CAPITAL UNIVERSITY OF SCIENCE AND TECHNOLOGY, ISLAMABAD Electric Machine Control Design for Hybrid Electric Vehicles by Athar Hanif A thesis… [609050]

CAPITAL UNIVERSITY OF SCIENCE AND
TECHNOLOGY, ISLAMABAD
Electric Machine Control Design
for Hybrid Electric Vehicles
by
Athar Hanif
A thesis submitted in partial fulllment for the
degree of Doctor of Philosophy
in the
Faculty of Engineering
Department of Electrical Engineering
October 2017

i
Copyright c
2017 by Athar Hanif
All rights reserved. No part of this thesis may be reproduced, distributed, or
transmitted in any form or by any means, including photocopying, recording, or
other electronic or mechanical methods, by any information storage and retrieval
system without the prior written permission of the author.

vi
List of Publications
Journal Publications
1. Journal Publication 1
A. Hanif , A. I. Bhatti and Q. Ahmed, "Managing Thermally Derated
Torque of an Electried Powertrain Through LPV Control", IEEE Transac-
tion on Mechatronics (Accepted for publication), 2017.
2. Journal Publication 2
A. Hanif , Q. Ahmed, A. I. Bhatti and G. Rizzoni "Linear Parameter Vary-
ing based Field-oriented Control for an Induction Machine based Electried
Powertrain", IEEE Transaction on Industrial Electronics (Under Review),
2017.
Conference Publications
1.A. Hanif , A. I. Bhatti, Q. Ahmed and G. Rizzoni, "Genetic Algorithm
optimized Multi-objective Controller for an Induction Machine based Elec-
tried Powertrain", Accepted in IEEE Conference of Control Technology
and Applications to be held in, August 27-30, 2017, Hawai'i, USA.
2.A. Hanif , A. I. Bhatti and Q. Ahmed, "Estimation of thermally de-rated
torque of an HEV drive using robust LPV observer", in American Control
Conference, 2016. Proceedings of the 2016, pp. 15301535, July 2016.
3.A. Hanif , A. I. Bhatti and Q. Ahmed, "Compensating the Performance and
Loss of Life of an Induction Machine based Electried Powertrain using Ro-
bust LPV Controller", in American Control Conference, 2018. Proceedings
of the 2018, Submitted, June 2018.
4.A. Hanif , S. M. N. Ali, Q. Ahmed, A. I. Bhatti, G. Yin, and M. H. Jaery,
"Eect of variation in rotor resistance on the dynamic performance of induc-
tion motor", in 2016 35th Chinese Control Conference (CCC), pp. 95249529,
July 2016.

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5. S. N. Ali, A. Hanif and Q. Ahmed "Review in thermal eects on the per-
formance of electric motors", in 2016 International Conference on Intelligent
Systems Engineering (ICISE), pp. 8388, IEEE, 2016
6.A. Hanif , Aamer Iqbal Bhatti, Abdul Rehman Yasin, Ghulam Murtaza,
and Qadeer Ahmed,"Sliding Mode Based Robust Observer Design for Field-
oriented Control of 3-phase Induction Machine Drive for Applications in
Hybrid Electric Vehicles", in Control Conference (CCC), 2014 33rd Chinese,
pp. 263268, IEEE, 2014.
7.A. Hanif , Aamer Iqbal Bhatti, and Qadeer Ahmed, "LPV Based Robust
Observer and Controller Design for Field-oriented Control of 3-phase Induc-
tion Machine Drive for Applications in Hybrid Electric Vehicles". Presented
in WEC-2013, NUST, 2013, Islamabad, Pakistan.
8. Athar Hanif, Faizan Pervaiz, Zeeshan Ali, Ali Abbas and Zohaib Qamar,
"Plug in type series hybrid vehicle: Concept, Design, and Implementation."
Proceeding of the International Conference on Mechanical and Electrical
Technology, 26-27 August, 2011, Dalian, China.

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Abstract
In order to achieve fuel eciency and reduce emissions into the atmosphere, the
automobile manufacturers have decided to escalate modern technologies such as
Electric Vehicles (EVs) and Hybrid Electric Vehicle (HEVs). Vehicles with elec-
tried powertrain exhibit degraded performance when operated in hot environ-
ments. When the operating and ambient temperatures rise, an electric drive
suers from torque derating, poor eciency and loss of lifetime (aging) as its
parameters change. Electric machine is the main component of an electried
powertrain. Among the available electric machines, induction machine has been
used for the traction system of EVs and HEVs because of the advantages in-
cluding reasonable cost, simpler control, enhanced power density and eciency,
consistent operation over wide speed range, elevated initial torque, technological
development and universal availability. Induction machines are also very robust,
have rugged construction and require little maintenance. Moreover, induction
machines are inherently de-excited with respect to inverter fault hence highly rec-
ommended to be used in automobile industries for precautionary measures. This
manuscripts presents the novel control schemes based on linear parameter varying
theory for enhancing the performance of an induction machine based electried
powertrain. Linear parameter varying control theory is extensively used in time
varying plants. Linear parameter varying observers and controllers based on linear
parameter varying dynamics deliver robust platform for the estimation and control
of electric drive system variables. In this dissertation, linear parameter varying
based observer is designed for an electried powertrain. The designed observer is
used to estimate the thermally derated torque and
ux of an electric powertrain.
This estimation is extremely helpful in controller design for the performance im-
provement of electric drive system. Secondly, a robust control scheme is designed
and developed in this thesis to address the torque derating problem. The designed
observer-controller pair is used to manage the thermally derated torque of an elec-
tried powertrain. The performance of the proposed linear parameter varying
based observer-controller pair is evaluated for a light duty electric vehicle against
Federal Urban Driving Schedule (FUDS) operating at various ambient tempera-
tures, which is a common controller evaluation approach adapted by automotive
community. Experiments are carried out on an induction machine electric drive,
realized by the NI myRIO-1900, using FUDS driving cycle to investigate that the

