Dynamic Performances in Sensorless System with [601055]

Dynamic Performances in Sensorless System with
Two-Phase Induction Motor

CR
CIUNA Gabriela

“Lucian Blaga” University of Sibiu, Romania,
Department of Computer and Electrical Engineering, Faculty of Engineering,
Postal address: 4 Emil Cioran Str., 550025 Sibiu, Romania, E-Mail:[anonimizat]

Abstract – In this paper is treated one of the most
effective and widely used methods to obtain good
dynamic performances for AC motor namely rotor flux
direct field oriented control. A key role in achieving
such adjustment is played by the rotor flux estimator.
This on the one hand provides the absolute value
which is used in the flux feedback control loop and on
the other hand it gives the position of the rotor flux
relative to the stator system. In the block diagram of
the driving system with direct field oriented adjusting
control there are used estimators derived directly from
the machine equations. Using Matlab/Simulink
simulation environment applied for a two-phase
induction motor model, simulations were made for
different imposed speeds and the characteristics of
each estimator block diagram were highlighted.

Keywords: two-phase induction motor, direct field
oriented control, flux estimators, Matlab/SIMULINK.

I. INTRODUCTION

As is well known asynchronous motor is superior to
DC motor from the point of view of cost, robustness and
reliability. However, a long time could not compete in
high performance applications, in which they requested
a change in speed within wide limits. Long time
asynchronous motor was only used in constant speed
drives or where it varies within narrow limits, [4].
Limitation of applications is mainly due to nonlinear
dependence between the torque developed by the engine
and currents absorbed from the network, dependency
which makes it difficult the control of electric drives.
The most frequently used solution to this drawback is
overcome by the field oriented control system, also
known as vector control. This type of induction motor
speed control is based on the observation that reference
system associated to spatial phasor of rotor flux, there is
a clear separation between the effects of the two
components of stator current phasor. These components
are: reactive, oriented on the rotating phasor of the flux
that it regulates and the second, active component, or the
orthogonal component that adjusts the machine torque.
In this paper is addressed the problem of estimating
rotor flux in order to achieve a direct vector control, directed by this flux for a two-phase asynchronous
motor. This method of control is one of the most
effective and widely used solutions to achieve good
dynamic performance with AC machines, [1]-[3]. There
are several solutions for estimating the state of a linear
system with variable parameters. Lately several methods
have been proposed to identify the flux and induction
motors parameters, especially the rotor speed. These
methods are based almost all on the flux estimation, [1].
Thus, in analogue control drives are preferred
estimators directly derived from the machine equations,
because their implementation is simpler, [1] These
estimators are under study in this paper. Rotor flux is
obtained by solving the equations of the machine
according to various measured sizes (stator current,
stator voltage, rotor speed). Another class of estimators
are linear state estimator respectively Gopinath [5] or
Luenberger estimator, [3],[5]. There is also a third
category that of optimal estimators or Kalman filters.
The latter two categories are used in the digital
controlled drives.

II. MATHEMATICAL MODEL OF TWO-PHASE
INDUCTION MOTOR

A mathematical model of the induction motor may
be described by the following set of ordinary differential
equations in the stationary reference frame )0 ( =aw ,[2]
[4],





YY
dtd
+iR=udtd+iR=u
s
ss
sss
sss sssss
b
b ba
a a

(1)







Y -YY +Y
s
rrs
rs
rrsrrsr srr
dtd
+iR=dtd+iR=
bb
baa
a
ww
00

where, the stator and rotor flux linkage are described by
the following equations,



YY
iL+iL=iL+iL=
s
rms
sss
ssrmsssss
b b ba a a
(2)



YY
iL+iL=iL+iL=
s
rrs
sms
rsrrssmsr
b b ba a a

The electromagnetic torque is given by the equation,

( )ab ba y ysr sr
rmi iLpLm – =23 (3)
where p is number of pole pairs.
A spatial state model of induction motor should be
presented in order to permit the control and the
parameter online estimation of the machine,

s
ss s ss
uB xAdtdx
× +× = (4)

where,
[ ]T
r r s ssi i xb a b a y y = – State vector in stator
fixed coordinate system
[ ]T
s ss
s u u ub a= – Input vector in stator fixed
coordinate system
As can be seen, the state electrical characteristics of
this case are stator current and rotor flux. For the full
model speed of the machine is a variable parameter and
not a size of state so that the model is considered.
Thus, in the fixed two-phase stator coordinate system
( )s sba, , we have the following model for
asynchronous machine, [2],





