control of Electrical Machines” in Tianjin University since 2009.
In this English edition, new materials have been added to cover the rapid advances of BDLC
motor drives. Thus the book is rewritten and organized as follows:
Chapter 1 provides an introduction to the history, current situation and development
prospects of BLDC motor drives and control.
Chapter 2 presents the basic principles and the mathematical models of BLDC motors. The
related mechanical properties, regulation characteristics and commutation transient processare investigated.
Chapter 3 is devoted to the modeling and control of BLDC motors based on MATLAB.
Practical examples are given and analyzed.
Chapter 4 focuses on the analysis of the most important issues related to the speed-control
system of BLDC motors, such as the classic double-loop speed-control system, various speed
control methods based on modern intelligent algorithms, the inﬂuences of the motor internal
parameters on system performances, and so on.
One of the most important research directions of BLDC motors, that is the analysis and
suppression of torque ripple, is investigated in Chapter 5. The causes and types of torque

ripple are analyzed. The cogging torque ripple and its minimization methods are studied.
Further, torque ripple reduction approaches based on ADRC, BP neural networks and fuzzy
genetic algorithms are presented, respectively.
Sensorless control, another research focus of BLDC motor control systems, is considered
in Chapter 6. Based on modern control theory and intelligent algorithm, various typesof position-detection methods of BLDC motor and a variety of control methods withoutposition sensors are studied. In addition, different means for motor starting and ways to widenthe speed range are proposed.
The software/hardware design approaches and related key technologies for the MCU- and
DSP-based BLDC motor control systems are addressed in Chapter 7.
Chapter 8 describes the particular applications of the BLDC motors in elevator doors,
elevator traction machines, inverter air conditioners, electric vehicles, electric bicycles, etc.
In addition, questions are supplied at the end of each chapter to facilitate class discussions
and as home assignments. Supplementary PowerPoint slides and simulation materials forstudying and teaching are provided too. Readers can download them from the book’s website(www.wiley.com/go/xia/dcmotor).
In future, permanent-magnet BLDC motor will be used in more applications, especially in
those that require a high level of accuracy and performance. Also, key technologies such as
sensorless control and torque ripple reduction will be more mature. Thus, this book will allow
people who are engaged in the control of BLDC motor drives to gain more knowledge aboutthe principles, simulation and hardware implementation of BLDC motor drives and controls.I hope it will also be useful for other electrical engineers and students who are related to thistopic. Some special issues, such as sensorless control, intelligent control, torque ripplereduction and hardware implementation will be valuable for the control of other motors.New progress in power electronics, control theory, and MCU will propel further developmentof the BLDC motor drives and controls.
This book is intended to be used as a reference book for related technicians in the ﬁeld of
design and control for BLDC motor drives, and a textbook for undergraduates and post-graduates who have learned the following courses: electrical machines, automatic control,motor control, MCU & DSP, and so on.
Over the years, the help and support from Associate Prof. Hong-wei Fang, Associate
Prof. Wei Chen, Dr. Qiang Geng, Dr. Yan Yan, Dr. Peng Song and Dr. Ying-fa Wang ofTianjin University have contributed greatly to the success of this book.
Finally, I must also thank my wife Tingna Shi and my son Yuxuan Xia for their love and
understanding, without which this task could not have been brought to fruition.
Chang-liang Xiaxiv Preface

List of Nomenclature
A real-time value of torque subsystem during its operation; the electrical
load
B magnetic ﬂux density
Bd magnetic load
B(y) radial ﬂux density in air gap of PM rotor, which is in trapezoidal
distribution along y
Bm maximum value of PM density distribution in air gap
Bv viscous friction coefﬁcient
bt stator tooth width
Ci center vector of Gaussian function at the ith hidden layer unit
Cj center of the jth hidden layer unit that is the closest to the input sample
D1 diameter of armature; stator outer diameter
D1,D2,… … ,D6diodes
Di1 stator inner diameter
dl wire diameter of the winding
E phase back-EMF
E0 gradient of the sloping part for back-EMF
eA,eBandeC phase back-EMF of phase A, phase B, and phase C, respectively
ec rate of change for motor speed error e
ei output error of the ith network
eL line back-EMF
emax largest positive error value in basic domain
esr stable error
ex phase back-EMF, in which subscript xdenote phase A, B and C
ey output of the fuzzy controller
ecx phase-induced EMF
f frequency of the back-EMF; ﬁtness of the mutation individuals
favg average ﬁtness for per generation population
fA(y),fB(y),fC(y) waveform coefﬁcient of back-EMF
fi ﬁtness of ith individual
fmax maximum population ﬁtness
f0larger ﬁtness in two crossover individuals
fst starting commutation frequency

fxt resonator frequency
g feedback gain coefﬁcient
HA,HB,HC output signals of Hall position sensors
H conjugate and transpose symbol
hm alnico thickness
I current amplitude
I phase current matrix
i steady phase current; detected armature current
ix phase current, in which subscript xdenote phase A, B and C
i/C3reference current
J moment of inertia
K gain constant of the integrator; sliding gain
KD differential coefﬁcient
KI integral coefﬁcient
KP proportional gain
Ke10,Kec0,Ku0 base values
K1,K2,K3 ﬁne-tuning parameters (all are non-negative)
KT torque coefﬁcient
ke coefﬁcient of line back-EMF, ke¼2pcm¼4pNSB m
Ke1,Kec quantization factors
Ke1 error quantization factor
Kec error change quantization factor
Ku scaling factor
L inductance; length
L0 nominal inductance
L1 stator iron core length
LA self inductance of phase A
Laf armature effective length
La equivalent line inductance of winding, La¼2(L–M )
L0equivalent phase inductance of winding, L0¼L/C0M
M population size; mutual inductance of phase winding
MAB,MAC,MBC phase mutual inductance
Mp system maximum overshoot
M controllability matrix
N number of winding turns
Na peripheral speed
Nr sampling frequency
n motor or rotor speed; numbers
nN rated speed
n/C3reference speed
P0 no-load loss, including the core loss and mechanical friction loss
P2 output power ( P2¼TLO)
PC copper loss
PCu armature copper loss ( PCu¼raI2)
PT loss of bridge power switches ( PT¼DUI)
Psi selected probability of the ith individualxvi List of Nomenclature

Pc crossover probability
Pe electromagnetic power ( Pe¼keOI)
Pm mutation probability
PN rated power
p number of conductors in series per phase; number of pole pairs
q number of slots per phase and per pole
Q1,Q2,… … ,Q6instant of phase commutation
Rx phase resistance, in which subscript xdenote phase A, B and C
R0 stator nominal resistor
R phase winding resistance matrix
ra line resistance of winding, ra¼2R
s switching function
S product of rotor radius and the effective length of conductors
S1,S2,… … ,S6 conduction signals
T1,T2,… … ,T6 power switches
T0 no-load torque corresponding to no-load loss ( T0¼P0/O)
Tc cogging torque
TD differential time constant
Te electromagnetic torque
TI integral time constant
TL load torque
TN rated torque
Tr rising time of the system response
Tst starting torque
T(k) the kth commutation instant
^Te tracking value of electromagnetic torque
Tb0 starting friction torque
te time constant
ts adjusting time
U phase voltage matrix
Ud DC bus voltage; DC voltage of the inverter bridge
UN neutral to ground voltage of the three phase windings
Uout output voltage of the integrator
usum sum of three-phase voltages
Uth threshold
4U voltage drop of the power switches of the bridge inverter
u number of existed hidden layer unit
uAG,uBG,uCG phase to ground voltages
uAB,uBC,uCA line voltages
ux phase voltage, in which subscript xdenote phase A, B and C
u(t0) step function
V electric voltage
VCE forward voltage of the power switch
VD forward voltage of the diode
Wm energy of air gap electromagnetic ﬁled
wij weight between network layersList of Nomenclature xvii

Xi N-dimensional input
y1 polar distance
yi network output; actual output of the ith neuron
Z slots of the armature coreZ(k) moment of the kth zero crossing point
a momentum factor; learning rate; leading conducting angle
a
p pole arc coefﬁcient
ask skewed slot coefﬁcient
b01,b02 coefﬁcients of observer
g learning rate
x damping ratio of the second-order system
e unmodeled dynamics
Z efﬁciency of the motor
l coefﬁcient of leakage permeance
l forgetting factor (0 /C20l/C201)
y relative angular displacement between rotor and stator; rotor position
angle
yB air-gap ﬂux density; platform width of air-gap ﬂux density waveform
yE electric angle at the decreasing moment of the line back-EMF
ye platform width of overall back-EMF
y/C3electric angle at the crossing point of the line back-EMF
si normalized constants of the ith hidden layer unit
d air gap; local gradient for weight correction of ith neuron
LA permeance of self-inductance of ﬂux in phase A
LAB permeance of mutual inductance ﬂux between phase A and phase B
o electrical angular speed of motor; electricity angle of motor
ok weighting coefﬁcient from the hidden layer to the output layer
on natural frequency of the second-order system
o*rotate speed reference signal
^o estimated signal
O mechanical angular speed of the motor
Or reference mechanical angular speed
j output function
C matrix of ﬂux linkage
cf0 nominal ﬂux
cm magnetic ﬂux linkage of each phase; maximum value of PM ﬂux linkage
of each winding, cm¼2NSB m
cpm(y) PM ﬂux linkage
crotor ﬂux of rotor permanent magnet
csum total ﬂux of each phase
Da(s) additive perturbation
Di(s) input multiplicative perturbation
Do(s) output multiplicative perturbationxviii List of Nomenclature

1
Introduction
Two typical deﬁnitions about the brushless DC motor (BLDC motor, BLDCM) have been
presented by scholars. Some of them considered that only the trapezoid-wave/square-wavebrushless motors could be called BLDC motors, and sine-wave brushless motors should becalled permanent magnet synchronous motors (PMSM) [1,2]. However, other scholars thoughtthat all the motors above should be considered as BLDC motor [3]. ANSI/IEEE Standard 100-
1984 has just deﬁned “Brushless Rotary Machinery” [4]. Moreover, in NEMA Standard MG7-
1987, a BLDC motor is deﬁned as a type of self-synchronous rotary motor controlled byelectronic commutation, where the rotor is a permanent magnet with rotor-position sensors [5],and the related commutation circuit could be either independent or integrated to the motor. Sofar, there has not been a uniﬁed standard about the classiﬁcation or deﬁnition of the BLDCmotor. By using the former deﬁnition, a BLDC motor is considered in this book as the trapezoid/square wave motor with the starting characteristics of series excitation DC motors and thespeed-regulation characteristics of shunt excitation DC motors. It has advantages like simple
structure, high efﬁciency and large torque, etc. Hence, it is widely used in national defense,
aerospace, robotics, industrialprocess control, precision machine tools, automotiveelectronics,household appliances and ofﬁce automation. The development history of BLDC motor, itsapplication ﬁelds, research status and the development tendency of related technology arepresented in this chapter.
1.1 History of BLDC Motors
In the modern society, electricity is the most popular secondary energy source. The application
of motors has spread to all kinds of ﬁelds in national economy and our daily life as the main
mechanic-electronic energy-conversion device for more than a century. In order to adapt to
different practical applications, various types of motors, from several milliwatts to millions of
kilowatts, including synchronous motors, induction motors, DC motors, switched reluctancemotors and so on, emerge as the times require. Although the synchronous motor hasadvantages of large torque, hard mechanical characteristic, high precision and efﬁciency,it has difﬁculties in speed regulation, which limits the range of its application. An inductionmotor has the advantages of simple structure, easy fabrication, reliable work and low price, but it
is uneconomical to regulate the speed smoothly over a wide range and it is not easy to start up.
Permanent Magnet Brushless DC Motor Drives and Controls , First Edition. Chang-liang Xia.
/C2112012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd.

Also, it is necessary to absorb the lagging ﬁeld current from the power system resulting in the
decrease of grid power factor. Moreover, its mechanical characteristic is soft and the power
factor is small. Without windings or a permanent magnet on its rotor, a switched reluctance
motor has a simple structure and low price. It can produce high torque at low speed. However,the noise and torque ripples limit its popularization and applications. DC motors are stillwidely used in electric power drive systems that have demands for start up and speedregulation, such as electric traction, rolling mill and hoisting equipment, because this type ofmotors have high efﬁciency and good speed-regulation performance. Nowadays, DC motors ofsmall capacity are still widely used in automation and control systems. But in traditional DCmotors, mechanical commutation is implemented by using brushes, which will result in
problems like mechanical friction that would shorten the lifetime, and create noise, electric
sparks, and radio interference, etc. In this condition, considering the disadvantages of highproduction cost and inconvenient maintenance [6–10], the range of applications in particularareas has been limited. Therefore, applications of small and medium size are in urgent need ofnovel high-performance motors.
The BLDC motor is developed on the basis of brushed DC motors. The modern machine
theory was established when Faraday discovered the electromagnetism induction phenom-enon in 1831. The ﬁrst DC motor was born in the 1840s. Conﬁned by the development of
power electronic devices and permanent magnet materials, BLDC motor was designed
successfully until more than one century later. In 1915, an American, Langmuir, invented themercury rectiﬁer to control grid electrode and made the DC/AC converter. Contraposing thedisadvantages of traditional motors, in the 1930s, some scholars started developing brushlessmotors in which electronic commutation was implemented, which made preparations for theBLDC motor. However, at that time, power electronic devices were still in the early stage ofdevelopment, scholars could not ﬁnd an appropriate commutation device. This type of motor,with less reliable work and low efﬁciency, was only used in the lab instead of being
popularized. In 1955, Harrison and Rye made the ﬁrst patent claim for a thyristor
commutator circuit to take the place of mechanical commutation equipment. This is exactlythe rudiment of the BLDC motor [11]. The principles of operation are as follows, when therotor rotates, periodic electromotive force (EMF) is induced in the signal winding, whichleads to the conduction of related thyristors. Hence, power windings feed by turns to achievecommutation. However, the problems are, ﬁrst, when the rotor stops rotating, induced EMFcannot be produced in the signal windings and the thyristor is not biased, so the powerwinding cannot feed the current and this type of brushless motor has no starting torque.
Furthermore, power consumption is large because the gradient of the electric potential’s
sloping part is small. To overcome these problems, researchers introduced the commutators
with centrifugal plant or put an accessory steel magnet to ensure the motor started reliably.But the former solution is more complex, while the latter needs an additional starting pulse.
After that, by numerous experiments and practices, the electronic commutation brushlessmotor was developed with the help of Hall elements in 1962, which inaugurated a new era inproductionization of BLDC motors. In the 1970s, a magnet sensing diode, whose sensitivityis almost thousands of times greater than that of the Hall element, was used successfully for
the control of BLDC motor. Later, as the electrical and electronics industry was developing, a
large number of high-performance power semiconductors and permanent magnet materialslike samarium cobalt and NdFeB emerged, which established a solid ground for widespreaduse of BLDC motors.2 Permanent Magnet Brushless DC Motor Drives and Controls

In 1978, the Indramat branch of Mannesmann Corporation of the Federal Republic of
Germany ofﬁcially launched the MAC brushless DC motor and its drive system on TradeShows in Hanover, which indicates that the BLDC motor had entered into the practical stage.Since then, worldwide further research has proceeded. Trapezoid-wave/square-wave and sine-wave BLDC motors were developed successively. The sine-wave brushless DC motor is theso-called permanent magnet synchronous motor. Generally, it has the same topology shown inFigure 1.1(a) as that of trapezoid-wave/square-wave brushless DC motors. It can be considered
as a PMSM where rotor-position detection is used to control the commutation in order to ensure
self-synchronization operation without starting windings. Meantime, these two kinds of motors
have the same equivalent circuit as shown Figure 1.1(b), in which L–Mis the equivalent
inductance of each phase. With the development of permanent magnet materials, microelec-tronics, power electronics, detection techniques, automation and control technology, especiallythe power-switched devices like insulated gate bipolar transistor (IGBT), integrated gate-commutated thyristor (IGCT) and so on, the BLDC motors in which electronic commutation isused are growing towards the intelligent, high-frequency and integrated directions.
In the late 1990s, computer techniques and control theories developed rapidly. Micropro-
cessors such as microcontroller units (MCU), digital signal processors (DSP), ﬁeld program-
mable gate arrays (FPGA), complex programmable logic devices (CPLD) made unprecedented
development, while a qualitative leap was taken in instruction speed and storage space, whichfurther promoted the evolution of BLDC motor. Moreover, a series of control strategies andmethods, such as sliding-mode variable structure control, neural-network control, fuzzycontrol, active disturbance rejection control (ADRC), adaptive control and so on [6,12–20],are constantly used in BLDC motor drive systems. These methods can improve the performance
of BLDC motor drive systems on torque-ripple minimization, dynamic and steady-state speed
response and system antidisturbance ability to some extent, as well as enlarge the applicationrange and enrich the control theory.
1.2 Applications for BLDC Motors
In recent years, small and medium size motor industries are developing rapidly. About theseindustries, incomplete statistics of proceeds and volume of sales in China during 2004–2008Inverter M
Rotor
position
sensors+
−DCi
R
L-M
e+
−U
−+
(b) Equivalent circuit (a) Topology
Figure 1.1 Topology and equivalent circuit of BLDC motor.Introduction 3

are shown in Table 1.1 [21]. In particular, the BLDC motor has achieved a brilliant expansion
in automotive, aerospace and household equipment industries, because it has the advantages ofhigh efﬁciency, long lifetime, low noise and good speed–torque characteristics. Somerepresentative application situations are described as follows.
1.2.1 Automotive BLDC Motor
Automobiles, as a convenient and efﬁcient vehicle, are very close to our daily life. In
developed countries, it has a high automobile popularization rate. In China, the automobile
industry had been conducted as a pillar industry in industrial policies that was establishedduring the Ninth Five-Year Plan period. In 2007, domestic production was 8 million. There areusually dozens or even hundreds of motors inside an automobile. As the automobile isdeveloping towards energy-saving and environmentally friendly, high-efﬁciency permanentmagnet motors including BLDC motors have a bright future. Some frequently-used perfor-mance indexes of motors that are used to drive the electric vehicles are shown in Table 1.2. Itcan be seen from Table 1.2 that the BLDC motor, which is included in permanent magnet
motors, has a good technical superiority [22].Table 1.1 Sales of small and medium electric motor during 2004–2008
Year 2004 2005 2006 2007 2008
Volume of sales (10 k kW) 7847 9702 10950 13009.5 13336
Product revenue (10 k RMB) 1 560 933 2 182 281 2 686 147 3 299 004 3 675 679
Table 1.2 Comparison between motors used in electric vehicles
Motor type
PerformanceindexDC motor Induction motor PM motor Switched
reluctance motor
Power density Low Intermediate High Very high
Peak efﬁciency (%) G90 90–95 95–97 G90
Load efﬁciency (%) 80–87 90–92 85–97 78–86
Controllability Simple Complex Hard for ﬁeld-
weakeningComplex
Reliability Normal Good Excellent Good
Heat dissipation Bad Bad Good Good
Size & weight Big, Heavy Normal, Normal Small, Light Small, Light
High-speed performance Poor Excellent Good Excellent
Construction Slightly worse Better Slightly better Excellent
Cost of motor ($/kW) 10 8–10 10–15 6–10
Cost of controller Low High High Normal
Combination property Slightly worse Normal Excellent Better4 Permanent Magnet Brushless DC Motor Drives and Controls

Besides the hardcore of automotive drives, motors can be used on the drives of air
conditioners, wiper blades, air bags, electric doors and power seats. Automotive air condi-
tioning is one of the most important accessory products on an automobile, and its performance
will change the passengers’ comfort directly. Also, it will inﬂuence their impression andevaluation about the entire automobile in an indirect way. The motor drive used in automotiveair conditioners is often operating with constant load, so it has lower requirements regardingthe dynamic response of the system. A motor and its control system have a direct relationshipwith the performance of automotive air conditioners. Certain key aspects of BLDC motordrives used in automotive air conditioners, has been studied in [23,24]. Similar to thetechniques of household air conditioners, air-conditioner compressor driven by a BLDC
motor is developing towards more energy-efﬁcient and comfortable directions. As the
techniques of power electronics, automation control and computer science are developing,BLDC motor speed-regulation techniques become mature gradually with higher quality andlower price. Therefore, BLDC motors will get a wider range of application, and be amainstream in speed-regulation techniques.
It is necessary to note that the usage and installation of position sensors would increase the
cost of motor drives and affect the reliability and lifetime of the control system. Moreover,automobiles usually have strict restrictions for the volume of the motor. However, sensors are
usually installed inside the motors, which will increase the volume. Consequently, the
sensorless control strategy will be an important development direction of automotiveBLDC motor drive systems.
1.2.2 BLDC Motor in Aerospace
Air-driven and hydraulic-type transmission devices are being replaced by motor-driveequipments, which is a tendency in the aerospace industry. Due to its particular application,
in aerospace industry, motors are required to be small size with simple structure. The special
structure and position-sensorless control method of BLDC motors make it possible for them to
be widely used in aerospace industry. In this condition, the BLDC motor is often operating
with variable load, which requests good high-speed regulation and dynamic response, forinstance, the application of gyroscopes and robotic arms. It is controlled by using semiclosedor closed-loop speed feedback, where advanced control algorithms are usually implemented inthe corresponding systems.
In aerospace, some BLDC motors, such as motors used in high-speed centrifugal pumps and
high-speed cameras, could reach the speed of tens of thousands of rev/min or more. Hence, it is
necessary to consider the requirements and solutions of mechanical and electrical performancewhen it operates at high speed. For instance, the bearing problem of a high-velocity rotating
motor can be solved by implementing an active magnetic bearing or bearingless design.
Moreover, there are signiﬁcant differences in voltage levels and frequency between universalpower and those in aerospace. Therefore, special requirements for rectiﬁer circuits andfrequency-conversion drive circuits should be taken into account in BLDC motor controlsystems, where soft-switching technology can be introduced to minimize the noise and loss
during high-frequency switching to improve the properties of the system. Meanwhile, to meet
the needs of high reliability, some special means, such as trapping techniques, redundancytechniques and so on, are adopted to prevent software sinking into dead circulation or gettingother problems.Introduction 5

1.2.3 BLDC Motor in Household Appliances
Recently, motor drivesusedinhouseholdappliances haveincreased about 30 per cent everyyear
worldwide.Thesemodernelectricappliancesaredevelopingtowardsenergy-saving,low-noise,intelligent and high-reliability directions. With the improvement of the living standard of thepeople and the increasing attention on energy saving and emission reduction from the
government, BLDC motors are chosen as the drive motor of household appliances increasingly.
In China, durable consumer goods, air conditioning and refrigerators, whose production has
ranked top in recent years throughout the world, have been popularized in cities. Both electricappliances have compressor motors that are usually induction motors. Usually, they have lowefﬁciency and a small power factor and these disadvantages may be overcome by usingfrequency-conversion technology. Compared with induction motors, BLDC motors have thefollowing advantages: (1) high efﬁciency; (2) the speed is not limited by power frequency,hence the rated speed can be designed higher, which is beneﬁcial to increasing the capacity anddecreasing the size; (3) the power factor is higher, by which the capacity required of the
inverter is reduced.
So, if the BLDC motor is implemented in the compressor, it will improve the properties of
the compressor signiﬁcantly and meet the requirements of energy saving and environmentprotection in modern society. Nowadays, 90 per cent of the induction motors used to drive thecompressors have been replaced by BLDC motors in Japan.
Because the compressor motors are sealed, whether in the condition of high or low
temperature, position sensors of BLDC motors will inﬂuence the reliability of the compressors.The position sensor takes the space inside the compressor, and the signal wires may have an
unfavorable inﬂuence. Therefore, position-sensorless control is preferable for BLDC motors of
the compressor. To reduce the cost and improve the stability of the control system for frequencyair conditioning compressors, current commutation signals are acquired by using the back-EMF-based method with a DSP and module IR2316. It achieves the position-sensorless controlof BLDC motor for frequency compressor systems, with a motor efﬁciency of 86 per cent [25].In addition, position-sensorless control is achieved by implementing the brushless linear DCmotor to drive the compressor directly [26]. The transmission mechanism of the eccentricwheel is removed in this system, which is convenient for the design and installation of the
compressor. This system, which is suitable for long-stroke linear motion system, is beneﬁcial to
reducing the size and the transmission loss, and improving the efﬁciency.
BLDC motors are also used as the spindle motor drive in VCD, DVD and CD players. Disk-
type coreless BLDC motors, which are cheap and usually used in this type of application, havebeen produced on a large scale. According to different requirements for torque, disk-typeBLDC motors as shown in Figure 1.2, can be classiﬁed as single-stator type and double-statortype, which is suitable for high-torque drive applications. A product of a DVD/CD playerdriven by BLDC motor is shown in Figure 1.3.
Moreover, the structure of multipole and external rotors, which is a mature technology, is
used in BLDC motors of electric bicycles. BLDC motors used in electric bicycles based onnanotechnology have been designed by a British Company, OLEXI-NANO. Due to its featuresof high efﬁciency, low temperature rise, high comfort level and stability, and so on, thecomprehensive properties of the electric bicycles are improved. In some areas of householdappliances such as vacuum cleaners, agitators, hair dryers, cameras, electric fans and so on,BLDC motors have gradually taken the place of current popular motors that include DC6 Permanent Magnet Brushless DC Motor Drives and Controls

motors, single-phase induction motors and variable-voltage variable-frequency (VVVF) drive
induction motors. BLDC motors cannot only overcome some disadvantages of traditionalhousehold motors but also reduce the energy loss, which brings a more comfortable lifestyleand properly realizes sustainable energy utilization for people.
1.2.4 BLDC Motor in Ofﬁce Automation
Most motors used in ofﬁce automation and computer peripheral equipments are BLDC motors,which is a combination of advanced technology and modern microelectronics. The adoption ofthe high-performance BLDC motor servosystem improves the quality and increases the valueof the products. For example, the BLDC motor used on the main shaft of the hard-disk drives
can rotate at high speed with the magnetic disk. The magnetic head, which achieves the
executive function for the data on the disk, takes a suspension motion over the surface ofthe disk about 0.1–0.3 mm to increase the read-write speed. BLDC motors can also be the
spindle motor for optical disc and ﬂoppy disc drives, and in that case, the BLDC motor has
Stator
StatorStator
RotorRotor
Figure 1.2 Structure of disk-type BLDC motor.
Figure 1.3 Application of DVD/CD players.Introduction 7

the advantages of low noise, low temperature and high temperature tolerance and it can
withstand shock and vibration to a certain extent, which improves the stability of the system.
Cooling fans driving motors for computers are usually required to have characteristics such as
low noise, compact construction, long lifetime and high speed. Hence, the BLDC motor usedin this area adopts an external rotor on which the magnetic steel pieces are usually made ofbonded NdFeB. In the area of digital cameras, the BLDC motor has also been widely used. Forinstance, the Japanese companies Toshiba and Sanyo have both produced the products ofBLDC motor drive cameras with the corresponding integrated drive chips TA8479F andLB8632V respectively. With a long history, laser printers driven by BLDC motors are apromising technology and have strong market competitiveness. Its speed can be controlled
accurately from thousands of rev/min to tens of thousands of rev/min [27]. Moreover, BLDC
motors have good applications in duplicators, facsimiles, recorders, LD video disk players,paper shredders and other ofﬁce equipments.
1.2.5 BLDC Motor in Other Industries
A BLDC motor control system is an electromechanical integration product that combines theadvantages of brushed DC motor and AC asynchronous motor control systems. As theperformances of power electronic device and rare-earth permanent magnetic materials areimproving and the price is reducing, BLDC motor drive systems, which have increasingapplications in industry, has been a main developing direction in the industrial motor drives.Considering performance and cost of the product, famous international motor manufacturershave carried out much research and development. Nowadays, BLDC motors occupy a greatportion in civil and military robots and manipulators, where there is a trend that they will take
the place of stepping motors and traditional DC servomotors driving robots. High-power
BLDC motors also have a good application prospect in some certain occasions, such as lowspeed, adverse circumstances or where good speed regulation performance is required. Forexample, in the applications of gearless elevator traction motor drives, pumped storage,transmission of rolling mills, they have the advantages of fast dynamic speed response, smalltracking error and static difference ratio, and wide range of speed regulation. Besides theabove, practical applications of BLDC motors consist of medical equipments, textilemachinery, printing machinery, digital control machine tools, etc.
1.3 Advances in BLDC Motor Drives
Currently, general BLDC motor control is relatively mature and China has developed aspeciﬁcation GJB1863 for it. Research of BLDC motors in developed countries is roughly thesame as that in China, whereas the United State and Japan have more advanced manufacturingand control technology. In particular, Japan is more prominent in civil aspects, while theUnited States is more advanced in the military arena. The current researches mainly focus inthe following areas: (1) Develop position-sensorless control technology to improve systemreliability and further reduce the motor size and weight. (2) Investigate methods of torque-ripple reduction for BLDC motors, from motor design and control aspects, to improve the
servoprecision and expand the scope of application. (3) Design reliable, compact and versatile
integrated BLDC motor controllers.8 Permanent Magnet Brushless DC Motor Drives and Controls

1.3.1 Position-Sensorless Control
The rotor position is directly detected by a position sensor in the traditional method of BLDC
motor-position detection, which is called the direct position-detection method. Voltage orcurrent signals of the motor, which are easily acquired, are processed with certain algorithmsto get the rotor position signals in the position-sensorless control method, which is also called
the indirect rotor-position-detection method. This concept started from the position estimation
method by using capacitor shifting, which was proposed by Mieslinger in 1966 [28]. The
commonly used indirect rotor-position-detection methods are shown in Figure 1.4.
The back-EMF-based method has a simple principle that is convenient to achieve and is
widely used. By using the computer, position-sensorless control was processed in 1985 byIizuka et al. [29] who made comprehensive analysis of software and hardware design for the
method, which improved the BLDC motor control to a new level.
During the end of the 1980s to the early 1990s, indirect detection methods of rotor position
developed in a diversiﬁed trend. Lin et al. [30] presented a rotor-position-detection method by
using phase current in 1989, considering the principle that if the phase current and the stator
ﬂux have the same phase, the rotor position of BLDC motor can be accurately reﬂected by thechange of phase current. In 1990, scholar Ogasawara [31] proposed the inverter switching stateestimation method, an ingenious method, which is shown in Figure 1.6 as the freewheelingdiode-based method. The basic principle of this method is still the back-EMF-based method,but the EMF is considered from the perspective of current, which is a novel and clever design.Matsui et al. [32] presented a detection method for rotor position based on transient current and
voltage equations. People began to understand the nature of BLDC motor rotor position
variation since the methods were presented in [31,32]. The stator ﬂux-based estimation
detection method was proposed in 1994 by Ertugrul et al. [33]. In this method, the ﬂux of each
stator winding is calculated by the phase voltage and the line current, in order to get the rotorposition signal from the ﬂux [33]. Although the computation complexity is higher, the error ofthis method is less and the range of speed regulation is wider. This method, which is an idealtesting method and has been applied to production, is not only suitable for BLDC motors, butalso for PMSM. In the same period, the rotor-position-detection method using a state estimatorand a Kalman ﬁlter was proposed [34]. Since this method requires a lot of calculations and was
limited by the actual conditions at that time, it did not arouse enough attention. In past decades,
Indirect rotor position
detection method
Back EMF-based methodInductance-based methodFlux linkage-based
methodFreewheeling diode-based
methodVariable structure-based
methodObserver estimation
methodIntelligent estimation
method
Figure 1.4 Indirect rotor-position-detection methods.Introduction 9

with the improvement of performance of MCU and the upgrading of DSP products, this
method has gained rapid development and been applied to actual control systems of BLDC
motors [35–37].
The terminal-voltage-based method, an indirect rotor-position-detection method, is actually
a changed form of the EMF-based method. It only detects the terminal voltage of each phase,so that the rotor position is acquired through the change of the terminal voltage, whereas thechange is actually the reﬂection for the variation of back-EMF in windings along with the rotorposition. However, the terminal-voltage-based method further simpliﬁes the interface circuit,which makes the back-EMF-based method more practical [9,18].
The variable-structure-based method refers to the position-sensorless control that is
achieved by making appropriate changes on rotor or stator structure. For instance, adding
an auxiliary rotor winding in the surface-mounted-type rotor BLDC motor to get rotor positionsignals [38], or setting nonmagnetic materials on the rotor surface in order to get the rotorposition from detecting the disconnected phase voltage variation caused by eddy-currentreaction [39]. In addition, Matsuse et al. obtained the rotor position by designing the closed
stator slot type motor [40].
As the development of intelligent control is promoting motor control, using fuzzy control,
neural networks and other intelligent algorithms to establish the relationship between voltage
signals, current signals and rotor position signals is a new approach to position-sensorless
detection, which has higher control precision [41–43]. However, compared with traditionalposition-sensorless control methods, it has more complex algorithms and takes more time incomputation, hence the cost is increased.
It is difﬁcult to achieve a direct start for a BLDC motor using position-sensorless control, so
the starting mode is always a research focus. The three-step starting technique by using theback-EMF-based method has been more mature. From the start to the stable operation of themotor, this method can be divided into the following three steps: position ﬁxing for rotor,
acceleration and switching. Other starting techniques under the position-sensorless control,
such as the rotor prelocation method, increasing-frequency and increasing-voltage synchro-nous methods and the short time measuring pulse rotor orientation starting method, havecertain applications.
1.3.2 Torque-Ripple Reduction
Torque-ripple reduction is always an important issue in BLDC motor control systems. As in
other motors, some phenomena like the cogging effect and the eddy-current effect cannot be
completely avoided in BLDC motor design. Therefore, cogging torque, which should be
considered in torque-ripple reduction of BLDC motors, can be restrained with good results by
using skewed and fractional slots.
In addition, electronic commutation is usually implemented in BLDC motors, and the
presence of motor winding inductance makes it difﬁcult for the phase current to achieve theideal square-wave current, which may also bring commutation torque ripple to the system.Therefore, to restrain the commutation torque ripple is also an important research, on which
many scholars have made a lot of efforts.
The principle of the BLDC motor and the necessity of existence of torque ripple are discussed
in[44].In[45,46],phasevoltageandcurrentaretransformedwithFourier-seriesdecomposition,and the torque model with fundamental and higher harmonics is derived. Moreover, the purpose10 Permanent Magnet Brushless DC Motor Drives and Controls

of eliminating torque harmonics is achieved by adjusting the conducting phase of the windings
to compensate appropriately. Although it has a large amount of computation, it has higher
control precision. Considering the fact that the total current is decreasing during commutation,
the overlapping commutation method is presented in [47] by preconducting the awaitingcommutationwinding,whichmakesallthreephasesconductedatthebeginningofcommutationto ensure that the amplitude of current is a constant value. The relationship among the amplitudeof commutation torque ripples, commutation intervals and speed is discussed in [48]. By usingthe optimum weight method of stator current harmonics, torque ripples caused by electromag-netic torque and cogging torque are effectively reduced with a current regulator and otherequipment in [49]. In 1997, Lim et al. [50] presented a method to eliminate the torque ripples by
regulating the turn-off angle of a voltage source inverter, which is not only suitable for the
constant-voltage constant-frequency (CVCF) systems, but also for the VVVF system. From theperspective of commutation instant, the relationships among commutation instants, back-EMFand torque ripple, and that between commutation time and motor speed are discussed in [51].In addition, torque ripples are effectively restrained by using a direct torque method to controlthe BLDC motor in [52]. Another torque-ripple reduction is achieved by dynamically changingthe input voltage in [53].
Chinese scholars have also done lots of research on torque-ripple reduction of BLDC
motors. Torque ripple caused by armature reaction is analyzed in [54]. The corresponding
methods to restrain the effects are proposed from aspects of magnetic circuit design andswitching phase control. In [55], by using back-EMF, phase current and motor speed as theinput signals and torque as the output to construct a torque estimator, the indirect measurementmethod with a torque estimator is presented. The method achieves the online estimation oftorque and makes appropriate compensation to different motor operating conditions. Althoughit requires complex computation, it can control the torque online and restrain the torque rippleunder most operating conditions without measuring the instantaneous torque. The BLDC
motor commutation torque-ripple reduction method based on an artiﬁcial neural network is
presented in [16]. In this method, two three-layer forward-feedback artiﬁcial neural networksare trained online and ofﬂine, respectively. The error feedback algorithm is used to modify theconnected weight value between each cell. One network is used for online commutation stateestimation, while the other is used for regulating the voltage instantaneously during com-mutation, which forms a voltage self-tuning regulator. This regulator, which makes the currentdecreasing rate approximately equal to the rate of rising during commutation by means ofregulating the terminal voltage, maintains the amplitude of the current at a constant value and
achieves the reduction of torque ripple. Note that accurate knowledge of parameters of the
system is not required in this method, so it shows good ability to adapt to environmental
changes. In [56], the motor is equivalent to a serial object that is constructed by two nonlinearsystems: a torque subsystem and a speed subsystem. The active disturbance rejection control
technique is used to design two ﬁrst-order active disturbance rejection controllers to achievethe inner and outer closed-loop control for the motor. By implementing the extended stateobservers (ESO) to observe the torque, torque-ripple reduction is achieved with the help oftracking differentiator (TD) and nonlinear states error feedback (NLSEF) [57]. The above-
mentioned technologies have contributed to the reduction of BLDC motor torque ripple, and
hence improved the performance of the control system.
Overall, the reasons for BLDC motor torque ripple are complex and corresponding control
methods can be used for different situations where each method has its own advantagesIntroduction 11

and applications. Meanwhile, the existing torque-ripple reduction methods, which do not
fundamentally eliminate the torque ripple, are pre sented as an improvement or compen-
sation for motor structure and control schemes. Thus, torque-ripple reduction remains for
further study.
1.3.3 Hardware Implementation
Similar to electrical components, BLDC motor controllers have experienced the developmentprocess from discrete element control to digital programmable integrated circuit. A commu-
tation logical signal circuit composed of gate circuits is shown in Figure 1.5.
In general, a BLDC motor designed with discrete components has complex structure and
large size, and its reliability and versatility are poor, which makes it unsuitable for massproduction. Therefore, application-speciﬁc integrated circuit (ASIC) controllers, FPGA,MCU and DSP controllers are widely used to control the BLDC motor.
Currently, many semiconductor manufactures from developed countries, can provide their
own ASIC for motor control. For example, American companies ON Semiconductor andMotorola developed the MC33035 and MC33039 BLDC motor control chips, and also
Micro Linear Corporation designed the position-sensorless control chips ML4425/4428.
HAHBHCForward/Reverse
Figure 1.5 Commutation logical signal circuit.12 Permanent Magnet Brushless DC Motor Drives and Controls

ASIC controllers have the advantages of simple structure, high cost–performance ratio and
fewer peripheral devices compared with discrete components. However, there are some
limitations and the expandability is not good, so it is difﬁcult to upgrade or change its
functions. Consequently, considering the controllers’ design of hardware and software andother function in the future, FPGA, MCU and DSP, which have the advantages of perfectfunctions and easy to control, could be implemented to control BLDC motor, with thecondition that the corresponding cost may be higher than that of ASIC controllers. FPGA canbe programmed with VHDL, Verilog or the C language, with the advantages of ﬂexibility,static reprogrammable and online dynamic reconstruction, which means the correspondinghardware can be easily modiﬁed with the interface functions deﬁned according to the users’
requirements. MCU and DSP both have ample peripheral interfaces. The difference is that
MCU is commonly used for simple motor control systems while the DSP is used for intelligentcontrol systems due to its powerful computing and data processing capabilities. Typical MCUor DSP control BLDC motor system is shown in Figure 1.6.
Economic and practical BLDC motor controllers can be achieved by using various types of
MCU. At the beginning, the most widely used MCUs were MCS-51/96 series products, whichhave now been extended to PIC16F877A, MSP430F149, MC68HC908MR16, LPC2101 andother products from different companies. Moreover, many companies have introduced speciﬁc
MCUs for BLDC motor control systems. Chip ST72141 from ST Company is a speciﬁc MCU
for BLDC motor, which consists of their back-EMF detection patented technology. C50Xseries chips from Siemens are also made for BLDC motor control systems. For example, insidethe C504 chips, there are hardware commutation circuits. When the three-phase rotor-positiondetector detects and transmits the position signal to the chip, the commutation signals in themain circuit can be controlled by the chip, which does not need to use software for processing.As a result, it can greatly reduce the difﬁculty of system development and improve thereliability of commutation. Also, the chip C508 can drive two BLDC motors at the same time.
Although the price of MCU is relatively lower, its processing capacity is ﬁnite, especially
when large volumes of data need to be dealt with for the requirements of real time and highprecision, the MCU often cannot meet the requirements of computing speed. In some speciﬁc
Peripheral
and display
equipmentsInterface
circuitMCU or
DSP
Drive
circuitBLDC
motor
Position detection circuitProtective
circuit
Figure 1.6 Typical BLDC motor control system.Introduction 13

applications, requiring cooperation with multiple motors, using an MCU and its interface
circuits makes the hardware circuit more complex, where it is difﬁcult to achieve digital
control for motor speed and current. In this condition, generally, DSP, FPGA and “DSP ț
FPGA” schemes can be implemented to design the BLDC motor control system. A BLDCmotor control system consisting of DSP, FPGA, signal conditioning comparison circuit andother subsystems is presented in [58], as shown in Figure 1.7. In the signal-conditioningcomparison subsystem, the signals from voltage and current sensors are conditioned andtransmitted to the DSP subsystem for A/D sampling. The signals from each phase arecompared with the bound of the chopping current from D/A part of the DSP subsystem.The comparison results, which are a series of high-level and low-level signals, are transmitted
to the FPGA subsystem, in which the speed signals are compounded and transmitted to DSP.
And then, according to the command signal, position signal and chopping signal from the DSP,control signals of power switches are compounded logically and generated. Commonly usedpower switches include MOSFETs, IGBTs, intelligent power modules (IPM) and so on. In theDSP subsystem, speed command, boot command and current/voltage feedback signals arereceived. The state of the motor and the bound of the chopping signal are also decided. Also, ithas the functions of data, alarm and state display and feedback output speed signals, etc.
At present, the DSP products have developed to the sixth generation, with abundant models
and speciﬁcations and low price. As the improved Harvard structure and pipeline mechanism
are introduced in DSP devices, its computing speed is much faster than that of MCUs, andespecially, due to highly specialized instruction set provided by DSP, the computing speed ofdigital ﬁlters is improved, which brings unique advantages on implementation of controllerrules, vector control and matrix transformation aspects. Besides, there are many such speciﬁcDSP chips that use the CPU as the core and integrate different peripheral components toachieve complex control functions. It reduces the requirements of peripheral components andthe cost of the system, which improves the reliability and is propitious for conﬁdentiality of
proprietary technologies. For example, TMS320LF2407 from the American TI Company is a
type of dedicated motor control DSP chip with low price and powerful functions. The motorcontrol scheme is greatly simpliﬁed by 2 EVENT managers, 6 CAPTURE units, 14 PWMoutput signals and teeming I/O interfaces. TMS320F2812 further improves the accuracy ofcomputation to 32-bit and develops the processing capacity of the system with the frequency
DSPA/D
D/AVoltage & current
ampli ȚerVoltage & current
sensor
BLDC
motorPosition sensorCurrent
comparator
FPGA
Power devices
drivesPower converter
Figure 1.7 BLDC motor control scheme based on DSP and FPGA.14 Permanent Magnet Brushless DC Motor Drives and Controls

up to 150 MIPS. A 128 kB ﬂash memory, 4 kB boot ROM, math tables and 2 kB OTP ROM are
integrated to the DSP of this series product, which greatly improves the ﬂexibility of the
applications. The codes and instructions are completely compatible with F240x series DSPs,
which ensures the sustainability for the project and product design. Many intelligent controlalgorithms are achieved with the powerful computation capability of DSP [14–19,59,60],which improves the accuracy and stability of motor control, thereby full digitalizationintelligent control of BLDC motor becomes the research focus in recent years. Althoughthe existing advanced control algorithms of BLDC motor based on the DSP are not matureenough, they will be widely used as the computing speed and memory capacity of DSP areimproving.
1.4 Future of BLDC Motor Drives
BLCDM is mainly composed of motor body, power drive circuit and position sensor, and it
involves motor technology, power electronics, detection and sensor technology, control theory
and technology. Hence, the emergence of new electronic technology, new power devices andcontrol methods, will further improve the development and application of BLDC motors.
1.4.1 Impacts of Power Electronics and Microprocessors on BLDC Motor
(1) Miniaturization and integration
The development of microelectromechanical system (MEMS) enables motor controlsystem development towards the direction of a highly integrated control and sensor circuit.For example, current, voltage, and speed signals feed back after being fused, which makesBLDC motor control systems simpler and more reliable. Moreover, as the BLDC motor
rotors are made of rare-earth permanent magnet materials and there is no heat source at the
rotor side, the internal temperature rise is smaller than that of traditional DC motor, whichenables the inverter control circuit to be installed into the motor. Take the 100-kW-typeBLDC motor from the French company Alsthom as an example, its total weight is only28 kg including the inverter, which is installed at the stator side. So the inverter and motor
are combined, which makes the BLDC motor and power electronics more closely and
improves the added value of products, and the whole control system hereby developstowards the direction of miniaturization and integration. It is worth noting that, currently,
due to the limitation of the technologies, these integrated products are mainly used in the
main drive motor of disk drive and low-power BLDC motor control systems like fan drivesused in equipments. For general industrial BLDC motor control systems, whether theelectronic circuit controllers are installed inside the motor, depends on many factors, suchas the actual operating condition, the cost of the system, the reliability of the circuit andmaintainability and so forth.
(2) Full digitalization of controllers
The improvement of BLDC motor performance, which is related to the permanent magnet
materials of rotors and electronic drive circuit, is closely bound up with the controllers.
Therefore, in order to improve the overall performance of the control system, we canconsider enhancing the performance of controllers. The emergence of high-speedmicroprocessors and high-density PLC technology provides a reliable guarantee andIntroduction 15

feasible solution. For example, in some of the applications that are strict on cost and space,
adding the position sensor is impractical and unacceptable, whereas the inherent high-
speed computation of DSP can be used to achieve position-sensorless control of BLDC
motor. Plenty of hardware, such as traditional PID analog circuits, digital signal proces-sing circuits and logical judging circuits, can be accomplished with software, thus furtherreducing the size of the hardware circuit and improving the reliability and efﬁciency of thesystem. In addition, some complex control algorithms can be realized with DSP, CPLDand FPGA chips, which not only improve the reliability of BLDC motor control systems,but also provide a solid foundation for development towards generalization of theinterface and full digitalization of the control system. Full digitalization enables the
structure of system hardware to be simpler and improves the application of ﬂexible control
algorithm. It is also easy for data transmission with the upper level and the remote controlsystem, which facilitates the monitoring and diagnosis of system failures. A typical blockdiagram of network remote control for a BLDC motor is shown as Figure 1.8. Remotespeed control of a BLDC motor can be achieved with speed and current regulator, thenetwork monitoring and diagnosis functions for the whole control system can be realizedwithin the supervision system.
(3) Green PWM modulation and high-efﬁciency realization
In BLDC motor control systems, when the three-phase six-state 120 degree two-phase
conduction mode is implemented in the inverter, each period has a sector that holds60 electrical degrees, where each power switch is conducted through a 120
/C14electrical
angle in each period. According to their different modulation modes during the conductedperiod, the control modes of PWM for BLDC motor can be classiﬁed as half-bridgemodulation and full-bridge modulation. The half-bridge modulation consists of four
types: H_PWM-L_ON, H_ON-L_PWM, ON_PWM and PWM_ON, whose characteristic
is that in each sector of 60 electrical degrees, one power switch remains normally open and
the other is used with PWM control. The full-bridge modulation mode H_PWM-L_PWM
can be described as follows, in each sector of 60 electrical degrees, the power switches onboth upper and lower legs are chopping at the same time. In these modulation modes,H_PWM-L_ON and H_ON-L_PWM are single-sideband modulation and the other three
BLDC
motorC1n* i*
Interface 1
Networkn
n
i*C2Drive
circuit
Interface 2
Supervision
system
Figure 1.8 Block diagram of remote network control for BLDC motor.16 Permanent Magnet Brushless DC Motor Drives and Controls

modes are double-sideband modulation. Each modulation mode has its merits and
demerits, so users should consider the torque ripple, system efﬁciency, position-sensorless
control methods and other factors to make a rational choice. When a BLDC motor control
system is driven by bipolar power transistor (BPT), the switching frequency of the drivecircuit is usually 2–5 kHz. The noise caused in this range of frequency is just in the humanaudible region, which is detrimental to human health. Meantime, when the windinginductance is not large enough, it will result in unsmooth current waveforms with largeripples. The range of switching frequency can be increased to tens of kHz after MOSFETsand IGBTs are used, by which both electromagnetic noise and current waveform areameliorated. Therefore, using soft switching and other new techniques to reduce switching
loss, prolong the switching life and guarantee unvaried or improved efﬁciency of the
system, the green PWM modulation for BLDC motor control systems can be achieved byincreasing the switching frequency of the drive circuit. While in the condition that theswitching frequency of power switch is restrained, new types of modulation can be used toincrease the operating frequency of PWM, so as to reduce the torque ripple and enhancethe system efﬁciency. Furthermore, motor drive power switches, especially the MOSFET,have a large voltage drop and loss when the current is large. Therefore, within theallowable range, high-voltage low-current power switches or power supplies should be
used for controlling, so that the ratio between the power switch voltage drop and DC bus
voltage is smaller, which can further improve the efﬁciency of the system.
1.4.2 Permanent Magnet and Design Considerations
Miniaturization, low weight and high efﬁciency of motors are closely linked to the devel-opment of the magnetic material. An early magnetic material is Al-Ni-Co, which wassuccessfully developed in the 1930s. It has higher remanent magnetic induction density
and lower coercivity. Co is contained in the alloy. It is expensive, whereas it has good
temperature characteristic and is widely used in instrument-type permanent-magnet machinesthat requires good temperature stability. The later developed ferrite magnetic materials, in
which barium ferrite and strontium ferrite are the two most common types, have lowerremanent magnetic induction density and higher coercivity with lower price, which made them
occupy the leading position for a long time. Rare-earth samarium–cobalt permanent magnetmaterial, the second generation of rare-earth permanent magnet material developed in the mid-1960s, has relatively high remanent magnetic induction density and coercivity, which greatly
increase the magnetic energy product. Its Curie temperature is up to 710–800
/C14C and the
magnetic stability is good. However, the price of this alloy is high, which limits its promotionand application. Hence, it is usually used in the aerospace and military products where theprice is not the main issue. In 1983, Japanese workers found the third generation of the rare-earth permanent magnet material Nd-Fe-B, leading to a revolution of magnetic materials. Thismaterial does not contain expensive alloying elements, and has a high magnetic energyproduct. Both neodymium and samarium are rare-earth elements, but the price of Nd is lowerand the reserves are ten times more than that of Sm. Accordingly, Nd-Fe-B material was
rapidly promoted and used in industrial applications and permanent-magnet machines [61].
Compared with traditional excited motors, permanent-magnet machines made of Nd-Fe-B
material have the advantages of easy construction, small size and light weight. In the samecondition, the number of turns of armature winding is decreased as the performance of magneticIntroduction 17

material is improving. Take the 70-W micromotor from the Philips Company of the Nether-
lands as an example, the volume of rare-earth PM motors is just one-quarter of the current-
excited motors and half of the ferrite excited motors. China is a country with rich mineral
deposits of rare-earth elements, of which the production counts for more than 90 per cent of thetotal output all over the world in recent years. In particular, the improved performance of third-generation Nd-Fe-B magnetic steel has provided a solid foundation for mass production ofBLDC motors and PMSMs. The recent nanocomposite permanent magnet material is com-pounded of hard magnetic phase with high coercivity and soft magnetic phase with highsaturated magnetic moments. The theoretical magnetic energy product of nanocrystal materialis more than 800 kJ/m
3, which is much more than that of Nd-Fe-B material. Although the
mineral resource of Nd-Fe-B is abundant in China, the productive procession and technological
management in this area obviously fell behind the developed countries. The good news is thatgood results have been achievedin the research of new rare-earth permanent magnet material byPeking University, Chinese Academy of Sciences and Central Iron and Steel Research Institute.It is believed that, in the near future, China will become a big player not only in production, butalso in processing and applications for rare-earth materials.
Throughout the history of motors, when a new permanent material appears, there is a new
revolution for the structure and functions of motors, which promotes the control theory,
computation algorithms and structural machinability to a new stage. In the future, as new
permanent-magnet materials emerge and the performance is improved, the research of BLDCmotor and related products can be further developed. Hence, the performance and functions ofmotors will be further improved, in particular it will be more widely used in industrial productsand civilian industry products. Note that adopting new conductive and insulating materials,and improving the performance of BLDC motors from the motor structure, are the importantdevelopment directions in the future. The bonded permanent magnet, orientation of permanentmagnet materials and magnetizing processing technology, which cannot be separated from
materials science, are required to be developed too.
1.4.3 New Types of BLDC Motor
In BLDC motor control systems, speed and torque ripple are always problems that require
further solution, especially in the application of audiovisual equipments, aerospace electricequipments and computers, where stable operation, high precision and low noise are
requested. Most of the motors used in these applications have low power, small size and
compact form, and thus are usually difﬁcult to change. To improve the performance, geneticalgorithms (GA), niche algorithms (Niche) and others are implemented to optimize the designof the motor. Through simulation, analysis and comparisons, the structure of magnetic polesand the shape of the air-gap magnetic ﬁeld are researched and appropriate pole-pair numbers,tooth numbers and slot dimensions are determined. Hence, the demands for power, speed andefﬁciency are satisﬁed. At present, many new types of BLDC motor are springing up, such asthe slotless type BLDC motor, the coreless-type BLDC motor, the axial-ﬁeld disc-type BLDC
motor and other types of BLDC motor. The slotless-type BLDC motor, in which the cogging
parts of stator core in traditional motors are abrogated and the stator windings are directlysettled on the yoke of the stator core, have a bigger air gap and the core loss is just the loss at theyoke, whereas in the coreless-type BLDC motor, iron loss is totally eliminated, so it has better18 Permanent Magnet Brushless DC Motor Drives and Controls

performance and is suitable for high-speed applications. Although both types above have
reduced the loss, the structure processing technique is more complex and techniques of
inserting winding and molding should be improved. The 2057 series coreless BLDC motor
promoted by the MicroMo Electronics Company, which can output torque up to 0.018 N m andspeed up to 58 000 r/min, are suitable for surgery, dentistry and other hand-held medicalequipments. The axial-ﬁeld disc-type BLDC motor is a type of motor that can achieve lownoise and vibration, small torque ripple, high efﬁciency and power density, under the conditionof small capacity. Corresponding with brushed DC motors, other types of BLDC motor consistof BLDC torque motors, BLDC linear motors, low-inertia BLDC motors, BLDC plane motors,BLDC spherical motors, and so on [62,63]. The optimization of the motor design scheme is
attributed to nonlinear programming problems of multiobject functions in [64], and it can
be achieved by implementing the fuzzy niche genetic algorithm. The designed motor has theadvantages of rapid increase of electromagnetic torque and small commutation torque ripple.The corresponding optimization ﬂowchart is shown in Figure 1.9. In conclusion, researching
Primary selection for design sheme based on the
rated values of motor
Determination of the range for optimized design
variables and encoding
OutputGenerating initial population randomly
N
YSolution for the parameters of magnatic circuit
using the Finite-Element method
Calculating performance indices of the motor
(parameters, loss and ef Țciency)
Get each individuals Țtness
Fuzzy niche genetic algorithm
New population
Convergence analysisStart
Figure 1.9 Flowchart of motor design optimization based on fuzzy niche genetic algorithm.Introduction 19

and developing from the aspect of motor structure is one of the major development directions
for BLDC motors.
1.4.4 Applications of Advanced Control Strategies
In modern industry, the requirement for motor performance is increasing. The improvement
can be achieved by optimizing the motor design and the control of power electronic devices.
Also, it can be realized by implementing the advanced control strategies. A BLDC motor
control system is a typical nonlinear and multivariable coupling system. The traditional PID
control algorithm is simple and easy to realize, but it is difﬁcult to meet the requirements ofhigh precision servocontrol systems. Nonlinear control methods, based on the modern controltheory and intelligent control theory, have established the foundation for high-qualitydynamic and stable performance and are widely used in BLDC motor control systems.Fuzzy control, neural network, variable structure control, robust control, adaptive control and
other advanced control strategies are adopted in the control of BLDC motor [58,59,65–80].
The problem with these methods is that the control is relatively complex, which is difﬁcult toimplement. However, as the development of digital control technology and the processingspeed of DSP are improving, more advanced control strategies will be used in BLDC motorcontrol systems, which will greatly enhance the performance of the control systems.Meanwhile, while the processing speed of DSP is limited, the practical applications ofcontrol algorithms should be focused on, in order to comprehensively promote the BLDCmotor control system towards the direction of small size, low weight, intelligence, high
efﬁciency and energy conservation.
1.5 Other Kinds of PM Motors
The introduction of high energy density rare-earth magnets such as Nd-Fe-B, has dramatically
increased the range of applications of PM motors. Besides the BLDC motor, other commontypes of PM motors used in industry are:
*Brush PM motors – Conventional DC machines with mechanical commutators and brusheswhere permanent magnets provide the excitation ﬁeld.
*PM synchronous motors – Conventional synchronous machines where permanent magnets
replace the DC rotor excitation winding.
*Line-start PM synchronous motors – Synchronous machines equipped with a squirrel-cage
induction-type rotor winding for line starting. Permanent magnets embedded in the cagesynchronize the motor.
*Doubly salient PM motor – Switched reluctance motor with PM embedded in the stator orrotor side, where the air-gap magnet ﬂux density is from both the winding and the permanentmagnet.
In addition, PM motors in which the magnetic ﬂux travels in the axial direction are classiﬁed
as axial-gap motors. They can have multiple disk or pancake-shaped rotors and stators. Thestator–rotor–stator conﬁguration is typical.20 Permanent Magnet Brushless DC Motor Drives and Controls

Questions
1. Describe some advances in BLDC motor drives.
2. Give some new types of BLDC motor and explain how they work.3. Describe the advantages of the application of advanced control strategies for BLDC
motors.
4. Explain why the BLDC motors are widely used in industries.
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80. Fang, H. W., Xia, C. L., Chen, Z. W., et al. (2007) Position servo control of brushless DC motor based on the
second discrete ﬁlter. IEEE International Conference on Robotics and Biomimetics, China, 1838–1842.24 Permanent Magnet Brushless DC Motor Drives and Controls

2
Mathematical Model and
Characteristics Analysis ofthe BLDC Motor
The mathematical model of the BLDC motor is fundamental for the corresponding perfor-
mance analysis and control system design. The structure characteristics and working modes ofthe BLDC motor should be considered when we are building its model. The BLDC motorgenerally consists of three parts: the motor structure, the power driving circuit, and the positionsensor. Moreover, there are various structures and different driving modes. In the ﬁrst section
of this chapter, we will introduce several existing structures and driving modes of BLDC
motors. The common mathematical models, which mainly include differential equationmodel, transfer function model, and state-space model, are presented in the second section.Finally, the steady and dynamic characteristics are analyzed and the variations of current andtorque during commutation are discussed in detail.
2.1 Structure and Drive Modes
2.1.1 Basic Structure
The main design principle of a BLDC motor is to replace the mechanical commutator by using
an electrical switch circuit. In traditional DC motors, the brushes are used for commutation,
making the directions of the main magnetic ﬁeld and the armature magnetic ﬁeld perpen-dicular to each other when the motor is running. For the purpose of realizing commutationwithout mechanical contact, brushes were abandoned after the “inverted DC motor” wasdeveloped in which armature winding and magnet steel are placed on the stator and rotor sidesseparately. In order to control the motor’s rotation speed and direction, a rotor-position sensor,a control circuit, together with a power inverter must be included in a BLDC motor system.Figure 2.1 shows a BLDC motor experimental system.
Compared with other kinds of motors, the BLDC motor is excited by a square wave, so that
the motor has lots of advantages, such as higher permanent magnet utilization, smaller size,
Permanent Magnet Brushless DC Motor Drives and Controls , First Edition. Chang-liang Xia.
/C2112012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd.

larger motor torque, higher efﬁciency and reliability. Therefore, the BLDC motor plays an
important role in product quality improvement, service life extension and energy saving.These superiorities are becoming even more evident along with the presence of higherperformance and lower price of new types of NdFeB.
The BLDC motor’s structure contains a stator with armature winding and a rotor with a
permanent magnet, which is similar to PMSM. The cross-sectional image of a four-pole BLDCmotor is shown in Figure 2.2.
2.1.1.1 Stator Cores
The stator structure of the BLDC motor is similar to that of a general synchronous motor or an
induction motor. Single- or multiple-phase symmetric windings are embedded in the iron core,which can be connected in “Y” or “ D” type. Considering the performance and the cost of
the system, the Y-type is mostly used, in which the three phase windings are connectedsymmetrically without a neutral point. Note that in the traditional brush DC motor, the
armature winding is placed at the rotor, whereas the armature winding is installed at the stator
side in the BLDC motor, causing less heating.
Figure 2.1 The BLDC motor experimental system.
coil PM materialrotorstator
N
NS S
Figure 2.2 Cross-sectional image of a BLDC motor.26 Permanent Magnet Brushless DC Motor Drives and Controls

2.1.1.2 Windings
The common winding types used in BLDC motors are concentrated full-pitch windings,
distributed full-pitch windings, distributed short-pitch windings, etc. The different types ofwindings can affect the waveform of the back-EMF and the performance of the motor.
(1) For the concentrated full-pitch winding, the wires of the same phase are placed in one
cog, and therefore the air-gap ﬂux density in the motor is the same. By adding the back-
EMF generated by wires of each phase, we can get the waveform of the total back-EMF,
which has a similar shape as the air-gap ﬂux de nsity. Furthermore, the platform width of
the back-EMF waveform is the same as that of the air-gap ﬂux density waveform. Thus,
the concentrated full-pitc h winding can produce a better trapezoidal back-EMF.
(2) For the purpose of cooling the winding effectively through the inner surface space of the
stator, the coil winding can be dispersed evenly at the surface of the stator, which is calleddistributed winding. Under normal circumstances, it is hard for the spatial distribution of
air-gap ﬂux density to form an ideal square wave.
(3) On the other hand, application of the short-pitch winding makes it possible to shorten the
connecting wires at the end of the winding. This can be helpful to save copper material and
weaken the torque harmonics.
2.1.1.3 PM Rotor
The BLDC motor’s rotor is constituted by permanent magnets with certain pole pairs
embedded in the surface or the inside of the iron core. At present, the permanent magnetsare usually made using rare-earth permanent magnetic materials like NdFeB, which have theadvantages of high coercivity and remanence intensity. The permanent magnetic steels, in theBLDC motors as well as the brushed motors, are used to produce a sufﬁcient magnetic ﬁeld inthe air gap. The only difference between them is that in BLDC motors, PM steels are installedon the rotor side, whereas they are placed on the stator side in brushed motors. Three typical
structures of the BLDC motor rotors are as follows.
(1) Surface-mounted PM rotor. For the surface-mounted PM rotor, on the surface of the iron
core there is mounted radial magnetized tile-shaped rare-earth permanent magnet.
Furthermore, the tile-shaped poles can be assembled by rectangle strips so as to cutthe costs of the motor. In the design procedure of the motor, the designer always adopts thisstructure with its pole arc width larger than 120 degree electric angle in order to generate asquare air-gap ﬂux density and decrease torque ripple.
(2) Magnet-embedded rotor. When the rectangular permanent magnets are embedded into the
iron core of the rotor, we call it a magnet-embedded rotor. Since the magnetism gatheringtechnology can provide larger ﬂux, the ﬂux under one polar pitch is produced by twoadjacent poles in parallel. In this case, magnetism-isolating technology or a stainless steelshaft should be adopted.
(3) Magnetic loop rotor. For the magnetic loop rotor, a rare-earth PM ring magnetized radially
in multiple poles through a special way is overlapped around the iron core. Note that it isusually used in low-power motors.Mathematical Model and Characteristics Analysis of the BLDC Motor 27