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proposed technique is eective and delivers robust performance. Another contri-
bution of this manuscript is the design and development of degradation control
scheme for an electric powertrain. In the synthesis of this control scheme, meeting
the road loads, ensuring ecient powertrain operation and minimizing the loss of
lifetime (aging) of an electric machine are considered as three essential but con-

icting targets. The eectiveness of the proposed control framework is tested for
a direct drive electried powertrain of a three-wheeled vehicle commonly found
in urban transportation for Asian countries. The urban driving schedule based
simulation results conrm that the lifetime of induction machine can be enhanced
by appropriate controller design without compromising its performance.

Contents
Author's Declaration iii
Plagiarism Undertaking iv
Acknowledgements v
List of Publications vi
Abstract viii
List of Figures xiv
List of Tables xviii
Abbreviations xix
Symbols xx
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Hybrid Electric Vehicles . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Types of Hybrid Electric Vehicles . . . . . . . . . . . . . . . 5
1.2.1.1 Parallel hybrid . . . . . . . . . . . . . . . . . . . . 5
1.2.1.2 Split hybrid . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1.3 Series hybrid . . . . . . . . . . . . . . . . . . . . . 5
1.3 Electric Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.1 Induction Machine . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Motivation and Objectives . . . . . . . . . . . . . . . . . . . . . . . 8
1.5 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.6 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . . 10
2 Electric Machines in Hybrid and Electric Vehicles 13
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 Propulsion Electric Machine Topologies . . . . . . . . . . . . . . . . 17
2.2.1 Induction Machines . . . . . . . . . . . . . . . . . . . . . . . 18
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2.2.2 Permanent Magnet Machines . . . . . . . . . . . . . . . . . 19
2.2.3 Switched Reluctance Machines . . . . . . . . . . . . . . . . . 21
2.3 Traction Operation Versus Industrial Operation . . . . . . . . . . . 21
2.4 Induction Machine for Traction System . . . . . . . . . . . . . . . . 23
2.5 Sizing of propulsion Machine . . . . . . . . . . . . . . . . . . . . . . 25
2.6 Research Scope in Induction Machine Control . . . . . . . . . . . . 26
2.6.1 Parameter Variations Eects . . . . . . . . . . . . . . . . . . 26
2.6.2 Review of Existing Estimators and Controllers . . . . . . . . 29
2.6.2.1 Estimation Problem . . . . . . . . . . . . . . . . . 30
2.6.2.2 Control Problem . . . . . . . . . . . . . . . . . . . 33
2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3 Mathematical Modeling of Induction Machine 37
3.1 Construction and Principle of Induction Machine . . . . . . . . . . 38
3.2 Induction Machine Modeling . . . . . . . . . . . . . . . . . . . . . . 40
3.2.1 d-q Model of a Three-phase Induction Machine . . . . . . . 43
3.2.1.1 d-q Model of a Three-phase Induction Machine in
Synchronously Rotating Reference Frame . . . . . 44
3.2.1.2 d-q Model of a Three-phase Induction Machine in
Stationary Reference Frame . . . . . . . . . . . . . 47
3.2.1.3 The Complete Dynamics of an Induction Machine . 49
3.3 Hybrid Electric Vehicle Drive System and Control . . . . . . . . . . 50
3.3.1 Field-oriented Or Vector Control of a Three-phase Induction
Machine Drive . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.3.1.1 Direct or Feedback Field-oriented Control . . . . . 51
3.4 Load Torque Prole . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.5 Model Based Analysis and Simulation . . . . . . . . . . . . . . . . . 55
3.5.1 Model Simulation and Discussion . . . . . . . . . . . . . . . 56
3.5.1.1 Positive Load Torque-Motoring Operation . . . . . 56
3.5.1.2 Positive and Negative Load Torque-Motoring and
Generating Operation . . . . . . . . . . . . . . . . 59
3.6 LPV Modeling of Induction Machine . . . . . . . . . . . . . . . . . 60
3.6.1 LPV Model Validation . . . . . . . . . . . . . . . . . . . . . 65
3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4 Estimation of Thermally de-rated Torque of an Electried Pow-
ertrain 70
4.1 Benets of Thermally Derated Torque Estimation . . . . . . . . . . 71
4.2 Advantage of LPV Control Technique . . . . . . . . . . . . . . . . . 71
4.3 Linear Parameter Varying Observer for Electried Powertrain . . . 72
4.4 Current and Flux Dynamics . . . . . . . . . . . . . . . . . . . . . . 74
4.4.1 Linear Parameter Varying Dynamics . . . . . . . . . . . . . 75
4.4.2 LPV Robust Observer . . . . . . . . . . . . . . . . . . . . . 75
4.4.2.1 Structure of Robust LPV Observer . . . . . . . . . 75
4.4.2.2 Observer Stability . . . . . . . . . . . . . . . . . . 76