– – –


 -+ – –


 -+ –
=
rr
rr
r rrr
r sr
r r s
s
T TT TT T TT T T
A
1 101011 1 1 101 101 1
wwsswss
ss
swss
ss
ss
s
(5)




=
0 00 01001
ss
s
LL
Bss

where,
ss
sRLT= ;
rr
rRLT= – Stator, rotor time constants
rsm
LLL2
1-=s – Total leakage factor III. ORIENTED CONTROL OF TWO-PHASE
INDUCTION MOTOR

A. Flux Estimators

Used flux estimators are derived directly from the
machine equations, where the rotor fluxes are obtained
by solving some of its equations. In analogue control
drives these solutions are preferred due to the simplicity
in implementation.
In the block diagram of the drive system with direct
vector control are used estimators VI, wI and wVI.
The naming convention is given according to their
inputs. Rotor flux estimation algorithms use voltages,
currents and speed of the machine depending on the
chosen model. For all flux estimators its modulus and
position is based on flux projections associated to stator
reference system, b a r rY Y, .
The implementation schemes of these three
estimators are shown in Fig.1 and Fig.2. These schemes
use the following sets of equations derived from the
relations (5),

dtdi
LLL LiRLLuLL
dtds
mrs m
ss
mr
s
mr r a
a aa -+ – =Y2 ˆ
dtdi
LLL LiRLLuLL
dtds
mrs m
ss
mr
s
mr r b
b bb -+ – =Y2 ˆ
(6)

Figure 1 VI, wVI Estimators
Relation (6) represents rotor fluxes dependence on
stator voltages and currents and is called “VI
estimator”. The expression of this estimator involves all
the main parameters of the model, except rotor
resistance.

Figure 2 wI Estimator
Estimator that uses the stator currents and rotor
speed as input (“wI estimator”) has the following form,
b a aawr r
rs
rm r
TiTL
dtdY- Y – =Yˆ1ˆ

a b bbwr r
rs
rm r
TiTL
dtd
Y+ Y – =Yˆ1ˆ
(7)

In these relations appear no stator parameters sR
and sL, but appears repeatedly the rotor circuit time
constant rT. Unlike the “VI estimator”, “wI
estimator” is as a system of linear differential equations.
Thus state is given by the rotor flux projections on the
two axes and the inputs in the system are the two stator
currents. Results therefore the standard form expression
of such a system.
Introducing the following notations,
sm
LLM=1
rm
LLM=2
and adding together two by two estimators equations (6)
and (7) is obtained estimator that uses rotor voltages,
currents and speed, wVI,

( )


–Y-Y-+Y
dtdiLTMM T uRL
MMTTdtds
ms rr r s
sm
srr a
b a aaw21
211 ˆ ˆ1ˆ
(8)
( )


–Y+Y-+Y
dtdi
LTMM T uRL
MMTTdtds
ms rr r s
sm
srr b
a b bbw21
211 ˆ ˆ1ˆ

All estimators described above are partial status
estimators. They estimated only a part of the state
system (4), the unmeasured part, namely the two
projections of the rotor flux (arYˆ,brYˆ).

B. Direct Field Oriented Control Using Flux
Estimators

Structure of a direct field oriented control system
based on rotor flux estimation is presented in Fig. 3, [6].
Measured feedback sizes are two-phase components of
stator voltage and current and rotor speed. They are
applied to the flux estimator input. Phasor analyser
“AF”, calculates the modulus and instantaneous position
of the rotor flux space phasor, in relation with which is
made the field orientation. Rotor flux modulus and rotor
speed are two feedback sizes in the two independent
control loops of the vector control system.

Figure 3 Block diagram of sensorless vector control system
with rotor flux estimation
Thus, in contrast to indirect vector control, in the
case of direct vector control uses a closed loop to control
rotor flux, [1]. Rotor flux controller takes as input the flux error, seen as the difference between imposed rotor
flux, *Yr and estimated rotor flux, arYˆ.
In Fig. 3 we can see the presence of block “DFOC”
(Direct Field Oriented Control) whose scheme is shown
in Fig. 4 and the power supply which is a PWM, which
presents a particular inverter class with intermediate DC.