2.1.1.4 Position Sensor
The position sensors installed in the motor can detect the rotor position and transform it into an
electrical signal, providing the correct commutation information for the logic switch circuit.Hence, the proper current commutation of the windings is obtained according to rotor positioninformation, and the PM rotor will rotate continuously because of the stepping rotatingmagnetic ﬁeld generated by the current in the air gap.
There are various kinds of position sensors and each has its own characteristics. At present, a
wide range of electromagnetic, photoelectric and magnetic sensors have been used in BLDCmotors. The Hall sensor, as a kind of magnetic sensor, has the advantages of compact volume,low price and convenient operation. Therefore, it is commonly used in BLDC motor controlsystems as the rotor-position detector.
2.1.2 General Design Method
The generally used methods of BLDC motor design mainly contain an electromagnetic designmethod (EMDM) and a ﬁeld-circuit method (FCM). The EMDM is used more frequently thanthe FCM for its simplicity. However, the FCM can be used to get more accurate results,
because it is allowed to check the magnetic ﬁeld of the design scheme with the ﬁnite element
method and make corresponding appropriate adjustments.
The EMDM is the traditional design method of BLDC motors. It mainly includes four steps:
(1) Conﬁrm the rotor structure according to the technical requirements; (2) Determine themagnetic load B
daccording to the rotor structure and the performance of permanent magnet;
(3) Decide the electrical load AbyBd; (4) Determine the basic size D,Laccording to AandBd.
Note that this method is easy to implement in practice. But its calculation precision isrelatively poor.
The FCM of BLDC motor design is based on the analysis of ﬁnite elements of magnetic
ﬁeld, where the magnetic and circuit parameters are obtained from the ﬁnite-element analysisand the electrical circuit, respectively. The high-precision analysis of magnetic ﬁeld (generallythe 2D calculation of the magnetic ﬁeld will meet the design requirements) is the mainadvantage of the method. But the amplitude and phase position of the equivalent current willchange when the magnetic ﬁeld is analyzed. So, the magnetic-ﬁeld analysis and the circuitcalculation must be carried out synchronously. Generally, the main procedure of the FCMdesign method is shown as Figure 2.3. As for the design optimization of BLDC motor, it will be
discussed in Section 5.5.
2.1.3 Drive Modes
2.1.3.1 Half-Bridge Mode
For Y-connected BLDC motors, the generally used three-phase half-bridge driving circuit is
shown in Figure 2.4. In the ﬁgure, LA,LBandLCrepresent the windings of phase A, B, and C,
respectively, and the power switches T 1,T2and T 3are connected to the t hree-phase windings
in series. The rotor position signals HA,HBandHCare used to drive the power switches after
being ampliﬁed so as to control the motor com mutation. During the commutation process,
the rotating step magnetic ﬁeld generated by each stator winding in the air gap has three28 Permanent Magnet Brushless DC Motor Drives and Controls

magnetic states in the range of 360/C14electrical angle, where each state holds on a 120/C14
electrical angle.
Although the three-phase half-bridge driving BLDC motor control system has the advan-
tages of fewer drive components, lower cost, easy to control, it is seldom used because of its
disadvantages of large torque ripples and low utilization of the windings. In this condition,each winding is conducted only 1/3 of the period.Determine the design
requirements
Determine the rotor structure style
Estimate A and Bδ, determine the basic size D,
L, and design the stator structure
Determine the magnetic steel, and design the
rotor structure
Calculate the magnetic circuit, solve the magnet working diagram,
analyze and adjust the no-load magnetic ﬁeld with ﬁnite element method
Design the windings
Design the electromagnetic parameters
Calculate the working characteristic
Calculate the starting characteristic
Results outputCheck A and Bδ
Check and adjust
Check and adjust
Figure 2.3 Flowchart of BLDC motor design.Mathematical Model and Characteristics Analysis of the BLDC Motor 29

2.1.3.2 Full-Bridge Mode
In the following content we will introduce the full-bridge driving circuit while taking the three-
phase Y-connected BLDC motor as an example. Figure 2.5 shows the schematic diagram of thefull-bridge driving circuit. In the diagram, power switches T
1,T2,T3,T4,T5and T 6are used to
turn on or turn off the currents of the windings according to the logic signals produced by Hallsensors. The mainly used conduction modes are the two-phase conduction mode and the three-
phase conduction mode.
1) Two-phase conduction mode
The principle of the two-phase mode is conducting two of the motor windings all the time as
well as suspending the third one. The conduction order and instant are determined by the rotorposition information that is generated by the sensors. In this condition, the synthetic rotatingmagnetic ﬁeld generated by the stator is a step ﬁeld instead of a continuous one. The bridgeconverter commutates once the rotor rotates a 60
/C14electrical angle, and the magnetic status
is consequently changed. So, there are six magnetic statuses and two phase windings areconducting in each state. The time of current ﬂowing continuously in each winding is 120
/C14
electric angles.
In the two-phase mode, there is only one upper bridge switch conducted at a time, which
produces the forward ﬂowing current in the corresponding winding, resulting in a torque.Similarly, another torque is produced by the backward current because of the lower bridgeswitch conduction. The sum of these torques constitutes the synthetic torque, which rotates 60
/C14T1T3
BA
CUdT2
Cd+
_LA
LB
LC
Figure 2.4 Half-bridge driving circuit.
T1 T5
BA
CUdT3
T4 T2 T6Cd+
_
Figure 2.5 Full-bridge driving circuit.30 Permanent Magnet Brushless DC Motor Drives and Controls

electrical angles at each commutation period. Therefore, the torque ripples are much smaller
than that of a half-bridge driving system because the direction of torque changes six times in
one cycle.
2) Three-phase conduction mode
In the three-phase conduction mode, there are three power switches of the bridge energized
every moment. Compared with the two-phase conduction mode, the three-phase conduction
mode has the same driving circuit as shown in Figure 2.5. The only difference between thesetwo modes is the order of conducting, and each power switch conducts 180
/C14in the three-phase
conduction mode.
The three-phase conduction mode can further increase the utilization of the windings as well
as reduce the torque ripples. However, it should be noted that the three-phase conduction modemay possibly lead to the upper and lower switches of the same bridge being conducted at thesame time.
The principle diagram of a D-connected three-phase full-bridge BLDC motor control
system is shown in Figure 2.6. As shown in the ﬁgure, there are few differences betweenD–connected and Y- connected driving circuits. The only thing we need to do is consider theconnection point of phase A and B in the D-connected motor as the point A in the Y-connected
motor, while the connection point of phase B and C as B point, and the connection point ofphase C and A as C point.
2.1.3.3 C-Dump Mode
In some applications of BLDC motors, good con trol performance, low cost and small size are
all required. In order to meet these requirements, a compromised method between half-
bridge control and full-bridge control was proposed by Walter and Stephen [1], which is
called a C-Dump driving circuit. As shown in the Figure 2.7, only four power switches areused in the C-Dump driving circuit of the th ree-phase BLDC motor. The four-quadrant
operation of the motor can be achieved thr ough this driving mode.
Compared with the full-bridge driving mode, there are fewer power switches and energy
losses under the C-dump driving mode. However, larger commutation torque ripples may beproduced.
T1 T5
Ud
T4 T6T3
T2Cd+
_A
CB
Figure 2.6 Full-bridge driving circuit for D–connected motor.Mathematical Model and Characteristics Analysis of the BLDC Motor 31

2.1.3.4 H-Bridge Mode
Figure 2.8 shows the principle of the H-bridge power inverter. The typical feature of the
H-bridge is that each winding is controlled by an H-bridge power inverter separately.The current of the BLDC motor can be controlled by this driving circuit easily. Moreover,
the four-quadrant operation can also be achieved with this driving mode.
Note that each H-bridge power inverter has 4 power switches for one phase winding. So, it
is usually used in single-phase or two-phase B LDC motors. A delay control of the driving
signals must be taken to prevent the upper and lower switches of the same bridge arm from
being conducting at the same time. This means that the switches of one side will conductunder the condition that the switches of the other side have been turned off reliably.Consequently, the dead-band time has to be longer than the turn-off time of the correspondingpower switch [2].
2.1.3.5 Four-Switch Mode
The structure of four-switch driving circuit is shown in Figure 2.9. In the topology, one bridge
of the full-bridge driving circuit is replaced with two capacitances. The neutral point of the twocapacitances is connected to the phase-C winding. Thus, two power switches are saved in thefour-switch driving circuit so that the system has lower cost and less loss, whereas the controlalgorithm will be more complicated [3].T1 T2 T3Ud
TrC0Cd D1D2D3
BA
C+
_
Figure 2.7 C-dump driving circuit.
T1 T3
T4 T2Ud+
_
Figure 2.8 H-bridge driving circuit.32 Permanent Magnet Brushless DC Motor Drives and Controls

2.2 Mathematical Model
2.2.1 Differential Equations
In this section, the differential equation model is built for a three-phase two-pole BLDC motor.
The stator has a Y-connected concentrated full-pitch winding, and the inner rotor has a
nonsalient pole structure. Three Hall sensors are placed symmetrically at 120/C14interval.
Furthermore, the following assumptions are made to build the differential equation of the
BLDC motor [4–6].
(1) Ignore the core saturation, as well as the eddy current losses and the hysteresis losses.
(2) Ignore the armature reaction, and the distribution of air-gap magnetic ﬁeld is thought to be
a trapezoidal wave with a ﬂat-top width of 120/C14electrical angle.
(3) Ignore the cogging effect and suppose the conductors are distributed continuously and
evenly on the surface of the armature.
(4) Power switches and ﬂywheel diodes of the inverter circuit have ideal switch features.
Hence, the simpliﬁed schematic diagram of the motor can be obtained as shown in
Figure 2.10.T3
BA
CUd
T2T1
T4Cd+
_C1
C2
Figure 2.9 Four-switch driving circuit.
Phase A
axis
eXiA
AψAiA
iB
iCA
B CX
Y Z NA θX B
CB
Y
AZC
SNdq
(c) Provision of positive direction (Phase A) (a) Structure of BLDC motor (b) Connecting type of winding
Figure 2.10 Schematic diagram of the BLDC motor.Mathematical Model and Characteristics Analysis of the BLDC Motor 33

Under the positive direction shown in Figure 2.10, the phase voltage of each winding, which
includes the resistance voltage drop and the induced EMF, can be expressed as
ux¼Rxixțecx ð2:1Ț
where
ux— phase voltage, in which subscript xdenotes phase A, B and C;
ix— phase current;
ecx— phase-induced EMF;
Rx— phase resistance. For three-phase symmetrical winding, there exists RA¼RB¼RC¼R.
The winding-induced EMF is equal to the change rate of the ﬂux. Since the positive
direction of induced EMF and ﬂux linkage deﬁned in Figure 2.10 is opposite to that of the
right-hand screw rule, the induced EMF can be written as
ecx¼dcx
dtð2:2Ț
Taking phase A for example, the ﬂux is given as
cA¼LAiAțMABiBțMACiCțcpmðyȚð 2:3Ț
where
cpm(y) — PM ﬂux linkage of phase A;
y— position angle of rotor, the angle between rotor d-axis and the axis of phase A;
LA— self-inductance of phase A;
MAB,MAC— mutual inductance of phase A with phase B and phase C.
The magnitude of cpm(y) depends on the magnetic ﬁeld distribution of the PM in the air gap.
The radial component of PM air-gap magnetic ﬁeld distributes as a trapezoidal proﬁle along
the inner surface of the stator, is shown in Figure 2.11.
As shown in Figure 2.11, when the rotor rotates anticlockwise, the winding AX moves in the
forward direction along the y-axis. Then, the effective ﬂux of phase Awill change with regard
to the rotor position. When the rotor position is a, the PM ﬂux of phase A is
cpmðaȚ¼NfpmðaȚð 2:4Ț
jpmðaȚ¼ðp
2ța
/C0p
2țaBðyȚSdy ð2:5Ț
where
Fpm(a) — PM ﬂux of phase A when the rotor position angle is a;
B(y) — PM rotor radial ﬂux density in the air gap, which is in a trapezoidal distribution
along y;34 Permanent Magnet Brushless DC Motor Drives and Controls

N— turns of winding;
S— product of rotor radius and effective length of conductors.
Substituting Equations (2.2)–(2.5) into Equation (2.1), we can get
uA¼RiAțd
dtðLAiAțMABiBțMACiCțcpmȚ
¼RiAțd
dtðLAiAțMABiBțMACiCȚțd
dtNSðp
2țy
/C0p
2țyBðxȚdx"#
¼RiAțd
dtðLAiAțMABiBțMACiCȚțeAð2:6Ț
where eArepresents the back-EMF of phase A.
Equation (2.6) includes a derivativeoperation of the product ofinductance and current, where
the self-inductance and the mutual inductance of the winding is proportional to N2(Nrepresents
the number of turns) and the permeance of the corresponding magnetic circuit. That is
LA¼N2LA ð2:7Ț
MAB¼N2LAB ð2:8Ț
where
LA— permeance of self-inductance ﬂux in phase A;
LAB— permeance of mutual inductance ﬂux between phase A and phase B.
The permeability of salient pole rotor differs in directions of the d-axis and the q-axis,
consequently the self-inductance and mutual inductance of winding changes with the rotor
position [7]. Therefore, the inductance also changes with the rotor position. But for the
nonsalient pole rotor, the ﬂux is isotropic in all directions. Hence, the permeability of themagnetic circuit cannot be affected by rotor position. So, the self-inductance and mutualinductance will not vary with time. The effect of rotor saliency on winding inductance is shownin Figure 2.12.S NB
θX
Aα
BmαN
SPhase A axis
Ω
0A XAd
(b) Flux distribution (a) Rotor position
Figure 2.11 PM ﬂux of phase A.Mathematical Model and Characteristics Analysis of the BLDC Motor 35

Generally, the surface-mounted salient-pole rotor is used for BLDC motors. In this con-
dition, the winding inductance will not change with the time. Further, as the three-phase stator
windings are symmetrical, the self-inductances will be equal, and so as the mutual inductance.
That is LA¼LB¼LC¼L,MAB¼MBA¼MBC¼MCB¼MAC¼MCA¼M. Substituting them
into Equation (2.6), we can get
uA¼RiAțLdiA
dtțMdiB
dtțMdiC
dtțeA ð2:9Ț
in which
eA¼d
dtNSðp
2țy
/C0p
2țyBðxȚdx"#
¼NS Bp
2țy/C16/C17
/C0B/C0p
2țy/C16/C17 hidy
dt
¼NSoBp
2țy/C16/C17
/C0B/C0p
2țy/C16/C17 hið2:10Ț
where ois the electrical angular speed of motor.θ=0ș
θ=180ș θ=270ș θ=150ș θ=240șθ=90ș θ=−30ș θ=60șA
dBA
d A
d
AA
dX
YA
XA XAX
AB
YXAB
YX
A
BY
XA
Bd
BA
B
A
BAd
ddA X
-30ș 60ș 150ș 240ș 330ș θ
MAB
0ș θLA
90ș 180ș 270ș 360ș
Figure 2.12 Effect of rotor saliency on magnetic circuit.36 Permanent Magnet Brushless DC Motor Drives and Controls

According to the distribution of magnetic density in the air gap as shown in Figure 2.11(b),
together with B(y) having a period of 2 pandB(yțp)¼–B(y), we can get
eA¼NSoBp
2țy/C16/C17
/C0B/C0p
2țy/C16/C17 hi
¼NSoBp
2țy/C16/C17
/C0Bp
2țyțp/C02p/C16/C17 hi
¼2NSoBp
2țy/C16/C17ð2:11Ț
Then, the y-dependent back-EMF wave of phase A is p/2 ahead of the distribution of the
magnetic density in air gap, and eAcan be expressed as
eA¼2NSoBmfAðyȚ¼ocmfAðyȚð 2:12Ț
where
Bm— maximum value of PM density distribution in air gap;
cm— maximum value of PM ﬂux linkage of each winding, cm¼2NSB m;
fA(y) — back-EMF waveform function of phase A.
Note that the fA(y) has a trapezoidal distribution with the rotor position, and its maximum
and minimum values are, respectively, 1 and –1. The corresponding waveform and its phase
relationship with B(y) and eAare shown in Figure 2.13. As for the three-phase symmetrical
windings, there also exist fB(y)¼fA(y–2p/3), and fC(y)¼fA(yț2p/3).
It can be seen from Equation (2.10) that eAis a rotating back-EMF that is produced by the
winding ﬂux linkage caused by the rotating rotor.
As the currents of the three phases satisfy
iAțiBțiC¼0 ð2:13Ț
eA
B(θ)
0 π/2 π 3π/2 2π 5π/2 3π 7π/2 4π
0 π/2 π 3π/2 2π 5π/2 3π 7π/2 4πB(θ)B(θ), eA
B(θ), fA(θ) θ
θfA(θ)
Figure 2.13 Phase relationship between B(y),eA, and fA(y).Mathematical Model and Characteristics Analysis of the BLDC Motor 37

Equation (2.9) can be further simpliﬁed as
uA¼RiAțðL/C0MȚdiA
dtțeA ð2:14Ț
Then, the matrix form of phase voltage equation of BLDC motor can be expressed as
uA
uB
uC2
435¼R00
0R0
00 R2435i
A
iB
iC2435țL/C0M 00
0 L/C0M 0
00 L/C0M2435
d
dtiA
iB
iC2435țe
A
eB
eC2435ð2:15Ț
According to Equation (2.15), the equivalent circuit of the BLDC motor can be shown as in
Figure 2.14.
In most practical applications of BLDC motors, the stator windings are Y-connected in
which there is no neutral point brought out so that the phase voltages are difﬁcult to detect.
Thus, the mathematical model based on phase voltage is not applicable in some cases. Incontrast, the line voltage is easy to measure. It is approximately equal to the DC bus voltagewhen the relevant power transistors are turned on. Therefore, the mathematical model based online voltage is more suited to the practical system.
The line voltage equation can be obtained through subtraction calculation of the phase-
voltage equation as
u
AB
uBC
uCA2
435¼R/C0R 0
0 R/C0R
/C0R 0 R2435i
A
iB
iC2435țL/C0MM /C0L 0
0 L/C0MM /C0L
M/C0L 0 L/C0M2435
d
dtiA
iB
iC2435țe
A/C0eB
eB/C0eC
eC/C0eA2435
ð2:16Ț
Similar to DC motors, the analysis of power and torque for the BLDC motor can be carried out
from the perspective of energy transfer. When the motor is operating, the power from the
source is absorbed, and although a little is turned into copper loss and iron loss, most of the
power is transferred through the air gap to the rotor by the torque effect. The power transferredto the rotor, which is called the electromagnetic power, equals the sum of the product of currentand back-EMF of the three phases. That is
P
e¼eAiAțeBiBțeCiC ð2:17ȚR
R
RL–MeA
eB
eCiA
iB
iCuA
uB
uC+
+
+L–M
L–M–
–
–
Figure 2.14 Equivalent circuit of the BLDC motor.38 Permanent Magnet Brushless DC Motor Drives and Controls

Ignoring the mechanical loss and stray loss, the electromagnetic power is totally turned into
kinetic energy, so
Pe¼TeO ð2:18Ț
where
Te— electromagnetic torque;
O— angular velocity of rotation.
Hence, from Equations (2.17) and (2.18), we can get
Te¼eAiAțeBiBțeCiC
Oð2:19Ț
Substituting Equation (2.12) into Equation (2.19), another form of the torque equation can be
represented as
Te¼p½cmfAðyȚiAțcmfBðyȚiBțcmfCðyȚiC/C138ð 2:20Ț
where pis the number of pole pairs.
When the BLDC motor runs in the 120/C14conduction mode and the corresponding transient
commutation process is ignored, the currents that have the same amplitude and the oppositedirection only ﬂow through two-phase windings of the Y-connected motor at any time. Notethat the symbols of f(y) at the ﬂat-top position are opposite to each other for different windings,
so Equation (2.20) can be further simpliﬁed as
T
e¼2pcmiA¼KTi ð2:21Ț
where
KT— the torque coefﬁcient;
i— the steady phase current.
In order to build a complete mathematical model of the electromechanical system, the
motion equation has to be included as
Te/C0TL¼JdO
dtțBvO ð2:22Ț
where
TL— load torque;
J— rotor moment of inertia;
Bv— viscous friction coefﬁcient.
Thus, Equations (2.15), (2.19) and (2.22) constitute the differential equation mathematical
model of the BLDC motor.Mathematical Model and Characteristics Analysis of the BLDC Motor 39

2.2.2 Transfer Functions
The transfer function is one of the most important concepts of control theory, and the transfer-
function-based mathematical models are widely used in automatic control ﬁelds. Some controldesign and analysis methods, such as the root-locus method and the frequency-responsemethod, are also developed based on the system transfer function.
The transfer function of the BLDC motor is signiﬁcant for the performance analysis and
control design of the motor. Compared with the traditional brushed DC motor, the windings ofthe BLDC motor are energized according to the rotor position, and the motor is usuallydesigned to be three-phase or multiphase. However, for each conducted phase winding, themechanisms of back-EMF and electromagnetic torque are all the same with those of thetraditional brushed DC motor, thus similar analysis methods can be adopted.
Suppose that the three-phase BLDC motor is controlled by the full-bridge driving in the
two-phase conduction mode, then when the windings of phase A and B are conducted, thereexists
i
A¼/C0iB¼i
diA
dt¼/C0diB
dt¼di
dt8
<
:ð2:23Ț
Thus, the line-voltage UABin Equation (2.16) can be rewritten as
uAB¼2Riț2ðL/C0MȚdi
dtțðeA/C0eBȚð 2:24Ț
Take the transient process out of consideration (i.e. ignore the trapezoid bevel edge), then the
steady eAandeBare equal in amplitude and opposite in direction when phases A and B are
turned on. So, Equation (2.24) can be expressed as
uAB¼Ud¼2Riț2ðL/C0MȚdi
dtț2eA¼raițLadi
dtțkeO ð2:25Ț
where
Ud— DC bus voltage;
ra— line resistance of winding, ra¼2R;
La— equivalent line inductance of winding, La¼2(L–M );
ke— coefﬁcient of line back-EMF, ke¼2pcm¼4pNSB m.
Equation (2.25) is exactly the armature voltage loop equation when two phase windings are
excited, and the corresponding equivalent circuit is shown in Figure 2.15.
Note that the equivalent circuit shown in Figure 2.15 could be adopted in three-phase half-
bridge driving and three-phase full-bridge driving modes of the BLDC motor with speciﬁc ke
andKTtoo.40 Permanent Magnet Brushless DC Motor Drives and Controls

In Equation (2.25), if the current can be expressed by angular velocity, then we can get the
transfer function of motor by obtaining the relationship between bus voltage and angular
velocity. So, substituting Equation (2.21) into Equation (2.22), we get
KTi/C0TL¼JdO
dtțBvO ð2:26Ț
First, when the BLDC motor runs with no load, the current is given as
i¼J
KTdO
dtțBv
KTO ð2:27Ț
Substituting Equation (2.27) into Equation (2.25), we get
Ud¼raJ
KTdO
dtțBv
KTO/C18/C19
țLad
dtJ
KTdO
dtțBv
KTO/C18/C19
țkeO ð2:28Ț
Also, it can be rearranged as
Ud¼LaJ
KTd2O
dt2țraJțLaBv
KTdO
dtțraBvțkeKT
KTO ð2:29Ț
By Laplace transformation of Equation (2.29), the transfer function of a BLDC motor can beexpressed as
G
uðsȚ¼OðsȚ
UdðsȚ¼KT
LaJs2țðraJțLaBvȚsțðraBvțkeKTȚð2:30Ț
Thus, the structure of a BLDC motor control system with no load can be built as shown inFigure 2.16.ra La i
keΩ+
−Ud+
_
Figure 2.15 Equivalent circuit of the BLDC motor with two phase windings excited.Mathematical Model and Characteristics Analysis of the BLDC Motor 41

Equation (2.30) implies that the BLDC motor can be considered as a second-order system,
so it can be rearranged as
GuðsȚ¼KT
raBvțkeKTo2
n
ðs2ț2xonsțo2
nȚð2:31Ț
where
on¼ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
raBvțkeKT
LaJr
— natural frequency of the second-order system;
x¼1
2raJțLaBvﬃﬃﬃﬃﬃﬃﬃLaJp ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
ðraBvțkeKTȚp — damping ratio of the second-order system.
It can be seen from Equation (2.31) that the two roots of the characteristic equation for the
BLDC motor’s second-order system are s1;2¼/C0xon/C6onﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
x2/C01p
. So the system response
time is determined by onandx. For unit step input, the convergence speed of the response
curve depends on on. A larger ongenerally leads to a faster convergence speed. Meanwhile,
the parameter xwill determine the character of eigenvalues and the shape of the response
curve. The system runs underdamping, critical damping and overdamping states, respectively,
when 0GxG1,x¼1, and xH1. The response curves for different damping ratios are shown
in Figure 2.17.I(s) Ud(s) Te(s) Ω(s)
Ea(s) −KT
kera + Las1 1
Js+Bv
Figure 2.16 Structure of BLDC motor control system with no load.
tΩ ξ= 0.2 ξ= 0.4
ξ= 0.6 ξ= 0.8 ξ= 1.0ξ= 0
0
Figure 2.17 Response curves of BLDC motor.42 Permanent Magnet Brushless DC Motor Drives and Controls

Let the mechanical time constant be tm¼raJțLaBv
raBvțkeKTand the electromagnetic time
constant be te¼LaJ
raJțLaBv, then Equation (2.30) can be rewritten as
GuðsȚ¼KT
raBvțkekT1
ðs2tmtețstmț1Țð2:32Ț
Generally speaking, the mechanical time constant is much larger than the electromagnetic
time constant, i.e. tm/C29te, so the transfer function expressed in Equation (2.32) can be further
simpliﬁed as
GuðsȚ/C25KT
raBvțkeKT1
ðs2tmtețstmțsteț1Ț
¼KT
raBvțkeKT1
ðstmț1Țðsteț1Țð2:33Ț
It is seen from Equation (2.33) that the transfer function of BLDC motor can be expressed bytwo inertia elements in series [8]. Figure 2.18 shows the corresponding speed respondingprocess with step input.
In Figure 2.18, we can learn the physical meaning of time constant in a transfer function.
When a step voltage is applied to the input, ﬁrst the current will respond to voltage change
through the 1/( st
eț1) link, and its time constant is te. Then, the speed will respond to the
current change through the 1/( stmț1) link, where tmis the corresponding time constant.
Figure 2.18 has shown the interconnection between armature current and angular speed.
If the effect of electromagnetic time constant is ignored, i.e. the armature inductance is
negligible, then Lacan be deemed to be zero, so Equation (2.32) can be simpliﬁed into a ﬁrst-
order model as
GuðsȚ¼KT
raBvțkeKT1
stmț1ð2:34Ț
The corresponding system structure diagram is shown in Figure 2.19.
Further, the step response of Equation (2.34) is given by
OðtȚ¼KTUd
raBvțkeKTð1/C0e/C0t=tmȚð 2:35Ț
Figure 2.20 shows the corresponding response curve.
Ud(s) I(s)
Ud(t) i(t) Ω(t)Ω(s)
ste + 11
stm + 11
raBv+ keKTKT
tt t
Figure 2.18 Speed responding process with step input.Mathematical Model and Characteristics Analysis of the BLDC Motor 43

It is known from Figure 2.20 that a smaller tmleads to a shorter settling time of O(t). For a
speed-control system, it is desirable that the delay time of speed response be short enough. If
the mechanical time constant is big, a rational closed control system should be designed to
increase the response speed. For example, a voltage or current ampliﬁer with large gain used inan analog control system as well as the larger proportional gain of PI controller in digitalcontrol system can all increase the open-loop gain of the system. Consequently, the rise time ofthe speed response will be reduced. However, too large a gain would bring more losses ofpower switches so as to reduce the efﬁciency of system. Furthermore, from the controlviewpoint, a large proportional gain may cause oscillation and instability. Therefore, thestability and the system response speed should be considered together in system design. The
response speed should be increased under the condition of stability.
In the following, the transfer function and speed step response of a BLDC motor when the
load torque is not zero will be discussed. In this condition, the load torque can be regarded as an
input of the system, as shown in Figure 2.21.
For such a system, the superposition principle holds. Thus, the output of the system equals
the sum of outputs when U
d(s) and TL(s) are applied to the system, respectively. In Figure 2.21,
when Ud(s)¼0 holds, then
/C0ke1
rațLasKTOðsȚ/C0TLðsȚ/C20/C211
JsțBv¼OðsȚð 2:36Ț
So
OðsȚðrațLasȚðJsțBvȚțkeKT
ðrațLasȚ/C20/C21
¼/C0TLðsȚð 2:37ȚKTI(s) Te(s)
Ea(s)ra1 Ud(s) Ω(s)
−
keJs+Bv1
Figure 2.19 System structure diagram of BLDC motor with the armature inductance neglected.
tΩ
tm 0raBv+ keKT0.6KTUd= Ωtm Ωtm
Figure 2.20 Speed step response of BLDC motor neglecting the armature inductance.44 Permanent Magnet Brushless DC Motor Drives and Controls

Then, the transfer function between load torque and speed is
GLðsȚ¼OðsȚ
TLðsȚ¼/C0rațLas
LaJs2țðraJțLaBvȚsțðraBvțkeKTȚð2:38Ț
Therefore, the speed response of a BLDC motor affected together by voltage and load torque is
given by
OðsȚ¼ GuðsȚUdðsȚțGLðsȚTLðsȚ
¼KTUdðsȚ
LaJs2țðraJțLaBvȚsțðraBvțkeKTȚ/C0ðrațLasȚTLðsȚ
LaJs2țðraJțLaBvȚsțðraBvțkeKTȚ
ð2:39Ț
2.2.3 State-Space Equations
In modern control theory, the motion state of control system relies on its state equation. The
state-space equation method is one of the most important analysis methods in modern controltheory. From the state equation we can get all the independent variables and then determine allthe motion states of the system. A group of ﬁrst-order differential equations with state variablesis used in the state-space method to describe the dynamic characteristics of the system. Since itis helpful to the realization of different digital control algorithms, the state-space method isbecoming more and more popular in designing control systems with the fast development ofcomputer techniques. Especially in recent years, computer on-line control systems such as
optimal control, Kalman ﬁlters, dynamic system identiﬁcation, self-adaptive ﬁlters and self-
adaptive control have been applied to motor control. All these control techniques are based onthe state equation.
The state equations of a BLDC motor can be obtained by the algebraic transformation of the
differential equation model. First, appropriate variables should be selected as state variables.The selection of state variables is not unique, but they should be independent of each other.Moreover, the number of state variables should be equal to the order of the differentialequation. Currents of three phase windings and the angular speed are selected here as state
variables, and the fourth-order state equation is then derived as
_x¼AxțBu ð2:40Țʵʵ
KT
keI(s) Ud(s) T (s)e
Ea(s)T
ΩL(s)
ra + L as1(s)
Js+Bv1
Figure 2.21 Structure diagram of BLDC motor with load torque.Mathematical Model and Characteristics Analysis of the BLDC Motor 45

where x¼iAiBiCO ½/C138T;
u¼uAuBuCTL ½/C138T;
A¼/C0R
L/C0M00 /C0pcpmðyȚ
L/C0M
0 /C0R
L/C0M0 /C0pcpmy/C02p
3/C18/C19
L/C0M
00 /C0R
L/C0M/C0pcpmy/C04p
3/C18/C19
L/C0M
p
JcpmðyȚpJc
pmy/C02p
3/C18/C19pJc
pmy/C04p
3/C18/C19
/C0Bv
J2
6666666666666643
777777777777775;
B¼
1
L/C0M00 0
01
L/C0M00
001
L/C0M0
000 /C01
J2
6666666643
777777775:
In Equation (2.40), the angular position of the rotor can be detected by a position sensor. As
the armature reaction is ignored, the PM ﬂux linkage c
pm(y) is only a function of y, which is
independent of current and speed. Hence, cpm(y) can be regarded as a coefﬁcient of the
equation. As ychanges with regard to time when the motor is running, matrix Ais time-
varying. Thus, the state equation represented as Equation (2.40) denotes a time-varying
multiple-input multiple-output (MIMO) continuous linear system.
The controllability of a linear system is the base of optimal control and optimal estimation,
so it should be determined. Assume the controllability matrix is
M¼M0M1M2M3 ½/C138 ð 2:41Ț
where M0¼B,MiðtȚ¼AiB,i¼1, 2, 3.
Then, matrix Mcan be transformed to
M¼l00 0
0l00
00 l 0
000 /C01
JM1M2M32
66643
7775ð2:42Ț
where l¼1=ðL/C0MȚ.
The matrix Mmeets the condition of rank [ M]¼4. So, the system represented by
Equation (2.40) is controllable and all the poles of the system can be arbitrarily placed by
state feedback.46 Permanent Magnet Brushless DC Motor Drives and Controls

2.3 Characteristics Analysis
2.3.1 Starting Characteristics
The starting characteristics are the variation curves of the speed and current in the process of
the speed rising from 0 to the stable value under constant DC bus voltage. At the instant of
starting, both the speed and back-EMF are 0, and the armature current can be represented as
I¼Ud/C0DU
rað2:43Ț
where DUis the voltage drop of the power switches of the bridge inverter.
The curves of speed and armature current in the starting process are shown in Figure 2.22.
It can be seen from Figure 2.22 that, since the voltage drop of the power switches and the
armature winding resistance are all small, the starting current will be large in a short period oftime. It may reach several times or more than ten times the normal operating current. Withinthe allowable range, the large starting current is helpful to the acceleration of the rotor so thatthe motor can quickly start even under full load. For example, if the motor runs under ratedoperating conditions, both the startup speed and back-EMF will be 0. Moreover, the armaturecurrent increases rapidly in the instant of starting. Thus, the electromagnetic torque is muchlarger than the load torque so that the speed increases rapidly. Consequently, the back-EMFwill increase so that the growth of armature current becomes slower until it reaches the
maximum. Then, the armature current begins to decrease. The decreased current will lead to a
decrease of the electromagnetic torque, so the rising acceleration of the speed becomessmaller. When the electromagnetic torque and load torque achieve the dynamic balance, thespeed will stay in the rating value, i.e. the BLDC motor will maintain steady-state operation.
Without considering the limit of the starting current, the shape of the speed curve in
Figure 2.22 is determined by the damping ratio of the motor. According to the transfer functionof the motor, when the damping ratio is 0 GxG1, the system is in the underdamped
condition, the speed and current will become stable after a process with overshoot and
oscillation, as shown in Figure 2.23. It can be seen that the shape of the speed step response in
Figures 2.22 and 2.23 are in accord with that in Figure 2.17. In practice, due to the restrictionson the armature current, the speed and current oscillations shown in Figure 2.23 will not appearwhen the motor is starting.
tI
t 0 0n
Figure 2.22 Curves of speed and current during the starting process.Mathematical Model and Characteristics Analysis of the BLDC Motor 47

In the motor control system, power switches of driving circuit are more sensitive to the
overcurrent. If the current exceeds its upper limit, the power switches will suffer from
breakdown in a short period of time. For example, the enduring time of overcurrent for IGBT isnormally less than 10 ms. Generally, large-capacity power switches are chosen to stand the high
starting current. However, the rated current of the motor is much smaller than the starting
current. Thus, the current of the power switch is less than its rated value during most of the
normal running. In this condition, the utilization efﬁciency of the switches decreases so that itscost increases. Therefore, in the design of the driving circuits, it is better to select suitablepower switches according to the starting characteristics and working requirements of themotor. In addition, the starting current has to be limited appropriately. Note that the startingcurrent should increase as much as possible to improve the dynamic response speed when thesafety of the power switches is ensured. Since the magnetic ﬁeld has a trapezoidal distributionin the air gap of the BLDC motor, then if the phase winding conducts in the trapezoidal bevel
edge of the back-EMF, the back-EMF will be smaller. Thus, the armature current is becoming
larger. So, compared to the traditional DC motor, the starting current of the BLDC motor maybe larger. This should be considered in the design of the driving circuits.
2.3.2 Steady-State Operation
2.3.2.1 Operating Characteristics
The operating characteristics indicate the relationships between armature current, motor
efﬁciency and output torque with a constant DC bus voltage Ud.
According to Equation (2.21), the armature current will increase with the increasing of load
torque so that the electromagnetic torque can balance the load torque. Hence, stable running ofthe motor is assured.
Since the input power of the motor can be given as
P
1¼UdI¼raI2țp
30kenIțDUI ð2:44Ț
and
P1¼PCuțPețPT ð2:45ȚI
t0t 0n
Figure 2.23 Overshoot and oscillation in starting process.48 Permanent Magnet Brushless DC Motor Drives and Controls

where
n— the motor speed;
PCu— the armature copper loss ( PCu¼raI2);
Pe— electromagnetic power ( Pe¼keOI);
PT— the loss of bridge power switches ( PT¼DUI), which is related to the characteristics of
power electronic switches and the voltage applied on the corresponding gate terminal of the
switch. Here, it is approximately considered a constant.
As shown in Equation (2.45), the input power consists of the electromagnetic power Peand
the loss PCuțPT.Peis the power consumed to overcome the back-EMF. It can be turned into
mechanical energy through the magnetic ﬁeld, which will act on the rotor in the form ofelectromagnetic torque. So, taking the loss of load into account, the power transfer can beexpressed as
P
e¼ðTLțT0ȚO¼P2țP0 ð2:46Ț
where
TL— load torque;
T0— no-load torque corresponding to no-load loss ( T0¼P0/O);
P2— output power ( P2¼TLO);
P0— no-load loss, including the core loss and mechanical friction loss.
Thus, the efﬁciency of the motor is given as
Z¼P2
P1¼P1/C0ðPCuțPTțP0Ț
P1¼1/C0PP
P1ð2:47Ț
Hence, Equation (2.47) can be further rewritten as
Z¼1/C0ra
UdI/C0PTțP0
UdIð2:48Ț
In order to ﬁnd the extreme value of Equation (2.48), the derivative of Zwith respect to Ishould
be equal to 0 as
dZ
dI¼/C0ra
UdțPTțP0
UdI2¼0 ð2:49Ț
Further, we can get
PTțP0¼raI2¼PCu ð2:50Ț
Note that the PTțP0in Equation (2.50) will not change with load variation, so it is deﬁned as
the invariable loss. But the copper loss PCuchanges with the load variation, so it is called theMathematical Model and Characteristics Analysis of the BLDC Motor 49

variable loss. Equation (2.50) shows that when the variable loss equals the invariable loss, the
maximum efﬁciency of the motor is achieved. Figure 2.24 shows the curves of armaturecurrent and efﬁciency of the BLDC motor with varied load torque and constant U
d.
2.3.2.2 Regulation Characteristic
Regulation characteristic denotes the relationship between the speed and Udwith constant
electromagnetic torque Te. If the loss of power switches is negligible, when the motor works in
steady state, there exist
Ud¼raIțp
30ken ð2:51Ț
and
KTI/C0TL¼p
30Bvn ð2:52Ț
Then
n¼30KT
pKTkețpraBvUd/C030ra
pKTkețpraBvTL ð2:53Ț
Figure 2.25 shows the n–Udcurves with different electromagnetic torques, where
Te1GTe2GTe3GTe4.
It can be seen from Figure 2.25 that there exists a dead zone in regulation characteristics.
When Udchanges within the dead zone, the electromagnetic torque is not big enough to
overcome the load torque to start the motor so that the speed is always zero. Only when the Ud
is greater than the threshold voltage can the motor start and run in the steady state. Moreover,
the greater the Ud, the bigger the steady-state speed.TLη
ηmax
I0
TLI
O O TN
(b) Efficienc y (a) Armature current
Figure 2.24 Curves of armature current and efﬁciency.50 Permanent Magnet Brushless DC Motor Drives and Controls

2.3.2.3 Mechanical Characteristic
Mechanical characteristics denote the relationship between speed and electromagnetic torque
with constant Ud. It can be derived from Equation (2.51) that
Te¼KT30Ud/C0pken
30rað2:54Ț
such that
n¼30
pKTUd/C0raTe
keKTð2:55Ț
From Equation (2.55), we can obtain curves of mechanical characteristics with different Ud,
as shown in Figure 2.26. In the ﬁgure, Ud1HUd2HUd3HUd4.
Note that Equation (2.55) is a linear equation. In practice, due to inﬂuences from the variable
loss and the armature reaction, the curve of mechanical characteristics is only considered asapproximately linear. As shown in Figure 2.26, with a certain DC bus voltage U
d, the speed of
the motor decreases on increasing the electromagnetic torque. Moreover, the curve will shiftupward as U
dincreases. Since the power electronic switches with nonlinear saturation
characteristics are used for the commutation of BLDC motors, the voltage drop of thepower switch will increase rapidly with increasing armature current when the motor runs near
the stalled condition. So, there will be a signiﬁcant downward bending phenomenon at the end
of the curve of the mechanical characteristics, as shown in Figure 2.26 [9].
As discussed above, the mechanical characteristics of BLDC motor are similar to those of a
separately excited DC motor. The no-load point of the mechanical characteristics may bealtered by changing the DC bus voltage. Therefore, the speed control of a BLDC motor isusually carried out by means of PWM modulation.n
UdTe1 Te2 Te3 Te4Te1<Te2<Te3<Te4
O
Figure 2.25 Regulation characteristics of BLDC motor.Mathematical Model and Characteristics Analysis of the BLDC Motor 51

2.3.3 Dynamic Characteristics
In this section, the dynamic characteristics of a BLDC motor refer to the motor transient
process with free acceleration and load torque variation. Figure 2.27 shows the simulationwaveform of the accelerating procedure for the BLDC motor from stall state to maximumspeed with no load and constant voltage power supply. The corresponding motor parametersare shown as follows: the stator resistance R¼0.620O, the stator equivalent inductance
L–M ¼1.000 /C210
/C03H,cm¼0.066 Wb, the moment of inertia J¼0.362 /C210–3kg m2,
the viscous friction coefﬁcient Bv¼9.444 /C210/C05N m s, the number of pole pairs p¼4, and
Ud¼300 V. The topology of the driving circuit is the DC power-supply–inverter structure,
where the inverter works in 120/C14conduction mode.
It can be seen from Figure 2.27 that the phase voltage and line voltage have a degree of slope
due to the effect of the trapezoidal back-EMF. Moreover, there are narrow pulses in the voltagewaveform. This is because of the voltage mutation caused by the conduction of thefreewheeling diode during the commutation period. The width of the narrow pulse isequal to the commutation period, which is dependent on the electromagnetic time constantand the running state of the motor. The variation of phase current and torque is similar to thatanalyzed in the starting process. The starting current and torque achieve more than 10 times
their rating values, respectively. But the steady current and torque are small at the no-load
condition. Note that the damping in the simulation is rather large, thus the speed curve inFigure 2.27 directly gets to the steady state without overshoot. The variation of the envelope ofback-EMF waveform is consistent with that of the speed curves.
The simulation results of the free acceleration process of the motor with the load torque
T
L¼6 N m are shown in Figure 2.28.
In this condition, the average of winding current is bigger, and the freewheeling process will
last a longer time during the commutation period, so that its inﬂuence on line or phase voltage
is also larger. Hence, in Figure 2.28, narrow pulses still exist in the voltage waveform at
the steady state. As for the current, the maximum of the starting current is approximately thesame as that in the no-load state. But the time is slightly longer to reach its maximum value, sothe heating of the motor and driving circuit is more serious. Generally, a series resistance or an
TeUd1
Ud2
Ud3
Ud4
O
Figure 2.26 Mechanical characteristics of BLDC motor.52 Permanent Magnet Brushless DC Motor Drives and Controls

0 0.01 0.02 0.03 0.04 0.05020406080Te/Nm
t/s
(d) Electromagnetic torque Te0 0.01 0.02 0.03 0.04 0.05−400–2000200400uAB/V uA/V iA/Vt/s
(a) Line voltage uAB
0 0.01 0.02 0.03 0.04 0.05−300−1500150300
t/s
(b) Phase voltage uA
0 0.01 0.02 0.03 0.04 0.05−50050100150
t/s
(c) Phase current iA
Figure 2.27 Dynamic process of free acceleration with no load.Mathematical Model and Characteristics Analysis of the BLDC Motor 53

decreasing voltage can be used to limit the starting current. In addition, the current and torque
ripple is more obvious in steady state in this situation.
The dynamic simulation results of the BLDC motor with step load are shown in Figure 2.29.In Figure 2.29, the motor starts with no load, and then accelerates freely to the steady state.
Note that when the load increases suddenly (i.e. jumps from 0 to 6 N m at 0.025 s), the motorspeed will decrease with the cycle of the phase voltage and phase current becoming longer.The increase in the current will lead to an increase of the torque so as to balance the increasedload torque. In addition, the amplitudes of the current and torque ripple are also increased.When the load decreases suddenly (i.e. varies from 6 N m to 4 N m at 0.045 s), the motorspeed will increase with the cycle of the voltage and current becoming shorter. Moreover, the
amplitude and the ripple of the current and the torque will become smaller. As discussed
above, the speed is high enough at 0.025 s, i.e. the back-EMF is large enough. So, the currentcannot quickly respond to the sudden increase of the load with constant bus voltage. Hence,the change of speed is relatively slow. In this condition, the boost circuits can be used toincrease the voltage so as to accelerate the response speed of the current. Similarly, when theload decreases suddenly, we can use the PWM control method to reduce the voltage of thearmature winding.
In summary, we can see that the response speed of dynamic process of BLDC motor is
quick. It is mainly determined by its merits, such as high power density, large torque output andsmall size. In addition, the simulation results show that the torque ripple of the BLDC motor is0 0.01 0.02 0.03 0.04 0.050200400600
t/sΩ/(rad/s)
(e) Angular velocity Ω
0 0.01 0.02 0.03 0.04 0.05-200-1000100200eA/V
t/s
(f) Phase back-EMF eA
Figure 2.27 (Continued ).54 Permanent Magnet Brushless DC Motor Drives and Controls

0 0.01 0.02 0.03 0.04 0.05–400–2000200400
t/suAB/V
(a) Line voltage uAB
0 0.01 0.02 0.03 0.04 0.05–300–1500150300
t/s
t/suA/V
(b) Phase voltage uA
0 0.01 0.02 0.03 0.04 0.05–50050100150iA/A
(c) Phase current iA
t/s0 0.01 0.02 0.03 0.04 0.05020406080Te/Nm
(d) Electromagnetic torque Te
Figure 2.28 Free acceleration process with load TL¼6 Nm.Mathematical Model and Characteristics Analysis of the BLDC Motor 55

t/s
t/s0 0.01 0.02 0.03 0.04 0.05–2000200400600Ω/(rad/s)
(e) Angular speed Ω
0 0.01 0.02 0.03 0.04 0.05–200–1000100200eA/V
(f) Phase back-EMF eA
Figure 2.28 (Cotninued ).
slightly large. This shortcoming has limited its applications in high-performance driving
systems. Hence, how to limit the torque ripple is one of the hot issues of the BLDC motor.
2.3.4 Load Matching
Of the various types of BLDC motors, if the motor with small mechanical time constant iscoupled with large inertial load, then it will lose the advantage of having a small moment ofinertia. On the other hand, when the motor with a big moment of inertia is used to drive lightload, the motor efﬁciency may be reduced. The most important property of a BLDC motoris that it is able to meet the power converter and load requirements. From this viewpoint, weshall consider the following fundamental issues with which to select the motor suitable for agiven load.
2.3.4.1 Torque Matching and Stable Running
One way to evaluate whether the torque capabilities of a motor meet the requirement of a given
load is to compare its mechanical characteristic curve with the corresponding speed–torquecurve of the load. At any time during acceleration or full speed, the amount of torque producedby the motor must exceed the load torque requirements. Further, to ensure the stable operationof the motor drive system, there should be a crossing point between the mechanicalcharacteristic curve and the speed-torque curve, as shown in Figure 2.30. It should benoted that the most accurate way to obtain the speed-torque curve of the BLDC motorand a given load is from the corresponding equipment manufacture. Besides the steady-state
torque and acceleration torque, the starting torque should be considered in practice too.56 Permanent Magnet Brushless DC Motor Drives and Controls

0 0.01 0.02 0.03 0.04 0.05 0.06–400–2000200400uAB/V
(a) Line voltage uAB
0 0.01 0.02 0.03 0.04 0.05 0.06–300–1500150300uA/V
(b) Phase voltage uA
0 0.01 0.02 0.03 0.04 0.05 0.06–50050100150iA/A
(c) Phase current iA t/st/st/s
Figure 2.29 Dynamic process of the BLDC motor with step load.
2.3.4.2 Mechanical Transmission
Generally, motor speeds and load speeds do not match up very well. This situation in the motor
industry makes the requirement for mechanical transmission of some type a necessity, andmost often it includes gear reduction, like in the BLDC motor application for elevator doordriving. Gear reducers have been engineered over the years in many forms, complex, simple,low and high accuracy, low and high efﬁciency. There are also belt and pulley reducers, clutchsystems, and recently more exotic systems like magnetic couplings, all with the intent of
matching the motor speed to the required speed of the load.
The most signiﬁcant contribution of gear reducers is the multiplication of torque output of
the motor, or said in reverse, the reduction of the load torque requirement by the ratio of the
reducer (minus efﬁciency losses). Due to the relatively low cost of mechanical solutions, gearreduction is the most inexpensive way to gain torque. In high-performance systems, a torqueincrease comes at a relatively high price if it has to be derived directly from the motor and drivesystem. This is based on the cost of power electronics and permanent magnets. In thiscondition, in order to match the load and motor, the input to the power converter is manipulatedMathematical Model and Characteristics Analysis of the BLDC Motor 57

by the controller. For further design information about the load matching of motor driving,
please refer to [8] and other related books.
2.3.5 Commutation Transients
Note that the current and back-EMF will both change during the transient process of thecommutation. Further, the interaction between them can result in commutation torque ripples.
Taking the three-phase symmetrical winding and Y-connected BLDC motor with full-
bridge driving as an example, the voltage equation can be given as
u
x¼RixțðL/C0MȚdix=dtțexx¼A;B;C ð2:56Ț(f) Phase back-EMF eAt/s0 0.01 0.02 0.03 0.04 0.05 0.06
t/s0 0.01 0.02 0.03 0.04 0.05 0.06
t/s0 0.01 0.02 0.03 0.04 0.05 0.06200
100
0
–100–200600
400200
080
604020
0eA/V Te/N m Ω /(rad/s)(d) Electromagnetic torque Te
(e) Angular speed Ω
Figure 2.29 (Continued ).58 Permanent Magnet Brushless DC Motor Drives and Controls

where
ux— phase voltage;
ix— phase current;
ex— phase back-EMF;
R— phase resistance;
L— self-inductance of phase winding;
M— mutual inductance of phase winding.
And the electromagnetic torque equation is
Te¼ðeAiAțeBiBțeCiCȚ=O ð2:57Ț
where Ois the mechanical angular speed of the motor.
From Equation (2.57), we can see that in order to maintain the electromagnetic torque
constant, the sum of eAiA,eBiBandeCiCmust be constant when the speed is kept constant.
Assume that the air-gap magnetic ﬁeld in the motor is the ideal trapezoidal wave with same
distributed shape as the back-EMF. Therefore, the armature current ixmust be square wave and
in phase with exso as to maintain the torque constant.
For the three-phase BLDC motor with full-bridge driving, only two phases of the armature
windings are conducted with the other phase nonenergized during the steady state, as shown inFigure 2.31(a).
Assume that phases A and C are conducted before commutation, then i
C¼–iA,iB¼0,
eC¼–eA, so it can be derived from Equation (2.57) that
Te¼2eCiC=O ð2:58Ț
Furthermore, assume that iC¼–I,eC¼–E, then the electromagnetic torque T¼2EI/Ois the
average torque. After the controller sends out the commutation signals, T 1will turn off with T 3
conducted, as shown in Figure 2.31(b).Tn
0Constant power load
Constant torque loadVariable torque loadn=f(Tem)
AB
Figure 2.30 Speed–torque curves matching between BLDC motor and various loads.Mathematical Model and Characteristics Analysis of the BLDC Motor 59

Hence, if the phase resistance is ignored and the back-EMF is assumed to be the ideal
trapezoidal wave, the change of the phase currents can be represented as
diA
dt¼/C0Udț2E
3ðL/C0MȚ
diB
dt¼2ðUd/C0EȚ
3ðL/C0MȚ
diC
dt¼/C0Ud/C04E
3ðL/C0MȚ8
>>>>>>><
>>>>>>>:ð2:59ȚeA
eB
eCR
R
RiCiBiA
T1D1
T4D4T3D3
T6D6T5D5
T2D2Ud
+++
–––
(a) Before commutation
eA
eB
eCR
R
RiCiBiA
Ud
+++
–––
T1D1
T4D4T3D3
T6D6T5D5
T2D2
(b) Commutating
eA
eB
eCR
R
RiCiBiA
Ud+ –
+
+–
–T
1D1
T4D4T3D3
T6D6T5D5
T2D2
(c) After commutation
Figure 2.31 The diagram of commutation.60 Permanent Magnet Brushless DC Motor Drives and Controls

Since the duration of commutation is very short, then we can assume that eA¼Ein this
process. The relationship between the phase currents and the time at the moment of
commutation can be derived from Equation (2.59) as
iA¼I/C0Udț2E
3ðL/C0MȚt
iB¼2ðUd/C0EȚ
3ðL/C0MȚt
iC¼/C0 I/C0Ud/C04E
3ðL/C0MȚt8
>>>>>>>><
>>>>>>>>:ð2:60Ț
At this moment, i
Astill exists. Thus, the current will ﬂow through the freewheeling diode until
iAdecreases to zero, as shown in Figure 2.31(c). During this process, iBincreases from zero
toI, and still satisﬁes
iAțiBțiC¼0 ð2:61Ț
After the commutation, iA¼0,iC¼/C0iB. We deﬁne t1as the time for iAdecreasing from Ito 0,
whereas t2as the time for iBincreasing from 0 to I. The corresponding variation process of
each phase current is shown in Figure 2.32.
From Equation (2.58) we can know that the torque is proportional to eCiCbefore
commutation. During the process of commutation, amplitude of iCis greater than Iwhen
t1Ht2(see Figure 2.32(a)). When t1¼t2(see Figure 2.32(b)), the amplitude of iCremains
constant. And when t1Gt2(Figure 2.32(c)), the amplitude of iCis less than I. Thus, from
Equation (2.60) we can get the time for iAdecreasing from Ito 0 as
tfa¼3ðL/C0MȚI
Udț2Eð2:62Ț
After tfapassed, iBcan be given as
iBðtfaȚ¼2ðUd/C0EȚ
Udț2EI ð2:63Ț
i
t0t1
(a) Ud>4E, t1>t2i
t0
iCiA
(b) Ud = 4E, t1=t2i
t0
(c) Ud<4E, t1<t2iB
t2iAiB iB
iC iCt2t2t1 t1
iA
Figure 2.32 Phase current in commutation under different conditions.Mathematical Model and Characteristics Analysis of the BLDC Motor 61

From Equation (2.63) we can obtain the following conclusions during the commutation:
(1) When UdH4E,t1Ht2, the torque increases.
(2) When Ud¼4E,t1¼t2, the torque remains constant.
(3) When UdG4E,t1Gt2, the torque reduces.
Thus, when Ud¼4E, changes of amplitude of iCcan be avoided so that the commutation
torque ripple will not appear. However, Ud¼4Eis not the steady state of the motor. In this
condition, the motor is in acceleration. The back-EMF Ewill increase with the increasing of
the motor speed such that UdG4E. Therefore, even in the steady state, commutation torque
ripple still exists in the BLDC motor, which is related to the speed [10]. Hence, by choosing a
proper commutation strategy, such as advanced conducting of the phase current and the PWMmodulation method, we can limit the commutation torque ripple to some extent.
Questions
1. What is the use of position sensor in BLDC motors?2. List at least four driving circuits for the BLDC motor control system and summarize their
advantages and disadvantages.
3. Try to model a BLDC motor with differential equation, transfer equation and state-space
equation, respectively, in MATLAB.
4. Explain why the current of the BLDC motor is larger at the starting time than that at the
steady state?
5. In what condition can the BLDC motor achieve its maximum efﬁciency?6. Why does the narrow pulse exist in the voltage waveform during the control of BLDC
motors?
7. Give some methods for limiting the commutation torque ripple of BLDC motors.8. Present some practical techniques of load matching for BLDC motor driving.
References
1. Walter, N. A., Stephen, L. H. (2003) Electric Motor Control . Thomson/Delmar Learning, Australia.
2. Xie, B. C., Ren, Y. D. (2005) DSP Control Technology and Its Application of Motor . Beihang University Press,
Beijing (in Chinese).
3. Fu, Q., Lin, H., He, B. (2006) A novel direct current control of four-switch three-phase brushless DC motor.
Journal of Chinese Electrical Engineering Science ,26(4), 148–153 (in Chinese).
4. Krause, P. C. (1986) Analysis of Electric Machinery . Kinsport Press Inc., Kinsport Town.
5. Pillay, P., Krishnan, R. (1989) Modeling, simulation, and analysis of permanent-magnet motor drives, part II: the
brushless DC motor drive. IEEE Transactions on Industry Application ,25(2), 274–279.
6. Pillay, P., Krishnan, R. (1989) Modeling, simulation, and analysis of permanent-magnet motor drives, part I: the
permanent-magnet synchronous motor drive. IEEE Transactions on Industry Application ,25(2), 265–273.
7. Gao, J. D., Wang, X. H., Li, F. H. (2005) AC Motor and Its Analysis . (2nd edn). Tsinghua University Press, Beijing
(in Chinese).
8. Kenjo, T., Nagamori, S. (1985) Permanent Magnet and Brushless DC Motors . Oxford University Press, New York.
9. Ye, J. H. (1982) BLDC Motor . Science Press, Beijing (in Chinese).
10. Xia, C. L., Wen, D., Wang, J. (2002) A new approach of minimizing commutation torque ripple for brushless DC
motor based on adaptive ANN. Journal of Chinese Electrical Engineering Science ,22(1), 54–58 (in Chinese).62 Permanent Magnet Brushless DC Motor Drives and Controls

3
Simulation for BLDC Motor Drives
The research of motor control systems has high requirements for hardware and exper-
imental conditions. Moreover, some experime nts may cause damage to the motor and other
equipment, which to some degree increases th e cost of the research, and also brings great
difﬁculty to the experiment. The introduction of computer simulation can effectivelyhelp to reduce such difﬁculties. When applied in modern motor control systems, computer
simulation plays a signiﬁcant role in helping researchers to design and analyze control
system more conveniently, as well as quickening product development and cutting down
the cost of research. At present, the software commonly used in simulation for motorcontrol systems involves MATLAB/Simulink, ACSL, SPICE, Saber, etc., among whichMATLAB/Simulink has fairly wide application. Simulink has a speciﬁc toolkit for motorcontrol system simulation, and its demos c over almost all the common types of DC and AC
driving system, including the models of high-pe rformance motor control strategies, such as
vector control, direct torque control, et c. In addition, Simulink has a user-friendly
interface, an easy operation method, and str ong capability of data analysis based on
MATLAB, all of which are vital to its wide applic ation. This chapter mainly introduces the
e x a m p l eo faB L D Cm o t o rc o n t r o ls y s t e mm odel based on MATLAB 7.1/Simulink 6.3, and
then the corresponding analysis of system performance is given in accordance withthe simulation.
3.1 S-Function Simulation
An S-function is a computer language description of a Simulink block, which can be used toexpand the simulation capability of Simulink. It can be written in MATLAB language, as wellas in computer languages such as C, C țț, Ada, FORTRAN, etc. S-functions are compiled by
MATLAB as MEX-ﬁles, and then will become dynamic linking subfunctions that MATLABcan automatically call and execute. Users can also construct their own S-function models torealize the function that is not found in the Simulink standard modules, so that the function ofthe simulation models will be more complete and more customized.
Permanent Magnet Brushless DC Motor Drives and Controls , First Edition. Chang-liang Xia.
/C2112012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd.