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4.4.2.3 Observer Construction . . . . . . . . . . . . . . . . 77
4.4.2.4 Synthesizing the Robust LPV Flux Observer . . . . 78
4.4.2.5 Selection of Observer Gain . . . . . . . . . . . . . . 79
4.5 Evaluation of Estimation Scheme . . . . . . . . . . . . . . . . . . . 79
4.5.1 Theoretical Scenario . . . . . . . . . . . . . . . . . . . . . . 80
4.5.2 HEV Powertrain . . . . . . . . . . . . . . . . . . . . . . . . 81
4.5.3 Thermally de-rated torque estimation . . . . . . . . . . . . . 83
4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5 Managing Thermally Derated Torque of an Electried Power-
train 86
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.2 Vehicle Dynamics and IM Modeling . . . . . . . . . . . . . . . . . . 89
5.2.1 Vehicle Modeling and Dynamics . . . . . . . . . . . . . . . . 89
5.2.2 Dynamics of IM . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.2.3 LPV Modeling of Induction Machine . . . . . . . . . . . . . 91
5.3 EV Performance Constraints and IM Parameter Estimation . . . . . 91
5.3.1 Performance Criteria . . . . . . . . . . . . . . . . . . . . . . 91
5.3.2 IM Performance Curve . . . . . . . . . . . . . . . . . . . . . 92
5.3.3 Rotor and Stator Resistance Estimation . . . . . . . . . . . 93
5.4 Control Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.4.1 Controller Structure . . . . . . . . . . . . . . . . . . . . . . 95
5.4.2 Robust LPV Current Controller . . . . . . . . . . . . . . . . 96
5.4.3 Design Methodology . . . . . . . . . . . . . . . . . . . . . . 99
5.4.4 Robust Torque and Flux Controller . . . . . . . . . . . . . . 101
5.4.5 Reference Current Calculation . . . . . . . . . . . . . . . . . 105
5.4.6 Reference Flux Calculation . . . . . . . . . . . . . . . . . . . 106
5.5 Comparison With Sliding Mode Control . . . . . . . . . . . . . . . 107
5.6 Standard Driving Cycle Analysis . . . . . . . . . . . . . . . . . . . 109
5.6.1 EV Specications and Simulation Detail . . . . . . . . . . . 109
5.6.2 Control Evaluation . . . . . . . . . . . . . . . . . . . . . . . 111
5.7 Experimental Verication . . . . . . . . . . . . . . . . . . . . . . . 116
5.7.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . 117
5.7.2 Open Loop Torque Derating Conrmation . . . . . . . . . . 118
5.7.3 Comparison with Sliding Mode Controller . . . . . . . . . . 118
5.7.4 Torque Derating Compensation against FUDS Cycle . . . . 119
5.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6 Degradation Control for an Induction Machine based Electried
Powertrain 124
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.2 Brief Theoretical Background of Multi-objective Control Problem . 128
6.3 Proposed LPV based FOC Framework for Traction Induction Machine129
6.4 Modeling of Electried Powertrain . . . . . . . . . . . . . . . . . . . 130
6.4.1 Vehicle Dynamics and Drivetrain Modeling . . . . . . . . . . 131

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6.4.2 Mathematical Model of IM . . . . . . . . . . . . . . . . . . . 132
6.5 Calculations for the Upper Limits on Stator Voltages . . . . . . . . 135
6.6 The Multi-objective Functions . . . . . . . . . . . . . . . . . . . . . 136
6.6.1 Case-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.6.2 Case-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.6.3 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.6.4 Eciency of Electried Powertrain . . . . . . . . . . . . . . 138
6.6.5 Road Load Error . . . . . . . . . . . . . . . . . . . . . . . . 138
6.6.6 Aging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
6.6.7 Temperature Measurement . . . . . . . . . . . . . . . . . . . 139
6.7 LPV based FOC Control Design . . . . . . . . . . . . . . . . . . . . 140
6.7.1 Torque and Flux Estimation . . . . . . . . . . . . . . . . . . 140
6.7.2 Multi-objective LPV Controller Synthesis . . . . . . . . . . . 141
6.7.3 Robust Flux and Torque Controller . . . . . . . . . . . . . . 145
6.7.4 Calculation for Reference Flux . . . . . . . . . . . . . . . . . 145
6.8 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . 146
6.8.1 Vehicle specications and simulation detail . . . . . . . . . . 146
6.8.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . 148
6.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
7 Conclusion and Future Directions 157
7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
7.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
7.3 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
8 Appendices 162
8.1 Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
8.1.1 Close-loop stability and synthesis of controller . . . . . . . . 162
8.2 Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
8.2.1 Induced L-2 norm of LPV systems . . . . . . . . . . . . . . 165
8.3 Appendix C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
8.3.1 Thermally derated torque's observer gains . . . . . . . . . . 165
8.4 Appendix D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
8.4.1 LPV current controllers gains . . . . . . . . . . . . . . . . . 168
8.4.2 Torque and
ux controllers gains . . . . . . . . . . . . . . . 171
Bibliography 172