Figure 4 The block diagram of DFOC

Speed controller takes as input the error rate obtained
as the difference between required and measured speed.
At output of direct vector control block are obtained
active and reactive components of stator current.

IV. SIMULATION RESULTS

The proposed algorithm was verified using real time
simulation on a Matlab/SIMULINK implementation of a
TPIM,( )min/ 1500 ; 230 ;35 rot nV UW Ps N N = = =
with known parameters, Table 1.

Table 1. The three-phase induction machine parameters
p=2 Rr=252,33W
16=sZ Ls=1,841H
17=sZ Lr=1,538H
2=m Lm=1,161H
Rs=415W J=3,3×10-5 kgm2

With the aid of the simulation environment,
simulations were performed for more prescribed speeds.
In Fig. 3 is a schematic diagram of the direct vector
control with “VIestimator”. To obtain vector control
using estimators wI, wVI, in Fig.3 we will just replace
the block “Estim VI” and outputs from the block
“TPIM” will be adjusted accordingly. Block diagrams
used in these cases are genuine, also the obtained results.

Figure 5 Speed system response for the reference at
W =380 rR

Apparently, in the simulations, the response of the
system to a reference speed level does not differ from
one estimator to another, regardless of the prescribed
value. In reality, different variations are observed if the
rotor resistance rR changes. Thus, Fig. 5 presents
graphs of the system in response to reference speed level
sec/ 07,157*radr=w for rotor resistance increased to
W =380rR . It is noted a fast response and a linear
evolution to the reference value in all three estimators
used. The most efficient proves to be “wVIestimator”.
Simulations were performed at no-load start of two-
phase asynchronous motor, and after 0,04s it was
applied the resistant torque Nm Trez 02,0= .

Figure 6 Speed system response for the reference at
W =120 rR

Figure 7 Speed system response for sec/ 10*rad r= w at
W =380 rR and W =120 rR
The same can be said for a decrease in rotor
resistance W =120rR , Fig. 6. The same simulations
were repeated for sec/ 10*radr=w , Fig. 7. In these cases it is noted the instability of the system regardless
of the value rR or the used estimator.
The role of used flux estimators, regardless of their
type, is to increase drives systems performances. Also
their removal reduces their cost, these systems are
known in the literature as sensorless systems. In Fig.8 it
is compared the two-phase induction motor operation
using and without flux sensor. As expected, sensorless
system proved to be more efficient in response.

Figure 8 Speed system response for the reference

V. CONCLUSION

This paper aims to highlight the performance of
sensorless drive systems use. This time it has been
removed the flux sensors from the system, and were
replaced by estimators derived directly from the
machine equation. The method is used in drives with
analogue control due to its simplicity. Of the three
estimators used, the most efficient proved to be
“wVIestimator”. It performed best in the variation of
rotor. If the drive does not depend on the variation of the
rotor resistance, either estimator would be more efficient
compared to drives using sensors.
In the case of direct vector control it has been found
an increase in the number of mathematical operations to
be made compared to indirect control. Currently this is
no longer a disadvantage because of the large computing
power of digital processors. The main advantage of
direct regulation is that it has a flux loop control through
the machine and thus it can be said that the motor
operates virtually flux steady.

REFERENCES

[1] P. Vas, “Sensorless Vector and Direct Torque Control”,
Oxford University Press, Oxford, 1998.
[2] N. P Quang, J. A. Dittrich “Vector Control of Three-
Phase AC Machines”, Springer, 2008.
[3] R. D. Doncker, D. W. J. Pulle, A. Veltman “Advanced
Electrical Drives”, Springer, 2011.
[4] A. Kelemen, Maria Imecs, “Vector Control of Induction
Machine Drives”, OMIKK Publischer, Budapest, 1992.
[5] T. Pan, “MATLAB în sisteme de acionare electric
automat, Universitatea Tehnic din Cluj Napoca, 1995.
[6] G. Crciuna, "Performances of Gopinath Flux Observer
Used in Direct Field Oriented Control of Induction
Machines", Advances in Electrical and Computer
Engineering, vol. 11, no. 1, pp. 73-76, 2011.