The S-function simulation example in this chapter is written in MATLAB language. The
structure of the simulation system is shown in Figure 3.1.
In the model, the commutation logic control and the motor are both realized by S-function
programming, and they are respectively masked as two subsystems: “Control” and
“BLDC_Motor”. The whole simulation model of BLDC motor control system is shownin Figure 3.2.
In the Figure 3.2, the module “Memory” is mainly used to delay the output Hall signal of the
motor with an integral step, so as to avoid algebraic loop in the simulation.T1 D1
T4 D4T3 D3
T6D6T5 D5
T2 D2UdBLDC motor
RL–M
L–M
L–MR
RiA
iB
iCeA
eB
eC+
+
+–
–
–+
–
Figure 3.1 The structure of a BLDC motor simulation system.
Figure 3.2 S-function simulation model for a BLDC motor control system.64 Permanent Magnet Brushless DC Motor Drives and Controls

The core of the subsystem “BLDC_Motor” is an S-function module named
“BLDC_Motor”, whose inputs include:
(1) The gate signal, Gates, is a vector, and its elements are the signals T1,T2,…, and T6, which
correspond to the gate signals of power devices in Figure 3.1. According to the output
signals of Hall position sensors and the control algorithm, the subsystem “Control”calculates the values of T
1,T2,…, and T6, which are Boolean variables, namely 0 or 1.
(2) The DC voltage Udof the bridge inverter is given by a constant module in Figure 3.2, and
thus its value can be adjusted as needed.
(3) The load torque TLis also given by a constant module and thus it is adjustable.
And the outputs of the “BLDC_motor” module include:
(1) Three phase to ground voltages uAG,uBGanduCG.
(2) Phase currents iA,iBandiC.
(3) The rotor speed n.
(4) The rotor position angle y, which stands for the angle between the rotor d-axis and the axis
of phase-A winding of the stator.
(5) The phase back-EMF of the windings eA,eBandeC.
(6) The neutral to ground voltage UNof the three phase windings.
(7) The electromagnetic torque Te.
(8) The output signals of Hall position sensors HA,HBandHC.
The variables in the model are all in SI unit except the rotor speed, whose unit is r/min.
Signal variables, including Hall signal and gate signal, have no units.
Double click the module “BLDC_Motor”, and there pops up a dialog box for parameter
setting, as shown in Figure 3.3.
The parameters of the motor mainly include:
(1) Stator resistance R(O), inductance L(H), mutual inductance M(H) and the back-EMF
coefﬁcient of each phase of the motor Ke(V/(rad/s)).
(2) Number of pairs of poles p, moment of inertia J(kg m2).
(3) Torque at no load T0(N m), the rotor angle at start-up y0(rad).
(4) Viscous friction coefﬁcient Bv(N m s), starting friction torque Tb0(N m).
(5) The voltage of the MOSFET while conducting VT(V), the voltage of the freewheeling
diode while conducting VD(V).
The main calculating process of the S-function corresponding to the module
“BLDC_Motor” is shown as follows:
(1) The calculation of back-EMF and Hall signal [1]. This is chieﬂy achieved by the lookup
table, among which the calculation of the peek value of back-EMF is shown as Equation
(2.12), and the lookup function corresponds to the back-EMF waveform distribution
function as shown in Figure 2.13.
(2) Calculate the differential of the current state variable. The modeling of a BLDC motor
needs to choose three phase currents, rotor speed and angle as state variables. The aim ofSimulation for BLDC Motor Drives 65

this part is to calculate the differential of currents. During this process, all the running
conditions should be taken into consideration before categorization on the basis of thevalues of T
1,T2,…, and T6. In order to avoid the situation that two power devices on the
same bridge are conducting at the same time, we should make sure of T1&T4¼T3&
T6¼T5&T2¼0. Now set the ﬂag variable as
flag¼T1jT4ðȚ /C2 4țT3jT6ðȚ /C2 2țT5jT2 ðȚ ð 3:1Ț
Hence, the value of ﬂag is an integer between 0 and 7, which represent 8 operating states of
the inverter, as shown in Table 3.1.
It can be seen from Table 3.1 that according to the different operating modes (120/C14
conducting or 180/C14conducting) of the inverter, when the PWM control mode and the
setting of dead zone are taken into account, the motor can be operated at any one of the8 states mentioned above. Thus, the windings of the motor can be in one of the conductingstates like no phase conducting, only one phase conducting, only two phases conductingand all the three phases conducting. The state that only two phases are conducting is rather
common when the ON_PWM control mode is implemented, in which case the circuit is
fairly complicated. Now ta ke the situation that ﬂag ¼2 for an example.
T h ef a c tt h a tﬂ a g ¼2 indicates that the upper bridge or the lower bridge of the phase B
is conducted, and thus the input voltage of ph ase B is easily obtained. To begin with, it is
Figure 3.3 A BLDC motor simulation parameter setting.66 Permanent Magnet Brushless DC Motor Drives and Controls

judged according to the value of the signal T3. If the upper bridge is conducted, then
uBG¼Ud/C0VT ð3:2Ț
Otherwise, the lower bridge is conducted, and the terminal voltage of phase B is
uBG¼VT ð3:3Ț
In this condition, the phase working in PWM control modes, either phase A or phase B, is at
PWM low level, during which the current ﬂows through the freewheeling diodes. The other phase
is open or in the state of commutation with freewheeling diodes. According to the different statesof circuit mentioned above, the phase current and terminal voltage of each phase can be
determined, and together with motor parameters and the three-phase back-EMF calculated in
stage (1), the derivative of current can be solved. In the program, the phase with zero crossingcurrent is simpliﬁed, both current and derivative of current are set 0. In the mode of unilateralmodulation, with the coaction of neutral point voltage jump and back-EMF of the windings, theterminal voltage of the unexcited phase will be higher than U
dor become negative, which cause
the current to ﬂow through another freewheeling diode of this bridge and increase inversely, thusforming the back-EMF current, as shown in Figure 3.4.Table 3.1 The operating states of the BLDC motor inverter
Flag Conducting state
0 No power device of the inverter conducting, no input voltage in any of the three phase windings.
1 T1,T3,T4andT6turned off, phase A and phase B open or freewheeling, phase C conducted.
2 T1,T2,T4andT5turned off, phase A and phase C open or freewheeling, phase B conducted.
3T 1and T 4turned off, phase A open or freewheeling, phase B and phase C conducted.
4 T2,T3,T5andT6turned off, phase B and phase C open or freewheeling, phase A conducted.
5 T3andT6turned off, phase B open or freewheeling, phase A and phase C conducted.
6 T2andT5turned off, phase C open or freewheeling, phase A and phase B conducted.
7 When there is a power device conducting in each phase of the inverter or when the three upper
bridges are conducting at the same time, there is no input voltage in the three phase windings; in
other cases, there are input voltages.
Figure 3.4 The back-EMF current.Simulation for BLDC Motor Drives 67

Table 3.2 Phase currents relationship
iA¼0 iAH0 iAG0
iC¼0 As the sum of three phase
current is 0, thus iB¼0,
and the motor is at the
moment of start-up.Phase C is turned off; phase A
is at the low level of PWM,
and freewheels through D 4;
iB¼/C0iA.Phase C is turned off, phase A
is at the low level of PWM,and freewheels through D
1;
iB¼/C0iA.
iCH0 Phase A is turned off;
phase C is at the low
level of PWM, and
freewheels through D 2;
iB¼/C0iC.Transient process during
which phase C freewheels
though D 2and phase A
freewheels through D 4;
iB¼/C0(iAțiC).Transient process during
which phase C freewheelsthough D
2and phase A
freewheels through D 1;
iB¼/C0(iAțiC).
iCG0 Phase A is turned off;
phase C is at the low
level of PWM, andfreewheels through D
5;
iB¼/C0iC.Transient process during
which phase C freewheelsthough D
5and phase A
freewheels through D 4;
iB¼/C0(iAțiC).Transient process during
which phase C freewheelsthough D
5and phase A
freewheels through D 1;
iB¼/C0(iAțiC).
The circuit state is closely related to the intensity and direction of current. Take the free-
wheeling phase for example, and then when the current decreases to 0, the structure of the circuit
changes as the freewheeling diode closes, resulting in the neutral point voltage and terminalvoltage jump, and consequently the derivative of current jump. While the motor is running, thevalue of current is shown in Table 3.2.
To calculate the differential of the current under different circumstances, it is necessary
to obtain the relevant voltage variable in advance. This calculation process can beperformed on the basis of categorized analysis of Table 3.2. Take the circumstance thati
A¼0,iCH0 for example. In this case, the current freewheels through the diode in
phase C, thus
uCG¼/C0VD ð3:4Ț
UN¼uBGțuCG ðȚ /C0 eBțeC ðȚ ðȚ =2 ð3:5Ț
UAG¼UNțeA ð3:6Ț
According to the voltage equation, the differential of the currents in phase B and
phase C are, respectively, given as
diB
dt¼ð ðuBG/C0UNȚ/C0eB/C0R/C2iBȚ=ðL/C0MȚð 3:7Ț
and
diC
dt¼ð ðuCG/C0UNȚ/C0eC/C0R/C2iCȚ=ðL/C0MȚð 3:8Ț68 Permanent Magnet Brushless DC Motor Drives and Controls

Note that once the current of the nonexcited phase decreases to zero, it will remain zero
before the next conducting instant. So, the differential of the current is also zero, namely
diA
dt¼0 ð3:9Ț
Similarly, the corresponding voltage variable and state variable differential can be
calculated for other conditions of iAandiC.
(3) The calculation of torque and angular speed. With the calculated three phase currents and
back-EMF, the electromagnetic torque is given as
Te¼p/C2Ke/C2fA/C2iAțfB/C2iBțfC/C2iC ðȚ ð 3:10Ț
The angular speed is also a state variable, and its state equation can be obtained according to
the motion equation of the motor. Note that the motion state of the motor is relevant to the
characteristic of the load. Here, the load is assumed to be a frictional constant torque load. Atthe instant of start-up, the electromagnetic torque has to offset the static friction and the loadtorque. Thus, the differential of angular speed is given as
dO
dt¼sgnTeðȚ /C2 absTeðȚ /C0 TLțT0 ðȚ /C0 Tb0 ðȚ ðȚ =J ð3:11Ț
When the angular speed is not equal to zero, the static frictional force in Equation (3.11)
turns into the sliding frictional force, so
dO
dt¼Te/C0sgnOðȚ /C2 TL/C0T0/C0Bv/C2O ðȚ =J ð3:12Ț
The simulation results for open-loop operation of the motor are shown in Figure 3.5.It can be seen from Figure 3.5 that, when no measures are taken to limit the current, both the
current and torque are too big at start-up, and the speed will rise to its maximum in a rathershort period of time. Due to the high speed, the compound back-EMF of the two windings aregreater than the line back-EMF, so the bus current ﬂows from the motor to the power source.Thus, the electromagnetic torque becomes negative and the motor works at braking state.In this situation, the mechanical energy of the rotor is transformed into electrical energy storedin the source, and the rotor speed starts to decrease. When the compound back-EMF is once
again lower than the line voltage on decreasing the rotor speed, the current begins to ﬂow from
the source to the windings again. Thus, the electromagnetic torque becomes positive, and themotor operates as a motor again.
3.2 Graphical Simulation
Simulink can employ all sorts of modules arranged as libraries to achieve dynamic system
graphical modeling. Besides the commonly used modules, Simulink provides module libraries
in the form of the toolbox for different research areas, including the power system simulationlibrary SimPowerSystem.Simulation for BLDC Motor Drives 69

0 0.01 0.02 0.03 0.04 0.05 0.06−1000100200300400
t/siA/A
(d) Phase current iA0 0.01 0.02 0.03 0.04 0.05 0.06−400−2000200400uAB/V
t/s
(a) Line voltage uAB
0 0.01 0.02 0.03 0.04 0.05 0.06−1000100200300400uAG/V
t/s
(b) Terminal voltage of phase A, uAG
0 0.01 0.02 0.03 0.04 0.05 0.06050100150200250300UN/V
t/s
(c) Neutral voltage UN
Figure 3.5 Simulation results of BLDC S-function modeling.70 Permanent Magnet Brushless DC Motor Drives and Controls

The SimPowerSystem library offers fairly accurate models of many components used in
power systems, such as power sources, transformers, motors, loads, etc. In the meantime, it
provides libraries of speciﬁc application systems, including various motor drive systemmodels. Moreover, it is a GUI-based tool with intuitive graphics capability and excellent
data-processing ability. Users can use SimPowerSystem for the modeling of motor drive
systems, as well as control strategies design, real-time recording of motor variables andqualitative or quantitative performance analysis of the motor operation. Note that when theSimPowerSystem library is employed for modeling, the following have to be paid attention to:
(1) The connection between electrical models and the common Simulink models. The
terminals of the modules in SimPowerSystem are usually denoted by the sign “ &”,
while the terminals of the ones in Simulink are usually denoted by the sign “ H”. These
two types of terminals cannot be connected directly. Some “interface modules”, like
controlled modules or measuring modules are used for the connection between them. Forexample, the output signals of the sources in Simulink, such as sinusoidal, stepping andconstant ones, must be transformed by controlled modules before they are connected tomodules in Powerlib, like inductance and capacitance. By contrast, signals like voltageand current in electrical modules must be transformed by measuring modules before beingconnected to modules in Simulink like “Math Operations” or “Sinks”.
(2) The measurement of voltage and current. In electrical models, branch voltage and current
are usually measured by voltage and current measurement modules or a multimetermodule. There is a positive or negative sign marked at the terminals of voltage and currentmeasurement modules, so that the polarity of the measured signal can be judgedconveniently. Slightly different from that, a multimeter module needs to select the0 0.01 0.02 0.03 0.04 0.05 0.06−1000100200300
t/sTe/Nm
(e) Electromagnetic torque Te
0 0.01 0.02 0.03 0.04 0.05 0.0601000200030004000
t/sn/(r/min)
(f) Rotor speed n
Figure 3.5 (Continued )Simulation for BLDC Motor Drives 71

pull-down menu in the parameter setting dialog of the electrical module, and then the
voltage and current signals are chosen to be measured. So that they will be displayed in the
multimeter module, which are ready to be selected by users.
(3) The connection of inductance and capacitance. Inductance cannot be directly connected in
series with a current source, while capacitance cannot be in parallel connection directly
with a voltage source. If the above direct connections are inevitable in the modeling, theinductance and capacitance can be connected in parallel with a certain resistance beforethey are connected.
3.2.1 Simulation of Double Closed-Loop Speed-Control System
Since double closed-loop speed-control system is one of the most common motor controlsystems, an example of the modeling for a BLDC motor double closed-loop speed-controlsystem based on SimPowerSystem is given below. The block diagram of the simulation systemis shown in Figure 3.6.
The whole system is comprised of four parts:
(1) The main power circuit. It is a VVVF AC–DC–AC circuit, mainly including a three-phase
AC voltage source, a bridge rectiﬁer, a bridge inverter and a DC ﬁltering capacitance. TheRMS value of line voltage of a three-phase AC voltage source is 217 V, and its frequency is50 Hz. Both the rectiﬁer and inverter are implemented by the “Universal Bridge” modulein SimPowerSystem, and the value of the DC ﬁltering capacitance is set to 4400 mF.
(2) The motor. The module “Permanent Magnetic Synchronous Motor” is selected with the
waveform of air-gap magnetic ﬂux density being trapezoidal and the width of its ﬂat part is120 electrical degrees.
(3) Measurement unit. This unit consists of several bus-selecting modules “Bus Selector”,
which is used to measure the variables of the motor when it is operating, such as voltage,current and rotor speed.
Figure 3.6 The block diagram the of BLDC motor double closed loop speed-control system.72 Permanent Magnet Brushless DC Motor Drives and Controls

(4) Controller unit. Double closed-loop speed regulation is implemented by the subsystem
named “Double Loop Controller”. Its input variables are the rotor position angle, the bus
current, the reference and measured speed, and it outputs six PWM pulses, of which the
frequency is 20 kHz, to the bridge inverter. The related block diagram of the controller is
shown in Figure 3.7.
Through the logic AND operation between the commutation signal and the PWM signal of
the BLDC motor, the controller will obtain the gate signal, which determines whether theinverter is on or off. The commutation signal is obtained by detecting the rotor position angle,which is transferred to the “Position Detector” unit after complementation and absolute valueoperation. In order to implement the electromagnetic braking and motor reversing rotation, the
“Position Detector” unit must be able to determine whether the controller adopts forward
rotation or reversing rotation commutation according to the error between the reference speedand the measured speed. When the speed is too high, electromagnetic braking can be achievedonly by changing the commutation sequence, so as to decrease the speed.
When two of the three windings of the motor are excited, the rotor will possibly be pulled to
one of the six different space positions, as shown in Table 3.3. Thus, the commutationsequence of the module “Permanent Magnetic Synchronous Motor” is determined.
According to Table 3.3, the schematic diagram of space vector of the BLDC motor can be
obtained, as shown in Figure 3.8. In Figure 3.8, the space of 360 degrees of electrical angle isdivided by the current space vector into six sectors, which are labeled by 0, 1, 2, 3, 4 and 5,respectively. The current space vector I
CBis located at the 0/C14axis, which is the reference
position of rotor angle. During simulation, the position of the rotor at any instant is trans-formed into the label of the corresponding sector. According to this label and the directioncommand, the subsystem “Position Detector” outputs the commutation signal.
Figure 3.7 Double closed-loop controller module diagram.
Table 3.3 Conducting phase and rotor position of the BLDC motor
Conducting phase AB AC BC BA CA CB
Rotor position angle (rad) p/3 2p /3 p 4p/3 5p /3 2pSimulation for BLDC Motor Drives 73

The PWM signal is generated by the subsystem “PWM Generator”, and its duty cycle is
calculated by a PI controller of the current loop.
Figure 3.9 is the simulation results of the BLDC motor double closed-loop speed-control
system with a constant reference speed.
In the ﬁgure, the reference speed is 2000 r/min, and the motor starts with a rating load.
Compared with the simulation waveforms in Figure 3.5, the waveforms of the line voltage and
terminal voltage of double closed-loop control are PWM waveforms, the envelope of which isthe same as the voltage waveform in Figure 3.5. The equivalent voltage of the winding
is determined by the duty cycle of PWM.
In the simulation system, the output of the speed PI controller is limited within twice the
rated current. From Figure 3.9, it can be seen that during the start-up procedure the phase
current arrives at the limited value within a rather short period of time, so that the motor startsat the permitted highest current. The torque changes in the same way as that of the amplitude ofcurrent. This means that during the start-up procedure the torque arrives at its permittedhighest value, and then with increasing speed and decreasing current, it decreases graduallyuntil settling down to the load torque. As they are limited, the current and torque are lower than
they are at open-loop operation during the start-up procedure. Thus, the rotor acceleration is
smaller and a longer time is necessary for getting to the rated speed.
Figure 3.10 shows the simulation results at the condition that the reference speed is a ramp
signal and the load changes from 0 to the rated value at 0.05 s.
In Figure 3.10, the reference speed varies from 0 to 2000 r/min during a period of 0.04 s.
The change of line voltage and terminal voltage is similar to that in Figure 3.9. They are allPWM waveforms, and the cycle of its envelope reduces with increasing speed.
As the motor starts with no load, and the reference speed is the ramp signal, the starting
current is rather small. When the rotor has ﬁnished its accelerating procedure and the loadtorque is still 0, the current is about 0. If the load changes to the rated value, the current willincrease quickly. During the start-up procedure, the rotor approximately rotates with constantacceleration, and thus the torque remains constant before 0.04 s. When the load changessuddenly, the electromagnetic torque increases with ascending current, so that the torque canIAB IAC
IBA ICA01
2
5
43ICB IBCA
C B
Figure 3.8 The BLDC motor current space vector.74 Permanent Magnet Brushless DC Motor Drives and Controls

−50050iA/A0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1−400−2000200400uAB/V
t/s
(a) Line voltage uAB
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1−1000100200300400uAG/V
t/s
(b) Terminal voltage of phase A, uAG
−50050100150200250UN/V
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
t/s
(c) Neutral voltage UN
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
t/s
(d) Phase current iA
Figure 3.9 Start-up process simulation of the motor with constant reference speed.Simulation for BLDC Motor Drives 75

be adjusted quickly. From Figure 3.10, it can be concluded that under the control of the double
closed-loop controller, the speed can track its reference fairly well when the motor runs withno load. The moment the load increases, the speed begins to decrease, and then the speed isincreased by increasing the output duty cycle of PWM. Thus, under the control of a PI
controller, nonstatic error control will be achieved. Moreover, this process will get faster with
appropriate parameter selection by the PI controller. So, it can be summarized that the BLDCmotor has a rather quick response and strong antidisturbance ability when controlled in doubleclosed-loop mode.
3.2.2 Advanced Conduction of Phase Current for BLDC Motor Control
When the reference speed is lower than the rated value, speed regulation can be achieved bychanging the terminal voltage of the windings. However, when the reference speed is higherthan the rated value, the back-EMF is fairly high, and the voltage of the winding can no longerbe increased. So that the windings current is not enough to generate higher torque, this will
cause the difﬁculty of increasing the speed of the motor. Thus, the range of speed is restricted.
Therefore, the key of speed regulation above the rated value is to avoid the restriction ofcurrent increasing imposed by back-EMF. For a separately excited DC motor, the mainmagnetic ﬁeld can be attenuated by adjusting the exciting current, so that the back-EMF isdecreased, and the rotor speed is increased. For a permanent magnetic synchronous motor,ﬁeld weakening and speed increasing will be achieved with the current vector control method.0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10102030405060
t/sTe/Nm
(e) Electromagnetic torque Te
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1−50005001000150020002500
t/sn/(r/min)
(f) Rotor speed n
Figure 3.9 (Continued )76 Permanent Magnet Brushless DC Motor Drives and Controls

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1−40−200204060
t/siA/A
(d) Phase current iAuAB/V
t/s0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1−400−2000200400
(a) Line voltage uAB
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1−1000100200300400uAG/V
t/s
(b) Terminal voltage of phase A, uAG
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1−1000100200300UN/V
t/s
(c) Neutral voltage UN
Figure 3.10 Simulation results with ramp input and varied load.Simulation for BLDC Motor Drives 77

As a permanent magnetic rotor is used in the BLDC motor, the ﬁeld excitation is not
adjustable. In addition, since the air-gap magnetic ﬁeld is trapezoidal, the analysis method
based on vector control has high error. Therefore, different from these two types of motor,when the reference speed is higher than the rated value, the advanced conduction of phasecurrent is usually adopted to expand the speed range of BLDC motor [2–7]. The corresponding
principle is shown in Figure 3.11.
Take phase A for example, Figure 3.11 shows the relation of the phase current i
Ain the
advanced conduction of phase current mode, the phase current i0in normal conducting mode,
and the phase back-EMF eA. Since the speed is fairly high at this condition, the rotor speed can
be assumed to be constant during the current varying period as shown in Figure 3.11. It can be
seen from Figure 3.11 that iAis leading i0in phase by aelectrical degrees. As it keeps
away from the maximum of the back-EMF, iAincreases rapidly during a period shortly after0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1−10010203040
t/sTe/Nm
(e) Electromagnetic torque Te
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.105001000150020002500
t/sn/(r/min)
(f) Rotor speed n
Figure 3.10 (Continued )
αθeA
i0iAe, i
0
Figure 3.11 The principle for advanced conduction of phase current.78 Permanent Magnet Brushless DC Motor Drives and Controls

phase A is conducting. The winding of phase A can store much magnetic ﬁeld energy,
compared with the situation in which the phase current is i0. Subsequently, as the line back-
EMF of the windings arrives and remains the maximum, the increase in the current gets slower.If the value of ais rather big, the current will decrease rapidly after its increase. Its waveform is
similar to a sinusoidal one. So, the torque ripple will be rather big as the back-EMF is a squarewave. As analyzed above, with the advanced conduction of phase current, when the back-EMFarrives at its maximum, i
Ais greater than i0, and the electrical torque increases. Thus, the speed
above the rated value is achieved. As a long time of operation at high current will cause severeheating of the motor, this operation mode is usually applied to constant power load, so as toensure that the current is remained about the rated value.
It is worth noting that the advanced conduction of phase current adopted in the BLDC motor
to increase the speed is essentially different from the ﬁeld-weakening method adopted inseparately excited DC motor for speed regulation. The air-gap ﬂux density of the BLDC motoris distributed in a trapezoidal waveform, of which the sloping edge is where the ﬂux density issmall and thus the magnetic ﬁeld is weak. In the normal commutation mode, the phase currentbegins conducting when the phase back-EMF is equal to the maximum, and the torque-generation process utilizes the magnetic ﬁeld to the utmost. In the mode of advancedconduction of phase current, only part of the magnetic ﬁeld at the sloping edge of the air-
gap ﬂux density takes part in the electromechanical energy conversion. This means that the
effective magnetic ﬁeld is reduced. Thus, a similar effect of ﬁeld weakening and speedincreasing is achieved like that of the separately excited DC motor. Note that the main ﬁeld ofthe motor is not changed here, only the air-gap ﬂux density distribution is changed. Since thesloping edge distribution area of the trapezoidal air-gap ﬂux density is limited, the magnetic-ﬁeld regulation and speed range expanding ability of the BLDC motor controlled by theadvanced conduction of phase current are inferior to those of the electrically excited DC motor.
Figure 3.12 shows the simulation block diagram of the BLDC motor controlled by the
advanced conduction of phase current.
In Figure 3.12, the structure of the main circuit is thoroughly the same as that of the double
closed-loop control system. They all employ the AC–DC–AC converter structure. Further, the
Figure 3.12 Simulation block diagram of the BLDC motor controlled by the advanced conduction of
phase current.Simulation for BLDC Motor Drives 79

motor starts in normal commutation mode with full load, and then shifts to the mode controlled
by advanced conduction of phase current at the steady-state speed. For the convenienceof observing how phase current varies with the leading conducting angle, the load torque is
set constant.
Figure 3.13 shows the corresponding waveforms of phase current and phase back-EMF of
the ﬁeld weakening speed-control system during the period between 3.5 ms and 5.5 ms, in
which achanges abruptly at t¼4 ms from 0
/C14to 30/C14.
It can be seen from Figure 3.13 that the phase and the shape of the phase current have
changed. In the normal commutation mode ther e exist apparent spikes in the vicinity of the
maximum of current, while in the advanced conduction of the phase current mode, thecurrent is almost ﬂat, with a trend of decreasin g. As analyzed before, this is mainly because
the advanced conduction mode causes the increasing of speed and back-EMF, bringing outthe difﬁculty in increasing the current. The simulation results also show that the RMS valueof phase current changed from 20 A to 22 A after the abrupt change of the angle a.T h i si s
caused by the increment of the current when the back-EMF is still small. Note that the
energy stored in the magnetic ﬁeld is closely related to the windings current. Thus,knowledge of the changing of phase current waveform is helpful for us to comprehendthe principle of the advanced conduction of phase current from the viewpoint of energytransfer. In this viewpoint, the energy transferred to the motor by the bridge inverter will be
transformed into the output mechanical energy of the motor and the magnetic energy stored
in the air gap, without regard to copper loss, iron loss and friction loss. When the BLDC
motor is controlled by the advanced conduction of phase current, power switches begin toconduct at the edge of the trapezoid back-E MF, and the corresponding phase current
increases rapidly. Before the end of the ﬂat t op of the trapezoid, power switches are cut off,
and the current of this phase decreases rapidly. If the DC bus voltage and load torque remainunchanged, the RMS value of bus current will also increase, and a greater proportion of theelectric energy from the power source will be t ransformed into mechanical energy, and thus
the speed of the motor is increased.
Figure 3.14 shows the corresponding simulation waveforms of electromagnetic torque and
speed response as analyzed above.
As shown in Figure 3.14, when achanges suddenly from 0
/C14to 30/C14, the electromagnetic
torque begins to increase, and the rotor starts to accelerate until the torques exerted on the rotor
iA/A
−150−100−50050100150
−60−40−200204060
eA/V
iA— — eA––3.5 4.0 4.5 5.0 5.5
t/ms
Figure 3.13 The waveforms of phase current and phase back-EMF.80 Permanent Magnet Brushless DC Motor Drives and Controls

reach the new equilibrium. Since the load torque is constant, the steady-state torque stays
unchanged after the change of a, and only the amplitude of torque ripple is slightly augmented.
Figure 3.15 shows the mechanical characteristics of the BLDC motor with different
advanced conduction angle. In order to observe the mechanical characteristic in a wide
range of torque, the load torque is set from 0 to 70 N m, almost triple the rated value.
As shown in Figure 3.15, the mechanical characteristics curve family of the BLDC motor
moves upward with the increasing of a, and the curve with a¼15/C14is the dividing line. When ais
less than 15/C14, the curves have only slight translation. Note that when ais equal to 7.5/C14,t h e
mechanical characteristic curve of the motor is nearly the same as that in the normal com-
mutation mode. However, when ais greater than 15/C14, there is an evident change in the
mechanical characteristics. For example, when ais equal to 30/C14, the speed of the motor with
rated load is 3700 r/min, which is 1.32 times the rated speed in normal commutation mode.
Figure 3.16 shows the variation for the RMS value of current with respect to the advanced
conduction angle.
Through comparison of the curves in Figure 3.16, it is apparent that when the value of ais
large, the phase current corresponding to the same load torque is also high, especially when
the speed is greater than the rated value. Therefore, the advanced conduction angle has a
signiﬁcant inﬂuence on the current RMS value variation with load change. Since higher phase
0 10 20 30 40 50 60 7020002500300035004000α = 0°
α = 7.5°
α = 22.5°
α = 30°
TL/N mn/(r/min)α = 15°
Figure 3.15 Mechanical characteristics corresponding to different advanced conduction angle.1020304050
3.5 4.0 4.5 5.0 5.5
t/ms27002800290030003100Te/Nm
n/(r/min )
Ten
Figure 3.14 Waveforms of electromagnetic torque and speed.Simulation for BLDC Motor Drives 81

current will cause higher average torque, a higher speed of the motor will be obtained
consequently, which is in accord with the results shown in Figure 3.15. Taking the currentrestriction of motor continuous working into consideration, the advanced conduction angle isusually not bigger than 30
/C14.
Questions
1. Brieﬂy describe the main calculating process of the S-function corresponding to the module
“BLDC_Motor”.
2. How many parts does the model of BLDC motor double closed-loop speed-control system
presented in this chapter consist of? And what are their functions, respectively?
3. Why is the advanced conduction of phase current adopted when the reference speed is
above the rated value? Describe the principle of this method.
4. Try to build a model of BLDC motor closed-loop speed-control system by yourself. Then
compare it with that presented in the SimPowerSystem library to see if they work in thesame way.
References
1. Pillay, P., Krishman, R. (1989) Modeling, simulation, and analysis of permanent-magnet motor drives, part II: the
brushless DC motor drive. IEEE Transactions on Industry Application ,25(2), 274–279.
2. Chan, C. C., Jiang, J. Z., Xia, W., et al. (1995) Novel wide range speed control of permanent magnet brushless motor
drives. IEEE Transactions on Power Electronics ,10(5), 539–546.
3. Yan, L. (2004) Flux weakening technology study on permanent magnet brushless DC motor . Hangzhou: Zhejiang
University, PhD Thesis, (in Chinese).
4. Janhns, T. M. (1984) Torque production in permanent-magnet synchronous motor drives with rectangular current
excitation. IEEE Transactions on Industry Application . IA- 20(4), 803–813.
5. Lawler, J. S., Bailey, J. M., Mckeever J. W., et al. (2002) Limitations of the conventional phase advance method for
constant power operation of the brushless DC Motor. IEEE SoutheastCon 2002, Columbia, 174–180.
6. Miti G K, Renfrew A C, Chalmers B J, (2001) Field-weakening regime for brushless DC Motors based on
instantaneous power theory. IEE Proceedings on Electrical Power Application . 2001, 148(3): 265–271.
7. Saﬁ, S. K., Acarnley, P. P., Jack, A. G. (1995) Analysis and simulation of the high-speed torque performance of
brushless DC motor drives. Electric Power Applications ,142(3), 191–200.0 10 20 30 40 50 60 700102030405060
TL/N mI/Aα = 0°
α = 7.5°
α = 22.5°α = 30°α = 15°
Figure 3.16 The variation of the RMS value of current with respect to the advanced conduction angle.82 Permanent Magnet Brushless DC Motor Drives and Controls

4
Speed Control for BLDC Motor
Drives
BLDC motor speed control plays an important role in modern motor control. The control
methods are usually divided into two main types: open-loop and closed-loop ones. Dual-closed-loop speed control is common in control systems. The inner loop is the current or torqueloop, while the outer loop is the velocity or voltage loop. When the motor works in normalmode or runs below the rated speed, the input voltage of the armature is changed through PWM
modulation strategy; while the motor is operated above the rated speed, we usually weaken the
ﬂux by means of advancing the exciting current or auxiliary ﬂux to achieve the aim. A BLDCmotor speed-control system generally involves many techniques. In this chapter, we mainlyfocus on the realization of the dual-closed-loop speed control, the intelligent speed-controlstrategies, and the inﬂuence of time-varying motor parameters (resistances, inductances, andmoment of inertia) on the motor speed control law.
4.1 Introduction
4.1.1 PID Control Principle
Traditional PID control has been one of the most developed strategies in the linear control
systems for over 70 years, which is still commo nly used in industrial control systems. The
PID controller has been used widely in indus trial applications owing to its simplicity,
robustness, reliability and easy tuning parame ters. The typical structure of PID control is
shown in Figure 4.1.
The standard PID controller calculates the deviation e(t) between the reference value and the
actual value. Then, the plant is controlled by the variable u(t) with a linear combination of
proportional–integral–derivative terms. The corresponding PID control law in continuous
form can be expressed as
uðtȚ¼KPeðtȚț1
TIðt
0eðtȚdtțTDdeðtȚ
dt/C18/C19
ð4:1Ț
Permanent Magnet Brushless DC Motor Drives and Controls , First Edition. Chang-liang Xia.
/C2112012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd.

where KPis the proportional gain, TIis the integral time constant and TDis the differential time
constant.
In practical control system, not all PID controllers are composed of three terms: propor-
tional, integral and differential. PID controllers contain various structure forms, such as
proportional controller, proportional–integral controller and proportional–derivative control-ler, and so on. Among them, the proportional–integral controller is the most commonly usedone in the BLDC motor control system. The differential term can effectively reduce theovershoot and maximum dynamic deviation, but it will make the controlled plant easilyaffected by high-frequency disturbances.
In order to improve system reliability, digital PID controller is often used in modern motor
control systems. In this situation, the continuous PID control algorithm cannot be useddirectly, and Equation (4.1) should be discretized. The difference equation of discrete PIDcontrol law, which is also known as the position PID control algorithm, is obtained as
uðkȚ¼K
PeðkȚțT
TIXk
j¼0eðjȚțTD
TðeðkȚ/C0eðk/C01ȚȚ"#
¼KPeðkȚțKIXk
j¼0eðjȚțKDðeðkȚ/C0eðk/C01ȚȚð4:2Ț
where KIis the integral coefﬁcient, KDis the differential coefﬁcient, Tis the sampling period,
e(k) and e(k/C01) are the deviation of inputs at the kth and the ( k/C01)th time, respectively.
A typical digital PID control system is shown in Figure 4.2.In digital motor control system, PID control law expressed as Equation (4.2) may induce
large error and has poor dynamic performance. Thus, the incremental PID control law based on
the recursive principle can be adopted, which is expressed as
DuðkȚ¼uðkȚ/C0uðk/C01Ț
¼K
peðkȚ/C0eðk/C01Ț ðȚ țKIeðkȚțKDeðkȚ/C02eðk/C01Țțeðk/C02Ț ðȚð4:3ȚP
I
DPlant
_r(t) y(t) u(t)
Figure 4.1 Diagram of a PID control system.
A/D Digital PID Motor
−y(t)
D/Ar(t)
Figure 4.2 Diagram of the digital PID motor control system.84 Permanent Magnet Brushless DC Motor Drives and Controls

Comparing Equation (4.2) with Equation (4.3), we could ﬁnd that the calculation com-
plexity of incremental PID control law is much smaller. Moreover, the positional PID control
law shown in Equation (4.2) could be deduced from Equation (4.3).
Once the structure of the PID controller is determined, the parameters of the PID controller
need to be adjusted. The parameter tuning methods for a continuous PID controller can be used
to determine the parameters of a digital PID controller. In practice, the proportional parameteris ﬁrst tuned, then the integral parameter, and ﬁnally the differential parameter. For a PIcontroller, one tuning method is ﬁrst to set the integral part to zero, then increase theproportional part until the system response is stable, ﬁnally tune the integral part to improvethe dynamic response ability and static stability. It is worth noting that the selections of
these three parameters are not isolated. In order to obtain the best control performance, they
should be considered as a whole in the tuning process. The system performance is also closelyrelated to the choice of sampling period T, so the designer should select it properly. According
to Shannon sampling theorem, the sampling frequency must be greater than or equal to twiceof the maximum frequency of the sampled signal in order to recover or approximately recoverthe discrete signal to its original continuous signal. Under this condition, the smaller thesampling period, the closer is the performance of the sampled data control system tothe continuous control system. As for closed-loop control systems, especially the motor
speed-control system, the controller is usually designed to trace the change of speed quickly.
Thus, the sampling period should be as small as possible, whereas the sampling frequency ishigh enough. In practice, taking the operating frequency of microprocessor, switchingfrequency of power electronics, time delay of sensors, and the restriction of the conversionability of A/D and D/A into consideration, the sampling period cannot be too small. Therefore,the system designer should select the sampling period reasonably according to the concretecircumstances. Let T
rbe the rising time of the system response and Nrbe the sampling
frequency, a simple empirical formula for estimating the sampling period Tis shown as
Nr¼Tr
T¼2/C04 ð4:4Ț
Compared with the continuous control system, the digital control system has the following
advantages:
(1) The digital devices have higher reliability, ﬂexibility and stability compared with the
analog devices.
(2) A digital control system has a higher antidisturbance ability.
(3) A digital control system is more ﬂexible, which has high control precision and could
implement complex control algorithms easily.
(4) A digital control system is more suitable to communicate with the top-level application
system or the remote control unit so as to construct a distributed control network.
With the development of computer technology and intelligent control theory, various types
of PID controllers have appeared, such as trapezoid integration PID, variable-speed integrationPID, fuzzy PID, neural-network PID, and so on. Note that these new PID controllers areproposed for those controlled objects that are characterized as nonlinear, coupling, delay,variable structure. These improvements not only enhance the system control performance, butSpeed Control for BLDC Motor Drives 85

also expand the application areas of PID controllers. Since each PID controller has its own
advantages, disadvantages and application areas, speciﬁc requirements and the control
performance should be considered when choosing the PID controller structure type.
During the design of a BLDC motor speed controller, it is essential to consider the system’s
working environment, load characteristics and position-detection methods. The target of
control is to achieve wide speed range, small static tracing error, good tracking performanceand antidisturbance ability. In a variety of control strategies, the dual-closed-loop PI controltechnology is the most mature and widely used. The outer loop of the dual-closed-loop speedcontroller is the speed loop (i.e. the voltage loop), aiming to stabilize the speed and resist-loaddisturbance. The inner loop is the current loop (i.e. the torque loop), aiming to stabilize current
and resist grid voltage ﬂuctuation. In the following two subsections, the antiwindup phe-
nomenon and the intelligent speed-control technologies are analyzed brieﬂy.
4.1.2 Antiwindup Controller
Using a PID controller for single-loop or double-loop speed regulation of BLDC motor hasbeen deeply studied. Usually, it can satisfy general speed-regulation requirements. However,since a BLDC motor is a multivariable nonlinear system, many new problems need to besolved further. Currently, most of BLDC motors adopt PID controller and PWM modulationfor speed control. Note that a current limiter is often followed in the speed loop, and PWM canbe regarded as another saturation limiter, as shown in Figure 4.3. Therefore, the BLDC motorspeed-control system has strong saturation characteristics. When the system enters into the
saturation state, the integral part of the controller will inevitably result in a typical windup
phenomenon. In more serious situations, it will make the system performance degrade greatly.
There are many ways to design an antiwindup controller, which can be mainly divided into
linear structure and nonlinear structure [1]. Their principles are all based on whether thesystem limits the amplitude of output or not (i.e. whether the output of the controller is equal tothe input of controlled objects) so as to prevent or limit the integral effect. The differencebetween the linear and nonlinear antiwindup controller is that there only exist switch elementsor other nonlinear elements in the latter. Antiwindup methods have been used in induction
motor and permanent-magnet synchronous motor control. Three new antiwindup design
methods have been proposed in [2], and they were performed in FPGA to control an inductionmotor. A current regulator based on antiwindup is used to realize the ﬂux-weakening control ofa surface-mounted permanent magnet motor in [3]. It needs no extra hardware and is easy toimplement in software.
All the traditional antiwindup controllers use the difference between the input and the
output of the limiter as the feedback signal to avoid or suppress the windup phenomenon in the
PID PID Inverter BLDC motorn*
n−i*
−
i Current limiter PWM equivalent
saturation limiteru
Figure 4.3 Diagram of double closed-loop speed-regulation system for a BLDC motor.86 Permanent Magnet Brushless DC Motor Drives and Controls

control system. Eleven different antiwindup design methods have been proposed in [4], and the
integrator clamping antiwindup controller is found to be the best one, whose structure is shownas Figure 4.4. A modiﬁed antiwindup controller based on the backcalculation and the
integrator clamping is presented in [1], the simulation results have demonstrated that its
application on the BLDC motor can make the system overshoot smaller to some extent. Butthis inﬂuence is not obvious and it also needs to reduce the system response speed to achievethis aim. Further, the algorithm of this kind of antiwindup controller is more complex. So, thesimple integrator clamping antiwindup PI controller is used here to control the BLDC motor.The corresponding variable structure control law of the controller is
_Z¼0 e/C1u
nH0;un$us
KI/C1eu n¼us/C26
ð4:5Ț
The speed regulation performance of a BLDC motor with PI and antiwindup PI controller is
shown in Figure 4.5.
It can be seen from Figure 4.5 that the antiwindup PI controller has good antidisturbance
ability, less overshoot and shorter settling time of the system, and can improve the speedresponse ability.KP
KI
0
>×
AND< > dt0
1unus+
+
η
∫•ηe
Figure 4.4 An integral clamping antiwindup controller.
00.10.2 0.30.4 0.50.6 0.7 0.8 0.9 10500100015002000250030003500
Anti-windup PIPI
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60500100015002000250030003500
Anti-windup PIPI
(b) Startin g with full load (load decreases at 1.2 s ) (a) Startin g with no load (load increases at 0.5 s ) n/(r/min)
t/s
n/(r/min)
t/s
Figure 4.5 PI and antiwindup PI control for a BLDC motor.Speed Control for BLDC Motor Drives 87

4.1.3 Intelligent Controller
Intelligent control emerges from the combination of automatic control and the concept of
artiﬁcial intelligence. The common intelligent control methods involve fuzzy logic, neuralnetworks and genetic algorithms, etc. They have been used widely in areas of the motorcontrol, motor parameter identiﬁcation and state estimation, fault detection and diagnosis.A typical BLDC motor block diagram of an intelligent control system is shown in Figure 4.6.An intelligent control algorithm is independent or not fully dependent on the controlled
plant’s accurate mathematical model. A fuzzy-logic control system based on expert
knowledge database needs less calculations, but it lacks sufﬁcient capacity for the newrules. On the contrary, a neural-network-based motor control system has a strong ability tosolve the structure uncertainty and the disturbance of the system, whereas it requires morecomputing capacity and data storage space. Genetic algorithms, ant-colony algorithms, andartiﬁcial immune algorithms are, respectively, created from the human evolution, biologyevolution, and artiﬁcial immune systems. They can optimize the controller parameters onlineor ofﬂine to achieve a better control performance. Of course, they need longer computation
time and larger storage capacity. In practice, in order to improve the reliability of the system, a
variety of combined intelligent methods like a fuzzy neural-network controller, a fuzzy-genetic controller, and a fuzzy immune controller are adopted so that they can take advantageof each other. The combination may be a simple superposition or a fully integration, as shownin Figure 4.7. From above, we can know that fuzzy control has the disadvantage of poorlearning ability and the advantage of good reasoning ability, while the neural network has poorreasoning ability but good learning ability. So, the combination of them can ensure thefuzzy neural network’s good learning and reasoning ability. Moreover, the integration of
genetic algorithm for a fuzzy neural network can optimize the fuzzy inference rules and theFuzzy logic control
Neural network controlGenetic algorithm controlr eu y
_BLDC Motor
Figure 4.6 Intelligent control diagram for a BLDC motor.
Neural network Fuzzy logicNeural
network
Genetic
algorithmFuzzy
logic
(a) Combination of two intelli gent control methods (b) Combination of three intelli gent control methods
Figure 4.7 Combination of intelligent control methods.88 Permanent Magnet Brushless DC Motor Drives and Controls

neural-network structure, and improve the system reliability and control accuracy. As far as we
know, it is difﬁcult for us to solve all problems in BLDC motor control systems by using only
one type of intelligent control methods. So in order to achieve a system-level optimal control
performance, intelligent control is usually combined with the traditional linear control andother modern control methods.
4.1.4 Representations of Uncertainty
Uncertainty of the controlled plant (for example, the BLDC motor) usually includesunstructured uncertainty and structured uncertainty. Let G
0(s) be a nominal transfer function,
which is a best estimate, in some sense, of the true plant behavior, and let G(s) denote the true
transfer function of the plant. Then for BLDC motor, the unstructured uncertainty can berepresented in three most commonly used models as follows:
GðsȚ¼G
0ðsȚțDaðsȚð 4:6Ț
GðsȚ¼G0ðsȚ½IțDiðsȚ/C138 ð4:7Ț
or
GðsȚ¼½ IțDoðsȚ/C138GoðsȚð 4:8Ț
where Da(s)— additive perturbation;
Di(s)— input multiplicative perturbation;
Do(s)— output multiplicative perturbation.
The additive model in Equation (4.6) may be used to pose some robust stabilization problems
that have nice solutions, but the multiplicative models in Equations (4.7) and (4.8) are often morerealistic, since D
ikk¥andDokk¥represent relative rather than absolute magnitudes.
In practical BLDC motor control systems, measurement errors such as current, voltage,
speed measurement errors caused by resolution of sensor, the perturbation from systemor external factors, and observation error such as torque, back-EMF observation errorcaused by observation algorithms or the accuracy of model all would lead to unstructureduncertainty.
It is well known that motor operation is strongly affected by the rotor magnetic saliency,
saturation, and armature reaction effects. In particular, the saturation of the rotor iron portionaround the magnets induces signiﬁcant distortion of the air-gap ﬂux. Subsequently, theinductance parameters vary as a function of the magnitude and phase angle of the motorcurrent. Moreover, the inductance variation affects both the plant gain and the open-loopelectrical time constant of the motor. Hence, the performance of the drive varies at differentdynamic and steady-state operating conditions.
Usually, the ﬂux density of the rotor permanent magnets is affected by the temperature
variation, and it will be ampliﬁed by variations in the stator-winding resistance and
the magnetic saturation in the motor. Also, the residual ﬂux density decreases as theSpeed Control for BLDC Motor Drives 89

temperature increases through a reversible process. In addition, the inaccuracy of the back-
EMF model may degrade the control performance under the condition of sensorless control.
Hence, in BLDC motor control systems, electrical parameters such as stator resistors Rs
and inductances Lsare sensitive to environment temperature and motor angle speed,
especially when the motor runs at high speeds and full load. Consequently, the electricaltime constant will vary with these factors. Random perturbations from load or unmodeleddynamics also affect the system performance. The uncertainty in a BLDC motor could berepresented as follows:
u
a¼R0iațL0dia
dtțorcf0țd ð4:9Ț
d¼DRi ațDLdia
dtțorDcțe ð4:10Ț
where R0,L0andcf0represent stator nominal resistor, nominal inductance and cf0nominal
ﬂux respectively, R¼R0țDR,L¼L0țDL,c¼cf0țDc, and erepresents unmodeled
dynamics.
In this way, the BLDC motor control system can be modeled more accurately and it will be
more suitable in practice.
4.2 Advanced Speed Control for BLDC Motor Drives
4.2.1 Fuzzy Control
As shown in Figure 4.8, a typical fuzzy-control system is composed of a fuzzy controller and a
plant. The fuzzy controller involves four components: fuzziﬁcation, knowledge database(including the database and rule base), fuzzy inference and defuzziﬁcation. Fundamentally,fuzzy control can reﬂect human reasoning. It is an intelligent control method that is
independent of the precise mathematical model of the controlled object. Whether the
controlled object is linear or nonlinear, a fuzzy controller can be implemented effectivelywith good robustness and adaptability.
Knowledge
Datebase
Fuzziﬁcation Fuzzy Inference Defuzziﬁcation
Fuzzy ControllerPlantReference
InputOutput
Figure 4.8 Typical diagram of a fuzzy-control system.90 Permanent Magnet Brushless DC Motor Drives and Controls

Due to the appearance and development of fuzzy theory, fuzzy control has been used widely
in motor-control applications. Since the motor load varies greatly in many motor applications,
good speed-regulation ability is often essential in all working conditions. Considering
the limitation on algorithm time consumption, nonlinear control methods based on fuzzylogic are ideal choices for motor control [5–8]. Currently, the fuzzy-control methods forBLDC motors can be mainly divided into three categories: standard fuzzy controller, fuzzy-PID switch controller and optimized fuzzy controller.
4.2.1.1 Types of Fuzzy Controller
(1) Standard fuzzy controller. A standard fuzzy controller for BLDC motor is shown in
Figure 4.9. Based on the principle of fuzzy controller shown in Figure 4.8, the input signal
is ﬁrst fuzziﬁcated, then the control table is constructed according to an expert knowledgedatabase, and ﬁnally the control signal is obtained through defuzziﬁcation.
In general, a one-dimensional fuzzy controller in Figure 4.9 is usually used for a one-
order controlled object. Because only one error signal is chosen as the input variable in thistype of controller, its dynamic performance is often poor. In theory, the higher the fuzzy
controller’s dimension, the better the control performance. However, higher dimension
will lead to more complex fuzzy-control rules and control algorithms. So generally thedimension of the fuzzy controller does not exceed 3. To date, the two-dimensional fuzzycontroller has been widely used. As shown in Figure 4.9(b), the feedback error eand its
differential _eare used as inputs and the control variable uis used as output.
(2) Fuzzy-PID switch controller. The control strategy is obtained by the integration with a
fuzzy controller and conventional PID control as shown in Figure 4.10. When the output ofthe fuzzy controller is zero, the system switches to the conventional PID controller.
Otherwise, the fuzzy controller works. Hence, the fuzzy controller can be used to improve
the robustness to uncertainties. It has been proved that the fuzzy-PID switch controller canalso reduce the overshoot and the settling time of the whole system.
(3) Optimized fuzzy controller. In order to achieve an optimal operation, a fuzzy controller is
used to optimize and adjust the parameters of traditional PID controller by using fuzzy
Fuzzy Controlleru e Fuzzy Controller
eu
d/dte
(b) Two-dimensional (a) One-dimensional
Fuzzy Controlleru
d/dted/dte e
(c) Three-dimensional
Figure 4.9 The structure of fuzzy controllers.Speed Control for BLDC Motor Drives 91

rules as shown in Figure 4.11. The controller’s parameters are adjusted online according to
the actual working conditions. It is an online intelligent parameters adjustment method.
(4) Other types. There are many other types of fuzzy controllers in BLDC motor control
systems. Moreover, with the development of the technology, more new fuzzy-controlstrategies will emerge. Figure 4.12 shows a precompensation fuzzy controller. In certainoccasions, the PID controller in Figure 4.12 can be removed (note that when there is no
PID controller, u
0is equal to r/C3), the basic idea is to use a fuzzy feedforward compensation
controller to compensate the actual reference input to get an ideal reference input signal,
then use the traditional double closed-loop controller to control the BLDC motor.
4.2.1.2 General Design Procedures of Fuzzy Controller for BLDC Motor
According to the practical needs in applications of BLDC motor control systems, the two-
dimensional fuzzy controller is usually adopted, i.e. using the motor speed error eand its
rate of change ecas inputs of fuzzy controller. Through fuzziﬁcation and fuzzy decision, a
one-dimensional output is obtained. Then the control signal after defuzziﬁcation is used forFuzzy Controlleru1 e
PID Controlleru2u
Figure 4.10 Fuzzy-PID switch controller.
PID Controllere
Fuzzy Optimizationu
rr *
Figure 4.11 Optimized fuzzy controller.92 Permanent Magnet Brushless DC Motor Drives and Controls

speed regulation. The two-dimensional fuzzy controllers have been widely used in fuzzy
controller for its good performance. The corresponding design procedures are as follows.
(1) Deﬁnition of dynamic signal. Here, the speed tracing error and its change are deﬁned as
eðkȚ¼n*ðkȚ/C0nðkȚ
ecðkȚ¼eðkȚ/C0eðk/C01Ț(
ð4:11Ț
where n/C3(k) — reference speed of kth sample,
n(k) — motor speed response of kth sample.
Leteybe the output of the fuzzy controller, i.e. ey¼f(e,ec), then the control surfaces
corresponding to the traditional PID controller and fuzzy controller can be shown as
Figure 4.13.(2) Quantization factor and scale factor. In order to increase the sensitivity of the control and
convenience for application of the fuzzy rule, the actual values of error eand its change ec
are quantized by using the quantization factors K
e1andKec, then they are mapped to the
fuzzy set domain X ¼{–m,–mț1,…,0 , …,m–1,m}. Generally, the system control
ey
eec
+1+1
−1−1ey
eec
+1+1
−1−1
(a) PID controller (b) Fuzz y controller
Figure 4.13 Control surface.Fuzzy
Compensatoru1 e
PID Controlleru0ur*
r−
Figure 4.12 Precompensation fuzzy controller.Speed Control for BLDC Motor Drives 93

performance will be improved by increasing m. Note that too large a value for mwould
increase the difﬁculty in determination of fuzzy control rules. Commonly, in BLDC motor
control systems, one can choose the fuzzy domain with 7 language variables including
negative big (NB), negative middle (NM), negative small (NS), zero (ZE), positive small(PS), positive middle (PM) and positive big (PB). Further, the output of fuzzy decisioncannot be applied into the control system directly. The output signal is required to beconverted from the fuzzy domain to the basic domain of actual output by using the scalefactor K
u, so that the output can be used to control the object.
(3) Member function. Different member functions such as the trapezoidal distributed
function, the triangle distributed function and the Gaussian-distributed function can be
chosen for various applications. Whether the selected member functions are proper or not
needs to be veriﬁed by theory, simulation and experiment. In order to facilitate theimplementation and ensure the reliable operation of the system, the triangle distributedfunctions, as shown in Figure 4.14, are generally selected as member functions of fuzzycontroller for BLDC motor.
(4) Control rules for fuzzy controller. According to expert experience, a fuzzy-control
decision table is obtained from the “IF-THEN” interference rules. Table 4.1 gives afuzzy decision table.
In the table, FD represents the output of fuzzy decision. Hence, 49 fuzzy control rules are
produced. Each of them can be expressed using the following form:
Ifeis NB and e
cis PM ;then FD is ZE
Ifeis PM and ecis NB ;then FD is ZE
Ifeis NS and ecis NM ;then FD is NM
…
…
4.2.2 Neural-Network Control
Artiﬁcial neural networks (ANN) were originated in the period of Freud psychoanalysis in the
early 19th century. Now they have been widely applied in the control of permanent magnetsynchronous motors, switched reluctance motors, ultrasonic motors, BLDC motors and othernew types of motors. The typical applications include position control, speed control, currentcontrol, parameter identiﬁcation and state estimation of the motors. At present, neural
NBN S NM ZE PM PS PB
−2 −4 −6 0+ 6 +4 +2
Figure 4.14 Member functions of fuzzy controller.94 Permanent Magnet Brushless DC Motor Drives and Controls

networks used in the applications of BLDC motor speed control mainly include back-
propagation (BP) neural networks, radial basis function (RBF) networks, wavelet networks,single neural networks and other types [9–17]. Here, an adaptive RBF network learning
algorithm with simple structure and fast convergence is presented. Then, it is applied to the
online estimation of power switch conducting signal of the BLDC motor for controlling theinverter directly. Finally, with the help of ofﬂine and online training for the network, the directcurrent control is obtained.
4.2.2.1 Adaptive RBF Network Learning Algorithm
An RBF network is not only biology based, but also consistent with the function approx-
imation theory, which is proved to be suitable for multivariable function approximation. Aslong as the set of central points is chosen rightly, a good approximation with advantage of
unique and best approximation point can be achieved with few neurons. The relation between
the network connection weight and the output layer is linear, so that it can adopt the linearoptimization algorithm guaranteeing global convergence. Based on these advantages of RBFnetworks, in recent years it has been paid more and more attention and used widely in areas ofpattern recognition, function approximation, adaptive ﬁltering and other ﬁelds.
The difﬁculty on applications of RBF networks is the proper selection of RBF hidden-layer
units, which has a signiﬁcant impact on the NN’s approaching capacity and performance.Thus, it will affect the size of the network. If the hidden units are few, then it cannot complete
the task of classiﬁcation or function approximation; while if there are too many hidden units,
the learning rate will be slowed down due to too many network parameters. Consequently, theinitial network parameters, speciﬁcity of training samples and outer interferences will have agreat inﬂuence on the network’s connection weight. Moreover, when small distortion existsbetween the input pattern and training samples, the correct generalization results may not beattained, and the increase of the network size has an adverse effect on applications.
Fortunately, the possible phenomenon of slow convergent speed or even nonconvergence
from the improper selection of the initial value of the hidden layer parameters was eliminated
by using the adaptive algorithm with dynamically adjusting network structure and para-
meters [18–21]. Generally, the adaptive RBF network’s initial numbers of hidden units canbe set to zero, then added adaptively according to certain rules in the training process, and thehidden units with less effect on the output signal can be deleted. This can effectively realizeTable 4.1 Fuzzy decision table
e
FD NB NM NS ZE PS PM PB
ec
NB N BN BN M N SN SZ EZ E
NM NB NB NM NS NS ZE ZE
NS NM NM NS NS ZE ZE PS
ZE NM NS NS ZE PS PS PM
PS NS ZE ZE PS PS PM PM
PM ZE ZE PS PS PM PM PB
PB ZE ZE PS PM PM PB PBSpeed Control for BLDC Motor Drives 95

the nonlinear mapping by using the least hidden-layer units, so that a simple and compact
network structure is obtained. For each new input sample ðXi;tiȚ, the adaptive algorithm
consists of the following six steps:
(1) The hidden layer output jkðXiȚand the network output yiare, respectively, calculated as
jkðXiȚ¼exp /C0Xi/C0Ci kk2
2si2 !
ð4:12Ț
and
yi¼fðXiȚ¼Xn
k¼1okjkðXiȚð 4:13Ț
where Xiis the N-dimensional input, Ciis the center vector of Gaussian function at the ith
hidden-layer unit, siis the normalized constant of the ith hidden-layer unit, okis the
weighting coefﬁcient from the hidden layer to the output layer.
(2) Calculate the network error between the expected output response tiand the actual
output yias
eikk¼ti/C0yi kk ð4:14Ț
and the deviation between the samples and existed hidden-layer units as
dj¼Xi/C0Cj/C13/C13/C13/C13j¼1;2/C1/C1/C1u ð4:15Ț
where uis the number of existed hidden-layer units.
Let
d
min¼minðdjȚð 4:16Ț
(3) If there exists
eikkHe;dminHlðiȚð 4:17Ț
lðiȚ¼maxðlmaxgi;lminȚð 4:18Ț
where eis the desired accuracy of the network, l(i) is the network’s approximation accuracy
of the ith input, which is reduced from lmaxtolmin, and gis the attenuation factor (0 GgG1).
Then a new hidden-layer unit is added, and the parameters of the new layer should satisfy
Ck¼Xi ð4:19Ț
sk¼1
qðXq
j¼1Xi/C0Cj/C13/C13/C13/C132Ț12=ð4:20Ț
where Cjis the center of the qth hidden-layer unit that is the closest to the input sample.
(4) If Equations (4.17) and (4.18) are not satisﬁed, then adjust the connection weight by
recursive least square method.96 Permanent Magnet Brushless DC Motor Drives and Controls

(5) If all the ncontinuous input samples satisfy
wkjkðXiȚ
yi/C13/C13/C13/C13/C13/C13/C13/C13/C20d ð4:21Ț
where dis the predeﬁned constant.
Then, the kth hidden-layer unit is deleted.
(6) Input new samples, and go to step (1).
4.2.2.2 Neural-Network Direct-Current Control for a BLDC Motor
In the BLDC motor speed-control system, the rotor position directly determines the ON/OFF
statesoftheinverterpowerswitches,whichisthefundamental basisforthedirectcurrentneural-network control of BLDC motor. Through ofﬂine and online training for the RBF network,nonlinear mapping between the motor stator voltages, winding currents and the ON/OFF statesof power switches are realized, so that the winding current can be controlled directly.
During ofﬂine training, the access of training samples is very important. A neural network’s
training samples could come from the simulating or experimental data. In order to make thenetwork obtained from ofﬂine training more close to the actual motor operation, the samplesused by ofﬂine training are generally the experimental data.
Note that only two of the three phases of the BLDC motor with Y-connected three-phase
stator windings are conducted at any time. Moreover, the summing current of the three phasewindings is equal to zero. So, the input sample vector can be taken as
X
i¼fiAðkȚ;iBðkȚ;iAðk/C01Ț;iBðk/C01Ț;uAGðk/C01Ț;uBGðk/C01Țg
where uAGanduBGare, respectively, the terminal to ground voltages of phases A and B.
Since the output sample are the ON/OFF states of the six power switches, it is difﬁcult to
detect the states of power switches directly. One method for solving this problem is to obtainswitch states depending on different rotor positions with 1 representing state ON, while 0represents state OFF according to the BLDC motor’s commutation logic. So the output vectorsof training sample can be represented as
Y
i¼fS1;S2;S3;S4;S5;S6g
where S1,S3andS5are the conduction signals of upper power switches for the three-phase
bridge inverter, while S2,S4andS6are the conduction signals of lower power switches for the
three-phase bridge inverter.
While the training sample is obtained, the ofﬂine training can be implemented according to
the adaptive training algorithm presented above. The whole ofﬂine training algorithm can be
realized through MATLAB software on a PC. With training of 3500 samples, the network
achieves the predetermined precision. After the ofﬂine training, the number and center of theRBF network hidden-layer nodes, and the initial values of connection weights are conse-quently determined. The initial structure of network is shown in Figure 4.15. Because theofﬂine training samples come from experimental data, the trained network could be consideredapproximately close to the motor’s actual condition. Moreover, the parameters of the hiddenlayer need not be tuned online.Speed Control for BLDC Motor Drives 97

The network connection weights are trained online by using recursive least square method
in supervision mode. The teacher of the network comes from the network output signals after
the logic process. The corresponding diagram of training is shown in Figure 4.16.
In order to avoid improper conduction of power switches, state signals need to be adjusted
and processed logically. So, the corresponding network output signal is represented as
SxðnȚ¼0
1
Sxðn/C01Ț8
><
>:^SxðnȚ/C200:25
^SxðnȚX0:7
Othersð4:22Ț
In which, the rules for logic procession are formulated as:
(1) At any moment, only one state of S1,S3, and S5is equal to be 1, and so is the state of S2,S4
andS6;
(2)S1andS4,S3andS6,S5andS2cannot be equal to 1 at the same time;
(3) If conﬂiction happens to the above two laws, then the network output signal must be set to
its closest state.ϕ
tϕ
6ϕΣ
Σ
Σ
……
……iA(k)
iB(k)
iA(k-1)
iB(k-1)
uAG(k-1)
uBG(k-1)S1
1(k)
Sj (k)
S6 (k)
Figure 4.15 Ofﬂine trained RBF network.
Sˆ (x = 1, 2, …,6) S (x = 1, 2, …,6)
ex (x = 1, 2, …,6)RBF Network Logic Process
−
Recursive Least Square Method
Figure 4.16 Online training diagram of RBF network.98 Permanent Magnet Brushless DC Motor Drives and Controls

The main procedures of the recursive least square learning rules are:
(1) As for the kth input, the network output function can be rewritten as
yðkȚ¼Xn
i¼1wijiðXðkȚȚ ¼wHðkȚuðkȚð 4:23Ț
where w(k) is the weight vector, u(k) is the RBF vector, Hrepresents the conjugate and
transpose symbol.
(2) Let the initial values of the recursive matrix Pand weight vector matrix wbe
Pð0Ț¼d/C01
0I;wð0Ț¼0 ð4:24Ț
where d0is a small and positive constant, and Iis the identity matrix.
(3) Then, calculate v(k),z(k),w(k), and P(k) according to the following equations as
vðkȚ¼l/C01Pðk/C01ȚuðkȚ
1țl/C01uHðkȚPðk/C01ȚuðkȚð4:25Ț
zðkȚ¼yðkȚ/C0wHðk/C01ȚuðkȚð 4:26Ț
wðkȚ¼wðk/C01ȚțvðkȚz*ðkȚð 4:27Ț
PðkȚ¼l/C01Pðk/C01Ț/C0l/C01vðkȚuHðkȚPðk/C01Țð 4:28Ț
where lis the forgetting factor (0 /C20l/C201),/C3represents the complex conjugate symbol.
Note that the online training algorithm only needs to adjust the connection weights between
the hidden-layer nodes and the output layer, which can be realized easily. Hence, the
computation time of the proposed algorithm is greatly reduced, so that the system’s dynamicresponse speed is improved.
Moreover, when the BLDC motor system works in position-sensorless control, a dual-RBF
network control mode can be used, as shown in Figure 4.17.
In Figure 4.17, the motor voltage and current are mapped nonlinearly into the rotor position
by the ﬁrst RBF network. The inputs of the network are the motor phase currents and phasevoltages (i.e. the voltages between the winding terminal and ground), while the output ofnetwork is the rotor’s position angle. The network is trained ofﬂine by using the proposedadaptive RBF network algorithm. All training samples come from experimental data.Therefore, the trained network could estimate the rotor position online.
The other RBF network in Figure 4.17 also uses the same learning algorithm to guarantee
the compactness of network structure. This network is used to achieve the nonlinear mapping
from the rotor position and the reference torque to the reference current. For three-phase
Y-connected BLDC motors with six states, only two of the three phase windings are conductedat any time. Under this condition, if the back-EMF of the motor is assumed to be an idealtrapezoidal wave, then the back-EMF can be determined by the rotor position angle and its rateof change (i.e. the speed). With the back-EMF known, when the torque is given and theSpeed Control for BLDC Motor Drives 99

operation in maximum torque mode is guaranteed, the current reference value without torque
ripple can be calculated. In other words, the reference current is the function of motor torqueand rotor position, the function relation could be accomplished by RBF network 2. By
comparing the estimated reference current with the actual current and regulating the current
through a PI controller, the current injected into the winding is controlled, so that the torqueripple of the speed-control system is restrained.
When a BLDC motor speed-control system runs with position sensors, the mentioned dual-
RBF network control above can be transformed into single neural-network direct controlmode, so that the speed loop adopts PI control while the current loop uses RBF networkcontrol, as shown in Figure 4.18. The dual-closed-loop control strategy of a single RBFnetwork with position sensors could also use the combination control mode where the speed
loop is neural-network control while the current loop adopts PI control.Speed
Reference
PITorque
Generator
Speed
CalculationTorque Reference Current
Reference
Phase CurrentVoltage− −
θˆBLDC
MotorRBF Network2
RBF
Network1PI
Inverter
ˆn
Figure 4.17 Dual-RBF network control without position sensors.
Reference
Speed
PIReference
TorqueReference
Current
Phase Current− −
d/dtθRBF Network
BLDC
MotorPI
InverterTorque
Generator
n
Figure 4.18 Single RBF network control with position sensors.100 Permanent Magnet Brushless DC Motor Drives and Controls

The proposed dual-RBF network position sensorless speed control algorithm is imple-
mented in TMS320LF2407 DSP, whose high-speed calculation capacity guarantees the
reliable online control for BLDC motor. The system control diagram is shown in Figure 4.19,
and the corresponding ﬂowchart of software program is shown in Figure 4.20.
The experimental waveform is obtained through an Agilent 54622A oscilloscope.
Figure 4.21(a) presents the current of phase A when the motor runs under rated speedInverter
SwitchesBLDC
Motor
TMS320LF2407PWMA/D
PCUd
Figure 4.19 System control diagram.
Initialization of
Variables and Event
Manager
Initialization
of Power
Drive
Double Closed-
Loop ControlMain
Program
Entrance
EndEnergize the
Winding in TurnEnd of Locating?N
Y
Figure 4.20 Flowchart of the main program.Speed Control for BLDC Motor Drives 101

with only the rotor position online estimation network and a load torque equal to 0.3 N m. The
corresponding output torque is shown in Figure 4.21(b).
It can be seen from Figure 4.21 that if there are no rotor-position sensors, the current could
still commutate correctly through position-sensorless speed control. However, there is a greatdifference between the actual current waveform and the ideal square wave. Figure 4.21 showsthat the amplitude of the torque ripple is about 30 per cent of the average torque.
Figure 4.22 is the current waveform of phase A and its corresponding output torque when
the real time reference current estimation is applied.
From Figure 4.22, we can see that the current waveform is clearly improved. In this case, the
amplitude of torque ripple is reduced to 4 per cent of the average torque. Thus, the robustnessand stability of the speed-control system are improved greatly. Therefore, the dual-BRF-based
neural-network control could realize position-sensorless speed control with less torque ripple
for BLDC motors.
4.2.3 Genetic Algorithm Optimization Control
In order to achieve precise speed control for BLDC motors, advanced algorithms such asgenetic algorithms, ant-colony algorithms, and artiﬁcial immune algorithms could be used tooptimize the control rules under different operating states, so that better optimized controlrules could be obtained to improve the control performance of BLDC motors [22–26]. Thissection mainly focuses on the application of genetic algorithm on BLDC motors.
4 A/div
1.2 ms/div
(a) Current waveform of phase A (b) Torque waveformt/msT/N m
00.10.20.3
1.0 2.0 3.0 4.0
Figure 4.21 Experimental results without reference-current estimation.
1.2 ms/div4 A/div
t/ms00.10.20.3
4.0 3.0 2.0 1.0T/N m
(b) Torque waveform (a) Current waveform of phase A
Figure 4.22 Experimental results with reference current estimation.102 Permanent Magnet Brushless DC Motor Drives and Controls