List of Figures
1.1 Oil Production, Demand and Import by Pakistan[1]. . . . . . . . . . 2
1.2 Based on the powertrain components arrangement, there are ba-
sically three schemes for the hybrid electric vehicles. (a)Parallel
hybrid, (b)Split hybrid, and (c)Series hybrid . . . . . . . . . . . . . 4
2.1 Parallel HEV Conguration. . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Schematic of an electric vehicle (EV) powertrain . . . . . . . . . . . 15
2.3 Electric Traction Motor (a) Torque-Speed Curve (b) Propulsive Ef-
fort Versus Speed [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 Motor Characteristics [2]. . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 Major traction and industrial machines. . . . . . . . . . . . . . . . . 18
2.6 Hybrid and electric vehicles. . . . . . . . . . . . . . . . . . . . . . . 22
2.7 Variations in (a) Drive cycle (b) Ambient temperature (c) Payloads
and (d) Operating temperature. . . . . . . . . . . . . . . . . . . . . 22
2.8 (a) Rotor and stator resistance variations (b) Operating voltages
imbalances and (c) Operating currents imbalances. . . . . . . . . . 23
2.9 Eect of ambient and operating temperatures on the dynamic torque-
speed characteristic curve for unipolar load torque. . . . . . . . . . 28
2.10 Eect of ambient and operating temperatures on the dynamic torque-
speed characteristic curve for bipolar load torque. . . . . . . . . . . 28
2.11 Direct Field-oriented Control Block Diagram With Rotor Flux Ori-
entation [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1 Idealized two pole three-phase induction machine [4]. . . . . . . . . 38
3.2 Coupling eect in three-phase stator and rotor windings of the ma-
chine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3 Equivalent two-phase machine. . . . . . . . . . . . . . . . . . . . . . 41
3.4 Stationary frame abctodsqsaxes transformation. . . . . . 42
3.5 Location of rotating dqaxes relative to stationary dqaxes. . . 43
3.6 Dynamic dqequivalent circuits of a 3 induction machine. . . 44
3.7 Proposed Induction Machine Drive Structure with Direct or Feed-
back Field-oriented Control. . . . . . . . . . . . . . . . . . . . . . . 53
3.8 Phasor Diagram for Direct Field-oriented Control in Synchronously
Rotating Reference Frame (SRRF)[3]. . . . . . . . . . . . . . . . . . 54
3.9 Aerodynamic drag force, Rolling resistance force, Road grade force
on a Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.10 Load Torque. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
xiv

xv
3.11 Induction machine load torque, electromagnetic generated torque,
rotor speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.12 Induction machine three phase current for the unipolar load torque. 58
3.13 Dynamic behavior of induction machine: Torque-speed curve. . . . 58
3.14 Bipolar load torque. . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.15 Induction machine phase currents for bipolar torque. . . . . . . . . 60
3.16 Induction machine load torque, electromagnetic generated torque,
rotor speed for bipolar torque. . . . . . . . . . . . . . . . . . . . . . 60
3.17 Dynamic behavior of induction machine: Torque-speed curve. . . . 61
3.18 Open-loop time response of an LPV model. Unit step demand in
us
dS;for 10 equally spaced values of nR;rR;rS. . . . . . . . . . . . . 65
3.19 Input voltages us
dSandus
qSto validate the nonlinear model and LPV
model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.20 Load torque input TLto validate the nonlinear model and LPV model 66
3.21 Validation plots of output currents is
dSandis
qSof the original non-
linear model and the LPV model. . . . . . . . . . . . . . . . . . . . 67
3.22 Validation plots of states s
dRands
qRof the original nonlinear
model and the LPV model. . . . . . . . . . . . . . . . . . . . . . . . 68
4.1 Overall scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.2 Robust LPV observer estimated results of : D-axis
ux(Top), Q-
axis
ux(Middle), and Torque de-ration(Bottom) at 200C, 200C,
and 400C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.3 Robust LPV observer convergence results of actual and estimated:
D-axis
ux(Top), Q-axis
ux(Middle), and Torque de-ration(Bottom). 81
4.4 (a) 3-phase Input voltages to the electric drive system. (b) Vdand
Vqfor the electric drive system. . . . . . . . . . . . . . . . . . . . . 82
4.5 Robust LPV observer estimated results for shortened FUDS test
cycle of : D-axis
ux(Top), Q-axis
ux(Middle), and Torque de-
ration(Bottom) at 200C, 200C, and 400C. . . . . . . . . . . . . . 82
4.6 Robust LPV observer convergence results for shortened FUDS test
cycle of actual and estimated: D-axis
ux(Top), Q-axis
ux(Middle),
and Torque de-ration(Bottom). . . . . . . . . . . . . . . . . . . . . 83
4.7 (a) 3-phase Input voltages to the electric drive system. (b) Vdand
Vqfor the electric drive system. . . . . . . . . . . . . . . . . . . . . 84
4.8 Robust LPV observer estimated torque de-rating under dierent
operating conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.1 Induction motor (used in this work) performance curve at 250Cand
400C(Torque derating at 400Cis vivid). . . . . . . . . . . . . . . . 93
5.2 Inner and outer loop strategy in induction machine. . . . . . . . . . 95
5.3 Constraints on S;T,andKSin term of a generalized plant. . . . . . 99
5.4 Simulation result for closed loop rotor velocity performance. ( a)
Load torque taken in closed loop simulation. ( b) Rotor velocity
tracking: reference (red) and actual (blue). . . . . . . . . . . . . . . 108
5.5 Vehicle level system architecture. . . . . . . . . . . . . . . . . . . . 110

xvi
5.6 Simulation results: Temperature prole for the controller observer
pair evaluation at dierent ambient temperatures. . . . . . . . . . . 111
5.7 Tracking of vehicle speed prole via a change prole of temperature
(at ambient temperature of 400C) with LPV controller observer pair.112
5.8 Induction machine speed. . . . . . . . . . . . . . . . . . . . . . . . . 113
5.9 Simulation results: Rotor and stator resistance variations over the
entire period of operation at dierent ambient temperatures. . . . . 113
5.10 Simulation results: Tracking of torque request prole via a change
prole of temperature (at ambient temperature of 400C) with LPV
controller observer pair. . . . . . . . . . . . . . . . . . . . . . . . . 114
5.11 Simulation results: Tracking of
ux request prole via a change
prole of temperature (at ambient temperature of 400C) with LPV
controller observer pair. . . . . . . . . . . . . . . . . . . . . . . . . 115
5.12 Simulation results: Induction machine direct and quadrature axis
(a) stator currents. (b) stator voltages: corresponding to the oper-
ation of electried powertrain at 400C. . . . . . . . . . . . . . . . . 116
5.13 Experimental setup of an IM drive system. . . . . . . . . . . . . . . 117
5.14 Experimental result: Induction motor (used in this work) perfor-
mance curve at 400C(Torque derating at 400Cis vivid). . . . . . . 119
5.15 Actual (blue) and estimated (red) experimental results for a refer-
ence (trapezoidal-wave) of 10 Nm. (a) Torque tracking. ( b) Stator
resistance variation. ( c) Stator current. ( d) Rotor
ux. . . . . . . . 120
5.16 Experimental result: Tracking of induction machine speed prole
via a change prole of temperature (at ambient temperature of
400C) with LPV controller observer pair. . . . . . . . . . . . . . . . 121
5.17 Experimental results: Tracking of torque request prole via a change
prole of temperature (at ambient temperature of 400C) with LPV
controller observer pair. . . . . . . . . . . . . . . . . . . . . . . . . 121
5.18 Experimental results: Tracking of
ux request prole via a change
prole of temperature (at ambient temperature of 400C) with LPV
controller observer pair. . . . . . . . . . . . . . . . . . . . . . . . . 122
5.19 Experimental results: RMSE and NRMSE values of induction ma-
chine: (a) Speed tracking (b) Torque tracking (c) Flux tracking. . . 122
6.1 Proposed LPV based FOC control framework for a traction induc-
tion machine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.2 Closed loop system block diagram . . . . . . . . . . . . . . . . . . . 142
6.3 IM winding temperature and resistance over the entire period of
operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
6.4 Vehicle speed prole for the validation of multi-objective LPV con-
troller with and without aging compensation during the operation
of electried powertrain. . . . . . . . . . . . . . . . . . . . . . . . . 149
6.5 IM speed under the validation driving schedule with and without
aging compensation. . . . . . . . . . . . . . . . . . . . . . . . . . . 150
6.6 Vehicle torques with multi-objective LPV controller: without and
with aging compensation. . . . . . . . . . . . . . . . . . . . . . . . 150

xvii
6.7 Power eciency for an electried powertrain after the compensation
of change in operating conditions with multi-objective LPV controller.151
6.8 Induction machine direct and quadrature axis (a) stator currents.
(b) stator voltages with aging. . . . . . . . . . . . . . . . . . . . . . 152
6.9 Induction machine direct and quadrature axis (a) stator currents.
(b) stator voltages without aging. . . . . . . . . . . . . . . . . . . . 153
6.10 IM winding temperature: simulation of driving cycle. . . . . . . . . 153
6.11 IM winding temperature: simulation of driving cycle with cooling
phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.12 (a) Average eciency of an electried powertrain. (b) RMSE values
of vehicle torque. (c) loss of lifetime of an IM. . . . . . . . . . . . . 155
8.1 Generalized plant diagram. . . . . . . . . . . . . . . . . . . . . . . . 162
8.2 Closed-loop system. . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