4.2.3.1 Optimization of Fuzzy Control Rules
Note that the nonlinearity of a controlled object usually increases the difﬁculty in determi-
nation of control rules for a BLDC motor fuzzy controller. Even the fuzzy control rules arealready obtained in certain conditions, it is difﬁcult for them to be used directly with systemvariation. Theoretical analysis and practical experiences have shown that the fuzzy controlrules could be optimized by the genetic algorithm, so that the control performance of thecontroller could be improved with better stability and higher control accuracy. Figure 4.23shows the encoded modes that are used for the fuzzy control rules optimized by the genetic
algorithm. In Figure 4.23, 10-bit binary codes are used to express the fuzzy decision rules. The
ﬁrst bit is the ﬂag, which indicates whether the rule is used or not. “1” indicates that the rule ispreserved, while “0” indicates that the rule is abandoned. The codes of 2–4 bits, 5–7 bits, and8–10 bits, respectively, represents the error e, the change of error ec, and the decision value FD.
All the three variables use 001, 010, 011, 100, 101, 110 and 111 to represent NB, NM, NS, ZE,PS, PM and PB, respectively. For example, in Figure 4.23, rule 1 represents that if eis PM and
ecis PS, then FD is NB, in which the ﬁrst bit 1 indicates that the rule 1 is preserved after
optimization. Rule 2 indicates that if eis PB and ec is NB, then FD is NM. The ﬁrst bit 0
indicates that the rule 2 will be abandoned after optimization. Table 4.2 presents the fuzzycontrol rules after genetic algorithm optimization.
Table 4.2 shows that 6 fuzzy control rules are abandoned and 4 rules are changed after
genetic algorithm optimization. Since the optimization procedure of fuzzy control rules usinga genetic algorithm is relatively complex, the high-speed performance DSP is also difﬁcult tofulﬁll the optimization algorithm online when the BLDC motor runs at high speed. Therefore,the optimization of fuzzy control rules is generally performed ofﬂine according to theexperimental data and then embedded into DSP.1 110 101 001 0 111 001 010Rule 1 Rule 2
…
Figure 4.23 Encoding modes of genetic algorithm.
Table 4.2 Fuzzy decision rules optimized by genetic algorithm
e
FD NB NM NS ZE PS PM PB
ec
NB NB NB NM NS ZE ZE
NM NM NS NS NS ZE ZE
NS NM NM NS NS ZE ZE PS
ZE NM NS NS ZE PS PS PM
PS ZE ZE PS PS PM
PM ZE ZE ZE PS PM PB PB
PB ZE PS PM PB PBSpeed Control for BLDC Motor Drives 103

4.2.3.2 Parameter Optimization of the Fuzzy Controller
The design of the fuzzy controller determines the performance of the fuzzy-control system,
while the performance of fuzzy controller is determined by the fuzzy rules or fuzzy inference.In general, after the fuzzy controller design is ﬁnished, its fuzzy rules or fuzzy inference areusually determined and cannot be adjusted. A large number of simulation and experimentalresults suggest that the quantization factor and the scaling factor of the fuzzy controller have a
great inﬂuence on its performance. Occasionally, the output characteristics of the fuzzy
controller may be changed. When the system characteristics are changed, the parameters of thefuzzy controller need to be adjusted in real time so that good dynamic and static characteristicsof the system can be achieved. Hence, a fuzzy controller with ﬁxed parameters lacks goodgenerality and adaptability. In this case, control rules with simple analytic expressions can beadopted to design the BLDC motor fuzzy controller with adjustable weight coefﬁcients.
In the design of a fuzzy controller for a BLDC motor, the input variable is required to be
converted from the basic discourse domain to the fuzzy set discourse domain. The error
quantization factor K
e1and the error change quantization factor Kecare used to achieve this
goal. Besides, the control value of each sampling from the fuzzy controller cannot be used on
the controlled object directly. It should be converted into the basic domain by using the scalingfactor K
u.
As for the inﬂuences of the parameters Ke1,KecandKuon the system response, we can ﬁx
any two of the three parameters and change the third parameter to analyze the control laws.The corresponding control laws are concluded as follows.
(1) The larger the K
e1, the faster the system response. Note that a large Ke1may cause big
overshoot and long adjusting time for the system. Moreover, an oscillating phenomenon
would appear in serious cases. While if the Ke1is too small, the system convergence rate
will be slower. Generally, the system static error will be reduced by increasing Ke1.
(2) The larger the Kec, the slower the system response. Usually, the smaller the Kec, the more
sensitive the system response. Hence, a faster rising rate is achieved. But too small a Kec
may cause oscillation in the system. Similarly, the static error will be reduced byincreasing K
ectoo.
(3)Kuis equivalent to the proportional gain in a normal control system. Generally, the larger
theKu, the faster the response rate. Note that large Kumay cause serious response
oscillation, while a small Kumay lead to a slower convergence rate. In the three
quantization factors, Kuis the most inﬂuential factor for system response.
So, it can be concluded that proper adjustment of the three parameters could increase the
system response speed, reduce the overshoot, and improve the static and dynamic performanceof the fuzzy controller. In addition, good dynamic performance and reliable stability
performance cannot be easily obtained by using fuzzy controller with ﬁxed parameters.
Therefore, it is necessary to adjust these parameters online according to the system dynamicerror eas the following equations:
K
e1¼Ke10țK1/C2e; jej/C20emax
2
Ke10țK1/C2emax
2;jejHemax
28
<
:ð4:29Ț104 Permanent Magnet Brushless DC Motor Drives and Controls

Kec¼Kec0țK2/C2e; jej/C20emax
2
Kec0țK2/C2emax
2;jejHemax
28
<
:ð4:30Ț
Ku¼Ku0țK3/C2e; jej/C20emax
2
Ku0țK3/C2emax
2;jejHemax
28
<
:ð4:31Ț
where Ke10,Kec0andKu0are the base values, K1,K2andK3are ﬁne-tuning parameters (all are
non-negative), and emaxis the largest positive error value in the basic domain.
From the above, we can see that increasing Ke1is equivalent to decreasing the basic domain
of error. Hence, the control effect of error variables is increased. In addition, it can be seen from
Equation (4.29) that when | e|/C20emax/2 is satisﬁed, the control effect will be increased by
increasing Ke1with the error increasing. When the error decreases gradually, in order to reduce
the overshoot, the control effect of error change should be increased, i.e. Kecshould be
increased. From Equation (4.31) we can see that Kuincreases with the error increasing, so that
faster convergence rate can be obtained.
The main procedures of how to use the genetic algorithm to optimize the fuzzy controller’s
parameters are shown in the following three steps:
(1) Determine the decision variables with their constraining conditions and the corresponding
encoding and decoding methods. In the optimization of parameters, base values Ke10,Kec0,
Ku0and ﬁne adjusting parameters K1,K2,K3are chosen to be decision variables. The
restraining conditions of decision variables are usually determined by the system stability
performance index. If the stable error is required to be less than d1, then
Ke1X1
2d1ð4:32Ț
Hence, according to experience, the range of base values are determined as Ke10: 0–120,
Kec0: 0–120, Ku0: 0–7. The restraining conditions of K1,K2andK3are the current
predetermined base values obtained by genetic algorithm optimization.
Construct the optimized model and determine the individual evaluation methodology.
One of the characters of a genetic algorithm is to use the objective function of the solvedproblem to obtain the next step’s searching information, where the usage of objectivefunction is reﬂected through evaluation of individual ﬁtness. Therefore, the ﬁtness
function is the key of genetic algorithm. The ﬁtness function is generally transformed
from the objective function. Here, the ﬁtness function is designed by using the weightcoefﬁcients combination method based on the system’s maximum overshoot M
p, adjust-
ing time tsand stable error esr, which is shown as
f¼aexp½/C0ðMp=Mp0Ț2/C138țbexp ½/C0ðts=ts0Ț2/C138țgexp½/C0ðesr=esr0Ț2/C138ð 4:33Ț
where Mp0,ts0,esr0are the corresponding expected index values; a,b,gare the weight
coefﬁcients, which satisfy the condition ațbțg¼1.
Equation (4.33) shows that the larger the value of the ﬁtness function, the better the
system performance.Speed Control for BLDC Motor Drives 105

(2) Genetic operations. Genetic operation is a simulating control of biology genetic inher-
itance, including the design of three genetic operators (selection operator, crossover
operator and mutation operator) and the determination of other operating parameters in the
genetic algorithm.
The selection operator, which indicates the chance for each individual to be selected is
proportional to its ﬁtness, can be represented as
Psi¼fi=Xn
j¼1fj ð4:34Ț
where Psiis the selected probability of ith individual, fiis the ﬁtness of ith individual, and nis
the population size.
The crossover operator is the main approach to produce new individuals in the genetic
algorithm. It is regarded as the major operator for its global searching capability. Here, thesingle-point crossover operator is used. However, the mutation operator is just the auxiliarymethod to produce new individuals because of its local searching capability. Here, the basic bitmutation operator is adopted.
As for the determination of operation parameters, the parameters that need to be determined
mainly include population size M, termination algebra T, crossover probability P
cand
mutation probability Pm. Here, Mis set to be 60 while Tis equal to 160. Hence, by using
the adaptive genetic algorithm proposed by Srinvivas, the parameters Pcand Pmare,
respectively, calculated as
Pc¼Pc1ðfmax/C0f0Ț
fmax/C0favg;f0Xfavg
Pc2; f0Gfavg8
<
:ð4:35Ț
and
Pm¼Pm1ðfmax/C0f0Ț
fmax/C0favg;fXfavg
Pm2; fGfavg8
<
:ð4:36Ț
where fmaxis the maximum population ﬁtness, favgis the average ﬁtness for per generation
population, f0is the larger ﬁtness in two crossover individuals, and fis the ﬁtness of the
mutation individuals.
Figure 4.24 gives the block diagram of the BLDC motor fuzzy-control system based on
optimization of a genetic algorithm. The corresponding ﬂowchart of optimized design for
fuzzy controller parameters is shown in Figure 4.25.
Figures 4.26 and 4.27 present the simulation and experimental results of the BLDC motor
system controlled by traditional PID and the genetic optimized fuzzy controller. From theﬁgures, we can see that the genetic optimized fuzzy controller has better speed-regulation
performance.
In the intelligent control systems for BLDC motor, the genetic algorithm can be combined
not only with fuzzy control strategy, but also with the neural network. For example, the106 Permanent Magnet Brushless DC Motor Drives and Controls

structure and learning rules of a neural network can be optimized by a genetic algorithm, so
that the corresponding performance of the intelligent controller is improved. In Figure 4.28,the speed loop adopts RBF network control optimized by a genetic algorithm, while the currentloop adopts traditional PID control. The RBF network structure in a speed loop is optimized bythe genetic algorithm, which can guarantee good stability and better antidisturbance ability ofthe system.
4.2.4 Sliding-Mode Variable Structure Control
Sliding-mode control is usually used for motor drive. One of the advantages of sliding-modevariable structure control is that its sliding mode has good adaptive ability against the systemdisturbance and perturbation. In particular, its high-speed switching characteristic has bettercontrol on the current ripple caused by load variation and winding commutation [27,28]. Theblock diagram of a single closed-loop sliding mode speed-control system based on the
extended state observer is shown in Figure 4.29. The part outside the dotted line is the motor
model, while the part inside the dotted line is the controller. The extended state observerestimates the load torque through the electromagnetic torque and speed of the motor. K
1,K2,
K3,K4andK5are parameters of the variable structure control systems.
4.2.4.1 Controller Design
From the principle of BLDC motor, the second-order model for BLDC motor can be described
by state equations as
_x1¼x2
_x2¼/C0ðraJțBvLaȚ
LaJx2/C0ðBvrațkeKTȚ
LaJx1țKT
LaJu/C0raTL
LaJ8
<
:ð4:37Ț
where x1is the motor’s angular speed, TLis the motor load, which is regarded as the motor
disturbance to be estimated by the extended state observer.eSpeed Reference Model
Speed Estimation
Defuzziﬁcation Fuzziﬁcation
ΔeUref
___
BLDC
Motor
Genetic
Algorithm
OptimizationKuKe
Kec 1-Z-1Driving System
Id
Figure 4.24 The block diagram of a fuzzy-control system based on optimization of genetic algorithm.Speed Control for BLDC Motor Drives 107

de/dtStart
Population size
generation, n=1
Selection, crossover,
mutation
Decoding
Fuzzy control rule
table
BLDC motor
Fitness calculation , control
quality evaluation
n= n+1
n >T ?
Output the
optimal parametersReference +
−
N
Ye
Figure 4.25 The ﬂowchart of optimized design for a fuzzy controller’s parameters based on a genetic
algorithm.
2200
1800
1400
1000
600
200
0 0.01 0.02 0.03 0.04 0.05n/(r/min)
t/s2200
180014001000
600200
0 0.01 0.02 0.03 0.04n/(r/min)
t/s0.05
(b) Genetic o ptimized fuzz y control (a) PID control
Figure 4.26 Simulation speed curves with load variation.108 Permanent Magnet Brushless DC Motor Drives and Controls

2500
2000
1500
1000
0
0.01 0.02 0.03 0.04 0.00GA
PIDn/(r/min)
t/s0.05500
Figure 4.27 Experimental speed curves with load variation.
RBF Speed
ControllerCurrent
ControllerPWM
Driving CircuitPosition
Detection
Current
Detection
Genetic Algorithm
Optimizationec i*
i_
n* UcnBLDC
Motor
_
Figure 4.28 Block diagram of a BLDC motor speed-control system based on a genetic neural network.
+ 1/(ra+Las)1 /(Js+B v) KT
TL+ ke
+Derivator K1
K2
K3
K4
K5c1+
+–– –
Extended
State ObserverSpeedΩrAccumulator
Figure 4.29 Variable structure control based on an extended state observer.Speed Control for BLDC Motor Drives 109

Let
e¼Or/C0O ð4:38Ț
where Oris the reference angular speed.
Substituting Equation (4.38) into Equation (4.37), we get
_x1¼x2
_x2¼/C0ðraJțBvLaȚ
LaJx2/C0ðBvrațkeKTȚ
LaJx1țðBvrațkeKTȚ
LaJOr/C0KT
LaJuțraTL
LaJ8
<
:
ð4:39Ț
where x1¼e,x2¼_e.
So, the parameters of AandBin_x¼AxțBuțFðtȚare, respectively, given as
A¼01
/C0ðBvrațkeKTȚ
LaJ/C0ðraJțBvLaȚ
LaJ2
435 ð4:40Ț
B¼0/C0
KT
LaJ/C20/C21
ð4:41Ț
LetCT¼[c11] and F(t)¼[0f(t)]T, then
fðtȚ¼ðBvrațkeKTȚ
LaJOrțraTL
LaJð4:42Ț
Further, considering the sliding-mode switching surface as
s¼CTx¼0 ð4:43Ț
Then, the sliding mode switching surface divides the whole state space into two parts: sH0
andsG0. So the controlling value u(x) of variable structure control can be deﬁned as
uðxȚ¼uțðxȚsðxȚH0
u/C0ðxȚsðxȚG0/C26
ð4:44Ț
where uț(x)$u/C0(x).
Note that the existing condition of the sliding mode is
lim
s!ț0_sG0;lim
s!/C00_sH0
Besides the existence of the sliding mode, the ability of the motion going into sliding mode
and its stability should be guaranteed too. Generally, different parameters can be used to
achieve different variable structure control strategies.
Moreover, by using the equivalent control law, the sliding mode equation can be obtained
directly without limit calculation.110 Permanent Magnet Brushless DC Motor Drives and Controls

Let _s¼0, then
CAx țCBu țCFðtȚ¼0 ð4:45Ț
The solution of Equation (4.45) is
ueq¼/C0 ðCBȚ/C01½CAx țCFðtȚ/C138 ð 4:46Ț
Hence, the ideal sliding mode equation is obtained as
_x¼½I/C0BðCBȚ/C01C/C138Axț½I/C0BðCBȚ/C01C/C138FðtȚð 4:47Ț
and the control input is rewritten as
u¼ueq/C0asgnðsȚI ð4:48Ț
Note that if the initial state of system is not near the area of s¼0, the state trajectory is
required to move towards the switching surface s¼0. This means that the reaching condition
of the sliding mode must be satisﬁed.
Further, if the Lyapunov function is chosen as V¼s2=2, by using Lyapunov stability
theorem, we get
1
2d
dtðs2Ț¼s_sG0 ð4:49Ț
This is exactly the condition of global sliding control mode, which indicates that any motion
point in state space has the approaching tendency to the switching surface s¼0. Obviously, if
the system satisﬁes the condition of global sliding control mode, it will satisfy the existing
condition and the reaching condition of sliding mode simultaneously.
From Equations (4.43) and (4.49), we obtain
sðc1_x1ț_x2ȚG0 ð4:50Ț
Then, substituting Equations (4.39), (4.46) and (4.48) into Equation (4.50) gives
s½/C0basgnðsȚțfðtȚ/C138G0 ð4:51Ț
So, sgn ðbȚaHfðtȚ=bj j . Hence, the value of ais determined. Then, by substituting aandueq
into Equation (4.48), the control value ucan be obtained.
Now, the torque equation of BLDC motor is recalled as
_O¼/C0Bv
JO/C01
JTLț1
JTe ð4:52Ț
Let
z1¼O
z2¼TL
u¼Te8
<
:ð4:53ȚSpeed Control for BLDC Motor Drives 111

Then, the second-order extended state observer of the system can be represented as
_z1¼z2/C0b01falðz1/C0xðtȚ;a1;dȚțb0u
_z2¼/C0b02falðz1/C0xðtȚ;a2;dȚ(
ð4:54Ț
where b01,b02— coefﬁcients of observer;
b0— estimated value of b;
falðz;a;dȚ¼jzjasgnðzȚ;jzjHd
z=d1/C0a;zj/C20d j :/C26
0Ga2Ga1/C201, and usually a1anda2are set to 1 and 0.5, respectively.
Thus, the load torque TLwill be estimated by the observer designed from Equation (4.54).
The corresponding variable structure parameters such as K1,K2,K3,K4andK5are shown in
Table 4.3. Table 4.4 shows the related parameters of the extended state observer.
4.2.4.2 Simulation and Experimental Results
The simulation curves in Figure 4.30 are the speed responses of the BLDC motor under the
control of the PID controller and the variable structure controller based on an extended stateobserver, respectively, in which, the load torque changes from 0.1 N m to 0.2 N m at 0.05 s.Comparing the proposed variable structure control with PID control, less speed ripple and ashorter recovery time are achieved by the variable control method. Hence, the variable
structure controller has less overshoot, a faster response speed and is not sensitive to the load
variation.
In Figures 4.31 and 4.32, the experimental speed-tracing curves under PID control and VSC
are shown, respectively. In the experiment, the input of the reference signal is the sinusoidalwaveform.
Figures 4.31 and 4.32 show that faster response speed and better trace ability of the system
can be obtained under the control of VSC with the extended state observer.
For the purpose of getting better control performance, the sliding-mode control combined
with other ﬁltering and estimation methods can be used [29]. If the Kalman ﬁlter is added to theTable 4.3 Parameters for variable structure control
K1 K2 K3 K4 K5
0.0001637 0.06710 0.0006 0.06710 18.08
Table 4.4 Parameters of extended state observer
a1 a2 b01 b02 d1 d2
0.75 0.25 7000 2000 0.1 0.01112 Permanent Magnet Brushless DC Motor Drives and Controls

sliding-mode control, the sliding-mode chattering can be reduced to some degree. Figure 4.33(a)
shows the block diagram of the BLDC motor driving system controlled by VSC with a Kalmanﬁlter. The corresponding simulation model in MATLAB is shown in Figure 4.33(b).
Since the system phase trajectory can reﬂect the chattering of sliding-mode variable
structure control, Figure 4.34(a) shows the system phase trajectory without Kalman ﬁlter,while Figure 4.34(b) is the system phase trajectory with a Kalman ﬁlter.
It is obvious from Figure 4.34 that a Kalman ﬁlter has a certain inﬂuence on reducing the
chattering in the sliding-mode variable structure control for BLDC motors. Hence, the Kalmanﬁlter can improve the control precision.
4.2.5 Grey Control
Grey control, a novel method solving indeﬁnite problems with little statistical information, isused to study uncertain systems together with theories like fuzzy mathematics, rough settheory and unascertained mathematics. Within the last 30 years, grey control theory has been
VSC Control 2000
1500
1000
500
00.04 0.12t/s0.08n/(r/min)PID Control
Figure 4.30 Speed response curves under the control of PID and VSC.
5 ms/div200 (r/min)/div
Figure 4.31 Speed-tracing curve under PID control.
5 ms/div200 (r/min)/div
Figure 4.32 Speed-tracing curve under VSC.Speed Control for BLDC Motor Drives 113

Sliding Mode Variable
Structure ControllerObject
−Kalman Filterryv y u
Process Noise w Measurement Noise vye
(a) Block diagram of control system
(b) Simulation model in MATLAB w
v Speed
Reference u
TLy
BLDC Motor x1
W0
TLu
Variable Structure Controller Speed
TLu
Yv Ye
Kalman
Filter
Figure 4.33 Sliding-mode variable structure control for a BLDC motor based on a Kalman ﬁlter.
(a) Without a Kalman ﬁlter
(b) With a Kalman ﬁlter0 500 1000 1500 2000 2500 3000
eec
3500 −5005
0
−5
−10−15x 10
5
0 500 1000 1500 2000 2500 3000
eec
3500 −50050
−5
−10−15x 10
5
Figure 4.34 System phase trajectory (— Phase trajectory, –- Sliding surface).114 Permanent Magnet Brushless DC Motor Drives and Controls

much developed and has been applied in many ﬁelds [30,31]. Grey control mainly consists of
eigengrey system control and grey system method-based control, such as grey-related control
and GM (1, 1) predictive control.
Grey theory doesn’t need distribution rules of membership functions, which makes it
superior in solving problems with inaccurate or incomplete information and small samples. A
motor control system is a typical grey system since the disturbances of internal parameters andmotor load can be considered as uncertainties. It can obtain expected control performances forthe induction motor, BLDC motor and reluctance synchronous motor by building a greycontrol model with grey system theory [32–34]. Therefore, grey control is feasible whenapplied to BLDC motors.
4.2.5.1 Controller Design
Currently, a BLDC motor control system is becoming more complex with novel control
algorithms implemented. In practice, it is difﬁcult for a motor control system to give deﬁnite
values to control inputs due to the complexity of problems, incompleteness of information andinaccuracy of data. Consequently, it is not easy for the speed of the BLDC motor to becontrolled accurately. In this condition, the system could be seen as a grey system where greypredictive control is utilized to improve the performance of the system.
A typical speed-control model of the BLDC motor can be simpliﬁed as
di
dt¼/C0ra
Lai/C0ke
LaOțu
La
dO
dt¼/C0Bv
JO/C0kT
Ji/C0TL
J8
>>><
>>>:ð4:55Ț
And its corresponding state equation is
_x¼AxțBuțFw
1¼/C0ra
La/C0ke
La
KT
J/C0Bv
J2
6643
775i
O"#
ț1
La
02
435u/C00
1
J2
435T
L ð4:56Ț
Considering the uncertainty of state parameters, it can be expressed as
_x¼AxțBuțFw ð4:57Ț
where w¼w1țw2, and w2¼V1x1țV2x2represent the disturbances caused by the uncer-
tainty of state parameters.
Generally, the unknown variable wthat cannot be measured directly can be estimated from
the measured data as
wðx;kȚ¼F/C01ð_xðtȚ/C0AxðtȚ/C0BuðtȚȚ ð4:58Ț
where t¼kT,Tis the sampling period, and k¼1;2;/C1/C1/C1;N.Speed Control for BLDC Motor Drives 115

In order to reduce the inﬂuence of uncertain parts on the system, improve control
performance of the system and increase its disturbance rejection ability, a grey estimator
is adopted to estimate the uncertain model parameter V¼½V1;V2;o1/C138and then wx ;kðȚ
is compensated properly. Such grey estimation doesn’t demand a continuous and real-
time operation, implying that data divergence in traditional real-time identiﬁcation willnot happen.
The grey estimator algorithm when GM (1, 2) control is used to predict and compensate the
speed-control system of BLDC motor is given as:
(1) Establish an initial discrete state sequence xð0Ț
iðkȚ, and compute the summation of the
discrete sequence xð1Ț
iðkȚ, where i¼1;2;/C1/C1/C1;n. The equal dimension new information
can be used for the modeling of xð0Ț
iðkȚ, meaning that at every sampling instant the most
initial information is eliminated and the latest information is added, which guarantees that
the GM (1, 2) model always reﬂects the latest actions of the system without extracalculation. It is expressed as
X
ð0Ț¼xð0Ț1ðȚ;xð0Ț2ðȚ;/C1/C1/C1xð0ȚnðȚ/C16/C17
/C0!NEXTXð0Ț¼xð0Ț2ðȚ;xð0Ț3ðȚ;/C1/C1/C1xð0Țnț1 ðȚ/C16/C17
(2) Calculate the vector D¼xð0Ț
1ð2Ț;xð0Ț
1ð3Ț;/C1/C1/C1; x0ðȚ
1nðȚhiT
and the corresponding
sequence xð1ȚkðȚ ¼Xk
i¼1xð0ȚiðȚproduced by the accumulated generating operation (AGO);
(3) Calculate the matrix B1¼/C0½xð1Ț
1ð1Țțxð1Ț
1ð2Ț/C138=2 xð1Ț
2ð2Ț1
/C0½xð1Ț
1ð2Țțxð1Ț
1ð3Ț/C138=2 xð1Ț
2ð3Ț1
………
/C0½xð1Ț
1n/C01 ðȚ ț xð1Ț
1ðnȚ/C138=2xð1Ț
2ðnȚ12
6666666643
777777775;
(4) Estimate the unknown parameters by using the least squares method as
^V
T¼ðBT
1B1Ț/C01BT1D¼½ ^V1;^V2;^w1/C138T:
Based on the above control law, the compensation control ucis introduced according to the
estimated ^V, where
u¼upțuc ð4:59Ț
uc¼/C0B/C01FXn
i¼1^Vixiț^w1"#
ð4:60Ț
Figure 4.35 shows the diagram of the speed-control system of a BLDC motor, in which dual
closed-loop control is applied. In addition, a PI controller is used in both loops.116 Permanent Magnet Brushless DC Motor Drives and Controls

4.2.5.2 Simulation Results
Figure 4.36 shows the simulation results of the BLDC motor under GM (1, 2) control with no
load and when the load is applied at 0.1 s, respectively.
It is seen from Figure 4.36 that grey GM (1, 2) speed control is better than simple PID
control for its smaller overshoot and faster dynamic response whether the motor is operatingwith no load or varied load.
Meanwhile, the grey control model GM (1, 2) can be used for the predictive compensation
control of external load disturbance and internal parameter perturbation comprehensively.Figure 4.37 shows the speed response of the BLDC motor under the predictive compensationcontrol of GM (1, 2) when both phase resistance and moment of inertia of the motor areincreased by 50% and the load variation is the same as that in Figure 4.36(b).
It is seen from Figure 4.37 that the internal parameter variation has little inﬂuence on speed
output, which is still able to follow the reference value of the system.
4.2.6 Other Intelligent Control Strategies
There are many good intelligent speed-control methods for BLDC motors, of which somecommonly used ones have been analyzed above. Meanwhile, there are some other intelligentspeed-control methods, such as fuzzy-control methods based on ant-colony optimization,PI PI
––Inverter
Grey
Compensation
ControllerBLDC
Motorn* i*
ucup
n i
Figure 4.35 Diagram of BLDC motor speed-control system.
00.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20500100015002000250030003500
(b) Varied load (a) No load 00.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2500
0100015002000250030003500Grey PI
PI
t/s n/(r/min)
t/s n/(r/min) Grey PI
PI
Figure 4.36 Simulation results of BLDC motor under GM (1, 2) control.Speed Control for BLDC Motor Drives 117

adaptive-learning neural-network control based on artiﬁcial immune feedback, and so
on [24,26,35].
The ant-colony algorithm is inspired by the fact that ants search for food by the shortest path,
as shown in Figure 4.38. Compared with genetic algorithms and simulated annealing algo-rithms, the ant-colony algorithm is outstanding since its combination of distributed computing,mechanism of positive feedback and greedy searching ability, which increases its parallelismand extensibility. On the other hand, the deﬁciency of the ant-colony algorithm is that it usuallytakes a long time to search and it is likely to fall into stagnation. It is demonstrated both
theoreticallyandpracticallythatinsomeconditions theoptimalfuzzycontrolrulesgeneratedby
the ant-colony optimization algorithm functions better than the rules generated by otheralgorithms such as genetic algorithms, which will improve the control performance.
The immune system is considered as “the second brain system” next to the nervous system,
which establishes self- and nonself-nonlinear adaptive networks from different kinds ofantibodies and identiﬁes foreign objects adaptively. Also, the immune system can control andeliminate the invading foreign antigens, playing an important role in handling dynamicchanging environment [26,36]. Figure 4.39 shows the simpliﬁed schematic diagram of the
biological immune system, in which the real lines represent positive effect and the imaginary
lines negative effect. Using the immune feedback law as the adaptive learning algorithm of00.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20500100015002000250030003500

t/s n/(r/min)
Figure 4.37 Speed response with parameter perturbation.
Food Nest Food Nest
Figure 4.38 The shortest path of ants’ searching for food.118 Permanent Magnet Brushless DC Motor Drives and Controls

artiﬁcial neural network increases the downward gradient of the neural network learning
algorithm, so as to reduce the deviation to a minimum faster for the neural network andincrease the learning step as much as possible. Therefore, the dynamic and static performanceand the control precision of the BLDC motor are improved. The problem of trackingcharacteristics for speed control that is poor when interfered strongly and inﬂuenced byintense nonlinear and uncertainties for a typical PID controller is solved.
4.3 Inﬂuences of Machine Parameters on Dynamic Response
and Speed Range
Similar to other types of motors, the parameters of a BLDC motor, such as resistance,inductance and moment of inertia, will change under different operating conditions, affectingthe speed performance of the BLDC motor. There exists a complex nonlinear relation among
resistance, inductance and moment of inertia, and the speed and torque of the motor, for which
a digital simulation method can be used here to analyze the effect of relative parameters onspeed control of the motor. The following simulation analysis is performed on a 220-V, 8-poleand 3-phase BLDC motor. The controller and motor parameters are shown in Table 4.5, and thedouble closed-loop PI control is used in the operation.
4.3.1 Armature Resistance
The transition of the stator current is determined mainly by the electrical time constant of thestator. It is obvious from the characteristic of the RL circuit that either increasing theTs Cell Th Cell B Cell
Antigen AntibodyInhibition
Stimulation
Attack
Figure 4.39 Simpliﬁed schematic diagram of biological immune system.
Table 4.5 Parameters of the controller and motor
Controller parametersKp1 TI1 Kp2 TI2
0.015 1 100 0.1
Motor
parametersRated Voltage
(V)Rated speed
(r/min)Rated torque
(N m)Phase resistance
(O)Back-EMF
coefﬁcient
(V/(rad/s))
220 3000 3 2.875 0.7
Phase inductance
(mH)Moment of inertia
(kg m2)Damping coefﬁcient
(N m s)Pole pairs Torque
coefﬁcient
(N m/A)
8.5 0.8 /C210/C031/C210/C034 1.2Speed Control for BLDC Motor Drives 119

inductance or decreasing the resistance would result in the increase of stator electrical
time constant, which consequently extends the process of currents reaching the steady-
state value. However, a decrease of resistance would lead to an increase of the steady-state
value of current, for which it cannot be considered simply that decreasing the resistance willcertainly retard the establishment of the commutating currents of a BLDC motor controlsystem. Meanwhile, the increase of BLDC motor stator resistance usually indicates that thenumber of its winding turns also increase, which decreases the efﬁciency and the averageoutput torque. When the stator resistance is decreased, the results are opposite. This is whysuch factors should be considered comprehensively when a BLDC motor is designed andchosen to establish a speed-control system.
Figure 4.40 shows the speed response of the motor under control of the given parameters
shown in Table 4.5 when the phase resistance is 2 O, 2.875 Oand 4 O, respectively. It can be
seen that the speed response has not been affected largely by the resistance when the speed iscontrolled by a double closed-loop mode. Therefore, the temperature effect of resistance canbe neglected in real closed-loop control. Figure 4.41 shows the dynamic response of theelectromagnetic torque when the phase resistance changes from 2.875 Oto 4Oat 0.5 s. It can
be seen from Figure 4.41 that when the resistance increases, the average torque falls, i.e. theoutput capacity of the motor decreases. Indeed, if open-loop control is adopted, the increase of
resistance would result in a remarkable fall in speed where the effect of resistance variation on
the system should be taken into account adequately.
Figure 4.42 shows the curve of maximum speed that the motor can reach when the stator
resistance is altered. It is seen that decreasing the resistance can expand the speed range tosome degree.
4.3.2 Armature Inductance
It should be noted that the inductance can hinder the change of current. The smaller theinductance, the faster the current changes. Figure 4.43 shows the dynamic speed response of
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 105001000150020002500300035004000

R=2Ω
R=2.875Ω
R=4Ω
t/s n/(r/min)
Figure 4.40 Speed response with resistance variation.120 Permanent Magnet Brushless DC Motor Drives and Controls

BLDC motor control system under double closed-loop PI control when the inductance is
varied from 8.5 mH to 5.5 mH at 0.5 s.
As seen from Figure 4.43, the decrease of inductance will slightly increase the steady-state
value of speed when the motor is under double closed-loop control. Instead, if the motor isunder open-loop control, the speed will increase much more, and such qualitative results can
be similarly obtained from the mathematical equations of a BLDC motor. Therefore, the
decrease of inductance, as for the decrease of resistance, can also expand the speed range.However, a large inductance can lessen the current rush, and the resistance and inductance willalso affect the efﬁciency and torque ripple of the motor. So, it is important to take the abovefactors into consideration comprehensively when it comes to the optimization of a motorcontrol system.0.49 0.495 0.5 0.505 0.51 0.515 0.520.050.10.150.20.250.30.350.4
t/s Te/ N m
Figure 4.41 Torque response with resistance variation.
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 330003200340036003800400042004400460048005000nmax/(r/min)
R/Ω
Figure 4.42 Relationship between motor resistance and maximum speed.Speed Control for BLDC Motor Drives 121

4.3.3 Rotor Inertia
Figure 4.44 shows the dynamic speed response when the moment of inertia of the motor is
changed from 0.8 /C210/C03kg m2to 0.4 /C210/C03kg m2at 0.5 s.
It is seen from Figure 4.44 that decreasing the moment of inertia deteriorates the speed
stability, which will be more conspicuous in open-loop control. Therefore, a large moment ofinertia is usually demanded in motor design to enhance the speed stability of the operation. If
varied speed control is required frequently, what the motor should follow is that its moment of
inertia is small to satisfy the dynamic speed-response requirement, which complies with thegeneral criteria of motor control systems.0.48 0.5 0.52 0.54 0.56 0.58 0.62999.82999.930003000.13000.23000.33000.43000.53000.63000.73000.8n/(r/min)
t/s
Figure 4.43 Speed response when stator inductance decreases.n/(r/min)
0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.62999.52999.62999.72999.82999.930003000.13000.23000.33000.43000.5
t/s
Figure 4.44 Speed response when moment of inertia decreases.122 Permanent Magnet Brushless DC Motor Drives and Controls

4.4 Practical Issues on Implementation
In the previous sections of this chapter, the inﬂuences of speed-control strategy and motor
parameters on the speed-control performance of a BLDC motor are analyzed. In practice, thecircumstances of the speed-control system, the type of load torque and the demands of thesystem vary greatly, thus it is necessary to take the following factors into consideration.
4.4.1 Type of Power Switches and Circuit Forms
The circuit of speed-control system is broadly comprised of the main circuit, driving circuit
and control circuit, of which the devices shoul d be selected according to their different
demands. For the main ci rcuit, the main factor to be considered is the type of power switches,
which includes diode, thyristor, MOSFET, IGBT, IPM, IGCT, etc. Different types of power
switches have different switching characters and power grades. When the topology of themain circuit is decided, the operating mode of each power device will be determined too andthe switching frequency, the voltage and curre nt grade can be calculated, consequently the
type of power switch will be determined. The driving circuit can be constructed withs e p a r a t e dd e v i c e s ,w h i c ha r ee a s yt or e o r g a n i z e ,w h i l ei tc a na l s ob eh i g h l yi n t e g r a t e dw i t ha
driving chip with small size, low loss and high reliability. As for the control circuit, the core
microprocessor should be selected carefully. The MCU can meet the needs of the conven-tional PI double closed-loop system, while DSP will be more appropriate for advanced
control of the BLDC motor, which involves compl ex calculations of multiplication, division
and matrix operations.
4.4.2 Detection of Rotor Position
Note that when space is limited and high re liability is demanded for the BLDC motor,
rotor position is usually detected by usin g a sensorless method, which has strong
antidisturbance ability and high reliability. T o date, there are various types of sensorless
control methods for BLDC motors. The corre sponding techniques will be discussed in
detail in Chapter 6.
4.4.3 Braking Circuit and Protection Circuit
In practice, rapid deceleration or shutdown of the motor is needed, which will produce brakingenergy, so that the motor is operating in the second or the fourth quadrant. If the energy-regeneration unit is designed in the circuit, the energy generated during the deceleration of themotor can be fed back to the DC bus, which will quicken the braking of the motor. If therectiﬁer circuit is uncontrollable, the braking energy is not able to be fed back, and unless anextra braking unit is introduced, the DC voltage will keep increasing until the main circuitdevices are damaged. A simple braking unit usually contains a braking resistance, on which the
braking energy is consumed and transformed into heat energy. Note that when this simple type
of braking unit is used, the system efﬁciency will be reduced. Thus, various regenerativebraking approaches should be considered in practice.Speed Control for BLDC Motor Drives 123

Meanwhile, during the practical operation of the BLDC motor control circuit, abnormal
events may occur to produce overvoltage and overcurrent phenomena, so corresponding
protection circuits are required to ensure the safety of power switches.
4.4.4 Antidisturbance Measures of Software and Hardware
In practical industrial control system, electromagnetic disturbance problems are more and
more severe with the wide application of various nonlinear power electronic devices, whichmake antidisturbance techniques much more important. Electromagnetic disturbances maydirectly damage the hardware of speed-control system, or cause the program in micropro-cessor out of control. Therefore antidisturbance measures of hardware and software play asigniﬁcant role in the design of a speed-control system.
The common hardware antidisturbance methods include increasing the internal impedance
of the power supply, adding smoothing reactors and ﬁlters, adopting a multipulse rectiﬁer
circuit, and proper topology design of the main circuit, and so on.
Besides the above hardware methods, software antidisturbance approaches, such as digital
ﬁltering, instruction redundancy, delayed conﬁrmation, and software reset, can be applied for
the control of BLDC motor too.
Questions
1. Compared with the continuous control system, what are the advantages of the digital
control system?
2. Why is antiwindup control usually required in the design of BLDC motor controller?3. What are the main characteristics of an intelligent controller?4. List some types of fuzzy controller, and give the general procedures of fuzzy controller
design.
5. Show how the fuzzy controller of a BLDC motor is optimized through genetic algorithm.6. What are the advantages and disadvantages of the sliding-mode controller?7. What is the principle of grey control? Try to explain it in your own words.8. What are the advantages of grey control and where does the main idea of the ant-colony
algorithm come from?
9. Summarize the inﬂuences of motor parameters on dynamic response and speed range.
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5
Analysis and Reduction
of Torque Ripple
Torque ripples reﬂected as periodic oscillations in torque will degrade the servo performance
of permanent magnet motors. Compared with PMSM, the torque ripples in BLDC motor aremuch more serious. The pulsation will not only cause acoustics and vibration, but severelylimit the performance of the system, especially in high-precision and high-stabilizationapplications. Minimization of the torque ripples in a BLDC motor drive system has been
an important and difﬁcult problem. Generally speaking, the pulsation in a BLDC motor can be
divided into two categories: cogging torque and commutation torque. The cogging torque isproduced by the different reluctance in the air gap caused by the existing of a stator slot. Theback-EMF pulsation caused by cogging torque is a periodic function of rotor position, whichwill lead to torque ripples. It is a great challenge to reduce cogging torque during machinedesign. However, researchers have developed various methods based on motor design that canminimize cogging torque by changing the structure of the motor. The existing methods mainlycontain skewing poles or slots, embedding a magnetic slots wedge, placing auxiliary slots and
teeth, designing fractional slots, and so on [1–5]. The commutation torque ripple in a BLDC
motor, due to current variation during commutation interval, also limits its application in high-performance servo system. The commutation torque ripple and its minimization methods willbe investigated in this chapter. First, the cogging torque ripple and its minimization methodsare analyzed. Then, the principle of the commutation torque ripple is presented. After that, theinﬂuences of back-EMF, commutation modes and PWM control on the commutation torquewill be analyzed. Further, torque-ripple-reduction methods based on time-division commu-tation, active disturbance rejection control technology, BP neural networks, and fuzzy niching
genetic algorithms will be discussed.
5.1 Cogging Torque-Ripple-Minimization Techniques Analysis
Cogging torque in BLDC motor can be deﬁned as the periodic electrical torque when the
armature winding is open. The presence of the stator slot will cause reluctance variation in the
Permanent Magnet Brushless DC Motor Drives and Controls , First Edition. Chang-liang Xia.
/C2112012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd.

air gap, thus the air-gap magnetic-ﬁeld distribution in space produces pulsations of back-EMF,
which will lead to torque ripple. Therefore, the cogging torque is also called the reluctance
torque [3]. In addition, this torque is caused by the interaction between the slot and the tooth of
the armature core and the magnetic ﬁeld of permanent magnet along with the direction of rotorcircumference, which make the rotor of the BLDC motor align with the stator in a particulardirection, so cogging torque can be named location torque too. Figure 5.1 shows the schematicdiagram of cogging torque.
The energy stored in the air gap varies with the relative position of rotor and stator between
its maximum and minimum. The relationship between the frequency of the electromagneticﬁeld energy and the slots of the armature core is shown as
f¼nZ=60 ð5:1Ț
where n— motor speed (r/min);
Z— slots of the armature core.
Thus, the cogging torque can be expressed as
T
c¼/C0qWm
qyð5:2Ț
where Wm— energy of air-gap electromagnetic ﬁeld;
y— relative angular displacement between rotor and stator.
Further, it can be illustrated as in Figure 5.2.The cogging torque is a direct expression of magnetostatic energy when the motor rotates.
The magnetostatic energy in a motor is approximately equal to that stored in the air gap,because the magnetostatic energy in the permanent magnet and the core, which can be ignored,is very small with respect to the variance of the magnetostatic energy in air gap. Magnetic ﬁeld
energy varies with the rotor angle as slots are present in the stator core. Meanwhile, it will
produce torque in the decreasing direction of magnetic-energy product. Cogging torque can beexpressed as a spectrum function whose fundamental frequency is equal to the least common
Stator
PM
Bg
0 xBδ
Figure 5.1 Schematic diagram of cogging torque.128 Permanent Magnet Brushless DC Motor Drives and Controls

multiple (LCM) of the poles number and the slot number. The other higher-order harmonics
are in inverse proportion to the square of frequency. So the higher the fundamental frequency,the lower its amplitude.
During variable-speed drive, vibration and noise produced by the cogging torque will be
ampliﬁed when the torque ripple frequency is equal to the mechanical resonance frequency of
the rotor or stator. Moreover, the existence of cogging torque will affect the servoperformance
of low-speed control and high-accuracy position control for a BLDC motor system.
Cogging-torque minimization is a challenge during the design procedure of a BLDC motor.
Optimization of the structure of a BLDC motor can reduce the cogging torque. To date,numerous methods, such as skewing slots and magnets, embedding magnetic slot wedge,auxiliary slots or teeth and a fractional number of slots per pole, have been proposed forreducing the cogging torque [2].
5.1.1 Skewing Slots and Magnets
Stator laminations having one slot pitch shift along the axial direction is one of the skewing
methods, which can eliminate cogging torques obviously and improve the stator wingding
distribution of BLDC motor. Skewing the magnet on the rotor by one tooth pitch is anotheralternative. The proper skew angle is signiﬁcant for reducing cogging torque. In theory,skewing one slot pitch will eliminate cogging torque altogether. But in fact, this cannot beachieved because of the edge effect and rotor asymmetry. Note that both magnet and statorskewing will make the corresponding stator design of BLDC motor more complex. Conse-quently, the mutual inductance and stray loss will be increased, while the shape of theWm
Tcθ
θo
o
Figure 5.2 The energy stored in the air gap and the motor cogging torque.Analysis and Reduction of Torque Ripple 129

back-EMF of the winding is more sinusoidal than rectangular. From this viewpoint, the torque
ripple will be increased with the average output torque reduced.
5.1.2 Embedding Magnetic Slot Wedges
Filling the open part of slots with magnetic wedges can also minimize the cogging torque
because it has a more uniform air-gap permeab ility, which makes the coenergy variation of
magnets decrease. The structure of a BLDC motor with magnetic wedges ﬁlled is illustrated
in Figure 5.3.
5.1.3 Auxiliary Slots and Teeth
This method can reduce the fundamental component of cogging torque by placing someauxiliary grooves on the PM surface or armature core [3] (see Figure 5.4), with a more uniformdistribution of the magnetic ﬂux density.
5.1.4 Fractional Number of Slots Per Pole
Another cogging-torque-reduction method employs the fractional stator slots in a BLDCmotor. It will increase the least common multiple of the poles number and the slot number, sothat the fundamental frequency of the cogging torque is increased [4]. Hence, the coggingtorque is reduced. In general, the higher the frequency of the cogging torque, the lower theamplitude of the cogging torque. A BLDC motor with fractional number of slots per pole is
shown in Figure 5.5.
One or more of the techniques discussed above should be used during the design procedure
of electrical machines. In this manner, the cogging torque of a BLDC motor can be reduced
substantially with the performance enhanced.N
S
Figure 5.3 Magnetic slot wedges.130 Permanent Magnet Brushless DC Motor Drives and Controls

5.2 Torque-Ripple Reduction with Time-Sharing Commutation
Strategy
5.2.1 Time-Sharing Commutation Strategy
Three-phase BLDC motor with full-bridge driving mode as an example is taken in this section.
In normal operation condition, there are two states (steady state and transient state) of a BLDCmotor under two-phase conduction mode. Generally speaking, the longer steady state of thetwo-phase conduction determines the amplitude of the electromagnetic torque. However,the transient state of the commutation will affect the performance of the motor too. In thecondition that load torque and rotor speed are invariant, meanwhile, two-phase conduction isN
SN
SA
B CA
C B
(b) With auxiliar y slots (a) Without auxiliar y slots
Figure 5.4 Schematic diagram of a BLDC motor with auxiliary slots.
N
SS
N
Figure 5.5 BLDC motor with fractional number of slots per pole.Analysis and Reduction of Torque Ripple 131

adopted in the three phase BLDC motor with full-bridge driving, we can obtain the waveform
of the electromagnetic torque as shown in Figure 5.6.
As illustrated in Figure 5.6 the electromagnetic torque of the motor is Te0when a two-phase
conduction mode is adopted. Electromagnetic torque, which is a periodic function, can beexpressed as
T
eðyȚ¼Teyțp
3/C16/C17
ð5:3Ț
Lett1¼p/3o, in which ois the electrical angle of the motor. Suppose that two-phase
conduction is adopted in the motor between 0 and t1, then analysis of the commutation can be
obtained in the interval [0, t1], since the electromagnetic torque is a periodic function.
The mean value of the torque ripple in the interval [0, t1] can be deﬁned as a criterion for the
commutation torque ripple, which can be expressed as
Tes¼ðt1
0jTe/C0Te0jdt
t1ð5:4Ț
where
Te0¼2EI
Oð5:5Ț
where E— phase back-EMF under two-phase conduction in the interval [0,t 1];
I— current amplitude under two-phase conduction in the interval [0, t1];
O— mechanical angular velocity in the interval [0, t1].
Suppose that the rotor speed of the motor is invariant during the interval [0, t1], then
E¼KeO ð5:6Ț
where Ke— coefﬁcient of back-EMF.
It can be seen from the equation of the electromagnetic torque of BLDC motor that phase
current and phase back-EMF play an important role on the electromagnetic torque. Mean-while, during the commutation intervals, back-EMF inﬂuenced by ﬂux leakage affects theTe
0 π/3 2π/3 πω tTe0
Figure 5.6 Waveform of electromagnetic torque in three phase BLDC motor with full-bridge driving.132 Permanent Magnet Brushless DC Motor Drives and Controls

phase current. Therefore, it is difﬁcult to analyze the torque ripple generated by phase current
and back-EMF simultaneously [1].
5.2.1.1 Effect of the Back-EMF
Commutation of a BLDC motor can be achieved by turning on or off the corresponding power
switches. If the turn-on and the turn-off power switches all belong to the upper half-bridge, it is
deﬁned as upper half-bridge commutation. Similarly, lower half-bridge commutation denotesthe turn-on and the turn-off power switches all belong to the lower half-bridge. Neglecting thevoltage of the power switches and freewheel diodes when they are conducted, the equivalentcircuit in the commutation can be obtained as Figure 5.7.
As illustrated in Figure 5.7, the equivalent circuits of the upper half-bridge and lower half-
bridge have no differences except that the current is reverse. In order to analyze the principle ofcommutation torque ripple, conduction switches from phase AC to BC in the upper half-bridge
is taken as an example.
How the back-EMF affects the commutation torque ripple separately is developed under the
assumptions stated below.
(1) Commutation transient process is neglected.
(2) Two phase windings are conducted at any time.(3) Ideal square waveform of the current is supposed.
The ideal waveform of back-EMF is 120
/C14trapezoidal, while the width of the ﬂat is less than
120/C14practically. The waveform of back-EMF is shown in Figure 5.8, where the dotted line is
the ideal 120/C14waveform of the back-EMF, and the solid line curve is the actual waveform of
R R
2 1Kcut Kon
iA iB3R
R2 1
KcutKoniAiB
3eB eA+
– –+
–
+eC–
+eB–
+eA–+
eC
RL LL L L
RLUdUdUd Ud
(a) Upper half-brid ge commutation (b) Lower half-brid ge commutation
Figure 5.7 Equivalent circuit in commutation of a BLDC motor.Analysis and Reduction of Torque Ripple 133

eA eBe
t t00t1
Figure 5.8 Schematic diagram of back-EMF waveform.
the back-EMF. In addition, suppose the back-EMF varies from the positive ﬂat to the negative
ﬂat monotonously.
Hence, if the current commutation starts at t0, then the current of the turn-off phase will
change into 0 from Iand the current of the turn-on phase will change from 0 to Iat the same
time. Also, currents between [0, t1] satisfy
iA¼Ið1/C0uðt0ȚȚ
iB¼Iuðt0Ț
iC¼/C0I8
><
>:ð5:7Ț
where u(t0) — the step function.
In the interval [0, t1], the electromagnetic torque will be
Te¼eAiAțeBiBțeCiC
O/C20Te0 ð5:8Ț
Thus, the mean value of the electromagnetic torque between [0, t1] is given by
/C22Te¼ðt1
0Tedt
t1ð5:9Ț
Substituting Equation (5.8) into Equation (5.9), yields
/C22Te¼ðt1
0eAiAțeBiBțeCiC
Odt
t1ð5:10Ț134 Permanent Magnet Brushless DC Motor Drives and Controls

Further, substituting Equation (5.7) into Equation (5.10), the average electromagnetic can
be expressed as
/C22Te¼I
Ot1ðt0
0eAdtțðt1
t0eBdt/C0ðt1
0eCdt/C18/C19
ð5:11Ț
Therefore, the average electromagnetic torque ripple between [0, t1]i s
Tes¼Te0/C0Te ð5:12Ț
If commutation of the motor happens at t0, then solving the best commutation moment can
be transformed to an optimization issue as
min
t02½0;t1/C138Tes¼min
t02½0;t1/C138ðTe0/C0TeȚð 5:13Ț
The derivative of the average electromagnetic torque ripple at t0is
d/C22Tes
dt0¼/C0I
Ot1ðeA/C0eBȚð 5:14Ț
Thus, the second derivative of the average electromagnetic torque ripple at t0is
d2/C22Tes
dt2
0¼/C0I
Ot1deA
dt0/C0deB
dt0/C18/C19
ð5:15Ț
Notice that both eAandeBare functions of t0. Therefore, if appropriate t0is chosen so that
eA–eB¼0 holds, the derivative of average electromagnetic torque ripple is 0 with the second
derivative greater than 0. Thus, the torque ripple has its minimum value. Further, eAis
monotone decreasing, while eBis monotone increasing around the commutation moment, and
the derivative of average electromagnetic torque ripple is greater than 0, consequently, there is
only one minimum value of the average torque ripple. If so, the minimum value of torqueripple will be achieved at t
0foreA–eB¼0. This means that if and only if the commutation
happens at t0corresponding to eA–eB¼0, the least value of average torque ripple will be
obtained. Similarly, deﬁne eA–eB¼eABas the line back-EMF of phase A and B, commutation
torque ripple will achieve the least value if the commutation happens at the zero-crossing pointof the line back-EMF. It must be emphasized that the best moment of commutation happens atthe time lag 30
/C14behind the zero-crossing point of phase back-EMF, which is a special case of
the phenomenon that the phase back-EMF is a 120/C14trapezoidal waveform and the rotor speed
is invariant.
The waveforms of back-EMF and electromagnetic torque at the best moment of commu-
tation t0are shown in Figure 5.9.
The higher the rotor speed, the greater the st eady state value of the back-EMF. Therefore,
the torque will decrease faster as the steady state value of back-EMF becomes greater. But theperiod of torque ripple will be smaller and th e average torque ripple does not varied with
rotor speed.Analysis and Reduction of Torque Ripple 135

5.2.1.2 Effect of the Commutation Transient Process
Neglect the variance of the back-EMF waveform and the PWM effect, and suppose the phase
back-EMF is equal to Eor/C0Eduring the transient process of commutation, then the steady-
state value of the phase current Iis
I¼Ud/C02E
2Rð5:16Ț
where Ud— DC voltage of the bridge inverter.
The current cannot be changed suddenly especially when the voltage source converter is
adopted because of the inductance of the windings. During the commutation switching fromphase A and C conduction to phase B and C conduction, the electromagnetic torque in [0, t
1]
can be obtained as
Te¼eAiAțeBiBțeCiC
O¼/C02EiC
Oð5:17Ț
Therefore, torque ripple is mainly determined by the current of the nonenergized phase if the
variance of back-EMF is neglected. Taking current of phase C as an example, the variationtendency of electromagnetic torque during the transient process of commutation is analyzed asfollows.
Usually, turning off and turning on certain phases in a BLDC motor happens synchronously.
Suppose the commutation happens at t¼0, then the voltage between phase A and phase C will
change from U
dto 0 while the voltage will be Udbetween phase B and phase C. If iAis assumed
to be 0 at t¼toff, the current of phase B will change from iB(toff-), which is the value of the
current before toff, into the steady-state value I. Since the motor is running in steady state
before commutation, i.e. iA(0–)¼I,iB(0–)¼0,iC(0–)¼/C0I, thus with the Laplace transform
the current equations in [0, toff] will be obtained as
2ðRțsLȚiAðsȚțð RțsLȚiBðsȚ¼2LI/C02E=s
ðRțsLȚiAðsȚț2ðRțsLȚiBðsȚ¼LI/C02E=sțUd=s
iCðsȚ¼/C0 ð iAðsȚțiBðsȚȚ8
>><
>>:ð5:18ȚeA eBTe,e
t t0 0 t1Te0
E
Figure 5.9 Waveforms of back-EMF and electromagnetic torque.136 Permanent Magnet Brushless DC Motor Drives and Controls

IftHtoff, the current equations will be
iAðsȚ¼0
2ðRțsLȚiBðsȚ¼2LiBðtoff/C0Ț/C02E=sțUd=s
iCðsȚ¼/C0 iBðsȚ8
>><
>>:ð5:19Ț
So, the time domain solutions of Equations (5.18) and (5.19) are given by
iA¼Ie/C0R
Lt/C0Udț2E
3R/C18
1/C0e/C0R
Lt/C19
;0Gt/C20toff
0; tHtoff8
><
>:ð5:20Ț
iB¼2Ud/C02E
3Rð1/C0e/C0R
LtȚ; 0Gt/C20toff
iBðtoff/C0Țe/C0R
Lðt/C0toffȚțUd/C02E
2Rð1/C0e/C0R
Lðt/C0toffȚȚ; tHtoff8
>><
>>:ð5:21Ț
iC¼/C0Ie/C0R
Lt/C0Ud/C04E
3Rð1/C0e/C0R
LtȚ; 0Gt/C20toff
/C0iBðtoff/C0Țe/C0R
Lðt/C0toffȚ/C0Ud/C02E
2Rð1/C0e/C0R
Lðt/C0toffȚȚ; tHtoff8
>><
>>:ð5:22Ț
Substituting Equation (5.16) into Equation (5.22), iCcan be simpliﬁed as
iC¼/C0IțUdț2E
6Rð1/C0e/C0R
LtȚ; 0Gt/C20toff
/C0IțI/C0iBðtoff/C0Ț ½/C138 e/C0R
Lðt/C0toffȚ;tHtoff8
><
>:ð5:23Ț
As shown in Equation (5.23), iCis monotone decreasing during [0, toff]. When tHtoff, the
amplitude of iCincreases monotonically to the steady-state value Ifrom /C0iC(toff–), which is the
value at the moment before toff. Thus, the electromagnetic torque during the transient process
of commutation is always lower than that in steady state, and the difference between them may
achieve its maximum at toff. The corresponding current and electromagnetic torque waveforms
are shown in Figure 5.10.Analysis and Reduction of Torque Ripple 137

So, the average electromagnetic torque ripple in [0, t1]i s
Tes¼2Eðtoff
0Udț2E
6Rð1/C0e/C0R
LtȚdtțðt1
toffI/C0iBðtoff/C0Ț ½/C138 e/C0R
Lðt/C0toffȚdt/C26/C27
Ot1
¼2EUdț2E
6RtoffțL
Rðe/C0R
Ltoff/C01Ț/C20/C21
țL
RI/C0iBðtoff/C0Ț ½/C138 ð 1/C0e/C0R
Lðt1/C0toffȚȚ/C26/C27
Ot1ð5:24Ț
As Equation (5.24) states, elec tromagnetic torque ripple that is caused by the variance of
the current could be affected by the rotor speed and the load torque. In the case that the load
torque of the motor is invariant, torque ripple will be much more serious when the amplitudeof back-EMF is large since the rotor speed is at a high level. If the rotor speed is invariantand the load torque of the motor is larger, the steady-state current Iwill become bigger. In
other words, the electromagnetic torque ripple will become larger as the rotor speed or theload torque increases.
5.2.1.3 Effect of Both Back-EMF and the Commutation Transient Process
The variance of back-EMF in [0, t
1] can bring about a change of the commutation current.
Suppose that the waveform of the back-EMF is an ideal 120/C14trapezoidal wave and the
commutation happens when eA–eB¼0 holds. Then, the back-EMF of phase A after conducted
can be obtained as
eA¼E/C06oE
pt;0GtGp
3oð5:25Ț
where o— electrical angular velocity of the motor.toff 0 t1iAiB
iCTe, i
tTe
Figure 5.10 Waveforms of current and torque ripple during commutation.138 Permanent Magnet Brushless DC Motor Drives and Controls

The Laplace transform of Equation (5.25) is
eAðsȚ¼E
s/C06oE
ps2ð5:26Ț
Hence, the current equations in [0, toff] are
2ðRțLsȚiAðsȚțð RțLsȚiBðsȚ¼2LI/C02E
sț6oE
ps2
ðRțLsȚiAðsȚț2ðRțLsȚiBðsȚ¼LIțUd/C02E
s
iCðsȚ¼/C0 ð iAðsȚțiBðsȚȚ8
>>>><
>>>>:ð5:27Ț
When tHt
off, the current equations will be
iAðsȚ¼0
2ðRțLsȚiBðsȚ¼2LiBðtoff/C0ȚțUd/C02E
s
iCðsȚ¼/C0 iBðsȚ8
>>>><
>>>>:ð5:28Ț
So, the time solutions of the phase currents are
i
A¼Ie/C0R
Lt/C0Udț2E
3Rð1/C0e/C0R
LtȚț4oE
pRt/C04oLE
pR2ð1/C0e/C0R
LtȚ;0Gt/C20toff
0; tHtoff8
<
:ð5:29Ț
iB¼2Ud/C02E
3Rð1/C0e/C0R
LtȚ/C02oE
pRtț2oLE
pR2ð1/C0e/C0R
LtȚ;0Gt/C20toff
iBðtoff/C0Țe/C0R
Lðt/C0toffȚțUd/C02E
2Rð1/C0e/C0R
Lðt/C0toffȚȚ; tHtoff8
>><
>>:ð5:30Ț
iC¼/C0Ie/C0R
Lt/C0Ud/C04E
3Rð1/C0e/C0R
LtȚ/C02oE
pRtț2oLE
pR2ð1/C0e/C0R
LtȚ;0Gt/C20toff
/C0iBðtoff/C0Țe/C0R
Lðt/C0toffȚ/C0Ud/C02E
2Rð1/C0e/C0R
Lðt/C0toffȚȚ; tHtoff8
>><
>>:ð5:31Ț
Compared with the effect of the commutation transient process on torque the current
amplitudes of phase A and phase C become bigger, while phase B will be smaller as stated inAnalysis and Reduction of Torque Ripple 139

Equations (5.29)–(5.31). In practice, this phenomenon will be more apparent as the waveform
of the back-EMF is not an ideal 120/C14ﬂat wave.
Generally speaking, the variance of back-EMF will give rise to electromagnetic torque
ripple. Commutation torque ripple can be suppressed to its minimum value when the line back-EMF is zero. If the effects of PWM are neglected, the minimum electromagnetic torque can beachieved at t
offbecause the current variance in the commutation transient process will cause
the electromagnetic torque to decrease. In addition, the amplitude of torque ripple will increaseas the rotor speed and load torque become higher. Torque ripple can be reduced if the propercommutation moment is chosen and this effect is related to the characteristic of the ripple. Ifthe torque ripple is increasing, the proper commutation moment will suppress the torque ripple
effectively. However, if the torque ripple is decreasing, this method can only reduce the torque
ripple partly. Note that the effects of rotor speed and load torque on torque ripple cannot bechanged in the reverse direction although proper commutation moment is chosen.
5.2.2 Analysis of Time-Sharing Commutation Strategy
Transient process of BLDC motor commutation is complex and of short duration. In addition,the commutation torque ripples become more obvious as the rotor speed and load torquebecome higher. In many cases, torque ripples can only be reduced partly in spite of the fact thata proper commutation moment is chosen to ﬁre the conduction phase and cut off theunenergized phase at the same time.
The moment of phase conduction or turn off can be controlled separately by the time-
sharing commutation strategy. The conduction of phases A and C switching to phase B and Cwill be discussed as an example as follows. The line voltage between phases B and C is equal to
U
dwhen phase B is conducted at ton, while the line voltage between phases A and C will be 0 as
phase A turned off at tcut(ton$tcut). Meanwhile, the current of phase A will become 0 at toff.
Thus, three switch modes can be chosen, which could be expressed as conduction after cut off
entirely, conduction after cut off and cut off after conduction. Different modes can producevaried effects on the commutation torque ripple, which will be discussed in the followingsections. Similarly, to analyze how the time-sharing commutation strategy affects commu-tation torque ripple separately, we suppose that phase back-EMFs are equal to Eor/C0Eduring
the commutation process.
5.2.2.1 Commutation Mode of Conduction After Cut Off Entirely
When this mode is adopted, we must cut off phase A ﬁrst, then conduct phase B until the
current of phase A is 0. In this condition, there exists t
cutGtoffGton.
Suppose tcut¼0, then the current of phase C can be obtained during [0, t1]a s
iC¼/C0Ie/C0R
LtțE
Rð1/C0e/C0R
LtȚ; 0GtGtoff
0; toff/C20tGton
2E/C0Ud
2Rð1/C0e/C0R
Lðt/C0tonȚȚ; tXton8
>>>>><
>>>>>:ð5:32Ț140 Permanent Magnet Brushless DC Motor Drives and Controls

Substituting Equation (5.16) into Equation (5.32), then iCcan be simpliﬁed as
iC¼/C0IțUd
2Rð1/C0e/C0R
LtȚ; 0GtGtoff
0; toff/C20tGton
/C0IțIe/C0R
Lðt/C0tonȚ; tXton8
>>>><
>>>>:ð5:33Ț
As Equation (5.31) states, the amplitude of i
Cwill drop dramatically during [0, toff] and will
be 0 during [ toff,ton]. But it will increase to Iwhen tHton. Thus, current variation will cause an
electromagnetic torque decrease during the transient process of commutation and the torque
will achieve its minimum value at toff. The corresponding current and torque waveforms are
shown in Figure 5.11.
So, during [0, t1], the average torque ripple can be expressed as
Tes¼2Eðt1
0ðIțiCȚdt
Ot1¼2Eðtoff
0Ud
2Rð1/C0e/C0R
LtȚdtțðt1
tonIe/C0R
Lðt/C0tonȚdt/C26/C27
Ot1
¼2EUd
2R/C20
toffțL
Rðe/C0R
Ltoff/C01Ț/C21
țL
RIð1/C0e/C0R
Lðt1/C0tonȚȚ/C26/C27
Ot1ð5:34Ț
Compare Equation (5.34) to Equation (5.24), it is worth noting that torque ripples, which are
caused by current variation, are more serious in the commutation mode of conduction after cutoff entirely than that in switching at the same time. Therefore, this method is not good toreduce torque ripple since it will decrease the output electromagnetic torque.−iCTe
t1 tTe, i
toff ton tcut 0
Figure 5.11 Current and torque ripple under commutation mode of conduction after cut off entirely.Analysis and Reduction of Torque Ripple 141