List of Tables
2.1 Electric Traction Systems Evaluation . . . . . . . . . . . . . . . . . 24
3.1 State Variables Used in the Modeling of The Induction Machine . . 46
3.2 Model's Parameters Description Used in Induction Machine Modeling 46
3.3 Induction Machine Specications . . . . . . . . . . . . . . . . . . . 56
3.4 Accuracy of the LPV model in comparison to the nonlinear model . 67
4.1 Parameters Values . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.1 Performance comparison of FOC-HOSMC and FOC-LPV to stator
resistance variations . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.2 Performance comparison of FOC-HOSMC and FOC-LPV to rotor
resistance variations . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.3 Specications of an induction machine and a light duty electric vehicle110
5.4 Performance indices comparison for proposed LPV based FOC con-
trol framework at dierent ambient temperature . . . . . . . . . . . 115
6.1 Specications of the three-wheeled vehicle induction machine . . . . 147
6.2 Specications of a three-wheeled vehicle used in urban transporta-
tion for Asian countries . . . . . . . . . . . . . . . . . . . . . . . . . 147
6.3 Optimal Value of Weighting Matrices coecients . . . . . . . . . . . 148
6.4 Loss of lifetime of IM at ambient temperature of 400Cand 200C. . 155
xviii

Abbreviations
IM Induction Machine
EVs Electric Vehicles
FOC Field-oriented Control
DFOC Direct Field-oriented Control
EPTP Electrical Power Transmission Path
MPTP Mechanical Power Transmission Path
PMM Permanent Magnet Machine
PMSM Permanent Magnet Synchronous Machine
PM BLDC Permanent Magnet Brushless DC
SRM Switched Reluctance Machine
HF Hybridization Factor
PEM Power of Electric Machine
PICE Power of Internal Combustion Engine
PHEV Power to push the Hybrid Electric Vehicle
SRRF Synchronously Rotating Reference Frame
SRF Stationary Reference Frame
d-axis Direct axis
GHG Green House Gases
q-axis Quadrature Axis
HEVs Hybrid Electric Vehicles
ICE Internal Combustion Engine
LPV Linear Parameter Varying
SMC Sliding Mode Control
xix

Symbols
nr Rotor angular speed
dR Rotor
ux of direct (d)-axis
qR Rotor
ux of quadrature (q)-axis
is
dS Stator current of direct (d)-axis
is
qS Stator current of quadrature (q)-axis
ne Synchronous speed
e Electromagnetic generated torque
eref Reference electromagnetic generated torque
ref Reference rotor
ux
L Load Torque
v(t) Vehicle's instantaneous velocity
PTR(t) Instantaneous tractive power
rs Stator resistance
rR Rotor resistance
lS Stator leakage inductance
M Magnetizing Inductance
lR Rotor leakage inductance
np Number of pole pairs
J Inertia
b Damping
nm Mechanical Speed
air Air mass density
Cd Aerodynamic drag coecient
xx

xxi
Af Frontal surface area of the vehicle
fad Aerodynamic drag force
M Mass of the vehicle
g Gravity acceleration
Cr Rolling resistance coecient
g Grade angle
froll Rolling resistance
fgrade Road grade force
Rw Radius of the wheel
Rf Ratio between the motor shaft and dierential axle of the vehicle
fe Electrical frequency

Chapter 1
Introduction
This chapter provides the preliminary knowledge to understand the rest of the
thesis.
1.1 Background
The world is facing severe energy crisis from the last few decades. As well as,
harmful emissions produced due to the burning of oil are polluting the environ-
ment. Due to the both problems, peoples are much attentive toward the energy
savings and environmental protection now a days. Use of oil in the transportation
sector is much high than the other available energy resources. Therefore, it is
producing the major problem for the both motives of energy savings and envi-
ronmental protection. Currently, a study is conducted by the Energy Information
Administration (EIA) [5], in United States, transportation sector is using 68% of
available amount of the petroleum resources from which 66% of these assets were
imported.
Correspondingly, in Pakistan (a developing country), Figure 1.1 depicts the oil
production, demand, and import [1]. It can be observed in Figure 1.1 that there
is a large gap between the oil production and its demand, in result, Pakistan
spending billions of USD to import fuels to meet its power demand. Oil is the
1

2
Figure 1.1: Oil Production, Demand and Import by Pakistan[1].
biggest contributor to transport sector in Pakistan, almost 48% of the oil resources
are used in this sector [1]. So it can be concluded that utilizing the oil ineciently
is not an economically feasible energy strategy.
Moreover, the submission of numerous limiting legislations to manage the pollu-
tant emissions, particularly the greenhouse gases (GHG) is also important element
of this discussion. For illustration, an international agreement (Kyoto protocol)
has been signed by all the countries to diminish the pollutant emissions especially
carbon emissions upto 5 :2% by 2012 than the value of carbon emissions in 1990
and so on [5]. It is clear from the literature that the transportation sector has
very poor energy conversion eciency of about 20% [5]. Therefore, due to the in-
creasing nature of the energy requirements, limited availability of energy resources,
lowest eciency of energy conversion and in
exible rules about emission [6], the
automotive leading industry is continuously practising unusual traction systems
(practical technologies) to reduce the dependence of transportation on the non-
renewable energy types ,as well as they are trying to improve the fuel savings
and the vehicle's eciency. Electric machine has been used in vehicles as an al-
ternative to the Internal Combustion Engine (ICE) by the automotive industry.
The electric means of transport was preferable because of its calm, consistency
and most signicantly the soundless operation, at the start of the 20th century.
However, electric means of transport was removed from the market, excluding for
some special uses due to the development of the ICE. Now a days, to reduce the
fuel consumption and diminish the exhaust emissions, the hybridization of existing

3
vehicles and electric powertrain is one of the viable solutions.
1.2 Hybrid Electric Vehicles
The vehicles with electric machine and internal combustion engine propulsion are
known as Hybrid Electric Vehicles (HEVs). HEVs utilize the electrical energy from
the batteries for its electric traction system with the combination of Atkinson Cycle
Combustion Engine (ACCE) in series or parallel to the former traction system.
The rst hybrid vehicle was built in 1898 by Dr. Ferdinand P. This vehicle had an
ICE to rotate the generator to charge the batteries. These batteries provide the
electric power to the electric motor to drive the vehicle [7, 8]. However, hybrid
vehicles have been ignored initially due the presence of heavy availability of the
fossil fuel at very low cost, lack of knowledge regarding the harmful emissions
and the development of the ICE technologies. These days the availability of oil
is becoming shorter and shorter. Also the cost of oil and insertion of harmful
emissions to environment is becoming high day by day. These are the alarming
notions for the automotive industry to deploy the alternative energy resources in
the vehicle as well as to meet the emission constraints imposed by the environment
governing bodies. Therefore, the automotive industry is constantly evolving to
meet two major demands of the world: (1) to meet consumer expectations and
(2) to meet Environmental Protecting Agency (EPA) requirements. HEVs have
successfully addressed the trade o between environmental and energy needs and
consumer demand for performance and utility. A hybrid vehicle contains two
power sources, usually a ICE is supplemented by one or more electric machines
powered by electricity stored in a battery. This not only helps in providing the
desired performance, decrease in emissions, and improved fuel eciency, but also
enables to recover energy wasted during braking. In summary, a HEV enables
fuel savings: (1) by avoiding engine idle (the engine is shut o whenever the
vehicle is stationary); (2) by allowing for downsizing of the ICE without losing any
performance; (3) by enabling electric-only drive mode for short distances under
operating conditions that would normally correspond to very low engine eciency;

4
Figure 1.2: Based on the powertrain components arrangement, there are basi-
cally three schemes for the hybrid electric vehicles. (a)Parallel hybrid, (b)Split
hybrid, and (c)Series hybrid
.
and (4) by allowing for the recovery of kinetic energy. The composite eect is a
signicant reduction in vehicle fuel consumption, typically highest for vehicles that
are predominantly used in urban cycles [9]. It may be kept in mind that the peak
ICE eciency is not more than 30% while comparing it with that of the electric
drives which is typically greater than 60%.

5
1.2.1 Types of Hybrid Electric Vehicles
According to the arrangement of components (ICE, Battery, Electric Machine
Drive) used in the power train of the EVs and HEVs, there are broadly three
types[8, 10, 11]:
1.2.1.1 Parallel hybrid
In Figure 1.2(a), an electric machine which act as a generator and motor is con-
nected to the ICE through mechanical coupling. It behaves like a generator to
charge the battery bank and behaves as motor to propel the vehicle whenever a
boost is required in the speed. It also acts as a motor below the speed of 60 Km=h .
Therefore, in this type of hybrid vehicles, engine is used at its optimal (highest)
eciency operating point. Brake energy is converted to the useful energy to charge
the battery as shown in Figure 1.2(a).
1.2.1.2 Split hybrid
In Figure 1.2(b), type planetary gear set is used to connect the generator and
engine, with third shaft is going to the vehicle's wheels. The engine charges
the battery bank and it provides the power to the electric machine connected
to the wheels through the power electronics circuits. Therefore, in this type of
hybrid vehicles, engine directly drives the vehicle through the planetary gear and
through the electrical path between generator, battery, and motor as shown in
Figure 1.2(b).
1.2.1.3 Series hybrid
In Figure 1.2(c), engine has no connection with the transmission but it is used
to run the generator to charge the battery bank. The battery bank provides the
power to the electric motor to drive the vehicle as shown in the Figure 1.2(c).

6
Therefore, this type of powertrain technology is also adopted for pure electric and
plug in type hybrid vehicles.
1.3 Electric Machine
Matured manufacturing and elevated eciency of electric machines have widened
their scope of applications in industry, domestic appliances, and in modern au-
tomotive systems. The uses of electric machine in the automotive other than
the propulsion include fuel pump, starter, power steering, alternator, etc. Now a
days, electric machines are used in dierent drive systems of hybrid electric ve-
hicles (HEVs) and electric vehicles (EVs) due to their availability in high power.
Induction machines, DC machines, switched reluctance machines, permanent mag-
net machines, all are suitable applicants for the traction system as well as for high
power starter-generator used in the electric and hybrid electric vehicles. Due to
the heavy use of high power electric machines in automotive, ecient operation
of control algorithms is the most crucial area of research to improve the torque
performance, eciency and lifetime of the machine and vehicle in the presence of
rise in surrounding and operating temperatures.
1.3.1 Induction Machine
The induction machine has advantages over the other electric machines used in
electric and hybrid electric vehicles. For example, it has wide speed range, low cost,
ruggedness, reliable, and complete deenergization because it has no brushes, one
piece rotor shaft inherently, availability, and its safer operation in hazardous en-
vironment. Therefore, it is best suited for the hybrid and electric vehicles [12{15].
However, the control of the induction machine is not straightforward. Due to this,
development of induction machine based drive system is complex. Initially, drive
system were built using the scalar control method in which only the magnitude of
the control variables are controlled. But these techniques are only useful for the