5.2.2.2 Commutation Method of Conduction After Cut Off
In this method, phase A is cut off ﬁrst, then conduct phase B before the current of phase A
becomes zero. In this condition, there exists tcutGtonGtoff.
Iftcut¼0, the current of phase C during interval [0, t1] can be expressed as
iC¼/C0Ie/C0R
LtțE
Rð1/C0e/C0R
LtȚ; 0GtGton
iCðton/C0Țe/C0R
Lðt/C0tonȚ/C0Ud/C04E
3Rð1/C0e/C0R
Lðt/C0tonȚȚ; ton/C20tGtoff
iCðtoff/C0Țe/C0R
Lðt/C0toffȚț2E/C0Ud
2Rð1/C0e/C0R
Lðt/C0toffȚȚ; tXtoff8
>>>>>><
>>>>>>:ð5:35Ț
By substituting Equation (5.14) into Equation (5.35), i
Ccan be simpliﬁed as
iC¼/C0IțUd
2Rð1/C0e/C0R
LtȚ; 0GtGton
/C0IțUdț2E
6RțiCðton/C0ȚțUd/C04E
3R/C20/C21
e/C0R
Lðt/C0tonȚ; ton/C20tGtoff
/C0IțiCðtoff/C0ȚțI ½/C138 e/C0R
Lðt/C0toffȚ; tXtoff8
>>>>>><
>>>>>>:ð5:36Ț
It can be seen from Equation (5.36) that the amplitude of i
Cdecreases dramatically during
[0,ton] and iCchanges monotonically during [ ton,toff] with its amplitude less than the steady-
state value I. However, when tHtoff,iCincreases gradually with its initial amplitude of iCless
than Iand the steady-state value equal to I. The corresponding current and torque waveforms
are shown in Figure 5.12.
−iCTe
t1 tTe, i
toff ton tcut 0
Figure 5.12 Waveforms of current and torque ripple under commutation method of conduction after
cut off.142 Permanent Magnet Brushless DC Motor Drives and Controls

Compared with the traditional simultaneous switching method, electromagnetic torque
ripple caused by current variation is much more serious by using this method. Thus, it has no
obvious advantage.
5.2.2.3 Commutation Method of Cut Off After Conduction
In this method, conduct phase B ﬁrst and then cut off phase A with tonGtcutGtoff.
Suppose ton¼0, then the current of phase C during interval [0, t1] can be obtained as
iC¼/C0Ie/C0R
Lt/C02ðUd/C02EȚ
3Rð1/C0e/C0R
LtȚ; 0GtGtcut
/C0iCðtcut/C0Țe/C0R
Lðt/C0tcutȚ/C0Ud/C04E
3Rð1/C0e/C0R
Lðt/C0tcutȚȚ; tcut/C20tGtoff
/C0iCðtoff/C0Țe/C0R
Lðt/C0toffȚ/C0Ið1/C0e/C0R
Lðt/C0toffȚȚ; tXtoff8
>>>>>><
>>>>>>:ð5:37Ț
Similarly, by substituting Equation (5.16) into Equation (5.37), i
Ccan be simpliﬁed as
iC¼/C0I/C0Ud/C02E
6Rð1/C0e/C0R
LtȚ; 0GtGtcut
/C0IțUdț2E
6RțUd/C04E
3R/C0iCðtcut/C0Ț/C20/C21
e/C0R
Lðt/C0tcutȚ;tcut/C20tGtoff
/C0IțI/C0iCðtoff/C0Ț ½/C138 e/C0R
Lðt/C0toffȚ; tXtoff8
>>>>>><
>>>>>>:ð5:38Ț
As stated in Equation (5.38), the amplitude of i
Cincreases gradually from Iduring
[0,tcut] and it will increase faster as the back-EMF decreases more marked. During
interval [ tcut,toff],iCdecreases monotonous ly with its initial value greater than I.T h e
smaller Eand Iare, the faster the amplitude of iCdecreases. When tHtoff,iCvaries
monotonously with its steady-state value equal to I. Note that the variation tendency of
iCdepends on the value of iCat the last moment. Current variation during the transient
process of commutation may cause electrom agnetic torque ripple, which will achieve its
maximum at tcut.
The waveforms of current and electromagnetic torque are shown in Figure 5.13. Torque
ripple during the transient process of commutation will increase in this mode.
As discussed above, only the commutation mode of cut off after conduction will make the
commutation torque increase among the three modes. Variation of the back-EMF during
transient process of commutation may decrease the electromagnetic torque. Therefore, theinﬂuence of back-EMF can be suppressed by the commutation mode of cut off afterconduction so that the commutation torque ripple is reduced.Analysis and Reduction of Torque Ripple 143

5.2.3 Optimal Time-Sharing Commutation
5.2.3.1 Optimum Time-Sharing Commutation Moment
Since the commutation method of cut off after conduction can increase the current of the
nonenergized phase, proper selection of tonandtcutcan offset the inﬂuence of the back-EMF
waveform on electromagnetic torque, so as to reduce the commutation torque ripple to acertain extent.
At the best moment for time-sharing commutation, the commutation torque ripple min-
imum average torque ripple can be obtained by the optimization problem as
min
ton;tcut2½0;t1/C138Tes¼ min
ton;tcut2½0;t1/C138ðt1
0jTe/C0Te0jdt
t1ð5:39Ț
The best moment of time-sharing commutation is related with the rotor speed, motor load,
etc. If the optimal time-sharing commutation moment can be identiﬁed according to theoperation states of the motor, torque ripple can be reduced effectively. The practical waveform
of back-EMF may cause a decrease of commutation electromagnetic torque. If commutation
happens at the moment that the line back-EMF is zero, the electromagnetic torque rippleachieves its minimum with the maximum average electromagnetic torque achieved.
Time-sharing commutation can make the commutation torque ﬁrst increase and then
decrease. And the electromagnetic torque will achieve its maximum at t
cut. Therefore, by
taking tcutas the zero-crossing point of line back-EMF, the effect of the transient process of
current commutation and the back-EMF on electromagnetic torque can be compensated.Deﬁne “ t
cut–ton” as the advanced conduction time, and then the electrical angle for the motor
running during this period is exactly the advanced electrical angle. After tcutis deﬁned, the
only need to know is the best advanced electric angle, so that the time-sharing commutationstrategy is achieved.
Note that the best advanced electrical angle is related to many factors. When the rotor speed
is high, the torque ripple that is caused by back-EMF is more serious, so that the advancedelectrical angle should be appropriately increased. In addition, while the motor load is heavy,the amplitude of the steady current is big with a longer transient process of currentcommutation, so the advanced electrical angle should also be appropriately increased.−iCTe
t1 tTe, i
toff ton tcut 0
Figure 5.13 Waveforms of current and torque ripple under commutation method of cut off after
conduction.144 Permanent Magnet Brushless DC Motor Drives and Controls

5.2.3.2 Fuzzy-Controller Design
In different motor operation modes, the rela tionship between advanced conduction angle
and the steady variables (i.e. the amplitude of back-EMF and current) cannot be described
in the traditional mathematical method. A fuzz y controller is free of accurate mathematical
model. Its output is usually determined according to the input signal and control rules withfuzzy reasoning [6–12]. Therefore, a two-di mensional fuzzy controller can be adopted
to determine the advanced conduction time, where the controller inputs are the per-unitvalue of the amplitude of the current and back-EMF, and the output is the advancedconduction angle.
First, per-unit values of EandIare mapped to [ /C01, 1], 5 fuzzy subsets can be deﬁned as PB,
PS, ZE, NS and NB, respectively. Suppose the detected EandIare of normal distribution, then
the membership of different fuzzy subsets can be gained. The fuzzy control rules of BLDCmotor by using the Mamdani minimum operation is shown in Table 5.1.
5.2.3.3 The Realization of Time-Sharing Commutation Strategy
Since the conduction moment precedes the zero-crossing point of back-EMF, it is difﬁcult to
give a commutation command according to the zero-crossing point of the line back-EMFduring the control process. In order to solve this problem, by using the approximate linearcharacteristics of the line back-EMF near the commutation moment, we can obtain the line
back-EMF corresponding to the advanced electrical angle. Hence, the commutation command
can be determined by the line back-EMF.
The relationship between the line back-EMF and electrical angle yis shown in Figure 5.14,
in which the line back-EMF near the commutation moment remains approximately linear.
The line back-EMF e
Land electric angle ywill meet
eL
y/C0y*¼2E
yE/C0y*¼k ð5:40Ț
where y/C3— electrical angle at the crossing point of the line back-EMF.
yE— electrical angle at the decreasing moment of the line back-EMF.
y— electrical angle corresponding to eL.
k— the slope.Table 5.1 Fuzzy rules for conduction moment
I
E NB NS ZE PS PB
NB NB NB NS NS ZE
NS NS NS NS NS PS
ZE ZE ZE ZE ZE PS
PS PS PS PS PS PB
PB PS PS PB PB PBAnalysis and Reduction of Torque Ripple 145

As stated in Equation (5.40), we can calculate the line back-EMF eoncorresponding to the
advanced electrical angle, then get the ecutwith the time of sampling, calculation, and
operation being taken into consideration. Thus, the time-commutation strategy is achieved so
that the commutation torque ripple of the BLDC motor can be reduced.
5.3 Torque-Ripple Reduction with Active Disturbance Rejection
Control
5.3.1 Principles of ADRC
An active disturbance rejection nonlinear c ontroller is based on the state observer and
disturbance compensation, which is composed of a tracking differentiator, an extendedstate observer and a nonlinear state feedba ck control law. Among them, the tracking
differentiator can ﬁlter the reference input si gnal and then achieve fast tracking without
overshoot, and extract the differential signal based on the generalized differential theory.The extended state observer can estimate the system status, model uncertainties and theexternal disturbances well. The nonlinear st ate feedback control law can generate control
signals by a nonlinear structure conﬁgurati on. In other words, the active disturbance
rejection controller deals with the system input and output by using a tracking differentiator
and an extended state observer, respectively. Also, the control input of system can beobtained through the combination of nonline ar state error and the feedforward compen-
sation [13–18].
Compared with the traditional PID control, an active disturbance rejection controller has
much signiﬁcant superiorities. First, it can provide reasonable arrangement of transitionprocess according to the tracking differentiator. Secondly, the nondifferentiable and discon-tinuous problem of error signal, and the noise of the differential signal can be solved with thegeneralized differential method. Meanwhile, the unmodeled dynamics and unknown external
disturbance are all resolved into a total disturbance of the system to be estimated by the
extended state observer. Therefore, an accurate model of the controlled object is not necessaryeL
θE θ* θ2E
0
Figure 5.14 The relationship between line back-EMF and y.146 Permanent Magnet Brushless DC Motor Drives and Controls

in practice, but the system is still robust. In addition, the ADRC nonlinear structure instead of
using a classical control conﬁguration in the form of linear weighted sum forms the nonlinear
state error feedback control law, which greatly improves the processing efﬁciency of the error
signal and the performance of the closed-loop control system.
5.3.2 ADRC Controller Design
5.3.2.1 Model of BLDC Motor
The main circuit of the three-phase BLDC motor is shown in Figure 5.15.
Using lumped parameters and ignore the armature reaction, the voltage balance equation of
the motor will be
ux¼RixțðL/C0MȚdix
dtțex ð5:41Ț
where ux— phase voltage;
ix— phase current;
ex— phase back-EMF.
The electromagnetic torque equation of the motor is
Te¼ðeAiAțeBiBțeCiCȚ=O ð5:42Ț
Moreover, the mechanical motion equation is
Te¼TLțBvOțJdO
dtð5:43Ț
T1 T5
Ud
T4 T6T3
T2Cd+
–A
CBeA
eB
eCR
R
RiCiBiA+ –
+
+–
–
Figure 5.15 Main circuit of a BLDC motor.Analysis and Reduction of Torque Ripple 147

5.3.2.2 Torque Subsystem Design of ADRC
Let
Tex¼exix=O
E¼KeO(
ð5:44Ț
where E— amplitude of ex;
Ke— coefﬁcient of back-EMF.
Then, Texcan be approximately taken as
Tex¼sKeix ð5:45Ț
where s¼1 ixX0
/C01ixG0(
.
As stated in Equation (5.41), one can obtain
_Tex¼/C0R
L/C0MTexțKe
L/C0Msux/C0Ke
L/C0Msex ð5:46Ț
Thus, we can deﬁne the disturbance of the torque subsystem as
w1x¼/C0Ke
L/C0Msex
u0x¼sux8
<
:ð5:47Ț
Then, three extended state observers of phase A, B and C are built to observe the
electromagnetic torque of the motor as
_z1x¼z2x/C0b1falðz1x/C0TexðtȚ;a1;d1Țțb0u0x
_z2x¼/C0b2falðz1x/C0TexðtȚ;a1;d1Ț(
ð5:48Ț
where b0¼Ke=ðL/C0MȚ.
Hence,
^Te¼z1ațz1bțz1c
a¼z2ațz2bțz2c(
ð5:49Ț
where ^Te— tracking value of the electromagnetic torque;
a— real-time value of the torque subsystem during its operation.
The greatest advantage of ADRC is that it does not rely on its object model. The tracking
value and real-time value of the torque subsystem are obtained by the extended state
observer to construct a ﬁrst-order ADRC contro ller that takes the bridge inverter output148 Permanent Magnet Brushless DC Motor Drives and Controls

voltage as control input, the electromagne tic torque as the measurement input in order
to reduce the torque ripple of BLDC motor. Here, the control input parameter bis chosen to
be 1/(2 L–2M).
Note that the torque observed by the extended state observer of torque subsystem is not the
actual motor torque, but the error between them is not signiﬁcant. Simulation and experimental
results show that the torque observer can meet the system requirements of torque-ripplesuppression.
5.3.2.3 Design of ADRC in Speed Subsystem
From the mechanical motion Equation (5.43), we further get
dO
dt¼/C0BvO
JțTe
J/C0TL
Jð5:50Ț
with the disturbance of the speed subsystem be deﬁned as
w2¼/C0TL
Jð5:51Ț
Thus, the ﬁrst-order ADRC of the speed subsystem can be designed, where Teis the control
input and Ois the measurement output.
So, two ﬁrst-order ADRCs can be designed by considering the motor equivalent to an
integral series model composed of two nonlinear subsystems to realize the double loop control
of a BLDC motor driving system. The outer loop is taken as speed control that provides thereference torque for the inner control loop. The inner loop is taken as torque control to reducethe torque ripple of the motor. The corresponding ADRC is obtained as shown in Figure 5.16,where the DC side voltage of the inverter is taken as the control input and the mechanicalvelocity as the measurement input.
In the ADRC, the external disturbance and internal disturbances of the system are in the
equivalent status. The extended state observer can track the output electromagnetic torquequickly, so that the online control of the torque subsystem is ensured. For a given referencetorque, the torque ﬂuctuations as disturbance can be estimated in real time by the extendedstate observer and compensated by adjusting the inverter output voltage. This can also keep thetorque steady.
ADRC1 ADRC2 Torque subsystem Speed subsystemΩ Te* *u Ω Te
Figure 5.16 Scheme of the ADRC to reduce torque ripple.Analysis and Reduction of Torque Ripple 149

5.3.3 Experimental Results
Here, the experimental test system is designed based on the DSP chip TMS320LF2407A of TI
Company to design and verify the active disturbance rejection control scheme for torqueﬂuctuations reduction in BLDC motor. The corresponding hardware block diagram is shown inFigure 5.17. The parameters of the ADRC are deﬁned in the MATLAB environment initially,and then certain adjustments are made during the experiment. The active disturbance rejection
control algorithm is implemented in TMS320LF2407A.
During the experiment, a 4-pole-pair Y-connected BLDC motor is used as a prototype,
which is controlled in the two-phase 120
/C14conduction mode. The rotor position is detected by
position sensors. DSP changes the position signal into the speed signal. Then the speed signal,
as the output of the speed subsystem, is put into ADRC1. The control variable calculated by thenonlinear feedback control law is taken as the given input of ADRC2. The output of the torquesubsystem can be calculated by three phase currents, and the control variable of ADRC2 willbe changed into the corresponding duty cycle square wave by the EVA of DSP to achieve the
PWM control for the motor. The torque is detected by a noncontact rotary torque sensor (range:
1 N m, accuracy class: 0.5%).
Figure 5.18 shows the torque waveform of open-loop operation. As can be seen from the
ﬁgure, the torque ripple can reach about 25% of the average torque.
Then, the motor is controlled by the active disturbance rejection control scheme with the
rated load ( T
L¼0.4 N m). Figure 5.19 shows the detected torques with the given speed being
equal to 300 r/min, 1000 r/min, and 1500 r/min, respectively.
As can be seen from Figure 5.19, the inhibitory effect of torque ripple is more feasible at
low speed. In this condition, the torque is more stable and the ﬂuctuations can be controlledwithin 1%.
Figure 5.20 shows the torque waveform of the motor with light load ( T
L¼0.05 N m) at the
rated speed condition. It can be seen from Figure 5.20 that the torque ripple has also been wellsuppressed when the motor runs with light load at high speed.
Three-phase
sourceCommutating
voltageInverter
MOSFET
driveBLDC
motor
PCPWM ADC
SCI CAP
Current sampleVoltage samplePosition
detection
TMS320LF2407A
Figure 5.17 Hardware control scheme.150 Permanent Magnet Brushless DC Motor Drives and Controls

0.6
0.4
0.2
0.0T/N m
0.52 0.51 0.50
t/s
Figure 5.18 Torque waveform of open-loop operation.
0.6
0.40.2
0.0T/N m
(a) n=300 r/min0.05 0.04 0.03
t/s
0.6
0.4
0.2
0.0
0.05 0.04 0.03T/N m
(b) n=1000 r/mint/s
0.6
0.4
0.2
0.0
0.05 0.04 0.03T/N m
(c) n=1500 r/mint/s
Figure 5.19 Torque waveforms for the motor running at different speeds.Analysis and Reduction of Torque Ripple 151

Comparing Figure 5.19 with Figure 5.20, it can be seen that the torque-ripple-reduction
effect of ADRC is independent with respect to the motor speed. At the rated torque or high
torque level, the torque ripple cannot be effectively suppressed mainly due to the limitation ofthe inverter voltage output. The DC voltage of the bridge inverter is limited to 40 V inexperiments. So, in high-speed operation and high-torque conditions, the torque ripple cannotachieve full compensation due to this voltage limitation. Since the torque ripple observation is
accurate, a sufﬁcient voltage output level of the inverter will suppress the torque ripple at high
speed too.
Generally speaking, by using ADRC, not only will better speed response of the motor be
achieved, but also the torque ripple and motor noise will be signiﬁcantly reduced. The ADRC-based closed-loop torque control can suppress the torque ripple caused by various factorsobviously, especially for motor commutation torque ripple.
5.4 Torque-Ripple Reduction with BP Neutral Network
5.4.1 BP Neural Network
5.4.1.1 Topology of BP Neural Network
A BP neural network is a kind of one-way transmission multilayer feedforward neural
network. It has a ﬂexible network structure with strong nonlinear mapping and adaptive
capabilities. Except for the input and output layer nodes, there are one or more layers of hidden
nodes in the network. Nodes of the same layer have no connection. Therefore, the output ofeach node only affects the nodes of the next layer. A BP neural network can be seen as acomplex nonlinear mapping from input to output. It can approximate to an arbitrarily complexfunction by compounding simple nonlinear functions. In theory, a continuous L
2-function can
be approximated by the BP neural network with only three layers to any desired degree ofaccuracy [19]. In addition, the learning of a BP neural network is essentially an unconstrainednonlinear optimization problem.
The commutation moment of a BLDC motor is determined mainly by the voltage and back-
EMF, whereas the back-EMF is related to the speed of the motor. Therefore, there is a certainrelation among the commutation moment t, speed n, and the terminal voltage u. A three-layer
BP neural network used in BLDC motor control system, with one input layer, one hidden layer,and an output layer, is shown in Figure 5.21.0.05 0.04 0.03T/N m
t/s0.15
0.10
0.000.05
Figure 5.20 Torque waveform for the motor running with light load at the rated speed.152 Permanent Magnet Brushless DC Motor Drives and Controls

In the network, there are two input nodes ( tandn), ﬁve hidden layer nodes and an output
node u. The network is mainly used to identify the relationship between uandt,n. The
logsigmoid function of the hidden layer and the tansigmoid function of the output layer are,
respectively, represented as
log sig ðxȚ¼1
1țe/C0xð5:52Ț
and
tan sig ðxȚ¼1/C0e/C02x
1țe2xð5:53Ț
Note that it is better to choose different output functions with varied running conditions to
enhance the network’s mapping function ability and improve its convergence speed.
5.4.1.2 Network Training
As is well known, network training is divided into online training and ofﬂine training. If the
ofﬂine trained network is used to the actual control system directly, it may not adapt to
environmental changes. On the other hand, online training can immediately update the model
with environmental changes, but it will lose accuracy for initial training. Therefore, acombination of online training and ofﬂine training can be used to enhance the trainingperformance. Usually, the ofﬂine trained network is adopted ﬁrst, and then the online trainingof network is applied when the motor is running.
The samples for ofﬂine training can be derived from simulations or experiments by
recording the time tof current rising from zero to the maximum, the corresponding speed
nand the terminal voltage u. If the motor parameters are determined, a series of different
samples of t(k),n(k) and u(k) can be obtained by changing the power supply voltage or the
motor load.
Here, 5000 simulation samples are used to train the network by modifying the voltage and
load 50 times. In this condition, the network will converge to the sample data in the secondperiod. As discussed above, the disadvantages the ofﬂine training can be compensated by thet
nu
Figure 5.21 Topology of the BP neural network.Analysis and Reduction of Torque Ripple 153

online training with real-time identiﬁcation of model parameters. The samples of online
training include the current, speed and power-supply voltage. The commutation moment tcan
be derived from the detected current. Then, taking tandnas the network inputs to obtain u, the
error between uand its expected value is thus used to correct the weights of the network so that
the merits of online training are obtained.
In the network-training process, it is nece ssary to modify the network weights between
neurons constantly, so that the error of the performance function is reduced to the requiredprecision gradually. There fore, the mapping of the network is approximated to the
true model.
The main disadvantages of a BP neural network include its slow learning speed and the
existence of a local minimum point. To solve these problems, many scholars have carried outextensive research and exploration, and have made many valuable achievements. The resultsshow that a BP neural network learning speed is related to the optimization of learningalgorithm, the choice of learning rate, and many other factors. So, in different learningenvironments, we can select different learning methods.
If appropriate learning methods are adopte d, the local optimization problem of the
network can be solved. The control strategy of adding inertia terms with its inertia factorequal to 0.92 is used in this section, so that onl y small oscillations o ccur in the BP neural
network training process. The training resu lts show that fast convergence of network is
obtained [20].
The formula for weight correction is
Dw
ijðkț1Ț¼gdiðkȚyiðkȚțaDwijðkȚð 5:54Ț
where wij— weight between network layers;
yi— actual output of the ith neuron;
di— local gradient for weight correction of ith neuron;
g— learning rate;
a— momentum factor.
For the output layer
dk
i¼ðdiðkȚ/C0yiðkȚȚj0ðviðkȚȚ ð5:55Ț
For the hidden layer
dk
i¼j0ðviðkȚȚX
odoðkȚwoiðkȚð 5:56Ț
where j— output function;
di(k) — teacher output of the ith neuron;
vi— input of the ith neuron.154 Permanent Magnet Brushless DC Motor Drives and Controls

5.4.2 Self-Tuning Regulator
Since the 1970s, due to the needs of space technology and process control, especially with the
development of microelectronics and computer technology, the adaptive control theory anddesign has made great progress. It has become an important branch of modern control theory.In contrast to traditional regulation principles and optimal control theory, adaptive control cangive good quality of control in the condition that the knowledge of the object model or
environment is less sufﬁcient.
A large number of engineering practices show that the adaptive control for complex
controlled object can often reduce costs, and improve the existing productivity and the quality
of products [21–23]. Currently, the most commonly used adaptive control contains the modelreference adaptive system (MRAS) and self-tuning regulator (STR).
Here, the self-tuning regulator is used for the BLDC motor control. The self-tuning
regulator separates the unknown parameters estimation and controller design. The unknownparameters are estimated online with a recursive estimation method, so that the estimated
parameters can be seen as the real parameters for system control. Moreover, the self-tuning
regulator is designed based on a BP neural network as shown in Figure 5.22.
In Figure 5.22, the network ANN2 is used to estimate parameters, while the network ANN1
for regulating the voltage. ANN1 and ANN2 have the same structure and weight. With ANN2online training, the updated weights are used for ANN2 and ANN1 together. The inputs of thenetwork ANN2 are t
2andn. The parameters (the weights between neurons) estimated by
ANN2 are taken as the true parameters to model ANN1. Since the inputs of ANN1 are t1andn,
we get t2¼t1. Thus, the voltage Un1under the ideal state is obtained by ANN1 to regulate the
power-supply voltage. Meanwhile, Un1is used as the teacher of network ANN2. The error
between Un1and the output of ANN2 Un2are used to correct the corresponding weights.
Finally, while the input and output of the network ANN1 and ANN2 have no signiﬁcantdifferences, the commutation torque ripple can be reduced. Note that ANN2 can correct theparameters of the system and update the weights of ANN1 online, so that the network modelwill always approach its actual model.
5.4.3 Experimental Results
The network training and adaptive control algorithm are achieved by VC țț 6.0. The current
signals of the last period are used to calculate the corresponding t1andt2by simple ﬁtting.
ANN1 ANN2
Regulator BLDC motorUdUn1Un2
e
nt2t1
Figure 5.22 Self-tuning regulator.Analysis and Reduction of Torque Ripple 155

Values of t1andt2are applied for the training of network ANN2 and the updating of network
ANN1. Meanwhile, t1andt2of the current period are recorded for network training and
adaptive voltage regulation of the next period.
Figure 5.23 is a record of the detected torque without adding the commutation torque-ripple-
reduction control strategy. As is seen from Figure 5.23, the torque ripple is more obvious. It
reaches about 25% of the average torque.
Figure 5.24 shows that the measured torque after the commutation torque-ripple reduction
control is implemented. It can be seen from Figure 5.24 that the ripple is dramatically reduced.
Note that the commutation current is simpliﬁed to linear during the transient process, which isnot fully consistent with the actual situation. Thus, the output torque still has small ﬂuctuationsand its value is about 1.2% of the average torque, as shown in Figure 5.24.
Figure 5.25 illustrates the effect of the adaptive control. As load increases suddenly, the
previous control model is no longer adaptive to the new environment. The online learning,
parameters re-estimation and model correction will make the system reach a new equilibrium
in a short time. Thus, there is a transition between the new equilibrium and the former one.The transition duration is related to the convergence speed of network learning. The fasterthe convergence, the shorter the transition time. Here, the system transition time is equal to5–6 cycles (about 14 ms).0.016 0.012 0.008 0.004 00.020.040.060.08
t/sTe/N m
Figure 5.23 Torque waveform without adding a commutation torque-ripple-reduction control strategy.
0.016 0.012 0.008 0.004 t/sTe/N m
00.020.040.060.08
Figure 5.24 Torque waveform with a commutation torque-ripple-reduction control strategy.156 Permanent Magnet Brushless DC Motor Drives and Controls

Torque ripple in a BLDC motor is mostly generated in the transient process of commutation,
while the commutation torque ripple is caused by the amplitude variation of the DC bus current
during the transient process of commutation. Controlling the winding voltage during the
transient process of commutation, so that the rise and fall rates of the corresponding phasecurrents are equal, can compensate the amplitude variation of the DC bus current and reducethe torque ripple. So, it can be concluded that in the control strategy described in this sectionbased on a BP neural network and self-tuning regulator, the exact parameters of the motor neednot be predicted, and the system can respond quickly to changes of the environment. Theresults show that the proposed method can greatly reduce the commutation torque ripple withhigh control accuracy and robustness.
5.5 Motor Optimization and Torque-Ripple Minimization
with Fuzzy Niche Genetic Algorithm
The platform width of the back-EMF waveform of a BLDC motor is 120/C14electrical angle
ideally, which is greater than that in actual operation. Also, the amplitude of the torque ripple
will increase as the platform width decreases. It is clearly seen that the platform width of
the back-EMF affects motor torque ripple. Therefore, whether it is computed accurately playsan important role in related optimization of motor torque ripple.
The structural parameters of BLDC motor, which have essential connection with the
motor torque ripple, have an effect on winding inductance and the platform width ofthe back-EMF waveform. In this section, the calculation of platform width based on the
structural parameters is presented, by which the theoretical basis for minimizing torque
ripple is provided. Also, the principle of niche genetic algorithm for multiobjective
optimization is given and a niche genetic algorithm based on fuzzy control is pr oposed
while taking the calculation complexity of motor design into account. The novel genetic
algorithm makes adaptive control of parameters possible and accelerates its rate ofconvergence. The validity of the novel algorithm is proved practically. Then it is appliedin the optimization of a BLDC motor, which improves the motor efﬁciency and minimizestorque ripple effectively.
0.04 0.03 0.02 0.01 00.020.040.060.08
t/sTe/N m0.004 N m load is added.
Figure 5.25 Torque waveform with a sudden load increase.Analysis and Reduction of Torque Ripple 157

5.5.1 Platform-Width Calculation of Back-EMF Waveform
5.5.1.1 The Platform Width of Back-EMF Waveform of Concentrated and Full-Pitch
Windings
Figure 5.26 shows the spatial distribution of the air-gap ﬂux density of a BLDC motor, where
bprepresents the length of pole arc, trepresents the polar distance and Bdrepresents the
amplitude of air-gap ﬂux density, respectively.
If the edge effect is neglected, the platform width of the air-gap ﬂux density waveform is
yB¼180/C2bp
tð5:57Ț
The back-EMF waveform of phase A is analyzed as an example in this section. The back-
EMF equation of phase A based on basic electromagnetic relation is given by
eA¼LafvXNa=p
n¼1BdnðȚ /C2 10/C03ð5:58Ț
where Bd(n),Laf,v,Naandprepresent the air-gap ﬂux density of the nth conductor, the
armature effective length, the peripheral speed, the number of conductors in series per phaseand the number of pole pairs, respectively.
The conductor peripheral speed is
v¼n
60/C2pD1/C210/C03ð5:59Ț
where D1represents the diameter of the armature.
It is obtained from Equations (5.58) and (5.59) that
eA¼KeOpXNa=p
n¼1BdnðȚ
NaBd¼EpXNa=p
n¼1BdnðȚ
NaBdð5:60Ț
Bδ(x)
Bδ
0τ
bpx
Figure 5.26 Spatial distribution of air-gap ﬂux density.158 Permanent Magnet Brushless DC Motor Drives and Controls

where the back-EMF coefﬁcient is
Ke¼NaD1LafBd/C210/C06
2pð5:61Ț
For concentrated and full-pitch windings, conductors of the same winding lie in the same
position x, which indicates that the air-gap ﬂux density remains unchanged. The overall back-
EMF waveform is obtained by synthesizing the back-EMF waveforms of all the conductors of
phase A, which looks like the waveform of the air-gap ﬂux density and whose platform width
yeequals that of the spatial distribution of air-gap ﬂux density, yB.
5.5.1.2 The Platform Width of Back-EMF Waveform of Distributed and Full-Pitch
Windings
In order to utilize the inner surface of the stator effectively and facilitate winding cooling,
the coils are dispersed evenly around the surface of the stator. Assume that the phase beltof phase A winding is 60
/C14and the number of slots per phase and per pole is q.I nt h i sw a y ,
the difference of back-EMFs generated by two adjacent conductors is 60/C14/qelectrical
angle, and the platform width of the overall back-EMF waveform is obtained fromsuperposition as
y
e¼yB/C060 1 /C01
q/C18/C19
ð5:62Ț
Now assume that the winding has inﬁnite conducts that are dispersed evenly around the
inner surface of the stator, then the summation can be expressed as integration. Therefore, the
back-EMF is given by
eA¼KeO3ðyțp=3
yBdxðȚdx
Bdp¼E3ðyțp=3
yBdxðȚdx
Bdpð5:63Ț
Assume that the distribution of the air-gap ﬂux density is square wave whose ideal
amplitude is Bd, which means
BdxðȚ ¼Bd; 2kpGxG2kpțp
/C0Bd;2kpțpGxG2ðkț1Țp(
ð5:64Ț
and its waveform is as shown in Figure 5.27.
Substituting Equation (5.64) into Equation (5.63) gives the back-EMF waveform of phase
A, which is relatively ideal and is a trapezoid with a 120/C14platform width, as shown in
Figure 5.28.
Usually, it is difﬁcult to attain ideal waveforms by using distributed windings since the
distribution of the air-gap ﬂux density is not a perfect square wave.Analysis and Reduction of Torque Ripple 159

5.5.1.3 The Platform Width of Back-EMF Waveform of Distributed and
Short-Pitch Windings
The advantage of short-pitch windings lies in the shortening of terminal parts of conductors.
Assume that the phase belt of phase A is 60/C14and distributed and short-pitch windings are
employed, the number of slots per pole and per phase, the polar distance and the pitch are q,t,
andy1, respectively. Therefore, the platform width of the overall back-EMF waveform from
superposition as
ye¼yB/C0180 1 /C0y1
t/C16/C17
/C060 1 /C01
q/C18/C19
ð5:65Ț
5.5.1.4 The Platform Width of Back-EMF Waveform using a Skewed Slot or a
Skewed Pole
The utilization of a skewed slot or a skewed pole can reduce the cogging torque ripple of the
motor. However, it also reduces the higher harmonics of the back-EMF waveform, whichnarrows the platform width of the back-EMF and increases torque ripple. The platform widthof the back-EMF waveform when the skewed slot coefﬁcient is a
skcan be expressed
approximately as
ye¼yB/C02ask ð5:66Ț−BδBδ
x π 2πBδ(x)
0
Figure 5.27 Schematic diagram of ideal air-gap magnetic ﬁeld.
eA
E
−Ex π 2π 2π/35 π/3 0
Figure 5.28 Back-EMF waveform in ideal conditions.160 Permanent Magnet Brushless DC Motor Drives and Controls

From what has been learned above it is evident that the shape of the back-EMF waveform
depends on the structure of windings, which will further have an effect on the commutation
torque ripple of the motor, therefore what should be considered synthetically in motor design is
the motor performance and applications with various winding structures.
5.5.2 Fuzzy Niche Genetic Algorithm
5.5.2.1 Multiobjective Optimization
Minimizing the torque ripple is just one of the objectives in motor optimization, and usually
the efﬁciency and cost of the motor should be covered. The optimization of motor design can
be concluded as nonlinear programming of multiobjective functions, each of them is usually anonconvex function that has more than one extreme point.
In multiobjective programming, sometimes several objective functions contradict with
each other, such as the efﬁciency, the speed and the platform width of the air-gap ﬂux densitywaveform of the BLDC motor, and so on. Therefore, solving a minimization problem is tosearch for the optimal solution, or a Pareto opt imal solution, when all objective functions are
taken into account synthetically. Although not ea ch objective function is optimized to its own
optimal solution when they are considered individually, it is not allowed for any objectivefunction to compromise in order to cater to o ther objective functions, by which multi-
objective optimization is distinguished from single-objective optimization. Meanwhile, thisis just the difﬁculty of mu ltiobjective optimization. Usually, a Pareto solution is not conﬁned
to one optimal solution. Instead, it is a set of sol utions (Pareto optimal set). Figure 5.29 shows
the Pareto optimal set of a BLDC motor whose objective functions consist of the platform
width of the air-gap ﬂux density waveform y
B, and the efﬁciency of the motor Z.
The complexity of multiobjective optimization is exponential with its scale, which consists
of the number of optimization variables and the number of values that each variable may take.Applying exhaustive method to the above problem belongs to an NP-complete problem, whichcannot be solved in ﬁnite time. Some conventional multiobjective optimization methods are
θBη
0
Pareto set
Figure 5.29 Schematic diagram of Pareto set of yBandZ.Analysis and Reduction of Torque Ripple 161

directional search based and converge fast, such as the weighted sum method, the goal
programming method and the game theory method. However, they often need derivative
information in calculations, which tend to converge at local optimal points caused by the
impact of objective functions0performance. The simulated annealing algorithm belonging to
random search methods is immune to the behavior of objective functions, but only one optimalpoint can be converged to. The randomness and implicit parallelism of a niche geneticalgorithm makes it possible to ﬁnd more than one local optimal point and obtain Pareto optimalsets, from which the best solution can be obtained according to certain preferences. Currentlythe niche genetic algorithm is known as one of the most effective methods to achievemultiobjective optimization. The following is the optimization of the motor based on a
niche genetic algorithm.
5.5.2.2 Niche Genetic Algorithm
Niche is a kind of survival environment. The niche genetic algorithm groups every generation
into categories, in which individuals having larger ﬁtness values are chosen as the excellentrepresentatives, or a population. Then, a new generation is produced through hybridization andmutation within a population or between populations, and then excellent representatives arekept through certain mechanism. In this way, new populations are produced continuallythrough clustering in the evolution, and populations are continually updated by newly obtainedexcellent individuals, through which populations are continually optimized.
The diversity of the solution remains in the niche genetic algorithm in evolution. Also,
global optimization is guaranteed, which is superior in optimizing multipeak functions that arecommon in mathematics and engineering. Compared to the conventional genetic algorithm,the niche genetic algorithm performs immensely well in increasing the convergence rate,enhancing global search ability and improving the quality of solutions. The niche geneticalgorithm is primarily implemented through the mechanism of preselection, crowding andsharing.
Among them, the limited competitive niche genetic algorithm based on the mechanism of
sharing limits the competition among design plans having different shape, structure and
characteristics, which is suitable for the optimization of the shape or structure of electro-
magnetic equipments.
5.5.2.3 Fuzzy Niche Genetic Algorithm
It is known that both the crossover probability P
cand the mutation probability Pmaffect the
convergence rate and the quality of the optimal solution for the niche genetic algorithm.
Generally, PcandPmare ﬁxed, and cannot adapt to the varied actual situation, which results in
the low efﬁciency of solving such computationally complex multivariable optimizationproblems as motor optimization for niche genetic algorithm. If P
candPmare adaptive,
then the convergence rate can be improved. It is complex to determine the optimal values of Pc
andPmonline since many factors should be considered and the exact expression is difﬁcult to
acquire. In order to handle the fuzzy information of the rules better, fuzzy control is utilized todetermine P
candPm. Making use of previous knowledge and experience, utilizing fuzzy
reasoning method, and considering the actual situation in evolution, a fuzzy controller reﬁnes162 Permanent Magnet Brushless DC Motor Drives and Controls

the crossover probability and mutation probability dynamically, then a fuzzy control table
containing the variation of crossover probability and mutation probability is produced. Finally,
the defuzziﬁcation is implemented based on the maximum membership degree method and the
crossover probability and mutation probability can be determined.
Fuzzy reasoning improves the optimization effe ct of the niche genetic algorithm greatly,
which endows the novel algorithm with better r obustness, global optimality and conver-
gence rate.
5.5.3 Optimization Design of BLDC Motors
5.5.3.1 Optimization Model
The optimization of the motor can signiﬁcantly improve the operating performance of the
motor, reduce material consumption, shorten the design cycle and enhance the product quality,which plays an important role in increasing the ratio of performance to price of the motor.After a proper multiobjective optimal algorithm and related performance evaluation criteriaare selected, the optimization model of the BLDC motor, including objective function,optimization variable and constraint condition, should also be determined.
In general, the cost and efﬁciency of BLDC motor or other performance indices are selected
as objective functions. In this section, the optimization of the motor based on a fuzzy nichegenetic algorithm is presented, which solves multiobjective optimization problems effectively.Therefore, besides the cost and efﬁciency of the motor, the optimization of the motorcommutation torque ripple is considered.
A lot of parameters are involved in motor design, of which the ones that have great inﬂuence
on objective functions are generally chosen as optimization variables, such as air gap d, wire
diameter of the winding d
l, winding turns per phase Na, stator outer diameter D1, stator inner
diameter Di1, stator iron core length L1, alnico thickness hm, pole arc coefﬁcient apand stator
tooth width bt, etc.
And the optimization variables are given by
X¼d;dl;Na;D1;Di1;L1;hm;ap;bt/C2/C3Tð5:67Ț
Inequality is the main form of the constraint condition in motor optimization, which can
be categorized into performance constraint and general constraint. The former is decidedby the technical performance indices, of which the power factor, efﬁciency, the starting
current, the starting torque, maximum torq ue and heat load are commonly used, and plays
the role of controlling those indices within the r ange that motor design requires. The latter
consists of constraints apart from technica l performance indices, including primarily
constraints about slot space-factor, stator cur rent density, stator tooth ﬂux density, stator
yoke ﬂux density, rotor current density, rotor tooth ﬂux density and rotor yoke ﬂux density,
and so on. The commonly used inequality const raints for the BLDC motor optimization are
shown in Table 5.2.
In motor optimization, the constraint values should be determined properly according to
different types of motor. The optimization will be encumbered with too strict constraint values
and the limit function will fail likewise when confronted with too arbitrary constraint values.Analysis and Reduction of Torque Ripple 163

Table 5.2 Constraint conditions
Indices Constraint conditions Indices Constraint conditions
Stator tooth ﬂux density Bt1min /C20Bt1/C20Bt1max Rated torque TNXTNmin
Stator yoke ﬂux density Bj1min /C20Bj1/C20Bj1max Starting torque TstXTstmin
Winding current density Jm/C20Jmmax Maximum torque TmXTmmin
Starting current Ist/C20Istmax Efﬁciency ZXZmin
Figure 5.30 Simulation results of electromagnetic torque for all the optimization plans.Table 5.3 Optimization plans
Criteria Plan I Plan II Plan III Plan IVVoltage (V) 36 36 36 36
Power (W) 150 150 150 150
Speed (r/min) 3620 3615 3618 3619
Efﬁciency (%) 79 78.1 80 77.3Platform width of back-EMF (
/C14) 96 115 110 105164 Permanent Magnet Brushless DC Motor Drives and Controls

Note that the difference among constraint functions in the magnitude order is fairly large.
In order to guarantee the same accuracy, normalization about the constraint conditions is
required to achieve the same or similar magnitude order.
5.5.3.2 Design Cases
In this section, the optimization is implemented by using fuzzy niche genetic algorithm for a
three-phase, Y-connected BLDC motor, and the parameters are given as: rated voltage:
UN¼36 V; rated power: PN¼150 W; rated speed: nN¼3600 r/min; efﬁciency: ZH75%.
In accordance with the above parameters the optimization of the BLDC motor based on a
fuzzy niche genetic algorithm is implemented, where the efﬁciency and torque ripple arechosen as the optimization objectives. The optimization schemes are shown in Table 5.3.
Figure 5.30 shows the simulated electromagnetic torque waveforms of the motor starting
process corresponding to the four motor design schemes.
It is seen from the simulation results that at rated conditions, the four proposed schemes
conform to the requirements of indices with different dynamic responses of torque during thestarting process. Among those schemes, plan II (see Figure 5.30(b)) surpasses the others intorque performance for its faster rising speed of electromagnetic torque and smaller com-mutation torque ripple.
Questions
1. How many types of torque ripples are there in the BLDC motor and what are they?2. How to minimize the cogging torque of the BLDC motor by using the methods of motor
design?
3. What is the commutation torque ripple and how to reduce it?4. What can affect the commutation torque ripple and how can they do this?5. Give the principle of ADRC.6. Draw the typical structure of a BP network.7. How to calculate the platform width of the back-EMF waveform with different winding
conﬁgurations?
8. Describe the principle and the characteristics of a fuzzy niche genetic algorithm.
9. List the main constraint conditions in motor optimization, including the performance
constraint and the general constraint.
References
1. Jahans, T. M., Soong W. L. (1996) Pulsating torque minimization techniques for permanent magnet AC motor
drives-a review. IEEE Transactions on Industrial Electronics ,43(2), 321–330.
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with skewing for torque ripple and cogging torque reduction. IEEE Transactions on Industry Application ,45(1),
152–160.
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4. Ishikawa T., Slemon G. R. (1993) A method of reducing ripple torque in permanent magnet motors without
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5. Zhu Z. Q. and Howe D. (2000) Inﬂuence of design parameters on cogging torque in permanent magnet motors.
IEEE Transaction on Energy Conversion, 15(4), 407–412.
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controller. Proceedings of the CSEE .25(11), 129–133 (in Chinese).
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University Master Thesis , 2005 (in Chinese).
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12. Chen W., Xia C. L. (2006) Sensorless control of brushless DC motor based on fuzzy logic. IEEE Proceedings of
the World Congress on Intelligent Control and Automation , China, 6298–6302.
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disturbance-rejection controller. Proceedings of the CSEE .27(14), 91–95 (in Chinese).
15. Li Z. J.Control of brushless DC motor based on active-disturbance rejection controller. Tianjin: Tianjin University
Master Thesis , 2004.
16. Xia C. L., Song Z. F. (2007) Rotor current control of doubly-fed induction generator based on active-disturbance-
rejection controller. Advanced Technology of Electrical Engineering and Energy .26(3), 11–14, 19 (in Chinese).
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20(11), 65–69 (in Chinese).166 Permanent Magnet Brushless DC Motor Drives and Controls

6
Sensorless Control for BLDC
Motor Drives
Many researches and preliminary achievements have been made for position-sensorless
control, which is always an important issue of BLDC motor drives. When operating undersensorless conditions, BLDC motors have some advantages like high reliability and anti-disturbance capability. Meanwhile, to some extent, they can overcome the commutationtorque ripples caused by inaccurate installation of position sensors. In this chapter, various
rotor-position-detection methods for BLDC motor are presented. Taking the three-phase
Y-connected BLDC motor with 120
/C14electrical angle between each phase for example,
position-sensorless controls based on modern control theories and artiﬁcial intelligencealgorithms are investigated. Different means of the starting operation and ways to widenthe speed range are proposed.
6.1 Principle of Sensorless Position Detection
Nowadays, position sensors used in BLDC motor drives are mainly electromagnetic types,photoelectric types and magnetic-sensing types. However, in some speciﬁc occasions, theapplications of a BLDC motor are limited by the existence of position sensors. This can
be mainly reﬂected in the following aspects:
(1) Position sensors may increase the volume of the system.
(2) Extra wiring between motor and control unit would be required, which causes the system
to be easily interfered with.
(3) Under certain conditions, such as high temperature, high pressure, high humidity, and
so on, position sensors work with poor sensitivity so that the system operates with lowreliability.
(4) Position sensors have a high precision demand for installation, as inaccurate commutation
caused by deviation of mechanical mounting will directly affect the operating performanceof the motor.
Permanent Magnet Brushless DC Motor Drives and Controls , First Edition. Chang-liang Xia.
/C2112012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd.

Therefore, sensorless control technology has received more and more attention. Further-
more, with the improvement of microcontrollers and the development of detection means and
control technologies, sensorless control technology has been rapidly developed. Some of
these technologies have been put into practice. According to different detection principles,the sensorless control methods for BLDC motor drives mainly include the back electromotiveforce (back-EMF)-based method, the ﬂux-linkage-based method, the inductance-basedmethod, and the artiﬁcial-intelligence-based method, etc.
6.1.1 Back-EMF-Based Method
Among all of the sensorless control methods, the back-EMF-based method is the most mature
and widely used one at present. In this method, the zero-crossing points of back-EMFs are
detected and made 30/C14electrical angle lag to get six discrete rotor-position signals in each
electrical cycle, from which commutation information is obtained by the logical switch circuit,and then the sensorless operation is implemented.
The relationship between zero-crossing points of the back-EMF and the commutation
instants is shown as Figure 6.1. In the ﬁgure, e
A,eB,eCare trapezoidal waves of three-phase
back-EMFs. They are phase-separated by 120/C14as shown in Figure 6.1. Q 1,Q2,…… and Q 6
are the commutation instants lagging the corresponding zero-crossing points of the back-EMF
30/C14electrical angle in the same period.
Nowadays, the challenge to the back-EMF-based estimation method is how to detect its
zero-crossing point accurately. Many scholars have made a thorough study and various
detection methods such as the terminal voltage sensing method, the back-EMF integration
eA
eB
eCωt
ωt
ωt0
0
0Zero crossing pointCommutation period
Q2Q6 Q4 Q5
Q1 Q3
Q1 Q2
Q3 Q4 Q5Q6
Q1Q2 Q3 Q4
Q5 Q6
Figure 6.1 Relationship between zero-crossing points and commutation instants.168 Permanent Magnet Brushless DC Motor Drives and Controls

method, the third-harmonic back-EMF method, the freewheeling diode method and the line
back-EMF method have been proposed.
6.1.1.1 Terminal Voltage Sensing
By detecting the terminal voltage of nonexcited phase winding, the zero crossings of the back-
EMFs can be obtained with software programming or hardware circuit. Then this method can
control the BLDC motor commutate properly. The means of how to get zero crossings of back-
EMFs by using software programming is described as follows.
The mathematic model of BLDCM can be written as
uAG¼RiAțðL/C0MȚdiA
dtțeAțUN
uBG¼RiBțðL/C0MȚdiB
dtțeBțUN
uCG¼RiCțðL/C0MȚdiC
dtțeCțUN8
>>>>>><
>>>>>>:ð6:1Ț
where u
AG,uBG,uCGare terminal voltages, UNis the neutral point voltage, and L–Mis the
equivalent inductance of each winding.
To illustrate the principle of terminal voltage sensing, we can suppose that phases A and B
are conducted while phase C is inactive, as shown in Figure 6.2. At this time, the back-EMFs of
phase A and B are on the opposite ﬂat parts of the trapezoidal wave, while that related tophase C is on the sloping part. Clearly, the latter will change with the rotor position. Then,
the back-EMF and current relationships of phases A and B in the BLDC motor can be,
respectively, represented as
e
AțeB¼0 ð6:2Ț
and
iAțiB¼0 ð6:3Ț
T1 T5
Ud
T4 T6T3
T2Cd+
_A
CBeA
eB
eCR
R
RiBiA+–
+
+–
–
UN
GD2D1 D3 D5
D4 D6
Figure 6.2 Current loop while phases A and B are conducted.Sensorless Control for BLDC Motor Drives 169

Adding the terminal voltages of phases A and B together, we can get
uAGțuBG¼RðiAțiBȚțð L/C0MȚdiA
dtțdiB
dt/C18/C19
țðeAțeBȚț2UN ð6:4Ț
Then, substituting Equations (6.2) and (6.3) into Equation (6.4) yields
UN¼uAGțuBG
2ð6:5Ț
Since phase C is inactive, then iC¼0 anddiC
dt¼0.
Thus, from Equation (6.1), we can get
eC¼uCG/C0UN¼uCG/C0uAGțuBG
2ð6:6Ț
Similarly, when phases A and C are conducted and phase B is inactive, we have
eB¼uBG/C0uAGțuCG
2ð6:7Ț
and when phases B and C are conducted and phase A is inactive, we obtain
eA¼uAG/C0uBGțuCG
2ð6:8Ț
It can be seen from Equations (6.6)–(6.8), six back-EMF zero-crossing signals in each cycle
will be obtained from terminal voltages, where a 60/C14electrical angle exists in each two
abutting signals. Hence, they can correctly provide commutation signals for the motor.
Commutation instants are decided by the electrical angles of back-EMF zero-crossing
points delayed 30/C14. The angles can be achieved based on the interval of the previous two zero-
crossing points as
Tðk/C01Ț¼ Zðk/C01Țț1
2DT
DT¼Zðk/C01Ț/C0Zðk/C02Ț(
ð6:9Ț
where T(k/C01) is the ( k/C01)th commutation instant, Z(k/C01) is the moment of the ( k/C01)th
zero-crossing point, and Z(k/C02) is the moment of the ( k/C02)th zero-crossing point. (Note that
the change of speed in the interval is neglected here.)
It is worth noting that each phase winding has two back-EMF zero-crossing points in an
electrical cycle. Therefore, we must distinguish them according to the reversals in polarity
after the back-EMF zero-crossing point or the conducting state of the windings. In addition, thecapacitor used in the terminal voltage detection circuit for voltage regulating and ﬁltering willcause the terminal voltage phase to shift. Thus, phase compensation should be performed in asoftware algorithm according to the parameters of the hardware circuit.
BLDC motors will run reliably within a certain speed range when the terminal voltage
sensing method is adopted. Figure 6.3 shows the experimental waveforms of phase voltage,line voltage and phase current.170 Permanent Magnet Brushless DC Motor Drives and Controls

(a)
(b)
(c)
Figure 6.3 Experimental waveforms with the terminal voltage detection method: (a) the phase voltage
waveform, (b) the line voltage waveform, (c) the phase current waveform.Sensorless Control for BLDC Motor Drives 171

The back-EMF zero crossing signals in the terminal voltage sensing method can be
calculated not only by software but also from a hardware circuit. Figure 6.4 shows a typical
hardware for terminal voltage sensing.
As depicted in Figure 6.4, the ﬁltered terminal voltage signals are input into the compara-
tors. Meanwhile, a virtual neutral point is constructed by using a symmetrical Y-connectionresistive load. If the back-EMF of the nonexcited phase is equal to zero, the correspondingterminal voltage for this phase will be equal to the neutral voltage. That is, if phase C is
inactive, u
CGwill be equal to UNwhile eC¼0. Therefore, back-EMF zero crossing signals will
be gained if we compare the output signals of ﬁlters with virtual neutral point signals as shown
in Figure 6.4.
6.1.1.2 The Back-EMF Integration Method
The back-EMF integration method compares the integration of the inactive phase back-EMF
with the threshold. It is the commutation instant of this phase when the integration of the back-EMF reaches the threshold. The relationship between the signals of back-EMF integration and
the commutation instants is shown in Figure 6.5.
In Figure 6.5, the back-EMF varies approximately linearly. Then, the function of the sloping
part can be represented as
eðtȚ¼/C6 E
0t ð6:10Ț
When the back-EMF in the nonexcited phase crosses zero, the integrator begins to work. In
this case we have
Uout¼ðt
0eðtȚ
kdt/C12/C12/C12/C12/C12/C12/C12/C12¼E0t2
2k/C12/C12/C12/C12/C12/C12/C12/C12ð6:11Ț+
−
+
−
+
−ZA
ZB
ZCuA
uB
uC
N
Figure 6.4 Back-EMF zero-crossing point detector.172 Permanent Magnet Brushless DC Motor Drives and Controls

where E0is the gradient of the sloping-part for back-EMF, Uoutis the output voltage of the
integrator, and Kis the gain constant of the integrator.
When the output voltage of the integrator Uoutis equal to the threshold Uth, the integrator
stops working, and outputs the commutation signals. The integrator will not restart working
until the next back-EMF crosses zero. In the control system, the commutation instant lags thezero-crossing point of the back-EMF with a 30
/C14electrical angle. Thus, at the phase
commutation instant, Equation (6.11) can be rewritten as
Uout¼1
2k/C1Keo
t/C1t2/C12/C12/C12/C12/C12/C12/C12/C12¼1
2kKeot/C12/C12/C12/C12/C12/C12/C12/C12¼1
2k/C1Ke/C1p
6/C12/C12/C12/C12/C12/C12/C12/C12¼U
th ð6:12Ț
where Uthis the threshold, Keis the coefﬁcient of the back-EMF.
To apply the back-EMF integration method, ﬁrst, Uthshould be calculated according to
Equation (6.12). Then, the control system makes a real-time comparison between UoutandUth
to determine the commutation instant. The advantages of this method are as follows: rotor
speed information is not necessary during the control process; lagging or leading commutation
of the motors could be done by regulating the threshold; and also it is insensitive to the switchsignal. The disadvantage is that there exist integration accumulated errors and threshold setupproblems.
6.1.1.3 The Third-Harmonic Back-EMF Method
The third harmonic of the back-EMF is used in this method to decide the commutation instant
of the BLDC motor. Above all, Fourier decomposition is applied to the back-EMF in three-phase windings. Then, multiple harmonics, including the fundamental and a series of oddharmonics, are obtained. So, the back-EMF can be given by
e
A¼E1sinyțE3sin 3yțE5sin 5yț……
eB¼E1siny/C02p
3/C18/C19
țE3sin 3 y/C02p
3/C18/C19
țE5sin 5 y/C02p
3/C18/C19
ț……
eC¼E1siny/C04p
3/C18/C19
țE3sin 3 y/C04p
3/C18/C19
țE5sin 5 y/C04p
3/C18/C19
ț……8
>>>>>><
>>>>>>:ð6:13ȚeA eB eC
0
Uout
150° 90° 30° 210° 270°ωt
ωte
0Uth
Q1 Q2 Q3 Q4Q5 Q6
330°
Figure 6.5 Relationship between the back-EMF integration signal and the commutation instant.Sensorless Control for BLDC Motor Drives 173

where yis the electrical angle of the rotor.
By adding the three-phase back-EMF in Equation (6.13), we can get
eAțeBțeC¼3E3sin 3y ț3E9sin 9y țE15sin 15 yț…… /C253E3sin 3y ð6:14Ț
It is obvious that the phase voltage equations of a BLDC motor can be written as
uA¼RiAțðL/C0MȚdiA
dtțeA
uB¼RiBțðL/C0MȚdiB
dtțeB
uC¼RiCțðL/C0MȚdiC
dtțeC8
>>>>>>><
>>>>>>>:ð6:15Ț
And note that the sum of three phase currents is zero, i.e.
i
AțiBțiC¼0 ð6:16Ț
Hence, by adding the three phase voltages in Equation (6.15), we obtain
usum¼uAțuBțuC
¼RțðL/C0MȚd
dt/C18/C19
ðiAțiBțiCȚțð eAțeBțeCȚ
¼eAțeBțeC/C253E3sin 3yð6:17Ț
After integrating, the third harmonic ﬂux is given by
c3rd¼ð
usumdt ð6:18Ț
Accordingly, usum, the sum of three phase voltages, contains information of the third-
harmonic components for the phase back-EMF. The third-harmonic ﬂux linkage can be
obtained by integrating the usum, whose zero-crossing point is exactly the commutation instant.
This can be illustrated as Figure 6.6.
To sum up, through software programming, the third-harmonic ﬂux can be obtained from
the three phase voltages uA,uBanduC. The zero-crossing point of the third-harmonic ﬂux is
exactly the commutation instant. Compared with the terminal voltage detection method, the
third harmonic back-EMF method has the following advantages such as wider range of speed,smaller delay of the phase, and so on. However, due to the continuous accumulation of noisesignal at low speed, errors will be made during the integration process, which will cause
inaccurate commutation.
6.1.1.4 The Freewheeling Diode Method
The freewheeling diode method is also known as the third-phase conducted method, in which the
rotor position is determined by detecting the switching condition of the freewheeling diode,which is reversely paralleled with bridge inverter. To illustrate the freewheeling diode method,an example is taken when phases A and B are conducted and phase C is inactive.174 Permanent Magnet Brushless DC Motor Drives and Controls

Q 1 Q 2 Q 3 Q 4 Q 5 Q 6ωt
ωtωteA
usum
ψ3rd0
0
0
Figure 6.6 Relationship among commutation time, back-EMF harmonic and ﬂux linkage.
The pulsewidth modulation implemented in the inverter is shown in Figure 6.7.
From the modulation shown in Figure 6.7, it is known that the power switch T 1on the upper
half-bridge of phase A is operating at the PWM chopping mode when phases A and B are
conducted, with the power switch T 6on the lower half-bridge of phase B conducted. This is
shown as the dark zone in Figure 6.7. During the modulation, when T 1is off, the freewheeling
diode D 4will be conducted. In such a case, the operating condition of the inverter is shown
in Figure 6.8.
From Figure 6.8, it is known that when T 1is off, current will ﬂow through the freewheeling
diode D 4.T h e nT 6and diode D 4compose a conducting circuit. Accordingly, uCG, the terminal
voltage of the nonexcited phase, is represented as
uCG¼eCțUN
¼eCțVCE/C0VD
2/C0eAțeB
2ð6:19Ț
where VCEis the forward voltage drop of the power switch, VDis the forward voltage drop of
the diode.
To conduct the freewheeling diode D 2, we must have
uCG</C0VD ð6:20Ț
Substituting Equation (6.19) into Equation (6.20), we obtain
eC/C0eAțeB
2</C0VCEțVD
2ð6:21Ț
When the back-EMF eCin the nonexcited phase approaches zero, the equation eAțeB¼0
holds, thus
eC</C0VCEțVD
2ð6:22ȚSensorless Control for BLDC Motor Drives 175

eA eB eC
T1
T3
T5
T4
T6
T2
Figure 6.7 PWM waveforms.
T1 T5
Ud
T4 T6T3
T2Cd+
_A
BeA
eB
eCR
R
RiBiA + –
+
+–
–D2
CD1D3 D5
D4 D6
Figure 6.8 Diagram for current ﬂow in freewheeling diode.176 Permanent Magnet Brushless DC Motor Drives and Controls

In general, VCEandVDare quite small compared with the back-EMF. When the back-EMF
eCbecomes negative, a current will ﬂow through the freewheeling diode D 2in the nonexcited
phase. In this condition, the negative point can be approximately considered as a zero-crossing
point of the back-EMF. Therefore, the position of the rotor can be determined by detecting theswitch state of the freewheeling diode.
The freewheeling diode method is realized by detecting the zero-crossing point of the back-
EMF from currents that ﬂow through the freewheeling diodes. Using this method, highsensibility and wider speed range can be obtained in the sensorless control for BLDC motordrives. Figure 6.9 shows the principle of the detection circuit. The disadvantage of thisdetection circuit is that six independent sources are needed in the additional detection circuit.
Thus, the detection circuit is a little complicated.
6.1.1.5 Line Back-EMF Method
In the phase back-EMF based sensorless control for BLDC motor drives, the commutation
instants of the windings are acquired through shifting of 30
/C14for the zero-crossing points of the
phase back-EMF in electrical angle. Note that the phase-shifting angle is closely related to theinstantaneous speed of the motor. In the variable-speed control of BLDC motor drives,
inaccuracy of commutation instants for the windings will occur in the sensorless control
with phase back-EMF detection. In contrast with the phase back-EMF detection method,the calculation of phase-shifting angle is not necessary in the line back-EMF method. Thecommutationinstants of thewindingsare decided directlythrough the zero-crossing pointsof theline back-EMF. Hence, this can effectively improve the commutation accuracy in speed control.
Figure 6.10 shows the relationship among the phase back-EMF, line back-EMF and the
commutation instants.
Note in Figure 6.10 that the zero-crossing points of line back-EMFs are exactly the
commutation instants of the BLDC motor. Thus, it is unnecessary to calculate the delay anglein the sensorless control with line back-EMF. So, by calculating the zero-crossing points ofline back-EMFs e
AB,eBCandeCA, the six commutation signals can be obtained, which can
ensure the reliable sensorless operation of the BLDC motor.
Compared with the phase back-EMF method, the line back-EMF method can be performed
at lower speed more easily. Thus, it has a wider speed range of applications. In addition, there is
T1
Ud
T4Cd+
_+−~Vref
+−
Vref~
Figure 6.9 Detection circuit with the freewheeling diodes.Sensorless Control for BLDC Motor Drives 177

no need to use the previous commutation instants for phase shifting in this sensorless control
approach. The motor can operate in such a sensorless mode with only the zero-crossing pointsof line back-EMFs determined.
It can be seen from the above that the purpose of each back-EMF-based method is to achieve
correct commutation for the windings by using the signals of rotor position, which can be
acquired from the back-EMF signals of the windings. The distinct advantage of the back-EMF-
based methods is its easy implementation.
6.1.2 Flux-Linkage-Based Method
The ﬂux-linkage-based method, which is different from the back-EMF-based ones, can obtainthe rotor position information by estimating the ﬂux. Note the well-known motor voltageequation is
U¼RIț
dc
dtð6:23Ț
where Uis the phase-voltage matrix, Iis the phase current matrix, Ris the phase winding
resistance matrix, and Cis the matrix of ﬂux linkage.
Hence, the ﬂux linkage can be obtained by using the measured voltages and currents as
c¼ðt
0ðU/C0RIȚdt ð6:24Ț
If the initial rotor position, motor parameters, and the relationship between rotor position
and ﬂux linkage are known, the rotor position can be determined by the ﬂux in Equation (6.24).
Figure 6.11 shows the principle diagram of the ﬂux-linkage-based method.
When the motor is controlled by the ﬂux-linkage-based method, the initial rotor position should
be detected so that we can have the initial ﬂux information required for the integral calculation.eA
eB
eABωt
ωt
ωt0
0
0Q1 Q2
Figure 6.10 Relationship among phase back-EMF, line back-EMF and commutation instant.178 Permanent Magnet Brushless DC Motor Drives and Controls

Note that due to the large integral calculation of this method, an accumulative error may be
produced when the motor is running at low speed. Moreover, this method is easily affected bythe motor parameters.
6.1.3 Inductance-Based Method
Both the back-EMF-based method and the ﬂux-linkage-based method determine the rotorposition depending on the movement of the rotor magnetic ﬁeld. As a result, neither of the twomethods can provide the initial rotor position for the self-starting of the motor at standstill.In order to solve this problem, an inductance-based method is adopted to determine the rotor
position at standstill. The basic principle of the inductance-based method is described as
follows. Above all, the amplitude of the current, which is generated by injecting speciﬁcsquare-wave voltage pulse into the winding, is measured. Then, the difference betweenthe inductances is obtained by comparing the amplitude of the currents. Thus, we candetermine the rotor position.
The total ﬂux of each phase consists of the ﬂux linkage of the rotor permanent magnet and
that generated by the stator winding current, namely
c
sum¼crotorțL0i ð6:25Ț
where csumis the total ﬂux of each phase, crotordenotes the ﬂux of rotor permanent magnet,
andL0¼L/C0M.
When current pulse ițori/C0is injected into the stator winding, different inductances, L0țand
L0/C0, are generated. Note that the direction of ițori/C0is the same as or counter to that of the
magnetic ﬁeld. Hence, L0țandL0/C0can be written as
L0ț¼csum/C0crotor
iț¼Dcț
iț
L0/C0¼csum/C0crotor
i/C0¼Dc/C0
i/C08
>><
>>:ð6:26ȚVoltage/current
detectionBLDC
motor
Flux calculationRotor position/
current calculation_I* I
Ψ*
θ*
Figure 6.11 Principle of ﬂux-linkage-based method.Sensorless Control for BLDC Motor Drives 179

Since the saturation effect of the stator core is taken into account, the ﬂux will change while
injecting current pulses with different directions. Figure 6.12 shows the relationship between
the current and the ﬂux linkage.
As shown in Figure 6.12, the ﬂux change Dcțproduced by ițis less than that produced by
i/C0, that is, L0ț<L0/C0. The nonlinear inductance L0is determined both by the magnetic pole’s
position and the stator winding’s current. Therefore, we can get the difference between theinductances by detecting the current pulses, and then determine the rotor position. The currentresponse with different inductances is discussed as follows.
Since the dynamic equation shown in Equation (6.15) can be simpliﬁed as
u
x¼RixțL0dix
dtțexx¼A;B;C ð6:27Ț
in which, when the rotor stands still, the back-EMF ex¼0.
Consequently, we obtain
ix¼ux
R1/C0e/C0R
L0t/C16/C17
ð6:28Ț
Hence, the current response, shown in Figure 6.13, will vary with different inductances.
Figure 6.13 shows that the response of the current ițis faster due to L0ț<L0/C0. Therefore,
by detecting the positive and negative phase currents in an appropriate time interval, thedifferences in inductances can be determined. Thus, the rotor position is determined accordingto the relationship between the inductance and rotor position.
The inductance-based method is well suited for the rotor initial position detection at
standstill. However, because the difference between the inductances is small with differentrotor positions, this method relies on high-precision current sensing.
6.1.4 Intelligence-Based Method
It is well known that an artiﬁcial intelligence algorithm has strong adaptability and good self-learning ability. Meanwhile, it is very suitable to be applied in sensorless control for ai– i+∆ψ+
∆ψ–ψsum
0 iψ
Figure 6.12 Relationship between current and ﬂux.180 Permanent Magnet Brushless DC Motor Drives and Controls

BLDC motor. The basic principle of rotor-position detection based on an artiﬁcial intelligence
algorithm is described as follows. Above all, the relationship is established between voltage,current and rotor position of the BLDC motor with the help of such theories as artiﬁcial neuralnetworks, fuzzy strategy, genetic algorithms, adaptive artiﬁcial immune algorithms, etc. Then,the rotor position or commutation signals for sensorless control are acquired through themeasured motor voltage and current signals. In this condition, an accurate mathematic modelof BLDC motor is not necessary. Thus, the artiﬁcial-intelligence-based method is suitable for anonlinear electrical machine control system, in which the generalization will be improved.
Furthermore, this method has fairly strong robustness to parameter variation and noise
measurement. Thus, it is capable of solving some complex problems that conventionaland other modern control methods would not be able to deal with. In such cases, theperformance of motor control will be enhanced. The advent of high-efﬁciency MCU andDSP has provided more development opportunity for this method.
The rotor-position-detection methods, including the back-EMF-based method, the ﬂux-
linkage-based method, the inductance-based method and the artiﬁcial-intelligence-basedmethod, all have their own limitations. So, these control methods should be chosen properly
according to different requirements and applications.
6.2 Sensorless Control Strategy
6.2.1 Sensorless Control Based on Disturbance Observer
In modern control theories, the design of controllers can be formulated as an integration design
of a state feedback controller and a state observer. This approach offers a solution for thedesign of a closed-loop system and performance improvement of the entire system. In thedesign of a state feedback controller, the state variables are needed. In practice, some of these
state variables cannot be measured directly. Hence, the state observation or state reconstruc-
tion are put forth to solve this problem.
According to the mathematical model of a BLDC motor, the voltage equation will be
transformed from nonlinear to linear if the back-EMF is assumed to be a constant disturbance.Thus, the zero-crossing point of back-EMF can be acquired through a disturbance observer,which is designed by using linear observer theory [1–3].i+
| i–|ux /R
Tt∆i
0i
Figure 6.13 Current responses with different inductances.Sensorless Control for BLDC Motor Drives 181

6.2.1.1 Design of Full-State Observer
Obviously, Equation (6.15) can be rewritten in the form of single phase as
dix
dt¼a11ixța12exțb1uxx¼A;B;C ð6:29Ț
where a11¼/C0R
L/C0M,a12¼/C01
L/C0M, and b1¼1
L/C0M.
In order to simplify the design of the observer, the back-EMF in Equation (6.29) is
assumed to be a constant disturbance, namely _ex¼0. Thus, the state variable model of the
BLDC motor is
_ix
_ex/C20/C21
¼a11a12
00/C20/C21
ix
ex/C20/C21
țb1
0/C20/C21
ux ð6:30Ț
y¼10½/C138ix
ex/C20/C21
ð6:31Ț
in which, phase voltage uxis the input variable, current ixis the output variable, and back-
EMF exis imposed on the system as a disturbance. The corresponding system diagram is
shown in Figure 6.14. It can be verified that the system is completely observable so that an
observer can be designed to observe the disturbance e.
Since the system expressed as Equations (6.30) and (6.31) is completely observable, the
full-order state observer can be designed as
d
dt^ix
^ex/C20/C21
¼a11a12
00/C20/C21^ix
^ex/C20/C21
țb1
0/C20/C21
uxțg1
g2/C20/C21
y/C010½/C138^ix
^ex/C20/C21/C18/C19
ð6:32Ț
^ixð0Ț¼0
^exð0Ț¼0(
ð6:33Ț
where g 1and g 2are the feedback gain parameters of the full-state observer.
ix
b1 ∫
a11a12
uxex
xi
Figure 6.14 The diagram of the BLDC motor.182 Permanent Magnet Brushless DC Motor Drives and Controls

Equation (6.32) can be rearranged as
d
dt^ix
^ex/C20/C21
¼a11/C0g1a12
/C0g2 0/C20/C21^ix
^ex/C20/C21
țb1
0/C20/C21
uxțg1
g2/C20/C21
y ð6:34Ț
Solving Equation (6.34), we have
d^ex
dt¼g2ðix/C0^ixȚð 6:35Ț
Thus, the error equation of the observer is
d
dte1
e2/C20/C21
¼a11/C0g1a12
/C0g2 0/C20/C21
e1
e2/C20/C21
ð6:36Ț
e1
e2/C20/C21
¼ix/C0^ix
ex/C0^ex/C20/C21
ð6:37Ț
From above, the full-state observer can be constructed as shown in Figure 6.15.
6.2.1.2 Pole Placement for the Full-State Observer
The eigenvalue polynomial of the full-state observer is
fðsȚ¼dets/C0ða11/C0g1Ț/C0 a12
g2 s/C20/C21
¼s2/C0ða11/C0g1Țsța12g2 ð6:38Ț
Suppose the expected poles are p1andp2, we obtain the expected eigenvalue polynomial
f*ðsȚ¼ð s/C0p1Țðs/C0p2Ț¼s2/C0ðp1țp2Țsțp1p2 ð6:39Ț
BLDC motor
1b
∫ a12a11 − g1
g2∫iˆxix xu
eˆx
eˆxdtdxiˆ
dtd
+
++−
Figure 6.15 Diagram of the full-state observer.Sensorless Control for BLDC Motor Drives 183

Let the eigenvalue polynomial of the observer equal the expected eigenvalue polynomial,
and then the coefﬁcients of like powers of son both sides are, respectively, equal. Thus, the
feedback gains g1andg2can be acquired by solving the desired characteristic equation.
6.2.1.3 Design of Reduced-Order Observer
Based on the phase voltages and currents, the full-state observer can reconstruct the phase
currents and the back-EMF. In practice, the phase currents can be obtained from currentsensors directly. Thus, a reduced-order observer can be used to estimate the back-EMF.
The reduced-order observer can be designed in several steps. First, the system state equation
should be decomposed according to the observable theory. Then, using a series of equivalenttransformations, we obtain the state equation and the output equation, which have to beobserved. Finally, the corresponding reduced-order observer is obtained according to thedesign methods of the full-state observer.
Let
z
x¼_ix/C0a11ix/C0b1ux ð6:40Ț
Then, by substituting Equation (6.40) into Equation (6.30), the state equation of a BLDCmotor after equivalent transformation can be expressed as
z
x
_ex/C20/C21
¼a12ex
0/C20/C21
ð6:41Ț
Hence, the reduced-order observer can be designed as
_ex¼gð^zx/C0zxȚð 6:42Ț
where gis the feedback gain coefﬁcient.
If the phase current ( ix) is detected directly, then ^ix¼ixholds. Hence, from Equation (6.40),
we have
^zx¼_^ix/C0a11^ix/C0b1ux¼_^ix/C0a11ix/C0b1ux ð6:43Ț
Combining Equation (6.43) with Equations (6.40) and (6.42), we can obtain the state
equations of the reduced-order observer as
_ex¼gð_^ix/C0_ixȚð 6:44Ț
From Equation (6.30), we can get
_ix¼a11ixța12exțb1ux ð6:45Ț
Furthermore,
_^ix¼a11^ixța12^exțb1ux¼a11ixța12^exțb1ux ð6:46Ț184 Permanent Magnet Brushless DC Motor Drives and Controls

Thus, according to Equations (6.46) and (6.44), the state equations of the reduced-order
observer are rewritten as
_^ix¼a11ixța12^exțb1ux ð6:47Ț
_ex¼gð_^ix/C0_ixȚð 6:48Ț
Equations (6.47) and (6.48) can also be written in vector form as
_^i¼A11ițA12^ețB1u ð6:49Ț
_^e¼Gð_^i/C0_iȚ¼A11GițA12G^ețB1Gu/C0G_i ð6:50Ț
where A11¼a11I;A12¼a12I;B1¼b1I;G¼gI,Grepresents the feedback gain matrix of the
observer.
Deﬁne the estimated error of the back-EMF as
«¼e/C0^e ð6:51Ț
Then the estimated error equation of the observer becomes
_«¼ _e/C0_^e¼A12Gðe/C0^eȚ¼A12G«¼a12gI« ð6:52Ț
Let the pole of the observer satisfy
a¼a12ga<0 ð6:53Ț
To ensure the asymptotic stability of the observer, the feedback gain coefﬁcient gis selected so
that the poles of the observer are on the left side of the complex plane. Note that the convergence
rate of the estimated error is proportional to the distance between the poles and the imaginary
axis. But when the poles are too far from the imaginary axis, the bandwidth of the observer willbe broadened. In such a case, the observer cannot suppress the disturbance and the noiseeffectively. Therefore, these factors should be considered in the procedure of pole placement.
In order to avoid the inﬂuence of the current differential item in the state equation, a new
variable xis deﬁned as
j¼^ețGi ð6:54Ț
Hence,
_j¼A
12GjțB1GuțGðA11/C0A12GȚi ð6:55Ț
^e¼j/C0Gi ð6:56Ț
Thus, the disturbance observer can be designed successfully, whose scheme diagram is
shown in Figure 6.16.
It can be seen from Figure 6.16 that there is a low-pass ﬁlter in the disturbance observer. It is
used to ﬁlter the high-frequency noise that is caused by the phase commutation. The outputs ofSensorless Control for BLDC Motor Drives 185

the observer contain the information about the zero-crossing point of the back-EMF. In
addition, the interference pulses, which are caused by the hypothesis that the back-EMF is a
constant disturbance, are comprised in the outputs of the observer. Thus, it is necessary to take
certain measures to eliminate the disturbances that are caused by these interference pulses.
6.2.1.4 The Elimination of Interference Pulses
1) The cause of interference pulses
Through the zero-crossing observation of the back-EMF, we can get the rotor position from
the outputs of the comparator circuit. Now, the rotor-position signals are denoted as SA,SB
andSC. The waveforms of these signals are the same, while their phases are offset 120/C14
from each other.
Usually, rotor-position signals SA,SBandSCcontain interference pulses. The causes of
the interference pulses are described as follows. In practice, the waveform of the back-EMFis an irregular trapezoidal wave due to the inﬂuence of the slot effect and armature reaction.Moreover, during the design process of the reduced-order observer, the back-EMFs areassumed to be constants. This will result in an estimated error. Thus, the interference pulsesare produced.
Therefore, the rotor-position signals not only contain the information about zero crossing
of the back-EMF, but also have some interference pulses. The interference pulses should beeliminated from the position signals so that sensorless control is achieved.
2) Principle of interference pulses elimination
The basic principle of interference elimination is making logic transformation (i.e. delay,latch, logical operations, etc.) for the rotor-position signals so as to reshape the waveforms ofthe rotor-position signals. The process of the logic transformation is discussed as follows.
The ﬁrst step is to obtain the gate signal of S
Aby making an XNOR operation between the
original SCand the corresponding signal with appropriate delay on SC. Afterwards, the width
of a low-level pulse in the gate signal is regulated greater than the width of interference byadjusting the delay time of S
C. Thus, we can eliminate the interference pulses by controlling
the gate signal of SA. Note that when the gate signal goes high, SAis conducted. On the
contrary, when the gate signal is low, SAwill be latched. This process of signal logic
transformation is illustrated in Figure 6.17.
In Figure 6.17, SCCis the signal with a delay on SC,SC/C8SCCis the gate signal, SA
represents the rotor-position signal related to phase A after the interference pulses have beeneliminated.u
ie eˆ +
+–
Ri ( L − M )id td
BLDC motor
Low-pass
ﬁlter
Figure 6.16 Scheme diagram of the disturbance observer.186 Permanent Magnet Brushless DC Motor Drives and Controls

Gate signals can be obtained from the transformation of three rotor-position signals. From
above, we can obtain the strobe signal of SAby logic transformation of SC. Similarly, the gate
signals of SBandSCcan be, respectively, obtained from SAandSB. The two main roles of the
gate signals are shown as follows.
(1)Determine the time to generate the interference pulses.
(2)From this moment, produce gate signals whose low-level width is greater than the
width of interference pulses.
We can eliminate the interference pulses by certain logic transformations, such as delay,
latch, and so on. Then, we will get the accurate zero-crossing information of the back-EMF. Figure 6.18 shows the waveforms of the actual Hall signal H
Aand the observed
rotor-position signal SArelated to phase A.
6.2.2 Sensorless Control Based on a Kalman Filter
In the dynamic system with random noise, a Kalman ﬁlter could achieve the minimum
estimation error by optimal estimation. It can be used in both stationary and nonstationary
applications. A Kalman ﬁlter uses the previous estimate and the latest input data to get newestimate data by using the recursive algorithm. So the ﬁlter only needs to store the previousestimate, and can meet the real-time requirement of the system. On the realization of aKalman ﬁlter, it is a recursive algorithm implemented by a computer in essence. Each recursivecycle includes two processes, in which the time and measurements of the estimated valuet
ttSA
000
SC
SC ⊕ SCC
SC ⊕ SCC
t0SAt0
Figure 6.17 Curves for logic transformation signals.Sensorless Control for BLDC Motor Drives 187

are updated. Figure 6.19 shows the state-space model diagram for a linear system with
random noise.
In Figure 6.19, Ukis the nonrandomized control input, Xkis the state of the system, w(k)i s
the random noise input, v(k) is the measurement of the noise, y(k) is the measurement of the
system output, Fk,Rk,Gk,Hkare the real matrices. Then, the sensorless control for BLDC
motor is achieved by estimating the position of the rotor based on the Kalman ﬁlter [4–6].
6.2.2.1 The Control Strategy of a Kalman Filter Based on Line Back-EMF
From Equation (6.1), we can get the terminal voltage model of the BLDC motor as
eAB¼uAG/C0uBG/C0ðL/C0MȚdðiA/C0iBȚ
dt/C0RðiA/C0iBȚ
eAC¼uAG/C0uCG/C0ðL/C0MȚdðiA/C0iCȚ
dt/C0RðiA/C0iCȚ
eBC¼uBG/C0uCG/C0ðL/C0MȚdðiB/C0iCȚ
dt/C0RðiB/C0iCȚ8
>>>>>>><
>>>>>>>:ð6:57Ț
Since the three line back-EMFs have the relationship
e
BC¼eAC/C0eAB ð6:58Ț01HA
SA
8
t/ms40 32 24 16SA(HA)
Figure 6.18 Waveform of Hall signal HAand the rotor-position signal SA.
RkGk
kZ–1 Hk
Φw (k)
Uk X k+1v (k)
ykXk
Figure 6.19 State-space model for a linear system with random noise.188 Permanent Magnet Brushless DC Motor Drives and Controls

then the voltage model of the motor can be simpliﬁed as
Ul¼2Rțd
dtðL/C0MȚ/C18/C19
0
Rțd
dtðL/C0MȚ 3Rțd
dtðL/C0MȚ/C18/C192
66643
7775I
lțEl ð6:59Ț
where
El¼eABeAC ½/C138T;
Ul¼uABuAC ½/C138T;
Il¼iABiAC ½/C138T;
iAB¼iA/C0iB
2;
iAC¼iAțiB
2:
Therefore, we can obtain the line back-EM F of the BLDC motor through detecting the
terminal voltage and current. Since there is no need for phase delay in the line back-EMF-
based sensorless control strategy, an extended speed range for BLDC motor drives is
achieved.
In practice, the line back-EMF signal usually includes unmodeled noise, detection noise and
burst noise. These noises, especially the burst noise, may lead to a false determination for the
zero crossings so that the motor will be uncontrollable. In general, the random noise can be
regarded as Gaussian white noise. Therefore, we could use a Kalman ﬁler to eliminate noisesand estimate the zero-crossing instants of the line back-EMF.
Based on the line back-EMF, the discrete state model of the BLDC motor is established as
X
kț1¼FkXkțRkUkțGkwðkȚð 6:60Ț
yk¼HkXkțvðkȚð 6:61Ț
where Xk¼½iABðkȚiACðkȚeABðkȚeACðkȚoðkȚ/C138T;
Rk¼T
2ðL/C0MȚ/C0T
6ðL/C0MȚ000
0T
3ðL/C0MȚ0002
66643
7775T
;
Uk¼½uABðkȚuACðkȚ/C138T;
yk¼½iABðkȚiACðkȚ/C138T;Sensorless Control for BLDC Motor Drives 189

Fk¼1/C0RT
L/C0M0 /C0T
2L/C0M ðȚ00
01 /C0RT
L/C0MT
6L/C0M ðȚ/C0T
3L/C0M ðȚ0
00 1 0 0
00 0 1 0
00 0 0 12
666666643
77777775;
H
k¼10000
01000/C20/C21
;
w(k) — measurement noise vector;
v(k) — system noise vector.
The Kalman ﬁlter consists of the predicted equation and the ﬁltering estimation equation.
The state equation and estimation error covariance matrices at time tkț1are predicated by the
state equation and inputs at time tk. The state prediction equation is
^Xkț1kj¼Fk^Xkkj/C01țKkðyk/C0Hk^Xkkj/C01Ț
¼ðFk/C0KkHkȚ^Xkkj/C01țKkykð6:62Ț
in which
Kk¼FkPkkj/C01HT
kðHkPkkj/C01HTkțRkȚ/C01ð6:63Ț
And the estimation error covariance matrix prediction equation is
Pkț1kj¼Fk½Pkkj/C01/C0Pkkj/C01HTkðHkPkkj/C01HTkțRkȚ/C01HkPkkj/C01/C138FTkțGkQGT
k ð6:64Ț
Finally, by making appropriate replacements in the usual Kalman gain formula, the estimate
and the error covariance can be updated by
^Xkkj¼ ^Xkkj/C01țPkkj/C01HT
kðHkPkkj/C01HTkțRkȚ/C01ðyk/C0Hk^Xkkj/C01Ț
Pkkj¼Pkkj/C01/C0Pkkj/C01HTkðHkPkkj/C01HTkțRkȚ/C01HkPkkj/C01(
ð6:65Ț
Thus, based on the line back-EMF estimated by a Kalman ﬁlter, a novel commutation
strategy is obtained. In such cases, if phases B and C are conducted, then eB>0,eC<0, and
the value of eAis between eBandeC.Therefore, there exist eAB<0,eAC>0 and eBC>0 in this
condition. Similarly, we can derive the signs of back-EMF in other conduction states. The
relationship between line back-EMF and the conduction phase winding has been shown inTable 6.1.
6.2.2.2 Simulation Results
Figure 6.20 shows the waveforms of the line back-EMF e
AB, which is obtained by solving the
state equation directly. Figure 6.21 is the line back-EMF estimated by a Kalman ﬁlter. The
actual value of the line back-EMF is shown in Figure 6.22.190 Permanent Magnet Brushless DC Motor Drives and Controls

Figure 6.23 shows the waveforms of the line back-EMF and Hall sensor position signals at
the motor starting stage.
It can be seen from Figure 6.23 that the speed of the motor will not affect the relationship
between the commutation instants and the zero-crossing points of the line back-EMF, while it
does inﬂuence the waveform of the line back-EMF.
6.2.3 Sensorless Control Based on Sliding-Mode Observer
6.2.3.1 Controller Design
A sliding-mode observer has been successfully used in estimating motor speed by rotor-
resistance identiﬁcation and other applications, because of its good robustness and the
antidisturbance ability for system measurement noise. Thus, a sensorless controller of aBLDC motor can be designed based on a sliding-mode observer [7,8]. A BLDC motorsensorless control scheme based on a sliding-mode observer is shown in Figure 6.24.
In Figure 6.24, the current reference signals are obtained from the speed controller based on
the error between the rotation speed reference signal o
*and the estimated signal ^o. The phaseTable 6.1 The relationship between line back-EMF and conduction phase winding
Line back-EMF Winding conducting state
eAB eAC eBC ABC
țțț Forward conducting Non-conducting Negative conducting
/C0țț Non-conducting Forward conducting Negative conducting
/C0/C0ț Negative conducting Forward conducting Non-conducting
/C0/C0/C0 Negative conducting Non-conducting Forward conducting
ț/C0/C0 Non-conducting Negative conducting Forward conducting
țț/C0 Forward conducting Negative conducting Non-conducting
Figure 6.20 Line back-EMF obtained by solving the state equation.Sensorless Control for BLDC Motor Drives 191

commutation signals are achieved through the commutation look-up table. Both ^oand ^yare
estimated by the sliding-mode observer. Based on the estimated speed and position signals, the
BLDC motor can operate in a sensorless condition.
According to the dynamic mathematic model of a BLDC motor, the sliding-mode control
model related to phase A can be written as
d
dt^iA¼1
L0uA/C0R
L0^iA/C01
L0^eAțKsgnð^iA/C0iAȚð 6:66Ț
where ^ denotes the estimated value of parameters, Kis the sliding gain.
Figure 6.21 Line back-EMF estimated by a Kalman ﬁlter.
Figure 6.22 Experimental line back-EMF.192 Permanent Magnet Brushless DC Motor Drives and Controls

From Equation (6.66), we can design the sliding-mode observer model of phase A, which is
shown in Figure 6.25.
In Figure 6.25, the phase voltage uAis the input signal, while the error between the
estimated stator current ^iAand the actual stator current iAis the feedback signal. However, the
error signal is restricted by a symbolic function before being fed back to the input terminal.
Sliding surface scan be implemented by stator currents. The switching function and error
function are
s¼^iA/C0iA¼es¼0
_es¼/C0R
L0es/C01
L0ð^eA/C0eAȚțKsgnðesȚ8
<
:ð6:67Ț
Figure 6.23 Line back-EMF and Hall sensor position waveforms.
Speed
controller
––Bridge
inverter BLDC
motor
Sliding
-mode
observeri
uCommutation
look-up tableˆθ
ˆω*ω Current
controller
Figure 6.24 BLDC motor sensorless control scheme based on a sliding-mode observer.Sensorless Control for BLDC Motor Drives 193

6.2.3.2 Stability Analysis
Considering s_s<0, sliding gain Kmust satisfy
s_s¼es_es
¼ð ^iA/C0iAȚ½/C0BRe s/C0Bð^eA/C0eAȚțKsgnðesȚ/C138<0ð6:68Ț
where B¼1
L0.
Since ^eAandeAare time varying, Kstill needs to satisfy the inequality
K<BR e sjj /C0 B^eA/C0eA jj ð6:69Ț
This means that if Kis small enough, the equivalent control works. Then the system will
stably run on the sliding surface. At this moment, es¼ _es¼0. Thus, Equation (6.67) can be
rewritten as
z¼/C0KsgnðesȚ¼/C0 Bð^eA/C0eAȚð 6:70Ț
It can be seen from Equation (6.70) that the back-EMF information of the BLDC motor is
included in the signal z. It can be used to estimate the rotor position and speed. According to
Equation (6.15), we need to know the phase voltage, the phase current and the derivative of the
phase current in order to obtain the back-EMF. The main advantage of sliding-mode observer-based sensorless control is that it is not necessary to calculate the phase current derivative.Besides, this sensorless control method has a good robustness to measurement noise.
According to the characteristics of a BLDC motor, the back-EMF can be written as
e
A¼ocmfAðyȚ
eB¼ocmfBðyȚ
eC¼ocmfCðyȚ8
><
>:ð6:71Ț1
L′∫
L′
Κ sgn
Adaptive lawuAdιˆA
dtiˆAi A
ˆω
ˆθ
1ˆeAL′+_
+
_+_
R
Figure 6.25 Sliding-mode observer.194 Permanent Magnet Brushless DC Motor Drives and Controls

where cmis the magnetic ﬂux linkage of each phase, fAðyȚis the waveform coefﬁcient of back-
EMF related to phase A, fBðyȚ¼fAðyț2p=3Ț, and fCðyȚ¼fAðy/C02p=3Ț.
Substituting Equation (6.71) into Equation (6.70), we get
/C0KsgnðesȚțB^ocmfAð^yȚ¼BocmfAðyȚð 6:72Ț
We can see from Equation (6.72) that the rotor position yon the right side can be
calculated by its estimated value on the left side. In this way, the estimated value is renewed.
In the current loop of the system, there are lots of switching ﬂuctuations in signal z, which
are produced by the sliding movement. Fortunately, low-pass ﬁlters can eliminate these
ﬂuctuations. In contrast, if the estimated rotor speed ^ois gained from the derivation of rotor-
position signal ^y, ﬂuctuations will be enlarged. These ﬂuctuations will deteriorate the
performance of speed control for BLDC motors. In such a case, it is very hard for low-pass ﬁlters to eliminate the ﬂuctuations. To solve this problem, adaptive methods are usuallyadopted to estimate the rotation speed. Thus, the estimated value will be less disturbed byswitching ﬂuctuations.
If^yis estimated accurately enough, we can let ^y¼y. Then, combining Equation (6.67) with
Equation (6.71), we get
_e
s¼/C0BRe s/C0Bcmð^o/C0oȚfAðyȚțKsgnðesȚð 6:73Ț
and if the Lyapunov function and adaptive law are deﬁned as
v¼1
2ð^o/C0oȚ2
^o_¼/C0hzfAðyȚ8
><
>:ð6:74Ț
where his a positive constant.
Further, from Equation (6.73), the equivalent control method can be expressed as
z¼/C0KsgnðesȚ¼/C0 Bcmð^o/C0oȚfAðyȚð 6:75Ț
Therefore, the estimated rotation speed ^ocan be calculated from the integral of Equa-
tion (6.74). Substituting Equation (6.74) into Equation (6.27), we can renew the estimated
rotor position ^y.I f ^ois accurate enough, and there exists _o¼0, then the sensorless speed
control for BLDC motors can be achieved.
Since
_v¼ð ^o/C0oȚ_^o¼/C0 ð ^o/C0oȚhzfAðyȚ
¼/C0 ð ^o/C0oȚhBcmð^o/C0oȚf2
AðyȚ
¼/C0hBcmð^o/C0oȚ2f2
AðyȚ/C200 ð6:76Ț
Thus, the system is Lyapunov stable.Sensorless Control for BLDC Motor Drives 195

6.2.4 Position-Sensorless Control Using Wavelet Neural Network (WNN)
6.2.4.1 Introduction to WNN
WNN is a feedforward artiﬁcial neural network (ANN) based on wavelet decomposition. It
combines a wavelet transform with ANN together by replacing a neuron nonlinear excitationfunction with nonlinear wavelet basis. WNN has many of the merits of a wavelet transform andANN. It not only realizes wavelet transform by adjusting the wavelet basis function adaptively,but also has good ability of function approximation. The structure diagram of a SISO WNN isshown in Figure 6.26.
In Figure 6.26, the hidden nodes of the network are all wavelet functions, w
iis the weight
from the ith hidden node to the output, aiandtiare the scale factor and translation factor of
the wavelet function for the ith hidden node, respectively. The optimum values of wi,aiandti
are obtained by training so that the network can approximate fðxȚwell.
6.2.4.2 Sensorless Control Based on WNN
1. Position detection of BLDC motor
Note that the voltage equation of BLDC motor is
uA
uB
uC2
6643
775¼R00
0R0
00 R2
435i
A
iB
iC2435țðL/C0MȚ
d
dtiA
iB
iC2435ț
d
dtcmðyȚ
cmðy/C02p=3Ț
cmðy/C04p=3Ț2435 ð6:77Ț
where c
mis a function of y,cmis related to the stator voltage and current. Therefore,
commutation signals can be calculated by stator voltages and currents for the sensorless
control [9–13].
2. Structure of WNN
Figure 6.27 shows the topology of a WNN that is used to detect the rotor position. This
WNN topology includes six input signals for the input layer, ten nodes in the hidden layer
and six switch signals of the output layer.
f(x)a1w1
wi∑ai x
wKϕ(⋅− t 1)
ϕ(⋅− t i)
ϕ(⋅− t k)ak
Figure 6.26 Structure diagram of a SISO wavelet neural network.196 Permanent Magnet Brushless DC Motor Drives and Controls

The Mexican-hat wavelet is chosen for hidden nodes, that is
jðxȚ¼ð 1/C0x2Țe/C0x2=2 ð6:78Ț
and the output can be expressed as
Y¼WTjðAX/C0TȚð 6:79Ț
where
X¼iAðnȚiBðnȚiAðn/C01ȚiBðn/C01ȚuAðn/C01ȚuBðn/C01Ț/C138T;/C2
T¼t1t2t3 … … t10/C138T;/C2
Y¼S1S2S3S4S5S6/C138T;/C2
A¼a1;1a1;2/C1/C1/C1 /C1/C1/C1 /C1/C1/C1 a1;6
a2;1……
………
a10;1/C1/C1/C1 /C1/C1/C1 /C1/C1/C1 /C1/C1/C1 a10;62
666643
77775;
W¼w
1;1w1;2/C1/C1/C1 /C1/C1/C1 /C1/C1/C1 w1;6
w2;1……
………
w10;1/C1/C1/C1 /C1/C1/C1 /C1/C1/C1 /C1/C1/C1 w10;62
666643
77775:a1,1
a1,jw1,1
w1,2
w10,6 a6,10s1
s2
s3
s4
s5
s6iA(n)
iB(n)
iA(n−1)
iB(n−1)
uA(n−1)
uB(n−1)ϕ ( . – t1 ) Σ
Σ
Σ
Σ
Σ
Σϕ ( . – tj )
ϕ ( . – t10 ) w10,5a6, j
Figure 6.27 Topology of WNN for rotor-position detection.Sensorless Control for BLDC Motor Drives 197

3. Ofﬂine training
How to obtain the training samples is very important for WNN ofﬂine training. Although
training samples can be obtained from simulation data, a further training must be done
based on the experimental data. This will make the WNN more suitable for the sensorlesscontrol of BLDC motors.
Now let the input sample set be { i
A(n),iB(n),iA(n/C01),iB(n/C01),uA(n/C01),uB(n/C01)},
and the output sample set is {g 1,g2,g3,g4,g5,g6}. Note that giis the switch state related to
theith bridge circuit. giis equal to 1 as the corresponding bridge circuit is conducted, while
being 0 as the circuit is turned off.
By training A,T, and Wwith a gradient descent algorithm, we deﬁne the minimize
objective function as
J¼1
2X
nX6
i¼1ðgi/C0SiȚ2ð6:80Ț
where nis the number of samples.
The adjusting law for the scale factor of the wavelet function is
am;jðnț1Ț¼am;jðnȚ/C0aqJ
qam;jð6:81Ț
where
qJ
qam;j¼/C0X
nX6
j¼1eiwi;jxm;nc0X6
m¼1am;jxm;n/C0tj ! !
ð6:82Ț
where ais the learning rate, xm;nis the mth input of the nth vector of sample data, and eiis
the output error of the ith network, i.e. ei¼gi/C0si.
The adjusting law for the translation factor of the wavelet function is
tjðnț1Ț¼tjðnȚ/C0aqJ
qtjð6:83Ț
where
qJ
qtj¼X
pX6
j¼1eiwj;ic0X6
m¼1am;jxm;p/C0tj !
ð6:84Ț
The weight control law of the wavelet function is
wj;iðnț1Ț¼wj;iðnȚ/C0aqJ
qwj;ið6:85Ț
where
qJ
qwj;i¼/C0X
peicX6
m¼1am;jxm;p/C0tj !
ð6:86Ț
Here, ofﬂine training method is developed in a PC by using MATLAB. After being
trained by 4000 samples, WNN can meet the predetermined precision. Then, the scale
factor, the translation factor and the connection weight of the output layer are all
determined.198 Permanent Magnet Brushless DC Motor Drives and Controls

4. Online training
Online training is adopted into the WNN to improve its adaptability and robustness. Hence,
the connection weights of the output layer can be adjusted by supervised learning. Thegradient descent method is employed again, and the external teachers for supervisedlearning are the output signals coming from the logic process. The training scheme is shownin Figure 6.28.
Actually, the output is not strictly 0 or 1, but ﬂuctuates around them. This indicates that
errors exist in output signals. However, the only signals needed by the motor bridge circuit
are 0 and 1. So output signals need to be ﬁltered, where the ﬁlter is designed as
S
0
iðnȚ¼0S iðnȚ/C200:25
1S iðnȚ/C210:75
S0
iðn/C01Ț0:25/C20SiðnȚ/C200:758
>><
>>:ð6:87Ț
where S0iðn/C01ȚandS0
iðnȚare the ( n/C01)th and the nth sample points of the ith ﬁltered
switch signal, respectively.
6.2.4.3 Simulation Results
The simulation is performed in MATLAB. Figure 6.29 shows the waveforms of sample signal
g1, output signal S1without ﬁltering, and the error ( e1) between g1andS1.
As shown in Figure 6.29, the output signals can track the sample signals properly, but they
are not strictly 0 or 1. This means that the output signal cannot achieve the on-off control of thebridge circuit successfully.
The waveforms of ﬁltered output signal S
0
1and error e01are shown in Figure 6.30.
From Figure 6.30, we can see that the output signal of the WNN can provide a qualiﬁed on-
off signal to the bridge circuit after being ﬁltered.
Figure 6.31 shows the waveforms of the sample signal, the output signal and the related
error, when the load is increased from 0 to 0.5 N m suddenly.
It can be seen from Figure 6.31 that the period of the commutation signal is 20 ms in the
beginning, and increases immediately to 24 ms when the load is changed. It can be concluded
that the dynamic response of the system is fast.
Figure 6.28 Online training scheme of WNN.Sensorless Control for BLDC Motor Drives 199

6.3 Starting Process for Sensorless Control
6.3.1 Determination of Initial Rotor Position at Standstill
Determination of the initial rotor position is critical for the reliable starting of a BLDC motor.
It directly affects the system’s maximum starting torque and minimum starting time. Atpresent, the inductance method is the main method for prediction of the initial rotor position.
The principle of the inductance method is described as follows. First, a special short time
Figure 6.29 Waveform of sample signal g1, output signal S1, and error e1.
Figure 6.30 Waveforms of ﬁltered signals S0
1ande01.200 Permanent Magnet Brushless DC Motor Drives and Controls

impulse voltage is injected into stator winding. Then, the initial rotor position is obtained by
differences among each stator winding’s inductance, which is determined by the currentresponse at a speciﬁc interval. Because the inductance of the windings is small and thereluctance of the PM is large in the BLDC motor, the inductance method requires a largeamount of computing time and high-precision current measurement. Another method fordetermination of initial rotor position is the rotor-locating method. By energizing one speciﬁc
phase winding, the rotor will be located at the deﬁned location. Thus, the initial rotor position
is known. The rotor locating method can be easily implemented. The disadvantages of thismethod are that the motor might rotate reversely and have a large current during the positionlocation period.
6.3.2 Starting Methods for Sensorless Control
At present, the back-EMF-based method is the most common technique used in sensorlesscontrol for BLDC motor drives. It is well known that the back-EMF will become zero or verysmall, when the motor is at standstill or running at low speed. This makes it difﬁcult for a motorto start by itself. To deal with this problem, many starting methods are presented. The mainmethods are: the three-step starting method, the prelocation starting method, the raising-
frequency and the raising-voltage synchronous starting method, and the voltage interpolation
method [14–17].
1) Three-step starting method
The three-step starting method includes three stages: determination of rotor location,
speeding up and operation mode switch. In the second stage, the motor is speeded up from
Figure 6.31 Waveforms of sample signal, output signal and their error when load changed suddenly.Sensorless Control for BLDC Motor Drives 201

stationary by the separate control method used in the synchronous motor. When the speed is
high enough, the motor is switched to the common position sensorless running mode tocomplete the starting procedure. Figure 6.32 shows the corresponding principle diagram ofthe three-step starting method.
Which power switch should be conducted ﬁrst depends on the initial rotor position
when the BLDC motor is at standstill. Since determination of the initial rotor position israther complex without position sensor, the rotor-locating method can be used to solvethis problem.
After the initial rotor position is determined, the main controller, i.e. the CPU in
Figure 6.32, will generate a series of synchronous signals SYA, SYB and SYC (Note thatthey are corresponding to rotor-position signals CPA, CPB and CPC, respectively),according to the rotation direction. Then the synchronous signals are compiled to generatethe trigger signals for the inverter. The frequency of the synchronous signal is increasedgradually, while the BLDC motor operates at separate control mode. When the motor runsat a low speed, the back-EMF is small so that the duty cycle of the inverter is also small.Then, the duty cycle of the inverter increases with the speed up. Hence, the normal
operation of the BLDC motor is ensured. By speeding up with the separate control method,
the BLDC motor may run in an unstable state. Thus, it is necessary to design a properacceleration curve. Note that the zero-crossing signal of the back-EMF should be strongenough for checking when the motor speeds up to the desired velocity. Meanwhile, themotor shifts to the back-EMF-based sensorless control mode.
The three-step starting method is easily inﬂuenced by many factors, such as load
torque, applied voltage, acceleration curve, moment of inertia, and so on. Under thecondition of small load or low inertia, the three-step starting method can usually be
implemented into practice. But it is easy to be unstable in the shifting stage, especiallyRotor Position
DetectionEncoder
Phase
Determination
Rotational Speed
Measurement
CPUSYA
SYB
SYC PWMSwitch CommandSIA
SIB
SICSignal Selection Circuit
CPA
CPB
CPC
Terminal Volta ge
Protection Signal
Synchronous
Signal Inverter Driving Signal
Figure 6.32 Principle diagram of three-step starting method.202 Permanent Magnet Brushless DC Motor Drives and Controls

when the motor has a heavy load. In this condition, the motor may fall out of step and
consequently fail in starting. Note that the motor parameters and load have a great inﬂuence
on the optimal acceleration curve during starting.
2) Prelocation starting method
During starting, two desired phase windings of motor are injected into the current and the
motor rotates to the corresponding position. Then, commutation is achieved by changingthe conduction condition of motor windings in turns. At each commutation procedure, it isnecessary to detect the zero-crossing point of the back-EMF for the nonexcited phase, andraise the applied voltage of motor by increasing the PWM duty cycle. When the zero-crossing points of the back-EMF can be reliably detected in Ntimes continuously, the
BLDC motor is switched to the back-EMF-based sensorless control mode.
The prelocation starting method has advantages like reliable starting up and easy
implementation. It can ensure the motor start at standstill and shift to sensorless controlsuccessfully under any initial rotor position. But this method needs an accurate shiftingtime. When the motor has different moments of inertia or starts up with varied load, it isnecessary to modify the prelocation and starting parameters so that the motor runsnormally.
3) Raising-frequency and raising-voltage synchronous starting method
The raising-frequency and raising-voltage synchronous starting method is usually achievedby hardware circuits. Figure 6.33 shows the basic principle diagram.
As shown in Figure 6.33, after the circuit is connected into the BLDC motor drivers, the
capacitor voltage U
C, which is added to the input of the voltage-controlled oscillator,
increases slowly. The output of the voltage-controlled oscillator, presented as a clock signalafter frequency division, is added to the ring-like distributor, whose outputs are trans-formed to commutation signals to control the power switches. Meanwhile, U
Cis added to
the input of PWM circuits to modify the duty cycle of PWM (i.e. to control the windings
voltage). So, the voltage and frequency added to the windings all rise with the increasing of
VCO DividerRing
Distributor
PWM Circuit
ComparatorDuty Cycle Signal
Switch SignalCommutation SignalR 1
R 2R 3
R 4CVcc
V ccUC
Figure 6.33 Principle diagram of the raising-frequency and raising-voltage synchronous
starting method.Sensorless Control for BLDC Motor Drives 203

UC, and the motor operates under the raising-voltage and raising-frequency mode. Further,
comparing UCwith the designed threshold value, and when UCis equal to the threshold, the
motor should be shifted to the sensorless control mode by a related logic circuit.
At a certain frequency and speed, the BLDC motor can start reliably under no-load,
half-load and other desired load conditions by the raising-frequency and raising-voltage
synchronous starting method, while the disadvantages of this method are that the designof such a starting circuit must consider motor parameters and the starting current needs tobe large.
4) Voltage interpolation starting method
(1) Starting principle
Suppose the acceleration torque is constant, we can obtain the time required for onerevolution of the motor as
t¼2ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
JpP
iTis
ð6:88Ț
whereP
iTi¼Te/C0BVO/C0TL.
As shown in Equation (6.88), if the load torque TLand the damping torque BvOare
assumed to be constant, the motor starting time has a direct relationship with theelectromagnetic torque T
e. However, Teis determined by the bus voltage U. Thus, the
DC bus voltage Udetermines the instant of phase commutation Q. So, by sampling the
DC bus voltage as well as the corresponding phase commutation instant, we can useinterpolation methods to simulate the relationship between UandQ. Then, the phase
commutation instant for BLDC motor drives is determined by the ﬁtting function.Figure 6.34 shows the ﬁtting curve in this condition.
(2) Starting process
Figure 6.35 shows the principle diagram for BLDC motor starting.As shown in Figure 6.35, the voltage interpolation starting method consists of thefollowing three stages.Stage 1: Prelocation, i.e. outputting certain two-phase conduction signals to make
the motor rotate to the corresponding position, and waiting the starting signals tobe determined.
Stage 2: Phase commutation starting, i.e. getting the phase commutation instant of
the motor by interpolation calculation and producing corresponding conductionsignals for the power switch by using effective values of DC bus voltage (or thePWM duty cycle).
Stage 3: End of starting, i.e. jumping out of the starting program and operating in
back-EMF-based sensorless control mode.
Figure 6.36 shows the waveforms of the starting signal (curve 1), actual measured Hall
signals H
A(curve 2), HB(curve 3) and HC(curve 4), and the speed modulation
signal (curve 5) when the BLDC motor starts with the voltage interpolation method
at no load.
In contrast with the traditional starting m ethods, those depending on experiences,
the main advantage of the voltage interpola tion starting method is that no extra starting
circuit is required for the sensorless control of BLDC motors.204 Permanent Magnet Brushless DC Motor Drives and Controls

0 10 20 30 40 50 60 70
Bus volta ge U /VQ2
Q1Q4
Q3Q6
Q5
51015202545
40
3035
0Commutation instant Q/msSample points
Fitting curves
Figure 6.34 Curve for the ﬁtting function between UandQ.
Rotor pre-location
Calculate effective values of
bus voltage
Running a round?Determine the interval of interpolation and get the
corresponding coefﬁcients
YNCalculate the
commutation instants
ENDENDCommutation and startRotor pre-location
Figure 6.35 Principle diagram for a BLDC motor starting based on voltage interpolation.Sensorless Control for BLDC Motor Drives 205

Questions
1. Explain how the BLDC motor runs based on the sensorless control with back-EMF-based
method.
2. Try to design an intelligent-based method for sensorless control of BLDC motor with your
own knowledge.
3. Give some starting methods for the sensorless control of a BLDC motor.
References
1. Xia, C. L., Yang, X. J., Shi, T. N. (2002) Position sensorless control of brushless DC motor based on the
disturbance observer”. Transactions of China Electrotechnical Society ,17(6), 25–28 (in Chinese).
2. Tomita, M., Senjyu, T., Doki, S., et al. (1998) New sensorless control for brushless DC motors using disturbance
observers and adaptive velocity estimations. IEEE Transactions on Industrial Electronics ,45(2), 274–282.
3. Yang, X. J. Sensorless control for brushless DC motor. Tianjin: Tianjin University Master Thesis, 2002 (in
Chinese).
4. Chen, W., Xia, C. L. (2006) Sensorless control of brushless DC motor based on fuzzy logic . IEEE Proceedings of
the World Congress on Intelligent Control and Automation, China, 6, 6298–6302 (in Chinese).
5. Terzic, B., Jadric, M. (2001) Design and implementation of the extended Kalman ﬁlter for the speed and rotor
position estimation of brushless DC motor. IEEE Transactions on Industrial Electronics ,48(6), 1065–1073.
6. Chen, Wei. Study on torque ripple suppression technique of permanent magnet brushless DC motor. Tianjin:
Tianjin University PhD Thesis, 2006 (in Chinese).
7. Shi, T. N., Lu, N., Zhang, Q., et al. (2008) Brushless DC motor sliding mode control with Kalman ﬁlter. IEEE
International Conference on Industrial Technology ,4, 1–6.
8. Lu, N. Sensorless control for BLDCM using an adaptive sliding mode observer. Tianjin: Tianjin University Master
Thesis, 2008 (in Chinese).
Figure 6.36 Experimental waveforms at starting.206 Permanent Magnet Brushless DC Motor Drives and Controls

9. Tian, Y., Shi, T. N., Xia, C. L. (2007) Position sensorless control using adaptive wavelet neural network for PM
BLDCM. IEEE International Symposium on Industrial Electronics , 2848–2852.
10. Shi, T. N., Tian, Y., Xia, C. L. (2007) Direct control of voltage based on adaptive wavelet neural network for PM
brushless DC motors. Transactions of China Electrotechnical Society ,22(9), 74–79 (in Chinese).
11. Shi, T. N., Tian, Y., Xia, C. L. (2007) Position sensorless control based on wavelet neural network for PM brushless
DC motors. Journal of Tianjin University ,40(2), 190–194 (in Chinese).
12. EI-Sharkawei, M. A., EI-Samahy, A. A., EI-Sayed, M. I. (1994) High performance drive of DC brushless motors
using neural network. IEEE Transaction on Energy conversion ,9(2), 317–322.
13. Tian, Y. Position sensorless control based on wavelet neural network for PM brushless DC motors. Tianjin: Tianjin
University Master Thesis, 2007 (in Chinese).
14. Shen, J. X., Lu, X. C. (1988) Detail analyses of 3-step start for LBLDC motor. Small & Special Machines ,26(5),
8–11 (in Chinese).
15. Liu, M. j., Wang, Q. (1999) The start method by means of rotor pre-setting for the brushless DC motor of electro-
motive force commutation. Small & Special Machines ,27(2), 8–10 (in Chinese).
16. Zou, J. B., Zhang, Y., Li, Z. Z. (1999) A driving circuit for sensorless brushless DC motor. Micromotors Servo
Technique ,32(2), 16–18, 47 (in Chinese).
17. Wu, S. G. Research on sensorless of brushless DC motor starting. Tianjin: Tianjin University Master Thesis, 2008
(in Chinese).Sensorless Control for BLDC Motor Drives 207

7
Realization of BLDC Motor Drives
Generally, a BLDC motor control system consists of two parts: hardware and software.
The hardware part is made up of a main circuit, a driving circuit, a microprocessor controlcircuit and a protecting circuit. The software part includes the main program, a timing interruptservice subroutine, and so on. This chapter will analyze the above contents, combining withengineering practices and speciﬁc design examples, and introduce some antidisturbance
methods for hardware and software design of motor control systems.
7.1 Main Circuit
Figure 7.1 shows the hardware system block diagram of a BLDC motor with position sensors.
Its main circuit is mainly made up of AC power, a bridge rectiﬁer and a bridge inverter.The input AC current is ﬁrstly rectiﬁed to DC current, and then transformed by a bridgeinverter it is used to drive the BLDC motor.
A single-phase or three-phase AC power supply can be used depending on different system
requirements and applications. Regarding a single-phase AC power supply, the commonlyused rectiﬁer circuits are showed in Figures 7.2(a)–(c), which are a full-bridge rectiﬁer circuit,
a half-bridge rectiﬁer circuit and a voltage-doubling bridge rectiﬁer circuit, respectively.
Practically, a boost rectiﬁer circuit shown in Figure 7.2(d) can be used to raise the DC voltageto meet the system’s requirements if the above rectiﬁed voltages are still too low to drive theBLDC motor.
Besides, a three-phase AC power supply can be used in BLDC motor control systems.
Consequently, a three-phase bridge rectiﬁer circuit is applied, which has the advantages ofsimple connection and good performance, such as the 6RI100G series of Fuji Corporation andthe SKD100 series of Semikron Corporation.
Bridge inverters, shown in Figure 7.3, usually have three phases and are formed by six
MOSFETs or IGBTs. Diodes D1–D6 noted in the ﬁgure are called feedback diodes in that theycan work as the passages that feedback the energy from the motor to the DC bus. Meanwhile,they are also called freewheeling diodes for their function of freewheeling the motor current.Beside the freewheeling diode, there is absorber circuit formed by a resistance, a capacitance
Permanent Magnet Brushless DC Motor Drives and Controls , First Edition. Chang-liang Xia.
/C2112012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd.

and another diode, which performs the function of suppressing the overvoltage and decreasing
the turn-off switching losses of the corresponding power switches [1].
Inverter circuits based on four-switch technique shown in Figure 7.4 are proposed in some
systems. They have great advantages of fewer power switches, lower costs and smaller
switching losses, but a more complex algorithm to generate control signals for power switchesand higher-performance requirements for microprocessors are demanded.
L
(b) Half-bridge rectiﬁer circuit
(d) Boost rectiﬁer circuit(a) Full-bridge rectiﬁer circuit
i
(c) Volta ge-doublin g rectiﬁer circuituu u
ui i
i+
Ud
+
Ud+
Ud+
UdL
LL
Figure 7.2 Common rectiﬁer circuits.A/DAC power
Rectiﬁer
InverterCurrent sampling
Voltage samplingSignal regulating
Signal regulating A/DMicroprocessor
PWM signal generator Drive circuit
Hall position
sensorLevel conversionRotor position
signalSignal capture unit
BLDC motor
Figure 7.1 Hardware block diagram of a BLDC motor.210 Permanent Magnet Brushless DC Motor Drives and Controls

For some low-capacity motor control systems, inverters constructed by MOSFET cannot
only meet the requirements of control system but also save costs. IRF530N, the ﬁfth-
generation MOSFET product of IR Corporation, is one of the commonly used MOSFETproducts and has an advanced manufacturing technology. Moreover it can drive a low-capacitymotor effectively for its small impedance and fast switching speed. Its drain breakdown
voltage is 100 V, the maximum drain current is 17 A under conduction conditions, and its delay
time of switching on and off is only tens of nanoseconds.
An IGBT inverter is widely used in high-capacity motor control systems. Its architecture is
essentially similar to that of a MOSFET, except that an additional P layer has been addedbetween the drain pole and the drain areas. The naming of its parts is similar to MOSFET.The device, combining the merits of a MOSFET and a GTR, has the advantages of highinput impedance, rapid response ability, good thermal stability, simple driving circuit, lowconduction voltage drop and good ability to withstand high voltage. So it is applied extensively
in some high-capacity motor control systems.
T3
BA
CUd
T2T1
T4Cd+
_C1
C2iCiA
iB BLDC
Motor
Figure 7.4 Inverter circuit based on four-switching technique.Ud+
−T1 D1 D3 D5
D4 D6 D2T3 T5
T4 T6 T2BLDC
Motor
Figure 7.3 Three-phase bridge inverter circuit.Realization of BLDC Motor Drives 211

FGA25N120 produced by Fairchild Corporation is one of thewidely used devices of IGBT. Its
maximum drain breakdownvoltage is 1200 V , the maximum drain current in conducting mode is
25 A, the turn-on delaying time is 50 ns, the turn-off delaying time is 190 ns, and the cost of the
device is low. Hence, it can readily meet the requirements of high-capacity motor controlsystems. As for some higher-capacity motor control systems, the device 1MBI200S-120 of FujiCorporation can be used since the maximum drain breakdown voltage that the device canwithstand is 1200 V, and the maximum drain current in conduction is 200 A.
7.2 Driving Circuit
7.2.1 MOSFET Driving Circuit
The MOSFET driving circuit can be constituted by discrete components as well as the special
drivers that have a simple circuit, high reliability and wide application. Among the variousdrive devices, IR2110 and IR2130 are widely used.
Driver IR2110, manufactured by IR Corporation, uses HVIC and latch-immunity CMOS
production techniques and outputs two drive signals. In IR2110, there is an upper-legsuspended bootstrap circuit that can greatly reduce the number of conventional drive
power supplies. Moreover, only one drive power supply is enough for three-phase bridge
inverter circuit.
IR2110 mainly consists of logical input, voltage translation and output protection. Its
operating voltage can be as high as 500 V, the range of grid drive voltage is ț10 toț20 V, and
the range of logical power voltage is ț3.3 to ț15 V. The above characteristics make it easy to
match the TTL and CMOS voltage level and IR2110 is extensively applied in small- andmedium-power driving circuits for its small volume and high speed. Figure 7.5 shows a drivingcircuit constituted by three IR2110. V
cc1andVcc2shown in Figure 7.5 are logical power and
drive power, respectively. They are isolated from each other in order to improve the reliabilityand safety of the circuit.
It is necessary to consider the following problems during the use of IR2110 [2].
(1) Reverse withstand voltage of power supply diodes must be higher than the operating peak
voltage of the driven MOSFET since the upper-leg driver supply in IR2110 is obtained bybootstrap techniques. Also, it is necessary to choose a fast recovery diode to prevent thetwo ends of the bootstrap capacitor from discharging.
(2) The volume of the upper-leg bootstrap capacitor, which is generally 1 mF (disk capacitor),
depends on the switching frequency of the driven power switch, the duty cycle and therequirements of the grid drive current.
(3) In three-phase bridge driving circuits for a BLDC motor, the bootstrap capacitor may
discharge due to the different voltage of VS pins on IR2110, which makes the upper-legpower switch not work when the control signal is effective and the underleg power switchis still in the operating condition. In order to avoid such a situation, the underleg powerswitch is conducted in advance to charge the bootstrap capacitor through logic control, or a
larger bootstrap capacitor should be chosen.
(4) In three-phase bridge driving circuits for BLDC motors, the insulation between high-
voltage bus and logic circuit is ensured by an antibias junction in IR2110. Serious
consequences will be caused if any junction in the structure is breakdown. So, optocouplers212 Permanent Magnet Brushless DC Motor Drives and Controls

or pulse transformers could be applied to isolate the logic circuit from IR2110 to avoid
such problems.
(5) Due to the low output impedance of the drive device in IR2110, it will cause fast turn-on
and turn-off of the devices and may lead to oscillation between the drain pole and thesource pole in the MOSFET if IR2110 is used to drive MOSFETappliances directly. Also,not only will RF interference be caused, but also the device may be in breakdown for highratio of d v/dtunder such conditions. To prevent this happening, a large resistance without
inductance whose value is about 100 Ocan be connected between the grid of MOSFETand
the output of IR2110.
IR2130, produced by IR Corporation, is a three-phase bridge driver with high performance.
It has only one drive power supply which is similar to IR2110. However, it can output six drivesignals, which makes system design easier. In addition, IR2130’s protective function is betterdesigned to make the circuit more reliable.
IR2130 can be used in circuits with the voltage not higher than 600 V, and its output upper-
leg and under-leg drive current peak values are 250 mA and 500 mA, respectively. Integrated inIR2130 are a current comparator, a current ampliﬁer, an under voltage monitor for its ownoperating power supply, an error-processing unit, a clearing blocked logic unit, three input
PWM1_IN
PWM4_IN
LO1COM2VCC3
NC4VS5VB6HO7
NC8VDD9
HIN10
SD11
LIN12
VSS13NC14U
IR2110Vcc1
PWM3_IN
PWM6_IN
LO1COM2VCC3
NC4VS5VB6HO7
NC8VDD9
HIN10
SD11
LIN12
VSS13NC14U
IR2110
PWM5_IN
PWM2_IN
LO1COM2VCC3
NC4VS5VB6HO7
NC8VDD9
HIN10
SD11
LIN12
VSS13NC14U
IR2110A
BCdU
1D 3D
4D 6D5T
2T3T
6T1T
4T1
2
35D
2DVcc1Vcc2
Vcc2
Vcc1 Vcc2
Figure 7.5 IR2110 driving circuit.Realization of BLDC Motor Drives 213

signal processors, three pulse-processing and level-shifting devices, three driving signal
latches for upper-leg power switches, three undervoltage monitors for upper-leg power switch
driving signals, six MOSFET drivers with low output impedance and an OR gate circuit.
In BLDC motor drive systems, six PWM pulse signals produced by a microprocessor serve
as six inputs of IR2130, three of them are used to drive the upper-leg and the other three signals
are applied to drive the under-leg. The three signals to drive under-leg power switches areinjected into control poles after ampliﬁcation. The other three signals to drive the upper-leg areinitially handled by a pulse processor and bootstrap circuit of a level shifter to maintain leveldisplacement and turned into three voltage-suspended drive pulse signals. Then, they arelatched through the corresponding three output latch devices and checked by strict driving
pulses. Lastly, the three signals are applied to control poles of the driven upper-leg power
switches after power ampliﬁcation.
IR2130 has the functions of overcurrent protection and undervoltage protection. When the
output voltage of the current detecting unit is higher than 0.5 V, the phenomenon of overcurrentor direct conduction in the circuit appears. In this condition, the current comparator in IR2130will reverse quickly, and the logic fault processing unit and
FAULT pin output low level
voltage and fault indications, respectively. Meanwhile, the six output drive signals are all lowlevel and power switches are all at the off state for protection. The undervoltage detector has a
similar operating process. When fault indication is low all the time and the circuit has no
output, it is generally in undervoltage protection mode. When fault indication oscillatesbetween high and low levels, and the circuit has output or not from time to time, it is inovercurrent protection mode. It is not until the clearance of the fault and input high-levelsignals into
LIN1– LIN3 at the same time that the fault latch state could be eliminated and the
devices operate in the normal state again. In addition, IR2130 has a logic protective function.When the two input drive signals into one leg are all effective, the corresponding two drivesignals output by IR2130 are low level, resulting in latching of this bridge leg [3]. Figure 7.6
shows the driving circuit of IR2130.
A
B
CUd
D1D3
D4D6T5
T2T3
T6T1
T4D5
D2+15V
PWM1_IN
PWM3_IN
PWM5_IN
PWM4_IN
PWM6_IN
PWM2_IN
CAO
LO314ITRIP9
VS318VB320
HO319FAULT8VCC1
HIN12
HIN23
HIN34
CAO10LIN15
LIN26
LIN37
CA-11
VSS12
VS013LO215LO116NC17VS222VB224
HO223
NC21VS126VB128
HO127
NC25U
IR21301
Figure 7.6 IR2130 driving circuit.214 Permanent Magnet Brushless DC Motor Drives and Controls

7.2.2 IGBT Driving Circuit
Similar to MOSFETs, an IGBT driving circuit can be constructed not only by discrete
components but also by integrated IGBT drivers that have better performance, smaller volumeand higher reliability. Among various IGBT drivers, EXB series drivers produced by FujiCorporation are widely used, among which EXB841 is one kind of high-speed driver.
EXB841 can drive an IGBT circuit with the current and voltage level of 400 A, 600 V or
300 A, 1200 V. It can be applied extensively to the 40 kHz switching operation as its delay timeof driving circuit signal is less than 1 ms. Figure 7.7 shows a typical application circuit of
EXB841, and the following aspects should be remembered when using EXB841 [4].
(1) The driving circuit wire between the grid pole and the source pole of IGBT should be
stranded wire and its length should be less than 1 m.
(2) The value of grid series resistance R
Gshould be increased if a high-voltage peak pulse is
engendered in the drain pole of the IGBT.
(3) The function of C 1and C 2is to absorb voltage changes aroused by power supply-line
impedance, instead of ﬁltering.
(4) The input and output circuits should be far isolated in space under high operating voltage,
though they are separated by an optocoupler.
7.2.3 Intelligent Power Module (IPM)
An intelligent power module (IPM) can be used as driving circuit to improve the reliability of a
bridge inverter. The IPM, a kind of modularized device, is integrated by the IGBT and circuitsthat have the functions of signal processing, self-protection and diagnosis. It can perform thefunctions of inverter circuits, driving circuits and other control circuits for a BLDC motor,
PWM1+5 V+20 V
+5 VBH1+20 VIN+15
IN-14OC
5OCC
4VSS9S1G3VCC2
D6
NC7
NC8
NC10
NC11
NC12
NC13U
EXB84147 uF 47 uF1
T11D
1C2CGR
A
U2
TLP521-1dU
Figure 7.7 EXB841 applied circuit.Realization of BLDC Motor Drives 215

which gives the motor controller the advantages of small volume, light weight, simple design
and high reliability. Therefore, an IPM is one of the ideal devices for high-performance BLDC
motor driving.
Many companies produce IPMs. For example, Fuji Corporation has already manufactured
complete IPM series products that have two voltage levels of 600 V and 1200 V and more
current speciﬁcations from dozens to hundreds of amperes. Among them, 7MBP75RJ120, is amedium-volume IPM, with its withstanding voltage and ﬂowing current as high as 1200 Vand75 A, respectively. Its principle terminal is screw M5. All electrical connections are screws andconnectors without soldering, which is easy to assemble and disassemble. Furthermore,overheat protection is designed in the module, which makes it very easy to use. Its typical
application circuit is shown in Figure 7.8
7.3 Rotor-Position Sensor Circuit
In the control system of a BLDC motor with position sensors, in order to get the maximum
torque, microprocessor controls the BLDC motor to commutate depending on the signals ofthe position sensors. Torque ripple can be reduced by the proper commutation instantsobtained from the position-sensor signals. Therefore, accurate position detection is very
important [5,6].
Position sensors in BLDC motors are used to detect the relative position of the rotor magnet
and provide the correct commutation information for the logic switching circuit, namely
transforming the position signals of rotor magnet to electric signals and then making statorwindings commutate properly. The commonly used position sensors mainly fall into elec-tromagnetic, photoelectric and magnetic types. A Hall position sensor, as one kind ofmagnetic-type sensors, is applied extensively for its simple structure and low cost.
A Hall position sensor, shown in Figure 7.9, is constituted by a Hall integrated circuit
ﬁxed on stator and sensor rotor ﬁxed on the main rotor in most BLDC motors. The sensorindicates the main rotor’s position since its rotor is rotating with the motor rotorsynchronously. Several Hall integrated circuits are ﬁxed on the motor’s stator at equalintervals and the sensor will produce a group of jumping signals when the main rotor passesby a pair of magnets. The more pole pairs of the main rotor, the more jumping signals aregenerated within 360
/C14mechanical angles. In an electrical cycle, a Hall position sensor
generates different switching states that have equal electrical angle from one to another.Take the three Hall position sensors with intervals of 120
/C14electrical angles in space for
example, each Hall position sensor will generate an output signal with 180/C14electrical angles
pulse width during every electrical cycle. As a result, the three output signals generated bythe three Hall position sensors are at 120
/C14electrical angle intervals, which will produce
three rising edges and three falling edges, corresponding to six commutation instants. Notethat position detection is not only used for commutation but also applied in velocityfeedback control.
Rotor position feedback signals, whose electrical level and jumping instants determine the
commutation state and instant of the motor, are fed into the corresponding input interface of
the microprocessor. As shown in Figure 7.10, the output signals H
A,HBandHCof a Hall
position sensor are processed through fast optocoupler isolation, then H0AH0BandH0Care
obtained after rectifying and capacitor ﬁltering to remove high-frequency interference, after
which they are input into the microprocessor for calculation.216 Permanent Magnet Brushless DC Motor Drives and Controls

GND U1VCC U4
Vin U3
ALM U2
GND V5VCC V8
Vin V7
ALM V6
GND W9VCC W12
Vin W11
ALM W10
GND13VCC14
Vin X16
ALM19Vin Y17
Vin Z18
Vin DB15
NP
BU
V
WU
7MBP75RJ1202
37
68 1
4 5U
HCPL-4504
U
TLP521-1V +5
V +5GND12
3
2
37
68 1
4 5U
HCPL-4504
U
TLP521-1V +5
GND24
5
2
37
68 1
4 5U
HCPL-4504
U
TLP521-1V +5
GND36
72
37
68 1
4 5U
HCPL-4504V +5
GND48
2
37
68 1
4 5U
HCPL-4504V +5
GND49
2
37
68 1
4 5U
HCPL-4504V +5
GND410
2
37
68 1
4 5U
HCPL-4504V +5
GND411
U
TLP521-112PWM1
ALMU
GND4dUA
B
CPWM3PWM4
PWM5PWM6
PWM2
DB
ALMALMV
ALMW1
V +5
V +5
V +5Vcc4 Vcc1
Vcc4
Vcc2
Vcc4
Vcc4
Vcc4Vcc3
Vcc4
Figure 7.8 7MBP75RJ120 applied circuit.

7.4 Microprocessor Control Circuit
7.4.1 Introduction
A microprocessor control circuit mainly consists of a microprocessor, interface circuits and
peripheral components. The microprocessor is the core component of the whole circuit. It canprocess the input data, complete various complex algorithms, send the control signals to thedriving circuit through the output port, send calculated results to peripheral components,
accept instruction from peripherals and act accordingly. So, proper selection of the micro-
processor is very important for normal operation of the whole circuit and the desired controlperformance [7].
It is necessary to conﬁrm the technique requirements of a BLDC motor control system at the
microprocessor choosing stage. The technique requirements mainly include functions that thesystem needs and performances that the system would obtain. Speciﬁcally, the requirementsconsist of the control strategy, structure, various control tasks, response time and steady-stateaccuracy of the control system, etc. Then, it is desired to make a comprehensive consideration ofMotor rotor
Bearing
Hall integrated
circuitMotor statorN N SSSensor roto r
Sensor stator
Figure 7.9 The structure of a Hall position sensor.
NOTVcc2
HA'
HB'
HC'HA
HB
HCVcc1U1
U2
U3
Figure 7.10 Rotor-position detecting circuit.218 Permanent Magnet Brushless DC Motor Drives and Controls

the microprocessor types. On the one hand, a microprocessor with much too high performance
should not be chosen since it would lead to increased complexity, higher cost and performance
waste. On the other hand, a microprocessor with much too low a performance should not be
chosen, or the technique requirements of the system may not be satisﬁed. In summary, thefollowing six aspects should be considered when choosing the microprocessor.
(1) Whether the microprocessor instruction set is abundant and whether it is easy enough to
achieve the algorithm of the system should be noted. Meanwhile, it shouldn’t be difﬁcult
to memorize and program, and confusion can be easily avoided.
(2) Whether the rated frequency and the operation speed can satisfy the requirements of the
BLDC motor control system.
(3) Whether the on chip source of the microprocessor is sufﬁcient, where the source mainly
covers the extensible memory space, the number of I/O ports, electrical level compatiblestandards, the channels and digits of A/D and D/A circuits.
(4) Whether the power dissipation, volume and working temperature of microprocessor can
meet the requirements of the system.
(5) Whether different business grade and industrial grade of the same type of microprocessor
can be compatible in packaging.
(6) The time to market, reliability, product volume and price of the microprocessor.
Generally, the performance of the selected microprocessor should be a little higher than the
system requirements, consequently hardware performance can be used to compensate part ofthe software functions to a certain extent, and make the system extensible and updatable in thefuture.
At present, the microprocessor suitable for a BLDC motor control system falls into mainly
microcontroller unit (MCU) and digital signal processor (DSP).
A MCU, which has the characteristics of high integrated level, powerful functions,
reasonable structure, rich instructions, large memory capacity, fast speed and strong anti-disturbance ability, is a chip integrated with CPU, ROM, RAM, I/O port and programmabletimer/counter, some even include an A/D converter. Now, Inter, Motorola, TI and othercorporations have had their own series MCU that are widely used in industrial control systems.For some motor control systems with a relatively simple control algorithm, a MCU is aneconomical choice.
A DSP chip is a microprocessor that is especially applied to digital signal processing. Its
main application is to achieve various kinds of digital signal processing timely and fast. Atpresent, the major DSP chip suppliers are TI, AD and Motorola, etc. Among them, TICorporation, which accounts for the biggest shares of DSP chip market in the world, hasmultiple series and a rich variety of DSP chips. According to the requirements of digital signalprocessing, DSP chips generally have the following characteristics.
(1) Harvard architecture with separated data bus from the program bus is widely used, which
has faster instruction execution speed comparing to the traditional Von Neumann
architecture.
(2) Assembly-line operation is mostly used to make the fetch, decoding and execution parallel
operation and to reduce the execution time of every instruction without increasing the
clock frequency.Realization of BLDC Motor Drives 219

(3) There are multiple on-chip buses, so that multiple operations can be executed in parallel.
(4) Independent multiplier and adder are equipped in a DSP, which make it easy to ﬁnish a
multiply and plus calculation within one clock cycle and to achieve ﬁlter and matrixoperation that need a large number of multiply-accumulate operations at faster speed.
(5) Direct memory access (DMA) controllers are mostly equipped with the on-chip multibus
architecture, which makes the transmission speed of the data block greatly improved.
(6) Hardware supports low overhead or zero overhead loop and jump.(7) Fast interrupt processor and timing controller are integrated in DSP, which makes it
convenient to construct a small-scale system.
Compared to universal microprocessor, DSP chip has relatively poor abilities of the
controlling and processing multitransactions. However, DSP chips produced in recentyears have absorbed some general microprocessor functions. Due to the above characteristics,DSP chips are widely applied in high-speed and high-accuracy motor control systems.
7.4.2 MCU Control Circuit
Among the series of microcontroller units, MSP430F1xx series from TI Corporation is a kindof ultra-low-power mixed-signal controller that can operate in an ultralow-power state underlow-voltage conditions. There are multiple kinds of MCU of this series available, which areextensively used in BLDC motor control systems, to be selected to meet the requirements ofdifferent users. The MCU of this series has 16-bit RISC structure and it can obtain high codeefﬁciency by using 16 registers and a constant generator in CPU. The power dissipation of thedevices can be minimized by selecting proper clock sources to meet the requirements of agiven battery power-supply system. When the device operates in low-power dissipation mode,
it can be woken rapidly by a digitally controlled oscillator (DCO). The wake-up time is less
than 6 ms and then the device is switched to activation mode. The MSP430F149 is introduced
to illustrate the BLDC motor control system based on a MCU as follows.
MSP430F149 mainly consists of one basic clock module that is constructed by one DCO
and two crystal oscillators, one watchdog timer, two 16-bit comparators with capture/compareregister, two 8-bit parallel I/O ports with interrupt function, four general 8-bit parallel I/Oports, one analog comparator, one 12-bit A/D converter, two serial communication ports withasynchronous, synchronous and SPI operation modes and one hardware multiplier.
MSP430F149 has advantages depicted as follows: rich addressing ways with only 27
instructions, which make it easy to remember, large number of inner registers, which canachieve multiple operations, look-up table approach processing methods with high efﬁciency,many interrupt sources, which can be nested arbitrarily and used ﬂexibly. All these char-acteristics ensure that a motor control program with high efﬁciency can be worked out.
Figure 7.11 shows the hardware circuit princi ple diagram of a BLDC motor sensor control
system based on MSP430F149. Port P1 of a MCU contains a capture unit that is used tocapture the rotor-position signal output by a Hall position sensor. Port P4 can generate PWM
waves to drive the bridge inverter. System fa ult signals are input into port P2 as interrupt
signals. Port P3 is used to communicate with PC. Port P5 is used to accept keyboard
instruction that leads the control program to act correspondingly. The function of each part isintroduced in detail as follows.220 Permanent Magnet Brushless DC Motor Drives and Controls

7.4.2.1 Commutation Control
The windings of a BLDC motor are usually Y connected and the two-phase conduction mode
is generally used. That means each conducting cycle has six conduction states. One state ischanged as the rotor rotates 60
/C14electrical angles. A MCU writes continuously the corre-
sponding control words to port P4 based on the output signals of position sensors to completecommutation operation. If MOSFETs in a bridge inverter are arranged as the sequence ofFigure 7.3 and the ports P4.1–P4.6 correspond to the grid control signals of T1–T6, the controlwords under the two-phase conduction mode could be as expressed in Table 7.1. Note that thecontrol words of port P4.0 and P4.7 are always zero.
7.4.2.2 Steering Control
Reverse rotation of a BLDC motor can be achieved by only changing the conducting
sequences of MOSFETs according to certain laws. The control words of reverse rotation
are shown in Table 7.2.AC power
Rectiﬁer
InverterMSP430F149
PWM signal generator
P4
Hall position
sensorLevel conversionRotor position signalSignal capture unit
P1 Drive
circuit
Fault interrupt
P2
Fault
signal Keyboard input
P5Keyboard
instructionUART communication
interface
P3Level conversionPC
BLDC motor
Figure 7.11 The hardware circuit principle diagram of a BLDC motor sensor control system based on
MSP430F149 MCU.
Table 7.1 Control words under two-phase conduction mode (forward)
Conduction phases P4.6 P4.5 P4.4 P4.3 P4.2 P4.1 Control words
A C 000011 0 6 H
B C 000110 0 C H
B A 001100 1 8 H
C A 011000 3 0 H
C B 110000 6 0 H
A B 100001 4 2 HRealization of BLDC Motor Drives 221

7.4.2.3 Capture Unit and PWM Wave Output Control
Capture unit interior to port P1 of MCU is used to detect the jumping edges of the Hall position
sensor input signals. The jumping edges can be the rising-edge, falling-edge or bi-edges. Once
the corresponding jumping edges are generated, the counting value is recorded and interrupt
signals are produced. Then, the rotor magnet position is instantly monitored, which greatlyreduces the system overhead.
Port P4 can be designed to run in PWM output mode, which is able to generate three-phase
symmetrical PWM waves by programming. Figure 7.12 shows the process of signals whenadding counting mode and set/reset output mode are used. Initially, the values of TBCL0 andTBCL1 are set, and then the signal generator begins to operate according to settings and thetimer starts to count. When the counting value is equal to TBCL1, the output is set depending
on the desired mode. However, when the counting value is equal to TBCL0, the output is reset
and the timer counts again and then PWM signals are formed in cycles.
7.4.2.4 Serial Communication Interface Circuit
MSP430F149 has two universal serial communication ports, but it cannot communicate with
the PC directly for their voltage levels do not match. Therefore, serial interface levelconversion chips are needed, among which MAX3232 produced by Maxim CorporationTable 7.2 Control words under the two-phase conduction mode (reverse)
Conduction phases P4.6 P4.5 P4.4 P4.3 P4.2 P4.1 Control words
A C 000011 0 6 H
A B 100001 4 2 H
C B 110000 6 0 H
C A 011000 3 0 H
B A 001100 1 8 H
B C 000110 0 C H
TBR (max)
TBCL0
TBCL1
0h
EQU0 EQU0 EQU0 EQU1 EQU1Output mode: set/rese t
Interrupt event
Figure 7.12 Adding counting-mode output example.222 Permanent Magnet Brushless DC Motor Drives and Controls

achieves preferable performance for its simple structure, low power loss, high integrated level,
and two receiving and sending channels without extra power supplies. Figure 7.13 is a typical
application of the chip.
7.4.3 DSP Control Circuit
Among the numerous DSP products, TI Corporation has the most abundant products. TheTMS320F240x and TMS320F281x series are widely applied in BLDC motor control systems.The BLDC motor control circuit based on TMS320F2812 is described as follows [8].
TMS320F2812, which has great signal processing and control functions, is produced by TI
Corporation and can supply a motor control system with a good platform. Its code andinstructions are completely compatible with those of TMS320F240x series DSP, whichensures the continuity of the project or product design. Compared to TMS320F240x series
DSP, TMS320F2812 improves the accuracy of calculation (32 bit) and the processing speed of
the system (150 MIPS).
TMS320F2812 mainly consists of one FLASH memory of 128k /C216 bit, one ROM
of 128k /C216 bit, one OTP ROM of 1k /C216 bit, two single-cycle access RAM (L0 and L1)
of 4k/C216 bit, one single-cycle access RAM (H0) of 8k /C216 bit, two single-cycle access RAM
(M0 and M1) of 1k /C216 bit, two event-manager modules, a variety of serial communication
interfaces, a high-speed and high-accuracy A/D converter module and a variety of conﬁg-urable universal I/O pins.
Figure 7.14 shows the hardware circuit block diagram of a BLDC motor sensorless control
system based on TMS320F2812. In this system, the rotor-position signal is detected by theback-EMF method, and double closed-loop speed-control system is constructed viaTMS320F2812. A DSP control system is similar to the corresponding MCU control system,R2INR1INT2OUTT1OUTV-V+
R2OUTR1OUTT2INT1INC2-C2+C1-C1+ C1
0.1 µF
C2
0.1 µFC4
0.1 µF
C5
0.1 µFC3
0.1 µF
MAX323216 1514
13 1211
10
8 976
5432 1+3.3V
TX2TX1
RX1
RX2+
+
++
+U11
6
2
73
8
4
9
5J1
16
2
7
3
8
4
9
5J2
Figure 7.13 MAX3232 serial communication interface circuit.Realization of BLDC Motor Drives 223

so they can refer to each other when being designed. Meanwhile, their different features should
also be noticed.
A BLDC motor control system based on TMS320F2812 DSP needs fewer external
components and has a high cost–performance ratio. The high-speed performance of a DSPis the basis of the implementation of real-time intelligent control strategies which largelyimproves the control accuracy, functions and anti-interference performance of the system.Figure 7.15 shows the application circuit.
7.5 Protecting Circuit
There are always abnormal conditions during the work of BLDC motor control system, whichmay cause great damage to the control circuit, driving circuit and the motor. So, proper
measures must be taken for protection. The common protection circuits contain an overvoltage
protection circuit, an overcurrent protection circuit and a logic protection circuit, etc. Thesecircuits are illustrated as follows.
7.5.1 Overvoltage Protection
The principle of overvoltage protection circuit can be explained as follows. The DC busvoltage could be obtained by the sampling circuits, which would be compared with thereference voltage. If the sampling value is greater, the comparator will output an overvoltage
protection signal to the microprocessor, and then the microprocessor can achieve the
overvoltage protection.
The DC bus voltage can be obtained in two ways. The ﬁrst method is to place a resistance
voltage divider on the DC bus, and transfer the measurement into the comparator. The outputAC power
Rectiﬁer
InverterTMS320F2812
PWM signal
generator
Comparison
of zeroDrive
circuit
Fault
interruption
Fault
signalReference
speedUART
Communica-
tion interfaceLevel conversionPC
phase-voltage
detectingSpeed
regulatorAD
samplingCurrent detecting
Current
regulator
−−
+ +
BLDC
motorSpeed
calculation Signal capture unit
Figure 7.14 Hardware circuit block diagram of BLDC motor control system based on TMS320F2812.224 Permanent Magnet Brushless DC Motor Drives and Controls

XA18158
XA17156
XA16152
XA15148
XA14144
XA13141
XA12138
XA11132
XA10130
XA9125
XA8121
XA7118
XA6111
XA5108
XA4103
XA385
XA280
XA143
XA018XD021XD124XD227XD330XD433XD536XD639XD754XD865XD968XD1073XD1174XD1296XD1397XD14139XD15147
XMP/MC17
XHOLD159
XHOLDA82
XZCS0AND144
XZCS288
XZCS6AND7133
XWE84
XRD42
XR/W51
XREADY161X1/XCLKIN77
X276
XCLKOUT119
TESTSEL134XRS160
TEST167
TEST266
TMS320F2812TRST135
TCK136
TMS126
TDI131
TDO127
EMU0137
EMU1146ADCINA0174ADCINA1173ADCINA2172ADCINA3171ADCINA4170ADCINA5169ADCINA6168ADCINA7167
ADCINB02ADCINB13ADCINB24ADCINB35ADCINB46ADCINB57ADCINB68ADCINB79
ADCREFP11
ADCREFM10
ADCRESEXT16
ADCBGREFIN164AVSSREFBG12AVDDREFBG13
ADCLO175VSSA115
VSSA2165VDDA114
VDDA2166
VSS1163VDD1162VDDAIO1VSSAIO176
TMS320F2812XMP/MC 10KR
14
23Y
33pFC8
0.1 uFC100R
S1
SW-PB10KR+3.3V
0.1 uFCAD1AD2AD3AD4AD5AD6AD7AD8
AD9AD10AD11AD12AD13AD14AD15AD16
1 2
3 4
5 6
7 8
9 10
11 12
13 14J1
JTAG10 KR
10 KRVDD (+3.3V)
10 KR
10KR
TMS
TDI
TDO
TCKTRST
EMU1 EMU0
TRST
TCK
TDITMS
TDO
EMU0
EMU110 uFC
10 uFC
24.9KR
+1.8V
0.1 uFC
0.1 uFC
1 uFC
1 uFC
0.1 uFCU 1BU
4 3 2 1
156
78
1
2345 6791 0
VDD (+3.3V)VDD (+3.3V)
VCC (+3.3V)
VCC (+3.3V)
(a) Debu gging interface and analo g interface 1A
Figure 7.15 TMS320F2812 application circuit.Realization of BLDC Motor Drives 225

V +1.8
uF 0.1C
uF 0.1C
0.1 uFC
uF 0.1C
uF 0.1C
0.1 uFC
uF 0.1C
uF0.1C
uF 0.1C+1.8 V
uF 0.1C
uF 0.1C
uF0.1C
uF0.1C
uF 0.1C
uF 0.1CuH 100 L
100 uH L0.1 uFC27
uF 10C26
GND1EN2IN13IN24
OUT25OUT16
PB7RST8U2
TPS7301uF 0.1C28+5 V
K 250R9
V +1.8
K 100R
250 KRuF 10C
GND1EN2IN13IN24
OUT25OUT16
SEN7RST8U
TPS3333uF 0.1C30V +5
250 KR12
10 uFC31DS
LampK 1R13V +5
DS
LampK 1R14
DS
LampK 1R15+1.8 VVDD23
VDD37
VDD56
VDD75
VDD100
VDD112
VDD128
VDD143
VDD154
VDDIO31
VDDIO64
VDDIO81
VDDIO114
VDDIO145
VDD3VFFL69VSS19
VSS32
VSS38
VSS52
VSS58
VSS70
VSS78
VSS86
VSS99
VSS105
VSS113
VSS120
VSS129
VSS142
VSS153
TMS320F2812W 1
Jumper1CU
3
10
113 2 11
211 19 18 17 16 15 14 13 12
25 24 23 22 21 20
29VDD (+3.3V)
VDD (+3.3V)VDD (+3.3V)VDD (+3.3V)
VCC (+3.3V)
VDD (+3.3V)
(b) Power-supply circuits
Figure 7.15 Continued .226 Permanent Magnet Brushless DC Motor Drives and Controls

GPIOA0/PWM192
GPIOA1/PWM293
GPIOA2/PWM394
GPIOA3/PWM495
GPIOA4/PWM598
GPIOA5/PWM6101
GPIOA6/T1PWM_T1CMP102
GPIOA7/T2PWM_T2CMP104
GPIOA8/CAP1_QEP1106
GPIOA9/CAP2_QEP2107
GPIOA10/CAP3_QEPI1109
GPIOA11/TDIRA116
GPIOA12/TCLKINA117
GPIOA13/C1TRIP122
GPIOA14/C2TRIP123
GPIOA15/C3TRIP124
GPIOB0/PWM745
GPIOB1/PWM846
GPIOB2/PWM947
GPIOB3/PWM1048
GPIOB4/PWM1149
GPIOB5/PWM1250
GPIOB6/T3PWM_T3CMP53
GPIOB7/T4PWM_T4CMP55
GPIOB8/CAP4_QEP357
GPIOB9/CAP5_QEP459
GPIOB10/CAP6_QEPI260
GPIOB11/TDIRB71
GPIOB12/TCLKINB72
GPIOB13/C4TRIP61
GPIOB14/C5TRIP62
GPIOB15/C6TRIP63GPIOD0/T1CTRIP_PDPINTA110
GPIOD5/T3CTRIP_PDPINTB79GPIOD1/T2CTRIP/EVASOC115
GPIOD6/T4CTRIP/EVBSOC83
GPIOE0/XINT1_XBIO149
GPIOE1/XINT2_ADCSOC151
GPIOE2/XNMI_XINT13150
GPIOF0/SPISIMOA40
GPIOF1/SPISOMIA41
GPIOF2/SPICLKA34
GPIOF3/SPISTEA35
GPIOF4/SCITXDA155
GPIOF5/SCIRXDA157
GPIOF6/CANTXA87
GPIOF7/CANRXA89
GPIOF8/MCLKXA28
GPIOF9/MCLKRA25
GPIOF10/MFSXA26
GPIOF11/MFSRA29
GPIOF12/MDXA22
GPIOF13/MDRA20
GPIOF14/XF_XPLLDIS140
GPIOG4/SCITXDB90
GPIOG5/SCIRXDB91
TMS320F2812PWM1
PWM2
PWM3
PWM4
PWM5
PWM6
PWM7
PWM8
PWM9
PWM10
PWM11
PWM121
2
3J2
J3
J4
J5
J6
J7K 10R16
R17
R18
R19
R20
R21
R22
R23
R24
R25
R26
R272.2 KXF_XPLLDIS
1
2
3K 10
2.2 K
XF_XPLLDIS1
2
3K 10
2.2 K
1
2
3K 10
2.2 K
1
2
3K 10
2.2 K
1
2
3K 10
2.2 KXMP/MC
SCITXDA
SCITXDA
SPISTEASPISTEA
MDXA
SPICLKASPICLKA
MDXACAP1
CAP2
CAP3
CAP4
CAP5
CAP6SCITRXDA
SCITRXDBSCITTXDBSPISIMOA
SPISOMIAT1PWMT2PWM
T3PWM
T4PWMU1D
XINT1
XINT2
XINT13
KEY1
KEY2
KEY3
KEY4VDD (+3.3V)
(c) External circuit interface
Figure 7.15 Continued .Realization of BLDC Motor Drives 227

signal of the comparator will be transmitted to the microprocessor by the optocoupler.
The optocoupler can ensure the isolation between the control circuit and the main circuit.The diagram of this detection circuit is shown in Figure 7.16.
The second method can be achieved by the voltage sensor with electrical isolation
architecture, so there is no need to use the optocoupler. However, the outputs of the voltagesensor not only could be put into the comparator after amplifying, but also can be transmittedinto the A/D module of the microprocessor directly, which could obtain a more accuratevoltage value of the DC bus. This method has higher ﬂexibility than the ﬁrst one, but its circuitwill be relatively complex. Figure 7.17 shows the diagram of the measurement circuit for theDC bus voltage with a Hall voltage sensor.+15 V
DC bus
voltage
Overvoltage
signalUdVcc
R1
R2R3
R4R5
R6R1R8
C1U1
Figure 7.16 Direct detection circuit of the DC bus voltage.
R
Secondary compensation current
Measurement resistance
RMoutputAMPSecondary compensation coil
Hall Magnetic coreHall voltage sensorDC bus voltage Ud
Primary
current
Figure 7.17 Measurement circuit of DC bus voltage with a Hall voltage sensor.228 Permanent Magnet Brushless DC Motor Drives and Controls

7.5.2 Overcurrent Protection
The overcurrent protection circuit is similar to the overvoltage protection circuit, and it also
has two methods. First, we can use the sampling resistance to convert current signals intovoltage signals on the basis of a voltage divider, so the operation status of the system can bejudged by the voltage signals. The circuit diagram of this method is shown in Figure 7.18.Since the current of the sampling resistance must not be too large, this method is usuallyapplied on low-capacity motor control systems.
Similar to the overvoltage protection circuit, the overcurrent protection circuit uses the current
sensor to detect the DC bus current. This method has higher ﬂexibility and better safety, so it has arelatively widerapplication. Inaddition,itcouldmakesampling valuesobtainedfrom the currentsensor as the current data in double-closed loop system, so we could simplify the design of thespeed-control system through calculating and controlling the sampling data directly.
During the starting process of a motor, the back-EMF is small, but the starting current is large,
so the motor might be damaged heavily at this moment. One always needs to add an overcurrentprotection circuit which is shown in Figure 7.19, to the motor control system. In the ﬁgure, u
0
represents the reference voltage. When the current of the system is large, the voltage drop of the
divider R1is also very large. Once the feedback voltage u1becomes larger than the reference
voltage u0, the comparator will output a low-level voltage to shutdown the power transistors T 2,
T4and T 6in order to reduce the current of the main circuit. On the contrary, if the feedback
voltage u1is smaller than the reference voltage, the comparator would output a high-level
voltage, T 2,T4and T 6will work normally. The protection system has a great advantage as it
doesn’t need a microprocessor to judge whether the system works in an overcurrent status or not.
So, the protection system could take an action rapidly according to the value of output of thecomparator even if the program of the system goes wrong. A current-detection circuit shown in
Figure 7.19 is usually used in the low-capacity motor system. As for high-capacity motor
systems, it is better to use the current sensor to detect the current of the system.
7.5.3 Logic Protection
The motor control system involves many complex logic circuits, and the circuit for thegeneration of PWM driving signals is the most important one. As for the circuit shown in+15 V
Overcurrent
signalDC bus current Vcc
R1 C1R2
R3R4
R5R6R7 U1
Figure 7.18 Direct detection circuit of a DC bus current.Realization of BLDC Motor Drives 229

Figure 7.19, if the two power switches in the same leg (such as T 1and T 4) conduct at the same
time, it will cause a short circuit. The short current would be very signiﬁcant. Therefore, many
microprocessors nowadays always set the dead time for the PWM generation unit in order toavoid being shorted. In addition, when the motor starts or the program goes wrong, the logicprotection circuit shown in Figure 7.20 is usually used for protection too. It can be seen fromthe ﬁgure that if the power switches in the same leg work at the same time, the XOR gate will
output a low-level voltage. After two AND gates, all of the control signals in this leg would
become low-level voltages. Thus, this logic protection circuit can protect the PWM unit frombeing shorted effectively, and its realization is simple.
7.5.4 Other Protection Circuits
7.5.4.1 Optocoupler Isolation Circuit
To avoid the high voltage or current signals in the main circuit disturbing the low voltage or
current signals in the control system, it usually applies the optocoupler isolation circuit toisolate them from each other, which would also improve the security of the system.
The use of optocoupler isolation is relatively simple. However, two points should be noted.
The ﬁrst is whether the optocoupler can satisfy the requirements of system. It is better to use aA
B
C
AND
u0
u1Ud
VccD1 D3 D5
D4 D6 D2
R1 R2 R4R3
C1T4 T6 T2T1 T3 T5
PWM1
PWM2PWM3
PWM4PWM5
PWM6BLDC
Motor
Figure 7.19 Overcurrent protection circuit in the starting process.
NOT AND
XOR PWM1
PWM4PWM1_IN
PWM4 _INNOT
Figure 7.20 Logic protection circuit.230 Permanent Magnet Brushless DC Motor Drives and Controls

high-speed optocoupler especially in some situations that need high switching speed. The
second is that the drive type for the input signals of the optocoupler must be determined. Sincethe optocoupler is a current-driven device, the connection mode shown in Figure 7.21(a)should be used when the input signals are high-level effective. On the contrary, the connectionshown in Figure 7.21(b) should be used. Note that if the input signal has both high-level andlow-level driving ability, then either mode could be used. But what should be paid attention tois the logical relationships between the input and output signals.
7.5.4.2 Capacitor Charging Protection Circuit
The relationship between capacitor current i
cand voltage ucis
ic¼Cduc
dtð7:1Ț
In the high-capacity system, the voltage of the DC bus is quite large, so the voltage change rate
of the capacitor is large at the instant of power-on. In this condition, the ﬁlter capacitance valueis also large. Thus, it can be obtained from Equation (7.1) that the instantaneous current of thecapacitor is also very large. Consequently, it may cause damage to the devices, so a capacitorcharging protection circuit is demanded with regard to the ﬁlter capacitor, which is shown inFigure 7.22. In Figure 7.22, K
1represents the double-contact relay. At the instant of power-on,Input
InputOutput OutputVcc2 Vcc2 Vcc1
(a) High-level drive mode (b) Low-level drive mode
Figure 7.21 Optocoupler application circuit.
2200 uF 2200 uF 2200 uFLoadK1
R1
1C2C3Cu
Figure 7.22 Capacitor charging protection circuit.Realization of BLDC Motor Drives 231

the capacitor was charged by the bridge rectiﬁer through the resistance R1and the normally
closed (NC) contact of the relay, thus the current of the capacitor is limited. When the current
of the capacitor gets higher than the action value of the relay, the relay will switch the NCcontact to the normally open (NO) contact rapidly, so that R
1will be disconnected, and the
capacitors that are paralleled cross the power source directly play the role of ﬁltering.
7.5.4.3 Power-off Protection Circuit
In motor control systems, it is necessary to store some important data or intermediate results of
calculations in the memory chip independent of the microprocessor sometimes. Hence, inorder to avoid the read and write errors of important data in the memory because of voltageinstability, or the data loss due to power off, a power-off protection circuit of the memoryshould be set. The corresponding circuit diagram is shown in Figure 7.23, where standbypower is needed besides the normal power. The standby power is applied in the event of normalpower failure, which makes sure the system works normally. Note that the voltage of the
standby power should be a little lower than that of the normal power supply.
7.6 Sensorless Control Circuits
7.6.1 Voltage Detection
The types of position sensors commonly used in BLDC motors are electromagnetic,
photoelectric, magnetic, etc. The BLDC motor adopting the electromagnetic position sensorneeds to install the opening transformer, a ferroresonance circuit, proximity switches and othersensor components on the stator. Considering the large volume and its poor anti-interferenceability, it is rarely used nowadays. Similarly, the large volume of the photoelectric position
sensor limits its application, especially the sinusoidal position sensor of which the high price
and poor reliability cannot be ignored. In contrast, a Hall magnetic position sensor is small insize and convenient to use, but it usually has certain nonsensitive magnetic areas that maycause detection errors of rotor position. All in all, the position sensor will cause severalproblems to a motor, such as more difﬁculty in system maintenance, increase of motor size,RAMVcc
GNDVcc
Normal power
Standby power
Figure 7.23 Power-off protection circuit.232 Permanent Magnet Brushless DC Motor Drives and Controls

and more complex motor design. In addition, the position sensor could hardly be embedded in
the small-scale motor systems, and it is difﬁcult for a position sensor to adapt to the harsh
working environment. So position-sensorless control strategies are demanded in many
applications for BLDC motor systems [9–11].
It is necessary to detect certain variables related to the rotor position to obtain the rotor
position in the sensorless control of a BLDC motor. The back-EMF-based strategy is the mostcommonly used, and it can detect the position of the rotor through the waveform of the back-EMF. However, the back-EMF cannot be detected directly in practice. Hence, indirectmethods for detecting and calculating the waveforms of back-EMF are required. The workin this section is all based on the assumptions that the motor has a three-phase Y-connected
winding, and a two-phase conduction mode is used to drive the motor.
7.6.1.1 Back-EMF Detection Circuit Based on Terminal Voltage
The waveforms and commutation points of BLDC motor are shown in Figure 6.1. It can
be seen from the ﬁgure that the commutation points lag 30
/C14electrical angles behind the
zero-crossing points of the back-EMF. Hence, the accurate detection of the zero-crossingpoints is very important.
The back-EMF detection circuit based on the terminal voltages is shown in Figure 7.24.
The zero-crossing detection equations of the back-EMF are obtained as
e
A¼uAG/C01
2ðuBGțuCGȚ
eB¼uBG/C012ðu
AGțuCGȚ
eC¼uCG/C012ðu
AGțuBGȚ8
>>>><
>>>>:ð7:2Ț
where u
AG,uBGanduCGrepresent the terminal voltages of the motor.
From Equation (7.2), it is known that only uAG,uBGanduCGare needed in order to get
the zero-crossing points of the back-EMF. In practice, u0AG,u0BGandu0CGare obtained after the
terminal voltage dividing and ﬁltering, and then the subtraction circuit is built according to
Equation (7.2), through which the zero-crossing points of the back-EMF is obtained. Note thatthe point G in the circuit is connected with the negative pole of U
d.
7.6.1.2 Back-EMF Detection Circuit Based on Phase Voltage
Further, in order to reduce disturbances, we can break the connection between point G and the
negative pole of Ud, and then the back-EMF detection circuit based on phase voltage is formed.
Assume that uNis the neutral point voltage of the motor windings. Then, according to the
symmetry principle, the voltage of point G has relationship as uG/C25uNwhen the back-EMF
crosses zero. Thus, we can obtain
eA¼uA
eB¼uB
eC¼uC8
<
:ð7:3Ț
where uA,uBanduCrepresent the phase voltages of the motor.Realization of BLDC Motor Drives 233

The corresponding circuit is shown in Figure 7.25, where the detection signals u0A,u0Band
u0Care, respectively, proportional to the phase voltages uA,uBanduCafter voltage dividing.
Then we can obtain the zero-crossing points of the back-EMF with Equation (7.3).
7.6.2 Filtering and Phase Shifting
7.6.2.1 Calculation of Phase-Angle Delay
In order to improve the signal quality, high-frequency electromagnetic interferences are
removed by ﬁltering, resulting in the phase shifting of the signals at the same time, whichshould be corrected appropriately.
According to the circuits shown in Figures 7.24 and 7.25, it is easy to calculate the phase-
shift angle of the detected signals. Take phase A in Figure 7.25 as an example, the relationshipbetween the original signal and processed signal, which is calculated according to thefundamental frequency of the back-EMF can be expressed as
u0A
uA¼R2
R1țR2țj2pfR1R2C1ð7:4Ț
where frepresents the frequency of the back-EMF.A
B
C
GUduAG
uBG
uCG
AGu'D1 D3 D5
D4 D6 D2R1
R2 C1BGu'R3
R4 C2u'CGR5
R6 C3
Ae'
Be'
Ce'Subtraction circuitT5
T2T3
T6T1
T4BLDC
motor
Figure 7.24 Back-EMF detection circuit based on terminal voltage.234 Permanent Magnet Brushless DC Motor Drives and Controls

Thus, the corresponding phase delay is
a¼arctan2pR1R2C1f
R1țR2ð7:5Ț
Further, in the complex high-order system, approximation is adopted sometimes to get
relatively accurate results. After the phase delay angle is determined, the correction of thezero-crossing points of the back-EMF can be achieved through software algorithms accordingto practical conditions.
7.6.2.2 Active Filter
In some situations requiring better waveform quality, an active ﬁlter is usually used to reshape
the detected signals. The functions of the active ﬁlter fall into two aspects. First, it can weakenor eliminate the PWM chopper pulses in the terminal voltage signals, so as to guarantee that
those pulses contained in the ﬁltered terminal voltages will not affect the follow-up treatment
of the back-EMF. Secondly, it extracts the back-EMF signal from the terminal voltage, andlimits its amplitudes within an appropriate range to avoid damaging the devices.
There are a number of classiﬁcation methods for active ﬁlters. According to the ampli-
tude–frequency or the phase–frequency characteristics near the cut-off frequency, the activeA
BC
GUduA
uB
uC
Au'D1 D3 D5
D4 D6 D2R1
R2 C1Bu'R3
R4 C2Cu'R5
R6 C3
Ae'
Be'
Ce'T5
T2T3
T6T1
T4BLDC
motor
Figure 7.25 Back-EMF detection circuit based on phase voltage.Realization of BLDC Motor Drives 235

ﬁlters can be divided as the Butterworth ﬁlter, the Chebyshev ﬁlter and the Bessel ﬁlter, etc.
To reduce the complexity of the system, the Butterworth ﬁlter is commonly used due to its
relatively ﬂat pass band.
The order of the active ﬁlter must be determined with comprehensive consideration and
calculation. If the order is too high, it wo uld not only increase the complexity and
instability of the circuit, but also increase the system error so that the ﬁnal results
would be inﬂuenced. On the contrary, if the order is too low, it will not achieve agood ﬁltering effect. Usually, the second- or thi rd-order ﬁlter is appr opriate. Furthermore,
the active ﬁlter should suppress the high-frequency interferences and retain the back-EMFsignals effectively.
7.6.2.3 Phase-Shift Filter Circuit
It can be seen from Figure 6.1 that the commutation points of the BLDC motor always lag 30
/C14
electrical angles than the corresponding zero-crossing points of the back-EMF. However,
phase shifting of 30/C14electrical angles is commonly hard to achieve in practice. In order to input
the output signals of the circuit into the microprocessor directly, a novel method is proposed,which is to introduce a phase-shift ﬁlter after the detected signals, thus the output signals,lagging 90
/C14electrical angles behind the corresponding zero-crossing points, can be regarded
as commutation signals.
During the design of the phase-shift ﬁlter circuit, it is necessary to consider both the
amplitude–frequency characteristics and the phase–frequency characteristics since the fre-
quency of the terminal voltage and phase voltage are changing with the speed of the motor.
In order to achieve the most satisfactory control performance, the ﬁlter should be able toeliminate the disturbances, retain the detected signals at the maximum extent, and keep thephase delay as close to 90
/C14electrical angle at the same time.
7.6.3 Current Detection
Generally, phase currents are required to be sampled in the position-sensorless control of aBLDC motor, and the sampling resistor or the current sensor are commonly used in currentdetection. However, both methods have their own limitations. So certain speciﬁc current-detection chips are used in some moderate-capacity motor systems, where the system doesn’t
need electrical isolation between the main circuit and the control circuit.
MAX472, an ideal current detection chip produced by Maxim Company, can achieve
bidirectional current sensing. Its internal structure and typical application circuits are shown in
Figures 7.26 and 7.27, respectively.
Assume that phase current i
loadﬂows to point B from point A, the comparator A 1in
MAX472 will output a high-level voltage, then T 1will be excited, and A 2outputs a low-level
signal to block T 2. Consequently, the pin 5 of MAX472 will output a high-level voltage. As the
positive terminal voltage of A 1is approximately equal to its negative terminal voltage, and the
current ﬂowing from pin 8 is also approximately equal to the current ﬂowing past RGand T 1,s o
the relationship between iloadandioutbecomes
iload/C2Rsense¼iout/C2RG ð7:6Ț236 Permanent Magnet Brushless DC Motor Drives and Controls

Hence, the relationship between uoutandiloadcan be expressed as
iload¼uoutRG
RoutRsenseð7:7Ț
As the phase current ﬂows from point B to point A, the relationship between the output voltage
uoutand phase current iloadremains unchanged. The only difference is that the pin 5 of MAX472
outputsa low-levelvoltage, thus thevalue and direction of the phase current can be judged by the
sampling value of uoutand the obtained output signal of pin 5. Furthermore, avoltage regulator is
needed on the end of the output to avoid an overvoltage. The selection of the sampling resistance
Rsenseshould make sure that the output voltage uoutcorresponding to the maximum sampling
current doesn’t surpass the maximum permissible input value of the A/D chip.+
A1+
A2
+COMPT1 T2
5SIGN8OUT7Vcc3 6
Figure 7.26 Structure diagram of MAX472.
SHDN
NC
RG1
GNDOUT
VCC
RG2
SIGNVcc
MAX472 phase current
iloadRsense
RG RG
R Rout
SIGNiout uoutB A
8
7
6
5 4321
Figure 7.27 Typical application of MAX472.Realization of BLDC Motor Drives 237

7.7 ASIC for BLDC Motor Drives
With the wide application of BLDC motors, more attention has been paid to this motor control
technology. Renowned semiconductor companies of several countries have produced ASICsfor BLDC motors. These highly integrated circuits have complex structure, most of which aremedium or large-scale integrated circuits. Generally, it contains linear and nonlinear devices.It can be used in low- and some high-power control circuits, and be applied in simple open-
loop control or high-precision closed-loop control systems. ASICs have many protection
circuits, such as overcurrent protection, overheat protection and overvoltage protection, etc.This improves the reliability of the control circuit. However, an ASIC for a BLDC motoralways has a ﬁxed control scheme, instead of user-programmable features, that makes it hardto update. Therefore, an ASIC is usually applied in certain BLDC motor control systems whichrequire relatively ﬁxed features and real-time high-quality control [12]. Here, MC33033 andTB6537P are introduced to illustrate the applications of ASIC for BLDC motor drives.
7.7.1 MC33033
MC33033 is a high-performance IC chip for BLDC motor control produced by the Motorola
Company. Because of its bipolar analog technology, it can be used in harsh industrial
environments. The IC contains all the features that can achieve open-loop control ofthree- or four-phase motors. MC33033 has units for undervoltage lockout, cycle-by-cyclecurrent limiting and internal thermal shutdown. In addition, it has functions of open-loop speedcontrol, forward/reverse control, operation enable and other typical motor control functions.And it has a 60
/C14=120/C14selection pin, which can be matched to sensors with 60/C14or 120/C14
electrical phasing.
MC33033 mainly contains a rotor position decoder used for determining the correct
commutation, a reference power supply source with temperature compensation used forthe Hall sensor, a sawtooth oscillator with adjustable frequency, an error ampliﬁer, a PWMcomparator, three upper-arm drivers with open collector and three high-current lower-armdrivers for high-power MOSFET. The working principle of the IC is introduced as follows.
The rotor-position decoder built in the MC33033 can not only monitor signals from three
input pins (pins 4–6), but also output the correct commutation signals for the bridge inverter.The input pins of the sensors can be connected to the Hall position sensor or the optocouplerdirectly, and they all have embedded pull-up resistances internally, which greatly simpliﬁes the
design of the peripheral circuits. In addition, they are compatible to the TTL level, and the
typical threshold voltage is 2.2 V.
The 60
/C14=120/C14selection pin allows connection of the MC33033 to the sensor with 60/C14, 120/C14,
240/C14and 300/C14electrical phasing conveniently. Theoretically, there are eight possible input
codes for the three input ports of the sensor, but only six of them are effective, and the other twoinvalid codes are usually caused by a line failure of the connection to the sensor. Base on the sixeffective codes, the position decoder could locate the rotor position within the range of 60
/C14
electrical angle.
The forward/reverse input interface (pin 3) changes the rotation direction of the motor by
changingthepowerturn-onsequenceofthestatorwindings.Whenthestateofthispinischanged,the output drive for the upper and lower arms of the same phase will be swapped. And then thecommutation sequence will be reversed, so that the rotation direction of the motor is changed.238 Permanent Magnet Brushless DC Motor Drives and Controls

The start/stop control of the motor can be achieved by the output enabling pin (pin 19).
When this pin is ﬂoated, it will be connected to the positive power supply through the internal
pull-up resistance. Then, the driving signals for the upper and lower arms of the bridge can
work normally. On the contrary, if this pin is grounded, the output driving signals for the upperarm of the bridge will be closed, and signals for the lower arm of the bridge will be forced lowtoo so that the motor is braked until it stops.
MC33033 contains a fully accessible error ampliﬁer for closed-loop speed control of BLDC
motors. The DC voltage gain of the error ampliﬁer is 80 dB with a 0.6 MHz gain bandwidth.The input voltage range is changing from 0 to V
ref. Note that in most open-loop control
systems, the ampliﬁer is conﬁgured as a voltage follower with its input connected to the
reference voltage source for setting the speed.
The frequency of the internal oscillator in MC33033 is programmed by selecting the
appropriate external resistor RTand capacitor CTparameters. The capacitor CTis charged from
the pin 7 through resistor RTin MC33033, and discharged by the internal discharge transistor.
The peak and valley voltages of oscillator are typically 4.1 Vand 1.5 V, respectively. In order to
reduce noise and improve the efﬁciency of the switch, the oscillator frequency is recom-mended to be 20–30 kHz.
The main task of PWM units is to achieve the effective control of motor speed by varying the
average voltage applied to each stator winding. When C
Tdischarges, the oscillator will set
both latches, allowing the corresponding top and bottom drive signals output. However, whenthe voltage of the C
Tis higher than the output of the error ampliﬁer, the PWM comparator will
reset the upper latch and shutdown the bottom drive output.
Continuous operation might cause the motor overload. This would make the windings
overheat or become damaged, which can be overcome by cycle-by-cycle current limiting. Thecycle-by-cycle current limiting regards each cycle as an independent unit, and monitorsthe real-time stator current. Once overcurrent occurs, the driving signals for the bridge inverter
are shut down at once, which will be kept blocked within the remaining period. The voltage
developed across the sense resistor R
sis monitored by the current sense input (pin 12), then it is
compared to the internal 100 mV reference voltage. If the current sense threshold is exceeded,the comparator will reset the lower latch, and terminate the drive output. The value of thecorresponding sampling resistor can be calculated by
R
s¼0:1
IstatorðmaxȚð7:8Ț
The capacitor CTcan be charged by the on-chip 6.25 V reference voltage regulator (pin 7)
in MC33033. This source can also provide a reference voltage to the error ampliﬁer, andcan supply 20 mA of current suitable for direct powering sensors in low-voltage applica-tions. In higher-voltage applications, it is necessary to add a suitable transistor so as toprovide a larger current up to 1 A, which meet s the requirements for power supply of the
external Hall sensor.
MC33033 contains a dual undervoltage lockout to prevent damage to the IC and the external
power switches. In low-power supply conditions, it can make sure that the IC and sensors arefully functional. The threshold voltage of the IC is 8.9 V. This ensures that the IC, which isconnected to a MOSFET, could output a sufﬁcient gate driving voltage. When directlypowering the Hall sensors from the reference voltage, improper sensor operation can result ifthe reference output voltage falls below 4.5 V. Hence, when the comparator detects powerRealization of BLDC Motor Drives 239

supply or reference voltage is too low, the top drives will be turned off and the bottom drive
outputs are kept at low level. Thus, the chip will be protected.
The open-loop control system of a BLDC motor with MC33033 is shown in Figure 7.28.
In the ﬁgure, the power switch is a MOSFET. At any given rotor position, MOSFETs on theupper and lower arms of the same bridge can not work at the same time, and the two excitedMOSFETs belong to different Totem poles. This switch structure ensures that the current canﬂow bidirectionally as the stator windings are connected to the DC bus and the ground.However, it may cause leading-edge peaks on the current waveform, so RC ﬁlter is added onthe current sense input (pin 12).
In order to achieve closed-loop control for a BLDC motor, it is necessary to build a feedback
voltage, which is proportional to the motor speed. The three-phase closed-loop control systemfor the BLDC motor based on MC33033 is shown in Figure 7.29, where the feedback voltage isgenerated by MC33039.
MC33039 is powered by the 6.25 V reference voltage (pin 7) of MC33033. The same Hall
sensor signals used by MC33033 for rotor-position decoding are utilized for MC33039. Basedon these signals, a pulse with deﬁned amplitude and time interval is generated by MC33039from its pin 5. Then, a DC voltage that is proportional to the motor speed is produced with theinternal integrator of MC33033. This voltage will establish the PWM reference level at pin 11
of MC33033, so as to achieve the closed-loop control. If the jumper at pin 18 is conducted, the
control system will be suitable for the motors having 120
/C14/240/C14electrical phasing. The system
can be easily be modiﬁed to accommodate 60/C14/300/C14Hall sensor electrical phasing by
removing the jumper.
7.7.2 TB6537P
TB6537P, produced by the TOSHIBA Company, is used for the position-sensorless control of a
BLDC motor. Because this chip can allow users design their own external driving circuits, it
can be used for driving various capacity motors. TB6537P is packaged by DIP18, and containsovercurrent protection, forward/reverse rotation control and lap turn-on functions. In addition,the IC has two types of PWM output (upper PWM and upper/lower alternate PWM). Theprinciple of the IC will be introduced in detail as follows.
Once the IC receives a PWM start instruction signal, a turn-in signal for forcible
commutation is output and the motor starts to rotate. The motor rotation will produceEMF on each phase winding. The generated voltage signals are converted to signals of
rotor position through the detection circuit. Then the position signals are transferred to pin 18.
Thus, the forcible commutation is automatically switched to turn-on signal for position signal.The forcible commutation frequency during the start of the motor is determined by
f
st¼fxt
6/C22bitț3ð7:9Ț
where
fst— starting commutation frequency;
fxt— resonator frequency;
bit — 14.240 Permanent Magnet Brushless DC Motor Drives and Controls

A
B
CUd
1D3D
4D6D5T
2T3T
6T1T
4T5D
2DR
R
R
R
R
R+20 V
R R R
W
W
WCRBT1AT2
F/R3SA4
SB5
SC6
REF OUT7
OSC8ERR IN+9
ERR IN-10
ERR OUT11
C OVER12GND13VCC14CB15BB16AB17
60/12018
EN19CT20U
MC33033R RC C
SA
SB
SC
VREF
RSR
C13 2 12 1
4
5
6
7
8
9
10
311 12
1
2
3T
T
Figure 7.28 Open-loop control circuit for a BLDC motor based on MC33033.Realization of BLDC Motor Drives 241

A
B
CdU
1D3D
4D6D5T
2T3T
6T1T
4T5D
2DR
R
R
R
R
R+20 V
R R R
W
W
WCRBT1AT2
F/R3SA4
SB5
SC6
REF OUT7
OSC8ERR IN+9
ERR IN-10
ERR OUT11
C OVER12GND13VCC14CB15BB16AB17
60/12018
EN19CT20U
MC33033R RC C
SA
SB
SC
VREF
RSR
C13 2 12 1
4
5
6
7
8
9
10
311 12
1
2
3T
TC1
B2
A3
A4FOUT5RT/CT6GND7VCC8U
MC33039RC
R
R
C213
13
144
5
Figure 7.29 Closed-loop control circuit of a BLDC motor based on MC33033.242 Permanent Magnet Brushless DC Motor Drives and Controls

Note that the frequency of forcible commutation during the start can be adjusted according
to the inertia of the motor and load. The frequency should be set higher as the number of motor
poles increases. And it should be set lower as the inertia of the load increases.
The external input PWM signals are output after transformation. The output PWM signals
should have proper frequency, so as to satisfy the requirements for electrical frequency and theswitching characteristics of the driving circuit. Since the position detection depends on therising edge of the PWM signals, position detection cannot be performed with 0% or 100%duty. Note that even if the reference duty cycle is 99%, the practical duty cycle may already be100% because of the existence of delay time. So the narrow pulse width should be larger than250 ns at the maximum and minimum duty cycle in practice.
The PWM output form is determined by the pin SEL_OUT of TB6537P as shown in
Figure 7.30. The system runs in upper PWM and upper/lower alternate PWM modes,
respectively, when the SEL_OUT is low and high.
As the position detection and the PWM signals are implemented synchronously, the
moment of the position detection is related to the frequency of PWM signal. When the IC
is used to control a high-speed motor, position signals are changing rapidly. Thus, if thefrequency of PWM signals is very low in this condition, it might cause detection errors. Inorder to avoid such problems, a proper PWM signal frequency should be selected. The rotor-position variation is calculated depending on two consecutive rising edges of PWM signals, asshown in Figure 7.31. Assume that f
pis the frequency of PWM signal, then detection time is
between 1/ fpand 2/ fP.
Upper turn-on signal
Output voltageLower turn-on signal
(a) SEL_OUT is low-level
Upper turn-on signal
Output voltageLower turn-on signal
(b) SEL _OUT is hi gh-level
Figure 7.30 Two PWM output forms of TB6537P.Realization of BLDC Motor Drives 243

During the start of forcible commutation, the advanced conduction angle is zero, and when
normal commutation is started, the advanced conduction angle will be automatically set with
LA0 and LA1. However, if both pins of LA0 and LA1 are set for high, then the advanced
conduction angles of forcible commutation and normal commutation are all 30/C14. The set of
advanced conduction angle is shown in Table 7.3.
When SEL_LAP is at high-level, each phase winding conducts 120/C14electrical angle, while
when SEL_LAP is at low-level, the IC works at overlapping conduction mode, in which the
conduction time of each phase winding is longer, and the conduction durations of differentphases overlap. The overlapping time is related to the set of advanced conduction angle.
Start/stop of motor is achieved by controlling the input pin of PWM signal. When the duty
cycle is zero, the motor stops. If the PWM signals work normally, and its average low-level
duration is longer than two resonator signal periods, the motor starts. In addition, the external
noise interferences of the input pin should be minimized.
The typical TB6537P application circuit, whose peripheral circuit is designed by using
discrete components, is shown in Figure 7.32. Note that the RC parameters and the powerswitches in the ﬁgure should be selected properly for different applications.
PWM
signal
Voltage
of the pinVoltage
of the pinReference
voltage
Position
signal
Actual detection time Ideal detection time
Figure 7.31 Relationship between position signal and PWM signal.
Table 7.3 Set of advanced conduction angles
LA0 LA1 Advanced conduction angle
LL0/C14
H L 7.5/C14
LH1 5/C14
HH3 0/C14244 Permanent Magnet Brushless DC Motor Drives and Controls

A
B
CdU
1D3D
4D6D5T
2T3T
6T1T
4T5D
2DR
R
R
R
R
R
R4
5
6
78
9
SLA01
LA12PWM3
CW_CCW4
SEL_OUT5
SEL_LAP6
XT7
XTIN8
GND9VCC10
UP11
UN12
VP13
VN14
WP15
WN16
OC17
WAVE18U
TB6537P R16
CR15
R CR
R
CR
R CRR
R
R+5 V
+5 V +5 V+5 V
+5 V
+5 V +5 V
1 2
YC
CPWM
CCW
LA0
LA1
SEL_OUT
SEL_LAP1
1
21
1
2
31110
1312
4314
17 65
1
2
3JR
R
1
2
3JR
R
1
2
3JR
R
1
2
3JR
R24
25
18
19
20
21
22
232
3 4
1LA0
LA1
SEL_OUT
SEL_LAP+5 V
Figure 7.32 Application circuit of TP6537P.Realization of BLDC Motor Drives 245

7.8 Software Design
7.8.1 BLDC Motor Driving with Position Sensor
7.8.1.1 Main Program
The ﬂowchart of the main program of a BLDC motor control system with a position sensor
is shown in Figure 7.33(a). For an initializatio n module, it contains not only the initiali-
zation of the system clock, the watchdog, the I/ O port status, system interruption and other
hardware systems, but also includes the initial ization of the corresponding variables. During
the initialization, in order to prevent accidental interrupt request, system interruption
should be disabled at the start of program, which will be enabled after initialization has
been performed.
In addition, the general timer should be set to provide the sampling period after the
initialization. Then the system will go into the cyclic-waiting state. Once the interrupt signal isreceived, the program will run into the timer interrupt service routine.
Start
Initialization of the
module and variables
Initialization of
hardware
Enabling the interrupt
and the timer
Starting the motor
according to rotor
position
Cyclic waiting for the
interruptTimer
interruptEntrance of
interrupt
On-site
protection
Reading capture unit
Calculating rotor
position and speed
Recovery site
operation
ExitAdjusting PWM
control signal
(a) Main program (b) Interru pt service routine
Figure 7.33 Flowcharts of a BLDC motor control system with position sensors.246 Permanent Magnet Brushless DC Motor Drives and Controls

7.8.1.2 Timer Interrupt Subroutine
The ﬂowchart of the timer interrupt service routine is shown in Figure 7.33(b). After entering
the interrupt, the program ﬁrst executes the onsite protection, and then the Hall sensor positionsignals will be detected by the capture unit, so as to calculate the rotor position and the speed ofthe motor. Thus, we could determine the commutation time and adjust PWM control signal.Furthermore, the conduction sequence of the power switches can be obtained. After all the
tasks have been performed, the program will execute site-recovery operations, and jump out of
the interrupt service routine.
Note that Figure 7.33 only shows a basic program process. The corresponding current
detection and fault protection programs are included in practical applications.
7.8.2 BLDC Motor Driving Without Position Sensor
The ﬂowcharts of a BLDC motor control system without position sensors based on
TMS320F2812 are shown in Figure 7.34. Usually, the back-EMF-based method is used to
Start
Initialization of the
module and variables
Initialization of
hardware and A/D
module
Enabling interrupt and
the timer
Starting the
motor without
position sensors
Cyclic waiting for
timer interrupt Timer
InterruptEntrance of
interruption
On-site
protection
Reading A/D module
and calculating values
of current and voltage
Calculating rotor
position and speed
Start A/D
conversion
Recovery site
and Exit
interruptionAdjusting PWM signal
according to double
closed-loop algorithm
(a) Main program (b) Interru pt service routine
Figure 7.34 Flowcharts of a BLDC motor control system with position sensors.Realization of BLDC Motor Drives 247

calculate the rotor position. The program is similar to that of the system with position sensors.
However, there are three different points, as follows.
(1) Since the stator phase current and the DC bus current need to be sampled, the initialization
should include the parameters of the A/D module in DSP as shown in Figure 7.34(a).
(2) Programs for reading the A/D conversion result and starting the A/D conversion should be
added to interrupt the service routine. Since the position sensors are removed, the capture
unit could be discarded as shown in Figure 7.34(b).
(3) Since the initial rotor position is unknown, the rotor start program is different.
7.8.3 Reliability
With larger scale BLDC motor control systems and more complex algorithms, the requirementfor reliability of the software have been given more attention, so it is necessary to add an
anti-interference program to improve the reliability [13]. There are a variety of factors that
have an inﬂuence on the motor. Some common measures, which can improve the reliability ofsoftware, are discussed as follows.
7.8.3.1 Anti-Interference Approaches for Switching Signals of Inputs and Outputs
Acquisition for switching signals is a common problem in motor control. In the control system,
higher requirements for the accuracy of signal acquisition and real-time control of the system arenecessary. However, in certain conditions, the requirements for accuracy and real-time controlmay contradict each other. If more attention is paid on the accuracy, it might take a longer timefor the program to meet the requirement of the system control resolution. On the contrary, if onlythe real-time control requirement is considered, the accuracy of signal acquisition may bereduced, which may cause frequent changes of switching signals, so that the control systemwould not work normally. Note that the interference signals are usually narrow pulses, and the
effective duration of switching signals are relatively long. According to this feature, we can
sample the same switching signal repeatedly at short intervals, and the interval is determinedaccording to thewidth of the effective signals and the speed of the motor. When the results of twoor more than two consecutive samplings are the same, the sampled signals are regarded as valid.
When the system outputs switching control signals, related interference may be conveyed to
the output interface as feedback through the shared line, then the output register might bechanged, so errors or malfunction may occur. The most effective software solution for thisproblem is to output the same data repeatedly. If possible, the repetition period should be as
short as possible, which would make sure that the control system isn’t able to respond to the
interferences before correct signals are sent, consequently the malfunction is avoided.
7.8.3.2 Anti-Interference Approaches for Analog Inputs
If the interference affects the input channels of analog signals, the results of the A/D module
will have a deviation from the true value, especially when the analog signals are weak. Usually,the reliability of A/D conversion results cannot be guaranteed by only one sampling.Consequently, multiple sampling with digital ﬁltering technology is applied. There are a248 Permanent Magnet Brushless DC Motor Drives and Controls

variety of digital ﬁltering methods, such as arithmetic mean ﬁltering, weighted mean ﬁltering,
sliding mean ﬁltering and inertia ﬁltering. In the control system of a BLDC motor, the
arithmetic mean ﬁltering, which is used to sample the same analog signal for certain times, can
be adopted. By taking the average of these signals as its sampling value, the inﬂuence ofsystematic random interference on the sampling results can be reduced.
7.8.3.3 Anti-Interference Approaches During Operation of Program
If the interference affects the microprocessor, the microprocessor might not work normally,
which leads the program to run away. In this condition, the program may take some operands
as operation codes, thus it would cause confusion in the whole program. In addition, if the
interferences affect the process of the data transmission, the error of data could also causesystem confusion. In summary, ﬁve typical approaches can be taken to suppress the inter-ferences during the operation of a program.
(1)Instruction redundancy
Single-byte NOP instructions are inserted into the program. In this condition, when theprogram runs away to certain NOP instruction, the confusion about operands and
operation codes can be avoided. Thus, the instruction can be executed correctly, so
that the program runs normally.
(2)Software trapThe software trap is a bootstrap used to capture the run-away program and force theprogram to go to certain error procession segment. Software traps are usually placedwhere normal program cannot reach, so these traps would not affect the efﬁciency of theprogram.
(3)Watchdog
If the run-away program falls into an accidental endless loop, then the above two strategies
are less effective. In this condition, nothing but a reset can force the program to run againso that the system runs normally. The most commonly used autoreset method is to use thewatchdog function of the microprocessor.
(4)Data-transmission veriﬁcationThe data transmission is easily disturbed between the host computer and the MCU. Inorder to solve this problem, the following two approaches can be adopted. The ﬁrst is tosend the critical data multiple times. This means only when the receiver receives the same
data in certain times, can the data be regarded as valid, so that the command can be
executed. Secondly, insert a check program in the communication protocol, andthe communication protocol should be coded according to certain rules. So, even ifthere are certain bits of data being disturbed during communication, the receiver can alsocorrect these errors. However, this approach makes the bit of communication data longerso that the real-time control performance will be reduced.
(5)Data protectionDuring the operation of the program, if the program itself isn’t allowed to be changed,
ROM can be conﬁgured in the system. This can avoid system malfunction and improve
system reliability. In addition, in order to avoid losing the critical data caused by suddenpower off, a nonvolatile memory such as FLASH can be adopted, by which the critical dataof the system can be protected effectively.Realization of BLDC Motor Drives 249

7.9 EMC Design
EMC of an electronic device refers to the ability to work in the designed level within the
required security range for electrical or electronic systems, equipment and devices in a givenelectromagnetic environment without causing damage or unacceptable performance degra-dation due to electromagnetic interference. A BLDC motor control system is composed ofthe high-voltage part, like power electronic devices, and the low-voltage part, such as the
microprocessor, digital logic gates and A/D converters. Since the low-voltage part has features
such as low power, low voltage and high frequency, it is vulnerable to the high-voltagepart. Hence, the EMC design of a BLDC motor control system falls into two aspects: one isto reduce the electromagnetic interference caused by the high-voltage part, and the other is toenhance the antidisturbance ability of the low-voltage part.
7.9.1 EMC Design of High-Voltage Part
The high-voltage part chieﬂy contains the main circuit of a BLDC motor control system. Inorder to reduce the electromagnetic radiation emitted by the high-voltage part, a shielding
box can be installed outside the main circuit. T he shielding box can be made from electrolytic
copper foil material and connected with the ground reliably. In addition, the cooling ﬁns forpower switches in the main circuit should be c onnected with the shiel ding box for reliable
heat dissipation.
If the DC bus between the bridge rectiﬁer and the inverter is too long, the distributed
inductance of the DC bus will be great, which may cause a large impulse voltage during the
switching instants of the power switches. Sometimes, the impulse voltage is more than 30% of
the DC bus voltage, which would lead to interferences in the low-voltage part. In order toreduce this impulse voltage, three measures can be applied. First, the length of the DC busshould be shortened as much as possible. Hence, its distributed inductance can be reduced.Secondly, according to the length of the DC bus, a proper parallel capacitor ﬁlter should beinstalled at the side of the bridge inverter, so as to absorb the distributed inductance on the bus.Finally, absorbing circuits should be paralleled at both ends of the power switches, so as toabsorb the impulse voltage. The commonly used absorbing circuits are shown in Figure 7.35.
Figure 7.35 Commonly used power-absorbing circuits.250 Permanent Magnet Brushless DC Motor Drives and Controls

Since driving signals for the power switches are relatively low, the shielding wire should be
used between the control part and the power switches. In addition, it must make sure that the
metal skin of shielding wires is connected to the shielding box reliably.
7.9.2 EMC Design of Low-Voltage Part
7.9.2.1 Power-Supply Design
This not only needs to supply the power for the main circuit in BLDC control system, but also
to supply the power for the microprocessor and the related peripheral driving circuit.
According to different devices, the power supply may include ț2.5 V, ț3.3 V, /C65 V and
/C615 V, etc. Therefore, the problem of matching and interference among them should be
considered.
At the design of the main power source, a switch-mode regulated AC–DC power supply is
usually employed for its simple structure. Moreover, it cannot be easily inﬂuenced by the
voltage and frequency of the power grid and can isolate the disturbance from the wire of powersupply. The switch-mode power supply should install a ﬁlter to eliminate the high-frequencyinterferences from the grid. Also, the input power cable is better to be the shielding wire.
Moreover, it should connect a parallel capacitor ﬁlter at the DC output of the switch-mode
power supply in order to reduce the power ripple. The linear power supply could be used for themicroprocessor in order to reduce interferences, which is usually isolated from other powersources. Note that the rating capacity of the power supply must be larger than the systemrequired, so that the system works normally.
7.9.2.2 PCB Design of Control System
The EMC design of a BLDC motor control system can be considered from the following three
aspects, i.e. ground protection, PCB placement and routing, and conﬁguration of a decouplingcapacitor [14].
(1)Ground protection
There are various ground wires in the motor control system, such as system ground,chassis ground (shielding ground), digital g round and analog ground, etc. In the real-
time control system, the com monly used anti-interference measure is grounding.
Proper combination of grounding and shiel ding can solve most of the interference
problems.
In the low-frequency circuits, when the working frequency is lower than 1 MHz, the
distributed inductance of the circuit boa rd routing and the components are very low,
while the circulation formed by a grounded circuit is very large, which will cause greatinterference to the system. Hence, one-poi nt grounding is applied for the circuit board
in this condition. When the working frequency is larger than 10 MHz, the groundimpedance becomes very large, so multipoint grounding is adopted in the circuit board
to reduce the ground impedance. When the working frequency ranges between 1 and10 MHz, the length of the ground wire should not exceed 1/20 of that of the minimumwavelength if one-point grounding is used . Otherwise, the multipoint grounding is
more appropriate.Realization of BLDC Motor Drives 251

The digital circuits, isolated from the an alog circuits, are always grounded at one
point with the latter. Usually, in the circ uit board there are not only the high-speed
digital circuits, but also analog circuits, which should be separated in the layout. In
addition, their ground wires mustn’t be c onfounded. Both ground wires of digital
circuits and analog circuit s should be connected to the power source ground at the input
of the power supply. Moreover, the ground are a of linear circuits should be expanded as
much as possible.
The ground wire should be as thick as possible. If the ground wire is too thin, the
grounding resistance will be great. Hence, the variation of current will cause a great
change in the voltage of ground, which will deteriorate the anti-interference perfor-
mance of the circuit board. So, the ground wire should be thick enough so that a current
as large as three times the rated current could ﬂow through it.
(2)PCB layoutThe circuit board of a BLDC motor control system always contains digital circuits andanalog circuits, and some control circuits even have power circuits. During the design ofthese circuits, it is better to achieve a reasonable partition to reduce the mutualinterference of each partition, and try to limit the current circulation in their ownregions. For example, the power circuit should be placed near the entrance of the power
source, so as to avoid interference caused by large power changes. The crystal and the
shell of the crystal oscillator should be grounded. Moreover, there should be enoughcopper covering the area of the clock region in order to suppress the interference of high-frequency clock signals. Note that digital c ircuits should be far from analog circuits
without interaction, and it is necessary to place a protective ground for analog signals thatare vulnerable to interference.
In practice, the number of vias on a circuit board should be minimized and 135
/C14lines
rather than the 90/C14lines should be used. In the places where the system is easy to
disturb, the arc lines are better. Common lines should not be too thick, generally 10–15mil is ﬁne. For a group of high-speed parall el signal lines, such as the data bus and the
address bus, the length of them should be a pproximately equal. In particular, the
serpentine line method can be used to keep them isometric. As for some long lines,
matching resistors are necessary in order to e nsure the integrity of signal. Furthermore,
the power lines and ground wires should be as thick as possible at different currentratings. In addition, the direction of power lines and ground wires should be inaccordance with that of data transmissi on, which will be helpful to enhance the
antinoise ability of the system.
It is also worth noting that the unused digital gate circuit and input ports of
operational ampliﬁer should not be idle. F ree microprocessor I/O ports should be
set as output ports at the initialization of software.
(3)Decoupling capacitor conﬁgurationDecoupling capacitors should be conﬁgured on key parts of the circuit board to improvethe system anti-interference ability. A 10–470 mF electrolytic capacitor should be con-
nected at the input of the power supply. And usually a 0.1 mF ceramic capacitor, which has
a low high-frequency impedance (lower than 10 Owithin 500 kHz to 20 MHz) and small
leakage current, is placed at the power input pin of each IC chip.
For devices having poor anti-interference ability and large current variation during
switching or memory devices such as ROMs/RAMs, a decoupling capacitor should be252 Permanent Magnet Brushless DC Motor Drives and Controls

directly inserted between their power line and the ground. Since the presence of an
impulse voltage at the reset pin of the microprocessor may change the state of a register, a
decoupling capacitor is needed at the reset pin too.
Further, decoupling capacitors should be placed as close as possible to devices, so as to
reduce the distributed inductance. In particular, with regard to some high-frequency
signals, if the line is a little longer, the distributed inductance will be very great. In thiscondition, the equivalent decoupling capacitor may be inductive and nonfunctional.Hence, the value of a decoupling capacitor should be selected according to the frequencyof major interferences, and capacitors with good high-frequency characteristic and smallparasitic inductance will be better.
Questions
1. What does the BLDC motor control system consist of?
2. Compare the advantages and disadvantages of MOSFET drive circuits and IGBT drive
circuits, respectively.
3. What should be considered when choosing a microprocessor?
4. Please brieﬂy introduce the principle of the DSP control circuits.5. List some typical protection circuits in the BLDC motor control system, and try to describe
their functions.
6. How to determine the rotor position in sensorless control of BLDC motors, and what are the
relationships between the rotor position and back-EMF?
7. Establish your own BLDC motor sensorless control system based on MC33033 and
TB6537P.
8. Try to draw the ﬂowchart of software for sensorless control of a BLDC motor.9. What should be paid attention to during the software design of a BLDC motor control?
References
1. Wang, Z. A., Huang, J. (2006) Technology of Power Electronics . Machinery Industry Press, Beijing (in
Chinese).
2. Li, Z. Q. (2005) Single neuron adaptive PID control for BLDC motor based on online identiﬁcation of RBF neural
network . Tianjin University, Tianjin Master thesis, (in Chinese).
3. Liu, D. (2007) BLDC motor speed control based on immune feedback . Tianjin University, Tianjin Master thesis,
(in Chinese).
4. Hu, C. Y. (1998) Modern Speed Control for AC Motor . Machinery Industry Press, Beijing (in Chinese).
5. Xia, C. L., Yu, W., Li, Z. Q. (2006) Disturbance rejection control for torque ripple of BLDC motor. Proceedings of
the CSEE ,26(24), 137–142 (in Chinese).
6. Xia, C. L., Li, Z. J. (2005) BLDC motor control based on ADRC. Proceedings of the CSEE ,25(2), 82–86
(in Chinese).
7. Li, Y. D. (2002) Digital Control System for AC Motor . Machinery Industry Press, Beijing (in Chinese).
8. Xia, C. L., Liu, D., Wang, Y. F. (2007) BLDC motor immune PID control based on fuzzy rules. Transactions of
China Electrotechnical Society ,22(9), 68–73 (in Chinese).
9. Xia, C. L., Wen, D., Fan, J. (2002) Position sensorless control for BLDC motor based on RBF neural network.
Transactions of China Electrotechnical Society ,17(3), 26–29, 76 (in Chinese).
10. Shi, T. N., Tian, Y., Xia, C. L. (2007) Position sensorless control based on wavelet neural network for PM brushless
DC motors. Journal of Tianjin University ,40(2), 190–194 (in Chinese).Realization of BLDC Motor Drives 253

11. Zhang, X. J. (2001) Position sensorless control for BLDC motor . Shanghai University, Shanghai PhD thesis, (in
Chinese).
12. Tan, J. C. (2006) Application of ASIC for Motor Control . Machinery Industry Press, Beijing (in Chinese).
13. Li, Z. J. (2004) BLDC motor control based on ADRC . Tianjin University, Tianjin Master thesis, (in Chinese).
14. T Y. (2007) Position sensorless control for BLDC motor based on wavelet network . Tianjin University, Tianjin
Master thesis, (in Chinese).254 Permanent Magnet Brushless DC Motor Drives and Controls

8
Applications of BLDC Motor
Drives
BLDC motor is widely applied in industrial products, ofﬁce automation, household, vehicles,
medical equipment and other ﬁelds due to its excellent performance. In this chapter, theapplications of BLDC motors in the elevator-door system, driving lift system, inverter airconditioner and the related technologies will be presented.
8.1 Elevator-Door Control System
8.1.1 Introduction
An elevator is indispensable in high-rise commercial and residential building, multistory
factories and other buildings. Nowadays, 70% of elevator faults occur in elevator doors, so theelevator-door system is critical to the entire elevator system. There are two major types of
elevator-door-motor systems: DC motor drive systems and AC motor drive systems. Both
of these door-motor systems have their own defects. The presence of electric brushes andcommutators in DC motors will result in high noise, poor maintenance and EMC performance.The structure of an AC motor is simpler, but it has the disadvantages such as large volume, lowefﬁciency, large vibration and shock, and so on. Thus, these two types of motor control systemcannot meet the requirements for architectural modernization and the development of theelevator industry. Therefore, the research on intelligence, small size, high efﬁciency, reliableoperation and easy maintenance for elevator doors, will be one of the developing directions of
the elevator industry.
According to the control signals sent by the host computer, elevator-door-motor system
drives the elevator-door motor to control the opening and closing of the car door and the
landing door in an elevator. The elevator door runs frequently, so fast and reliable operation ofelevator doors for ensuring the normal working of an elevator is quite important. A high-performance elevator-door system should have advantages of smoothness, low noise, highefﬁciency and security, so as to shorten the waiting time, improve the transport capacity of theelevator, and ensure the safety of passengers.
The experimental system of an elevator door is shown in Figure 8.1.
Permanent Magnet Brushless DC Motor Drives and Controls , First Edition. Chang-liang Xia.
/C2112012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd.

The elevator-door system consists of the door motor, the controller of door motor, the
driving device of door motor, the mechanical parts of door system, the security detection
system, and so on, as shown in Figure 8.2.
8.1.1.1 Elevator-Door Controller
The elevator-door controller is primarily used to control the door motor installed at the top of
the elevator car, and drive the landing doors by a mechanical linkage to open and close the
landing doors and the car doors along the given curve quickly and accurately.
8.1.1.2 Structure of Elevator Door
The mechanical part of the elevator door mainly consists of car doors, landing doors, door
locks, door-protection devices, and so on. Among them, the car door and landing door play an
Figure 8.1 The experimental system of an elevator door.
Controller M
PowerDoor motor
Control SystemWormGear Gear Strap
Door Door
Figure 8.2 Block diagram of elevator-door control system.256 Permanent Magnet Brushless DC Motor Drives and Controls

important role in protecting passengers in the car from colliding with the elevator hoistway
and preventing the waiting passengers from falling into the elevator hoistway. The car door,
set near the landing door, is the channel for passengers to go into and out of the car.
The landing door or ﬂoor door, which is the opening and closing device set at the entrance tothe elevator hoistway of each ﬂoor, is used to ensure the safety of passengers. Further, thelanding doors must be locked in time when the door reaches the closing point toensure the safety of passengers, too. Currently, there are two structures of the car doorand landing door: the single door and the double door opening from the middle. To improvethe rapidity of the door system, the double-door structure is mostly adopted in high-performance elevator-door systems.
8.1.1.3 Safety Detection Subsystem
In order to prevent the passengers from being injured when they are going into or out of the
elevator, the safety detection subsystem is set in the elevator control system to detect whether
there are passengers going through the elevator door when the door is closing. If there arepassengers going into or out of the elevator car (including situations where passengers aresomewhere in front of the car door or the door being prevented from closing by passengers),the car door should stop closing immediately and reopen, to make sure that passengers go intoand out of the elevator safely. Currently, there are two common types of safety detectionsubsystem: a contact detection device and a noncontact detection device. A contact detectiondevice is mainly based on the safety edge, while the noncontact detection device includes a
photoelectric detection device (photosensor), ultrasound monitoring device, electromagnetic
induction detector and infrared light curtain detector and other forms.
8.1.1.4 Technology Requirements of Elevator-Door Motor System
The elevator-door control system drives a gear box and mechanical transmission through the
door motor to complete the process of opening and closing for the car door and the landingdoor. The opening and closing for the elevator car is a speed-changing process including start,stop, acceleration and deceleration. In order to guarantee the opening and closing for elevatordoor smoothly and rapidly, and avoid the collision at the beginning and the end, speed-regulating control of the elevator-door motor is essential. The common curve of opening and
closing for elevator door is shown in Figure 8.3.
As shown in Figure 8.3, the door motor runs at low speed to ensure a smooth opening in the
initial opening stage, then the elevator door accelerates to high-speed operation. When
the elevator is going to open completely, the door motor should also run at low speed toavoid the collision. Similarly, the elevator door starts slowly in the initial closing stage, andthen accelerates to high-speed operation. When elevator is going to be completely closed, theelevator door slows down to low-speed operation, and closes slowly too. Considering thesafety of passengers, the average speed of closing should be lower than the average speed of
opening so as to avoid clipping. During the closing process, in order to prevent the elevator
doors from hurting human bodies, a limited speed of elevator is set. Similarly, during theopening process, the speed should not be too high. So the maximum speed of opening andclosing for the door is set in advance.Applications of BLDC Motor Drives 257

The elevator-door system is closely related with the safety and comfort of passengers.
On the elevator-door control, a number of technical requirements have been introduced.
Currently, European Standard CEN-EN81-1, the most common criterion of elevatormanufacturing and installation, prescribes that the maximum kinetic energy of an elevator
door in the direction of closing should not exceed 10 J. For example, if the total mass of the
elevator door is 80 kg, the corresponding maximum velocity of closing is 0.5 m/s. Thecorresponding limited speed curve of elevator door is shown in Figure 8.4.
In the closing process, if the elevator door is stopped by impediment and the stopping torque
reaches the set value, the elevator-door system should terminate the closing process and openthe elevator door, then shut down again after a short waiting time. If the elevator door stillcannot be closed after repeating three times, the waiting time of closing the door should begradually extended to prevent the motor temperature from being too high.
In the early elevator-door control systems, travel switches and tachometer generators were
used to complete the control of opening and closing for the elevator door. Because of the singleVopen_max
Vclose_maxVopen_min
Vclose_minOpen
Closetravel
slopeslope
slopeslope
++++
−-− −
Vopen_min
O
Figure 8.3 Elevator-door operation curve.
Vmax/(m/s)
m/kgNot allowed range0.8
0.6
0.4
0.2
120 100 80 60 40 20 0
Figure 8.4 Limited speed curve of elevator door.258 Permanent Magnet Brushless DC Motor Drives and Controls

operating parameter and low reliability, this method was unable to meet the requirements of
the modern elevator control technology. Therefore, in order to avoid installing position
sensors, door systems should study the width of the elevator door by itself at the time of initial
installation, namely detecting the required distance that the elevator door runs from fullyclosed to fully open and storing these parameters for future use. The closed position of elevatordoors can be conﬁrmed by way of opening slightly, then shutting down three times with largetorque. When the width of the door or environmental condition is changed, the controller ismanually made to run again under the self-learning operation mode.
For the elevator-door control system, the technical requirements are as follows:
(1) The elevator-door motor installed in the elevator car controls the opening and closing
process of door. When the elevator car reaches the stop points of any levels, the doorknives and other mechanisms ensure that the current level landing door and elevator cardoor are linked to achieve the car door and landing door opening and closingsynchronously.
(2) The elevator door can run smoothly, and there is no severe vibration and noise. According
to national standards, the noise of opening and closing of door should not be more than65 dB.
(3) When the elevator door is fully open or closed, a certain capability of locking the rotor is
required.
(4) To be safe, when the car door and the landing door are closed, electrical and mechanical
conﬁrming and displaying equipments are needed to guarantee that the door is completelyclosed.
8.1.2 Hardware Design
The elevator-door system driven by a BLDC motor based on sensorless control consists of aBLDC motor, a main power circuit, a driving circuit, voltage and current sampling circuits, aDSP control circuit, and protection circuits for overvoltage, undervoltage and overcurrent, asshown in Figure 8.5.
In the elevator-door-control system, TI’s DSP TMS320F2812 is used for the controller. This
processor has high signal processing and control capability. It has integrated many kinds ofadvanced peripherals, and provides a good platform for the realization of motion control.
The single-phase 220 V, 50 Hz AC current is transformed into 22 V, 50 Hz AC current by the
transformer in the main power circuit of the system, and then rectiﬁed by the full-bridge
PowerMain
circuitBLDC motorElevator
door
Control
circuitSampling Driving
Host
computerCommunication
State output
Parameter
settingFault
display
Figure 8.5 Elevator-door system driven by a BLDC motor based on sensorless control.Applications of BLDC Motor Drives 259

rectiﬁer module, after which the voltage Udon the DC side of the inverter circuit is obtained
through a voltage-stabilizing capacitor, and then the BLDC motor is driven through a bridge
inverter with MOSFETs.
In addition, the system has the function of communicating between the host computer and
the slave MCU. Then, the operation parameters of the elevator-door system can be controlled
and set through the monitor program in the host computer directly.
8.1.2.1 Inverter Circuit
To ensure the safe operation of power devices, the bridge-inverter circuit has a turn-off snubber
circuit, namely the damping snubber circuit. Besides, MOSFET switches are very sensitive to
overvoltage between the gate and source, so some appropriate protective methods must betaken. The bridge inverter with damping snubber circuit is shown in Figure 8.6.
In Figure 8.6, the internal freewheeling diodes provide freewheel paths for winding
currents. When the motor is working in the stage of electromagnetic brake, the motor’sregenerative energy can be fed back to the DC bus through the freewheeling circuit, so that theMOSFET power switches are protected.
At the moment of turning off or turning on the MOSFET, due to the larger rate of change of
the winding current, the induced EMF is large. Then, if the induced EMF is not limited, thepower switches will be damaged. Therefore, the buffer circuit should be put next to each powerswitch, as shown in Figure 8.6, to slow down the rate of changes of voltage and current, inwhich C
1–C6are used to restrain the growth rate of voltage of T 1–T 6when they are
turned off, and resistors R1–R6can restrain the growth rate of the discharge current ﬂowing
from C1–C6to T 1–T 6when they are turned on.
Besides the above-mentioned protective methods, normal operation of the MOSFET
also needs an appropriate driving voltage and power. While discrete components are used
to achieve these functions, the circuit design is relatively cumbersome. It is also difﬁcultto determine the parameters of the devices, and to guarantee the reliability of the circuit.At present, speciﬁc integrated circuits ar e widely used to drive the power devices in
Figure 8.6 Three-phase bridge-inverter circuit.260 Permanent Magnet Brushless DC Motor Drives and Controls

industrial applications. This can overcome the shortcomings of disc rete components and
improve the reliability of the control circuit e ffectively. In the design, a speciﬁc gate drive
IC for power MOSFET IR2110 manufactured b yI Ri su s e d .T h eI Cc a ns i m u l t a n e o u s l y
drive two output signals, thus it is usually used to drive the upper and lower arms of the
same bridge.
The driving circuit is related to normal operation of the whole control system. So the
following design principles should be followed in the design process of driven circuit:
(1) provide sufﬁcient power for power switches of a bridge inverter;
(2) having essential protective functions;
(3) strive to reduce the self-loss of driving circuit;
(4) achieve electrical isolation from the control circuit;(5) be able to transfer driving signals quickly.
8.1.2.2 Overcurrent Protection
The DC bus current is converted to a voltage signal through sampling resistance, then sent to
the voltage comparator after ampliﬁcation and ﬁltering, and compared with the predeﬁnedreference value. If the current exceeds the set value, the comparator output toggles, then theinterrupt response of DSP takes place. Thus, the overcurrent protection is achieved.
8.1.2.3 Voltage Protection
The bus voltage differential sampling circuit is used to implement the voltage-protection
circuit. At the same time, overvoltage and undervoltage protection are achieved by setting the
upper and lower limits of the main circuit.
8.1.2.4 LED Display Circuit
In order to achieve a real-time display for speed and other status information of the motor
during operation, an LED display circuit is added to the control system. A designed LEDdisplay circuit is shown in Figure 8.7.
In Figure 8.7, CD4511 is the seven-segment decoder driver chip produced by TI. The chip
converts binary data into decimal data, and then produces corresponding signals to drive theseven-segment LED for displaying decimal numbers. Since CD4511 has strong load capacity,the circuit does not need an additional drive circuit. During the operation process, only thechip-selecting signal and the binary data, which will be displayed on the CD4511, are coming
from the DSP. Then, the data display is achieved.
8.1.3 Software Design
The elevator-door-control system usually adopts a modular programming method to achieve
the related functions, such as sensorless control of the BLDC motor, self-learning on doorwidth, automatic opening and closing of the door, and block torque detection [1].Applications of BLDC Motor Drives 261

8.1.3.1 Sensorless Control
First, the terminal voltage and phase current are sampled by hardware detection circuits,
then the line back-EMF of the BLDC motor is calculated based on a Kalman ﬁlter algorithm.When the zero-crossing point is detected, the controller changes the drive signal to implementthe commutation of BLDC motor, ensuring the normal operation of the BLDC motor.
Meanwhile, according to the average time interval between the two commutation points,
the motor speed can be calculated approximately. Speed deviation is obtained by comparing
the motor speed with the speed reference. Then it is controlled by a PI regulator, so that
the current reference signal is obtained. After that, the reference current with thefeedback current are compared. Finally, the control of the motor achieves the double-loopspeed control by adjusting the duty cycle of the PWM signal. During the operation ofthe motor, the rotor position of the motor and the moving distance of the elevator doorcan be calculated by the times of phase commutation. Speed reference values on correspond-ing points are determined by the given operation curve of the elevator door, so as toachieve the speed-operation curve of the elevator door in the process of opening and closing
the door.
The ﬂowchart of sensorless control for BLDC motor is shown in Figure 8.8.
8.1.3.2 Self-Learning of Door Width
For ﬁrst installation, the self-learning subroutine of the door width should be run to measure
the width of the elevator doors, which is the moving distance from the elevator door openingcompletely to closing completely. In addition, parameters of the door width about operationcurves of the door motor also include the low-speed operation point, the accelerating operationpoint, the high-speed operation point and the decelerating operation point. Then the para-meters are saved, and the maximum speed, minimum speed, acceleration and deceleration
values are set in the control system according to the requirement. Hence, it is ensured that these
settings are suitable for different working conditions. The ﬂowchart of a door-width self-learning subroutine is shown in Figure 8.9.
Figure 8.7 LED display circuit.262 Permanent Magnet Brushless DC Motor Drives and Controls

At the end of the self-learning subroutine of the door width, the control system will
record the measured width of the elevator door and the initial location of the elevator. By using
the initial position and the moving distance, the location of the elevator door can be conﬁrmed
to determine whether the elevator door is completely open or completely closed. Hence, a
dead-space switch in a traditional door device is not needed. Then, the complexity ofinstallation is reduced and the operation reliability of the device is improved. After deter-mining the location of the elevator door, the real-time speed command signal is givenaccording to the operation curve of the elevator door, and the elevator door operation iscontrolled in accordance with the curve. In the actual program, a smooth curve is usually usedfor the speed operation of the elevator door to ensure its opening and closing quickly andsmoothly.
The parameters of the operation curve, such as the minimum speed and the maximum speed
of the door’s opening, the minimum speed and the maximum speed of the door’s closing,slope, accelerating distance and decelerating distance of door’s closing, decelerating distanceof door’s opening are set by a potentiometer. Then, they are converted to a speed commandstable for controlling the elevator door, and the commands table is stored in FLASH orEEPROM to ensure that these parameters are not lost after being restarted and make to surethat the elevator door works normally.
In addition, after the control device of elevator door has run a certain time, the system should
automatically reconﬁrm the required running distance from fully closed to fully open, thuseliminating the accumulated error generated in the operation process.Detect terminal voltage and phase
current
Calculate line back-EMF
NStart
Zero crossing ?
Y
Change driving signal
for phase
commutation
Obtain motor speed
by timer
Record the times of
commutation
Figure 8.8 Flowchart of sensorless control for BLDC motor.Applications of BLDC Motor Drives 263

8.1.3.3 Opening and Closing of Door
The subroutine for opening and closing of elevator door is mainly responsible for controlling
the operation status of the motor and achieving the operation curve of the elevator door as showin Figure 8.3. When the elevator door receives commands to open or close door from the hostcomputer, the elevator car doors driven by the door motor run forward or reverse smoothly inaccordance with the given curves. When the elevator door reaches the fully open or fullyclosed position, the controller sends corresponding signals to the host computer, then thecurrent status of the elevator door is conﬁrmed.
8.1.3.4 Detecting Stalling Torque
In the opening and closing process of the elevator door, the stalling torque is calculated
according to the motion equation of the motor. When the calculated stalling torque is greaterthan the setting value of the stalling torque, it is considered that there are some obstacles, so theelevator doors stop closing, or open again. If the door cannot be closed after three times of trial,the waiting time for the door’s closing should be prolonged gradually to prevent overheating of
the motor. Meanwhile, the obstacle should be pushed away in a slow way by the elevator door
so that the door can close.Open door completely
Close elevator door
NStart
Motor stalled?
Y
Record the times of
commutation
Compare with last record and
count once when matching
Record the times of
matching
Reach two times of matching?
EndN
Y
Figure 8.9 Flowchart of self-learning subroutine of door width.264 Permanent Magnet Brushless DC Motor Drives and Controls

8.2 Elevator Traction Machine System
8.2.1 Introduction
With the accelerated process of urban modernization and sustainable development of the
construction industry, the elevator market is also developing rapidly. An elevator is a more
complex mechatronic piece of equipment providing transport services for high-rise buildings.
In recent years, new requirements for high-performance drive system are being proposed.More comfortable, small size, energy saving, reliable and accurate speed control are becomingthe developing directions of elevator drive systems.
An elevator is mainly composed of a traction machine, a guide system, a door system, a car
door, a counterweight balancing system, an electric drive system, a power control system and asecurity system [2,3]. Among them, the traction machine is composed of a motor, a tractionwheel and an electromagnetic braking device. According to whether there is a gear box
between the motor and traction wheel, it is divided into gear and gearless traction machines.
The gearless elevator traction machine is shown in Figure 8.10.
An elevator traction machine and its drive system are the major components of the elevator
drive system. As the power source for driving the elevator, their performances directly affect theperformance index of the elevator such as start up, braking, acceleration, deceleration, landingaccuracy and comfort. Currently, a gear traction machine is the main method used in elevatortraction drive systems. Gear transmission systems adopt a mechanical decelerator, worm gearsor a planetary gear, resulting in many shortcomings such as complex system structure, hard
maintenance work and high noise. The low efﬁciency of gear transmission also results in
increasing the energy consumption and running costs of the whole system. In addition, the large
31
2
4
Figure 8.10 Schematic diagram of gearless elevator traction machine (1: Electromagnetic braking
device, 2: Brake arm, 3: Traction wheel, 4: Brake disk).Applications of BLDC Motor Drives 265

size of the gear box and traction machine makes the volume of the on-top machine room larger
and the architecture cost increases, inﬂuencing the overall beauty of the building. The gearless
elevatortractionmachineofaBLDCmotorhastheadvantagesofcompactmechanicalstructure,
energy saving, low noise, and high transmission efﬁciency. Therefore, the further research ofgearless elevator traction machines has far-reaching signiﬁcance of improving the technicalcontent of the elevator and competitiveness in international markets. A physical photo of aBLDC motor elevator traction machine is shown in Figure 8.11.
The designed BLDC motor gearless elevator traction device includes a BLDC motor, a
traction wheel, an electromagnetic braking device, a brake disk, and the controller. The brakedisk and traction wheel are mounted on the rotor shaft of the BLDC motor. The BLDC motor is
used to drive the traction wheel and provide the torque needed to drag the car. Its stator adopts
concentrated winding, and radially magnetized permanent magnets are mounted on thesurface of the rotor. The traction wheel drags the elevator car moving up and down throughthe wire rope. The brake arm controlled by the electromagnetic brake is used to lock thetraction wheel under power failure and other fault conditions. The controller is used to controlthe BLDC motor in four-quadrant operation. This kind of gearless elevator traction machinedevice has advantages of high efﬁciency, low cost, small size, large torque, wide speedregulating range, and higher safety and reliability.
8.2.2 Characteristics of a BLDC Motor Gearless Elevator Traction Machine
A BLDC motor gearless elevator traction machine is a gearless elevator traction machinedriven by a BLDC motor. This kind of motor doesn’t need an excitation current and has high
Figure 8.11 Physical photo of the BLDC motor elevator traction machine.266 Permanent Magnet Brushless DC Motor Drives and Controls

efﬁciency, low noise, and it can work in strict accordance with the speed required by the
elevator, resulting in better comfort for passengers. Thus, it is favored by the elevator
manufacturing industry. Its main characteristics are given as follows:
(1) Environmental protection and energy saving. High magnetic ﬂux-density permanent
magnetic material is used in the BLDC motor, no excitation coil is required. Hence,
miniaturization and high efﬁciency of the motor system is achieved. Also, by adopting theway of gearless traction, the previous gear box is no longer needed.
(2) Lower vibration and noise. A BLDC motor gearless elevator traction machine without
gears eliminates the noise and vibration generated by gearing mesh of a gear traction
machine. Meanwhile, the motor speed is signiﬁcantly reduced, so the noise caused by
high-speed rotation of the motor is avoided.
(3) Safe and reliable. A permanent-magnet motor can constrain or lock the operation of
system by a proper control mode. In addition, the electromagnetic brake is mounted directlyon the rotor. When the brake works, the braking force acting directly on the rotor stopsthe operation of the traction machine, effectively preventing the elevator from slipping.
(4) Excellent and stable performance. As a result of the frequency control and nongear
system, a traction machine does not produce torque ﬂuctuations and effectively improves
the running stability of the system.
8.2.3 The Technical Requirements of the Elevator Traction Machine
The movement characteristics of the elevator traction machine include repetitive work,
variable speed, frequent starting, forward and reverse rotating. Compared with taking thetransport in the horizontal direction, the human body is more sensitive to speed changing ofvertical movement of the elevator. Therefore, the speed curve of the elevator, which can
improve not only the efﬁciency of the elevator but also the comfort of passengers, needs to be
designed to obtain higher operating performance of the elevator.
The ideal speed curve of an elevator should meet the following two requirements.
(1) Acceleration is an important parameter to the operation curve of the elevator. The
maximum acceleration a
maxmust not exceed 1.5 m/s2. If the acceleration is too large,
people will be severely uncomfortable or feel dizzy. The average acceleration aavmust not
be less than 0.5–0.7 m/s2. If the acceleration is too small, it will not only extend the process
of acceleration, lowering operating efﬁciency, but also make humans feel ﬂuctuations inthe change of the speed, and they may become uncomfortable.
(2) The rate of acceleration change in elevator technology is known as the physiological
factor. The rate of acceleration change cannot exceed 1.3 m/s
3. The speed curve of the
elevator should be a smooth transition in the corner, because it is decided by the body’sphysiological characteristics. A human is not only sensitive to the acceleration but alsomore sensitive to the rate of acceleration change. If the rate of acceleration change islarger, humans will feel dizziness or pain.
It can be seen from the analysis above that when the speed curve of the elevator is designed,
it is necessary to choose the right acceleration and rate of acceleration change, so as to meet therequirement of ride comfort and improve the operation efﬁciency. Therefore, when theApplications of BLDC Motor Drives 267

elevator starts, it should speed up slowly, and have a smooth transition to the steady-state
operation. The ideal speed curve of the elevator should be designed as a parabolic shape, asshown in Figure 8.12.
In Figure 8.12, the elevator starts accelerating slowly from the stationary state, passing
slowly from the stationary state to the operation of acceleration at the rate of accelerationchange p
1, and continues to accelerate at acceleration a1, going to the highest speed
through a smooth transition to the uniform state at rate of acceleration change p2, then enters
the stage of deceleration at the rate of acceleration change p3after running for a certain time.
Finally, it decelerates at acceleration a2, and transits to the stop state at rate of acceleration
change p4.
During the operation, the elevator traction machine starts and brakes frequently, and the
loads are changed markedly. Usually, there are the following technical requirements to be met.
(1) The elevator traction machine should have characteristics such as intermittent and
repeating operation, variable speed, frequent starting, forward and reverse operation.
(2) When it starts with a full load, the starting current should be as little as possible to avoid
inﬂuence on the motor windings from a large current.
(3) It should have large enough starting torque so that the car is capable of starting up and
accelerating at full load.
(4) It requires hard mechanical characteristics, i.e. when the load of the elevator changes, the
speed of the elevator will not change drastically.
(5) In order to make sure that the passengers feel comfortable, it should have low vibration
and noise, as well as high transmission efﬁciency.
8.2.4 Hardware Design
The BLDC motor gearless traction system consists mainly of a BLDC motor, a rectiﬁer/
inverter circuit, a drive circuit, a sampling circuit, the position detection circuit, a controlSpeed
Open gate
Speed ReferenceOrientation Timep1a1p2
p4p3
ttt t t tt1
2q d s
fka2
0
Figure 8.12 Operation curve of elevator traction machine.268 Permanent Magnet Brushless DC Motor Drives and Controls

circuit and an interface circuit. The whole structure diagram of the system is shown in
Figure 8.13.
8.2.5 Software Design
When an elevator traction machine works, it is required that the elevator can automaticallygain the operation direction according to the status of the elevator and elevator-calling signal,and achieve the given speed curve. When the elevator descends, it responds sequentially to the
down elevator-calling signals from lower layers than the one that the elevator is currently on.
When the elevator ascends, it responds sequentially to the up elevator-calling signals fromhigher layers than the one that the elevator is currently on. It should make sure to take all therequests of going downstairs before the ones of going upstairs, or in the inverse sequence.Therefore, when the elevator runs in the automatic operation mode, the following functionsshould be implemented.
(1) According to the current running state of the elevator and elevator-calling signal, the
direction of the operation is determined automatically, and the system responds sequen-
tially to the requests. When the elevator reaches the top ﬂoor or the bottom ﬂoor, thedirection is changed automatically. In addition, the elevator runs according to the designedspeed curve of the elevator.
(2) Open door automatically according to the leveling signal, and count the layers automat-
ically. When the elevator is running, the operation status of the elevator and the number ofthe layer are displayed inside and outside the building simultaneously.
(3) The elevator-calling signals are stored and recorded in a real-time way. When the elevator-
calling layer is reached, the corresponding elevator-calling signal should be canceled intime.
(4) When the frequency converter of the traction machine or the elevator-door system has
broken down, it should stop running immediately and produce related alarm signals. Then,the elevator goes to the nearest ﬂoor slowly and remains in waiting mode.Speed
regulatorCurrent
regulatorPWMo
utputEXB841
drive
circuitIGBT three-
phase inverter
Traction
wheelThree-phase
AC
Three-phase
bridge
rectiﬁerI/O
controlFailure
analysisHost
computer
A/D
converter
Commutation
logic
decision
QEP
circuitPhotoelectric
encoderCurrent
sampling DSP
n* i*
_ _Serial
communications
interface
(SCI)
BLDC
motorni
Figure 8.13 The BLDC motor gearless traction control system.Applications of BLDC Motor Drives 269

According to the above requirements, general functions of the elevator traction machine
control system are achieved. The ﬂowchart of the designed elevator traction machine control
system is shown in Figure 8.14.
8.3 Inverter Air Conditioner
A variable-frequency air conditioner is a new kind of high-efﬁciency equipment that can
automatically regulate the speed of the compressor motor according to the indoor load.
Compared to the traditional ﬁxed-frequency air conditioner, a variable-frequency air condi-tioner has the advantages of high efﬁciency, fast temperature regulating, small temperatureﬂuctuation, and adapting to a wide range of environment temperatures.
Among most of the current domestic variable-frequency air conditioners, the compressors
are driven by induction motors with high noise, low efﬁciency and power factor. The applicationPower on
System initialization,
elevator being at the bottom
ﬂoor
Elevator-calling signalN
YMalfunction interrupt?
Check in elevator-call signalFault processing
subroutineY
N
Read the status of the
elevator
Run according to the
operation rules
Reach the target layerN
Y
Traction machine leveling
Elevator door being
open and waiting
Close the door
Finish all of registered
signalsN Y
Figure 8.14 Flowchart of the elevator traction machine control system.270 Permanent Magnet Brushless DC Motor Drives and Controls

of a BLDC motor for driving the compressor can effectively overcome these shortcomings, and
signiﬁcantly reduce the overall size of the compressor system. Currently, Hitachi, Sanyo,
Toshiba and other companies have used a BLDC motor as the driving motor of the air-
conditioner compressor.
Through a microprocessor chip, the variable-frequency air conditioner controls the speed of
the compressor and the fan. The structure diagram of a variable-frequency air-conditionercontrol system is shown in Figure 8.15.
8.3.1 Control Function of Indoor Controller
Generally, the following functions should be achieved for the indoor controller [4].
(1) Receive input signal to control the switching of the air conditioner.
(2) According to different working environments, ﬁve operating modes: cooling, heating,
dehumidiﬁcation, auto, and defrosting, are achieved.
(3) The indoor temperature is detected in real time by using a sensor. According to the
difference between the given temperature and the actual indoor temperature, and thetemperature changing rate, the speed of the compressor is controlled. Then, temperaturedetection of the indoor heat exchanger and protection function are achieved.
(4) According to different modes selected by the user, the indoor fan runs at four modes: high
speed, medium speed, low speed and auto.
(5) When the air conditioner works, the current operating status is displayed.
(6) After the air conditioner starts to work, the air deﬂector is open, and the swing of air
deﬂector can be controlled by the shutter motor.
8.3.2 Control Function of Outdoor Controller
For the outdoor controller, it should have the following common functions.
(1) All of the outdoor temperatures are detected in real-time mode by sensors, and signals of
the outdoor environment temperature, coil temperature, and discharge temperature of the
compressor are sent to the indoor controller.Indoor controllerIndoor
fanShutter
motor
Input Outdoor controller
State
displayingPosition
sensorless
detectionOutdoor
Temperature
Sampling Inverter circuitOutdoor
fan
BLDC
motorData
communicationPower
Indoor
temperature
sampling
Figure 8.15 Structure diagram of variable-frequency air-conditioner control system.Applications of BLDC Motor Drives 271

(2) According to the outdoor environment temperature and the compressor speed, the speed of
the outdoor fan is controlled.
(3) It is controlled coordinately with indoor unit.
In addition, the position sensors installed in the BLDC motor increase the system cost, while
they affect the structure compactness of the compressor. Therefore, position-sensorless control
of the BLDC motor is mostly adopted in the compressor. The schematic diagram of sensorlesscontrol for a BLDC motor is shown in Figure 8.16.
In Figure 8.16, the whole control system consists of the current loop and speed loop. In the
speed loop, the voltage signal is processed through the program of a position-sensorless
control algorithm to obtain the speed n. The deviation between the reference speed n
/C3and the
calculated speed nis processed through the speed regulator to obtain the reference current i/C3.I n
the current loop, the reference current i/C3and the detected armature current iare calculated by
the current regulator to generate a PWM signal with variable duty cycle. Thus, the BLDC
motor is driven through the inverter circuit to drag the compressor.
8.4 Electric Vehicles
Fuel vehicles consume a large amount of oil resources, and discharge a lot of exhaust gas,which seriously pollute the environment, bring noise and other inevitable negative impacts.The Chinese Environmental Protection Center has demonstrated that the emission of vehicleexhaust gas pollution is the main pollution source, and EPA also estimates that vehicle
emissions account for as much as half of all the cases of cancer attributed to outdoor air
pollution. Faced with such a grim situation, research and development of electric vehicles havedrawn worldwide attention.
8.4.1 Pure Electric Vehicles
Electric vehicles have advantages of less pollution, saving oil consumption, simple structure,easy maintenance, and long service life. Thus, in the ﬁelds of energy, environmental protectionand energy saving, it shows excellent development potential. In addition, electric vehicleshave advantages of rapid torque response, short process of acceleration, direct control of thewheel speed, easy implementation four-wheel independent drive and four-wheel steering, high
safety and reliability of braking. These make electric vehicles show signiﬁcant merits and
–Speed
regulationSpeed
calculation
Current
regulationPosition sensorless
control
Current
detectionDriving circuit Inverter
–n* i*
iBLDC
motorn
Figure 8.16 Schematic diagram of sensorless control of a BLDC motor.272 Permanent Magnet Brushless DC Motor Drives and Controls

strong market competitiveness. A structure diagram of an electric vehicle derived by a BLDC
motor is shown in Figure 8.17.
The motor and control technology are the keys to electric vehicles. They should have
characteristics of wide adjustable speed range, high speed and starting torque, small size, lightweight, high efﬁciency, and regenerative braking to ensure good operating performance ofelectric vehicles. With the improvement of motor drive systems and its digital intelligentcontrol methods, the application of variable structure control, fuzzy control, neural-networkcontrol, expert system, genetic algorithm and other nonlinear intelligent control technologieswill enhance the performance of electric vehicle control system and its antidisturbancecapability, and improve the responding ability. Then, the overall performance can be
signiﬁcantly improved.
Currently, electric vehicles mostly adopt a DC motor, an induction motor, a switched
reluctance motor, the BLDC motor, and so on. Among them, the BLDC motor used as the drive
motor retains good characteristics of speed regulation, control and operating. It overcomes theshortcomings of the mechanical commutation, and has many advantages such as highefﬁciency, high power density, maintenance-free operation, high-speed operation, and soon. So it perfectly meets the basic requirements of drive motors used in electric vehicles [5].
The electromagnetic design of a BLDC motor used to drive electric vehicle should mainly
aim at increasing the rotation speed of the motor. Then, motors with characteristics of smallsize, light weight, high power and torque density are provided to meet its operatingrequirements. Meanwhile, BLDC motors can also be applied to other parts of the car. Forexample, they can be used as the driving motor of the auto air conditioner [6,7].
8.4.2 Hybrid Electric Vehicles
A hybrid electrical vehicle (HEV) is a vehicle that combines a conventional internalcombustion engine (ICE) propulsion system with an electric propulsion system. The hybridvehicles can beneﬁt from the best features of both conventional ICE vehicles and electricvehicles. The hybrid vehicle offers a long drive range and rapid refueling as for conventional
vehicles. Also, it can provide high efﬁciency with low loads, and deliver better acceleration at
low speeds. Since HEV is an emerging technology in the automotive market, the manufac-turers are designing and producing hybrid systems for passenger cars, light-duty vehicles, andeven heavy-duty vehicles. In general, the internal combustion engine provides the main powerDisplay and outputBattery
management
Operation
managementBattery
Electronic
controllerBLDC
motorTransmission
mechanismWheels
Figure 8.17 Structure diagram of the electric vehicle.Applications of BLDC Motor Drives 273

during the long-distance drive, while the electrical motor can either complement the ICE or
power the vehicle in electric-only mode during the urban service, where the ICE is less
efﬁcient. Improving battery capacity and technology may enable longer electric drive range
and reduce the need for the ICE contribution. At present, only hybrids combining a petrol ordiesel combustion engine with an electric motor are commercially available, the costs andtechnical bottlenecks still restrain the deployment of the hybrid vehicles.
There are basically three kinds of hybrid electric vehicles. One kind is using the engine as
the main driving power, and the electric motor is used as a secondary power unit. This kind ofoperation of a hybrid electric vehicle as shown in Figure 8.18(a) is called the parallel mode. Inthis mode, engines are used as the main power to drive the vehicle. The electric motor can
produce a strong driving force in the course of restarting, while the starting and accelerating of
the vehicle engine will consume a large amount of fuel. The electric motor is used as anauxiliary driving way to reduce the consumption of fuel. The structure of this mode is simple,which only needs to add an electric motor, a battery, and a related controller to the system. Thesecond kind of hybrid electric vehicle is that at low speed, the vehicle is driven only by electricmotor. When the velocity increases, the vehicle is driven by the engine and the electric motor.This kind is called the series-parallel mode, which is shown in Figure 8.18(b). Note that in thismode, power-sharing devices, generator and other devices are needed, so the structure is
complicated. Another kind of hybrid electric vehicle is where the electric motor is the only
driving power, which is called the series mode as shown in Figure 8.18(c). In this mode, theengine is used as the power source of the generator, and the vehicle is driven only by theelectric motor. At the same time, the engine is required to charge the battery.
8.5 Electric Bicycles
With the improvement of people’s living standards, environmental protection has drawnincreasing attention. So the green nonpolluting electric bicycle has become a current major
(c) Series modeFuel tank
Power
inverterBatteryICE
BLDC
motorMechanical
transmissionFuel tank
Power
inverterBatteryICE
BLDC
motorMechanical
transmissionGenerator
(b) Series-parallel mode (a) Parallel mode
Fuel tank
Power
inverterBatteryICE
BLDC
motorMechanical
transmissionGenerator
Figure 8.18 Structure diagram of HEVs.274 Permanent Magnet Brushless DC Motor Drives and Controls

development trend. Applying the BLDC motor to electric bicycles instead of the traditional
DC motor fully utilizes the signiﬁcant advantage of electronic noncontact commutation of theBLDC motor, which effectively extends the service life of electric bicycles, with convenient
speed regulation, ease of control, and smooth operation [8].
At present, the control mode of an electric bicycle is mostly to drive electric bicycle directly
by an in-wheel motor. The in-wheel motor is mounted on the bicycle wheel to directly drive the
bicycle, which can signiﬁcantly reduce noise of transmission and improve system efﬁciency.Figures 8.19 and 8.20 are, respectively, the structure diagram and the actual product picture ofa wheel BLDC motor.
Since high-efﬁciency rare-earth permanent magnet material is adopted in the rotor to
replace exciting windings, electric bicycles driven by a BLDC motor thus have higher
operation efﬁciency.
8.6 Others
8.6.1 The Applications in the Fan and Pump
With the rapid economic development, energy conservation has become an important issue. In
China, power consumption of fans and pumps accounts for more than 60% of the total powerconsumption of motors. Therefore, the development and application of related energy-savingtechnology in the ﬁelds of fans and pumps play an important role in the practical imple-mentation of our country’s energy-reduction strategy.
Fan equipment is mainly used for drying and cooling systems, where power consumption
accounts for about 20% or more of the national power output. In the traditional control method,the output power is mainly wasted in the closure process of the bafﬂe and valve. Note that the
shaft power of the fan and pump is proportional to the cube of the rotational speed. When the2
5 71
3
64
Figure 8.19 The structure diagram of a wheel BLDC motor (1: Wheel hub, 2: Rotor core, 3: Magnet
steel, 4: Stator core, 5: Stator winding, 6: Shaft, 7: Bearing).Applications of BLDC Motor Drives 275

rotational speed decreases, the shaft power will also decline rapidly. Thus, the use of variable-
speed regulation in ﬂow control can improve mechanical efﬁciency and achieve signiﬁcant
energy saving.
Currently, the BLDC motor has been successfully used to drive axial fans, cross-ﬂow fans,
electric fans, scavenger fans and other small fans of household air conditioners. Due to the
improvement of motor efﬁciency, the power consumption of small fans is decreasedsigniﬁcantly, and the related performance and quality of system have been greatly improved.
8.6.2 The Application in the Washing Machine
With the continuous improvement of consumption level and the quality of life, the demandof environmental protective and intelligent washing machines is increasing. Washingquality, drying quality, noise and vibration of the washing machine depend largely on the
performance of the motor. Therefore, the motor used in washing machines should be
developed towards high-power density, energy saving, environmental protection (lownoise) and intellectualization, which require the motor of washing machines to provideproper speed and torque according to the different washing modes, namely achieving variable-speed operation. In traditional washing machines, the single-phase induction motor is used todrive the washing machine via a belt drive and gear reducing. Although the motor has a simplestructure and low cost, the efﬁciency of this drive system is low, and it is difﬁcult to achievespeed regulation.
Figure 8.20 The wheel BLDC motor.276 Permanent Magnet Brushless DC Motor Drives and Controls

The pulsator washing machine driven directly by a BLDC motor does not need the belt and
reduction gear. So the wide speed range of a BLDC motor can change the water ﬂow in the
washing machine, and a variety of washing modes are achieved with less noise.
8.6.3 The Application in Medical Instrumentation
Because of the need for surgery, the power system of orthopedic medical devices should
achieve continuous speed regulation in a wide range to meet the requirements of differentoccasions, such as drilling, milling gap, reciprocating saw, swing saw and grinding. In theexisting orthopaedic hospitals of our country, motors used to drive medical instrumentation aremostly single-phase DC series motors, of which the motor commutator and brush are prone toproduce sliding friction between the mechanical wear, sparks and noise. This seriously affectsnot only the operative level of the medical staff, but also the psychological emotion of patients.Along with the development of the medical treatment level and the improvement of people’s
living standard, a new generation of low-noise, wide range of speed, small volume, and light
weight of BLDC motor drive systems is urgently needed. Therefore, the BLDC motor isexpected to be widely used in medical devices.
Questions
1. In what ﬁelds can the BLDC motor be applied?2. What are the main hardware components of the elevator-door-control system?3. What are the main characteristics of the elevator traction machine driven by the BLDC
motor?
4. Give more than 5 other applications of BLDC motor that are not included in this book.
References
1. Chen, W. Study on torque ripple suppression technique of permanent magnet brushless DC motor . Tianjin: Tianjin
University, PhD Thesis, 2006 (in Chinese).
2. Yang, L. C. (2000) The Design, Installation, Maintenance of Elevator Traction Machine. Machinery Industry Press,
Beijing (in Chinese).
3. Xu, J. Q., Yu, S. B., Xu, Y. L., et al. (2002) Present state and perspectives of driving system for elevator. Small &
Special Machines, 30(3), 5–7 (in Chinese).
4. Song, H. L. Study on air conditioner control system of BLDC motor . Harbin: Harbin Institute of Technology, PhD
Thesis, 2003 (in Chinese).
5. Chen, Q. Q., Zhan, Y. J. (2001) The 21st Century Green Transport-Electric Automobile . Tsinghua University Press,
Beijin (in Chinese).
6. Xia, C. L., Xue, X. D., Shi, T. N. (1999) Design of the brushless DC motor for the air conditioner in the automobile.
Micromotors Servo Technique ,32(3), 7–8 (in Chinese).
7. Xia, C. L., Shi, T. N., Wen, D. (2001) Simulation of non-bridge brushless DC motor for the air conditioner in the
automobile. Micromotors Servo Technique ,34(3), 7–9 (in Chinese).
8. Xia, C. L., Xue, X. D., Shi, T. N. (1997) Optimum design of brushless DC motor for electromotive bicycle. Small &
Special Machines, 25(3), 13–15 (in Chinese).Applications of BLDC Motor Drives 277

Index
AC asynchronous motor 8
acceleration torque 56, 204
AC–DC–AC converter 79
active disturbance rejection control 3, 11, 127,
146, 150
adaptive control 3, 20, 155–157
advanced conduction 76, 78–82, 144, 145, 244air gap 18, 20, 27, 28, 33, 34, 37, 38, 48, 59, 72,
78–80, 89, 127–130, 158–161, 163
angular position 46
angular velocity 39, 41, 54, 132, 138
antiwindup 86, 87
application-speciﬁc integrated circuit (ASIC) 12armature reaction 11, 33, 46, 51, 89, 147, 186armature winding 17, 25, 26, 47, 54, 127
asynchronous motor 8
automotive 1, 4, 5, 273auxiliary rotor winding 10
back-EMF 6, 9–11, 13, 27, 35, 37, 38, 40, 47–49,
52, 54, 56, 58, 59, 60, 62, 65, 67, 69, 76, 78–80,
89, 90, 99, 119, 127, 128, 130, 132–136, 138,
140, 143–148, 152, 157–161, 164, 165,168–170, 172–175, 177–182, 184–195,201–204, 206, 223, 233–236, 247, 253,
262, 263
back-EMF-based method 6, 9, 10, 168, 178, 179,
181, 201, 206, 247
basic structure 25
bipolar power transistor (BPT) 17
brake 260, 265–267
brush 20, 26, 277brushless DC motors (BLDC motor,
BLDCM) 1–21, 25–33, 38–45, 47, 48, 50–52,
54, 56–59, 62–67, 72–74, 76, 78–82, 83, 84,
86–92, 94, 95, 97, 99–101, 103, 104, 106–109,
111–117, 119–121, 123, 124, 127–133, 136,
140, 145–147, 149, 150, 152, 155, 157, 158,
161, 163, 165, 167–169, 173, 174, 177, 179,181–184, 186, 188, 189, 191–194, 196,
200–206, 209–212, 214–216, 218–221, 223,
224, 230, 232–236, 238, 240, 241, 246–253,255, 259–263, 266–269, 271–277
centrifugal 2, 5
centrifugal pump 5
ceramic capacitor 252
chopper pulses 235
coercivity 17, 18, 27cogging effect 10, 33
cogging torque 10, 11, 127–130, 160, 165
coil winding 27commutating current 120
commutation 1–3, 6, 10–13, 19, 25, 28, 31, 39,
51, 52, 58–62, 64, 73, 79–81, 97, 107, 127,131–146, 152, 154–157, 161, 163, 165, 167,168, 170, 172–175, 177, 178, 181, 185,
190–193, 196, 199, 203–205, 216, 221, 233,
236, 238, 240, 243, 244, 247, 262–264, 269,273, 275
commutation torque 10, 11, 19, 31, 58, 62, 127,
132, 133, 135, 140, 143, 144, 146, 152,
155–157, 161, 163, 165, 167
commutator 2, 25, 277
Permanent Magnet Brushless DC Motor Drives and Controls , First Edition. Chang-liang Xia.
/C2112012 Science Press. Published 2012 by John Wiley & Sons Singapore Pte. Ltd.

comparator 14, 186, 203, 213, 214, 220, 224,
228, 229, 236, 238, 239, 261
complex programmable logic device (CPLD) 3
computation capability 15computer peripheral equipment 7
concentrated full-pitch winding 27, 33
conductor 158copper material 27
core loss 18, 49
coreless BLDC motor 6, 19current control 94, 95, 97
current sensing 180, 236
DC machine 20
DC motor 1–4, 6, 8, 15, 25, 26, 40, 48, 51, 76, 79,
255, 273, 275
differential equation 25, 33, 39, 45, 62digital control 8, 14, 20, 44, 45, 85, 124, 273
digital signal processor (DSP) 219
diode 2, 9, 52, 61, 65, 67, 68, 123, 169, 174–177,
209, 210, 212
distributed function 94
distributed inductance 250, 251, 253distributed winding 27
double-stator type 6
doubly salient PM motor 20
driving circuit 25, 28, 30–33, 48, 52, 109, 123,
209, 211–215, 218, 224, 243, 251, 259, 261, 272
dynamic characteristics 25, 45, 52
dynamic response 5, 48, 85, 99, 117, 119, 120,
124, 199
eccentric wheel 6
efﬁciency 1, 2, 4, 6, 16–20, 26, 44, 48–50, 56, 57,
62, 120, 121, 123, 147, 157, 161–165, 181, 220,
239, 249, 255, 265–268, 270, 273, 275, 276
electrical angle 16, 29, 30, 33, 73, 132, 144–146,
157, 159, 167, 168, 170, 173, 174, 177, 216,
236, 238, 244
electric bicycle 274, 275
electrical vehicle 273
elevator door 57, 255–264, 269, 270, 277
elevator traction machine 265–270, 277EMC 250, 251
EMF 2, 9, 10, 34, 240, 260
energy conversion 1, 79energy loss 7energy product 17, 18, 128
energy saving 4, 6, 26, 265–267, 272, 275, 276
equivalent circuit 3, 38, 40, 41, 133estimation 9, 11, 46, 88, 94, 95, 102, 107, 112,
116, 155, 156, 168, 187, 190
extended state observers (ESO) 11
external load 117
fan and pump 275
Faraday 2feedback controller 181
feedback gain coefﬁcient 184, 185
ferrite magnetic materials 17ﬁeld-circuit method (FCM) 28
ﬁeld programmable gate array (FPGA) 3
ﬂoppy disc drives 7ﬂux 9, 20, 27, 34, 35, 37, 46, 72, 79, 83, 86, 89,
90, 130, 132, 158, 159, 161, 163, 164, 168, 174,
175, 178–180, 195, 267
ﬂux linkage 9, 34, 37, 46, 168, 174, 175,
178–180, 195
ﬂux-linkage-based method 168,
178, 179
four-quadrant 31, 266
frequency conversion 5, 6
frequency response 40friction loss 49, 80
frictional force 69
full-bridge 16, 30–32, 40, 59, 131, 132, 209,
210, 259
full-pitch windings 27, 158, 159
fuzzy control 3, 10, 20, 88, 90–92, 94, 103, 104,
106–108, 117, 145, 157, 162, 163, 273
gain 44, 57, 84, 89, 104, 173, 182, 184, 185, 190,
192, 194, 239, 269
gate circuit 214, 252
gate signal 65, 73, 186
gate terminal 49gearless 8, 265–269genetic algorithm optimization 102, 103,
105, 109
grey control 113, 115, 117, 124
half-bridge 16, 28–31, 133, 175,
209, 210
Hall element 2
Hall sensor 28, 191, 193, 238–240, 247
hardware design 9, 259, 268heating 26, 52, 79, 271high efﬁciency 1, 2, 4, 6, 16, 17, 19, 20, 57, 181,
220, 255, 266, 267, 270, 273, 275
hysteresis losses 33280 Index

impedance 124, 211, 213–215, 251–252
induced electromotive force (induced EMF) 2,
34, 260
induction motor 1, 4, 26, 86, 115, 273, 276inertia 19, 39, 43, 52, 56, 65, 83, 117, 119, 122,
154, 202, 203, 243, 249
initial rotor position 178, 179, 200–203, 248insulated gate bipolar transistor (IGBT) 3
intelligent power module (IPM) 215
insulation 212inverter 3, 6, 9, 11, 15, 16, 25, 32, 47, 52, 65–67,
72, 73, 80, 86, 95, 97, 100, 101, 117, 136,
148–150, 152, 174, 175, 193, 202, 209–212,
215, 220, 221, 224, 238, 239, 250, 255, 260,
261, 268–272, 274
inverter air conditioner 255, 270
Kalman ﬁlter 9, 112–114, 187, 188, 190,
192, 262
laminations 129
Laplace transformation 41
laser printer 8linear DC motor 6
linear motion system 6
load matching 56, 58, 62
loss 5–7, 17–19, 32, 38–39, 49–51, 80, 123, 129,
233, 232, 261
magnetic ﬁeld 18, 25, 27–30, 33, 34, 48, 49, 59,
76, 78–80, 128, 160, 179
magnetic pole 18
maximum efﬁciency 50, 62maximum speed 52, 120, 121, 257, 262, 263
mechanical characteristic 1, 2, 51, 56, 81
mechanical loss 39mechanical time constant 43, 44, 56medical instrumentation 277
microprocessor 85, 123, 124, 209, 210, 214, 216,
218–220, 224, 228, 229, 232, 236, 249–253, 271
microcontroller 3, 219, 220
microcontroller unit (MCU) 219
micromotor 18minimizing torque ripple 157
moment of inertia 39, 52, 56, 65, 83, 117, 119,
122, 202
multiple-input multiple-output (MIMO) 46
NEMA 1
neural-network control 3, 94, 100, 102, 118, 273neutral point 26, 32, 38, 67, 68, 169, 172, 233
niche algorithms 18
no-load condition 52
no-load loss 49no-load torque 49
nominal ﬂux 90
nominal inductance 90nominal resistor 90
nominal transfer function 89
nonlinear states error feedback (NLSEF) 11
observer 9, 107, 109, 112, 146, 148, 149,
181–186, 191–194
operating conditions 11, 47, 89, 119
operating frequency 17, 85
operating parameters 106
optical disc drives 7overload 239
pancake-shaped rotors and stators 20
parallel operation 219
permanent magnet 1–4, 15, 17, 18, 20, 25–28,
86, 94, 127, 128, 179, 267, 275
permanent-magnet synchronous motor
PMSM 86
permeability 35, 130
permeance 35phase shifting 117, 118, 234, 236
PI controller 44, 74, 76, 85, 87, 100, 116
PID 16, 20, 83–86, 91–93, 106–109, 112, 113,
117, 119, 146
pitch 27, 33, 129, 158–160
platform width 27, 157–161, 164, 165pole placement 183, 185
position control 94, 129
position-sensorless control 5, 6, 8–10, 12, 16, 17,
99, 167, 196, 233, 236, 240, 272
power density 4, 19, 54, 273, 276
power electronic switch 49, 51
power factor 2, 6, 163, 270
power switch 16, 17, 31, 32, 48, 51, 95, 123, 175,
202, 204, 212, 214, 240, 260
power transistor 17principle 9, 10, 25, 30–32, 44, 78, 80, 82, 83, 84,
91, 107, 124, 127, 133, 157, 165, 167, 169,
177–179, 181, 186, 200, 202–205, 216, 220,221, 224, 233, 238, 240, 253
protection 6, 123, 124, 202, 212, 214–216, 224,
229–232, 238, 240, 246, 247, 249, 251, 253,
256, 259, 261, 267, 271, 272, 274, 276Index 281

PWM generator 74
PWM modulation 16, 17, 51, 62, 86
quadrant 31, 123, 266rare-earth permanent magnetic materials 8, 27
ratings 252rectiﬁer circuit 123, 124, 209, 210
regenerative braking 123, 273
reluctance motor 2, 4, 20, 273reluctance torque 128
rotating magnetic ﬁeld 28, 30
rotation speed 25, 191, 195, 273
rotor 1–3, 7–10, 13, 15, 20, 25–30, 33–40, 46,
47, 49, 65, 69, 70, 72–78, 80, 89, 97, 99, 100,
102, 122, 123, 127–129, 131, 132, 135, 138,
140, 144, 150, 163, 167–169, 173, 174,177–181, 186–188, 194–197, 200–203, 205,
210, 216, 218, 220–223, 232, 233, 238, 240,
246–248, 253, 259, 262, 266, 267, 275
salient pole 35, 36
saturation 33, 51, 86, 89, 180series excitation DC motor 1
short circuit 230
short-pitch winding 27
single-phase induction motor 276skewed slot 160
sliding-mode variable structure control 3, 107,
113, 114
slot-type motor 10
slotless-type BLDCM 18
software design 209, 246, 253,
261, 269
speed control 16, 44, 51, 72, 74, 80, 82,
speed regulation 83, 85, 86, 90, 94, 95, 97,
100–102, 107, 109, 115–117, 119, 120,122–124, 129, 149, 177, 195, 223, 229, 238,
239, 262, 265
stabilization 89, 127
starting circuit 204
starting methods for sensorless control 201
starting torque 2, 56, 163, 164, 200,
268, 273
state-space equation 45, 62
static characteristics 104static stability 85stator 6, 7, 9, 10, 11, 15, 18, 20, 25–30, 33, 34,
36, 38, 52, 65, 89, 90, 97, 119, 120, 122,
127–130, 159, 163, 164, 179, 180, 193, 196,201, 216, 218, 232, 239, 240, 248, 266, 275switch 16, 17, 25, 28, 30–33, 48, 49, 51, 86, 91,
92, 95, 97, 123, 140, 168, 173, 175, 177, 196,
198, 199, 201–204, 210, 212, 214, 232, 239,
240, 251, 260, 263
synchronous motor 1, 3, 26, 72, 73, 76, 86,
115, 202
three-phase conduction mode 31
three-phase two-pole BLDC motor 33
three-phase winding 26, 45, 65, 67, 97, 99thyristor 2, 3, 123
time constant 43, 44, 52, 56, 84, 89, 90, 119, 120
time-sharing commutation strategy 131, 140,
144, 145
tooth ﬂux 163, 164
torque constant 59
torque ripple 3, 10, 11, 12, 17–19, 27, 54, 56, 62,
79, 81, 100, 102, 121, 127–133, 135–147,
149–153, 155–157, 159–161, 163, 165, 216
tracking differentiator (TD) 11, 146transfer function 25, 40, 41, 43–45, 47, 89
transformer 232, 259
transient process 40, 52, 58, 68, 133, 136–141,
143, 144, 156, 157
two-phase conduction mode 16, 30, 31, 40, 131,
132, 221, 222, 233
ultrasonic motor 94
uncertainty 88–90, 115
variable-voltage variable-frequency (VVVF) 7
variable 3, 5, 7, 9, 10, 20, 50, 51, 59, 65, 66, 68, 69,
83, 85, 87, 91, 104, 107, 109, 110, 112–115, 129,150, 161, 163, 177, 182, 185, 267, 268, 270–273
viscous friction coefﬁcient 39, 52, 65
voltage comparator 261voltage regulation 156voltage source inverter 11
voltage-controlled oscillator 203
washing machine 276, 277
wavelet neural network 196
winding current 52, 97, 164, 179, ,260winding inductance 10, 17, 35, 36, 157
winding voltage 157
Y-connection 172
Y-type 26
zero-crossing point 135, 144, 145, 168, 170,
172–174, 177, 181, 186, 203, 262282 Index

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