7
constant speed operation [3]. In 1970's, a new eld-oriented control (FOC) tech-
nique was developed by Haase and Blaschke to achieve the high performance drive
system based on induction machine [16]. In this technique, both the magnitude
and phase of the control variable are changed to control the machine operation.
This technique is based on the machine's model in a rotor reference frame. Instead
of having superior performance over scalar control, this method also suers from
some severe drawbacks, when it is adopted for high dynamic performance applica-
tions like hybrid and electric vehicles where exact and precise tracking is needed.
These drawbacks include: the machine model is highly non linear, components
of rotor
ux which are the two states of the machine's model are actually not
accessible, and some of the machine's parameters (rotor resistance, stator resis-
tance etc.) change signicantly during the operation. These changes have severe
eect on the eld-oriented control (FOC) of induction machine drive system for
the applications in hybrid and electric vehicle than in other industrial applica-
tions. Because the operating conditions in hybrid and electric vehicles change
constantly depending upon the trac situations, drive cycles, load on the vehicle,
and temperature, causing wide variations in speed. A signicant change in rotor
and stator resistances occurs linearly with the change in ambient and operating
temperatures, depending upon the temperature coecient of the resistance of the
material as well as these are also eected by the skin eect [3, 17, 18]. The vari-
ations in rotor and stator resistances as well as wide variation in speed make the
overall performance of the direct eld-oriented control (DFOC) based induction
machine traction system for HEVs and EVs poor. Because the whole operation
of the induction machine propulsion system based on direct eld-oriented control
(DFOC) is dependent on the exact and precise generation of the unit vectors ( cose
andsine). Various methods are described in [10, 12, 13, 19{21] to overcome the
rotor resistance variations only.

8
1.4 Motivation and Objectives
With the hasty development in automotive engineering, the researchers in auto-
motive eld have struggled hard to build up the schemes and make use of the
diverse novel technologies to achieve fuel economy improvement and decrease in
the emission of vehicles. For these purposes the ecient control of the power-
train of vehicle has been of impressive signicance. The electric machine converts
the electrical energy stored in the battery bank of the electrical vehicles (EVs)
and hybrid electric vehicles (HEVs) into mechanical energy to achieve the ecient
operation of electric drive (traction) system.
Therefore, the foremost motivation of this research is to achieve the overall bet-
ter torque performance, eciency and minimizing the loss of lifetime (aging) of
a traction induction machine based electried powertrain deployed in the electric
vehicles (EVs) and hybrid electric vehicles (HEVs) with the design and implemen-
tation of advanced and robust controllers. Secondly, this research also addresses
and provides the optimum solution against the parameter variations of induction
machine. The induction machine parameters change as the operating condition
changes. Operating conditions for HEV propulsion system will change constantly.
Trac situations, driving cycles, etc.are the reasons of the variation in speed. Also
temperature has the eect on parameters, which is in
uenced by ambient season,
loading, etc.In spite of all these, induction machine must track the reference
ux,
which is desired to reduce the energy consumption in HEVs and EVs. Also torque
demanded by the controller must be exact and ecient.
The primary objective of this research is to develop the novel (robust and ad-
vanced) controllers for the ecient control of the hybrid and electric vehicle's
traction machine. The others objectives are:
Design and implementation of a novel and robust observer for induction
machine to estimate the thermally derated torque to achieve the ecient
control of traction system.

9
Design and implementation of novel and robust controller based on the novel
and robust observer to manage the thermally derated torque (improve the
performance) of traction system for hybrid and electric vehicles.
Design and implementation of degradation control of an traction induction
machine for hybrid and electric vehicles.
1.5 Contributions
The main contribution of this thesis is the development of robust control schemes
to estimate and manage the thermally derated torque, enhance the eciency of an
electried powertrain and minimize the loss of lifetime (aging) of a traction ma-
chine. The designed control scheme for HEV and EV powertrain overcomes the
surrounding and operating temperatures eects on torque generating capability
of a traction machine by delivering higher performance. Another control scheme
is proposed to maximize the powertrain eciency and mitigate the electric ma-
chine based electried powertrain degradation while simultaneously providing the
desired closed loop performance.
The presented and conducted research work has following main contributions:
Development of Linear Parameter Varying (LPV) model for traction induc-
tion machine to cope with the change in operating and ambient tempera-
tures.
Estimation of thermally derated torque and
ux of an traction drive
Development of method for conrmation of torque derating in traction ma-
chine
Compensation of thermally derated torque
Eciency improvement control technique
Traction machine aging minimizing control technique

10
1.6 Organization of the Thesis
Rest of the thesis is organized as discussed below:
Chapter 2 discusses the types of the propulsion machines, their pros and cons, and
their comparison based on the controllability, reliability, power density, technolog-
ical maturity, eciency, availability, and cost. A study based on aforementioned
factors is done and concludes that induction machine is the excellent and decent
choice for the Electric Vehicles (EVs) and Hybrid Electric Vehicles (HEVs). This
chapter also describes the primary requirements of the electric traction drive for
EVs and HEVs. The eects of change in operating and surrounding temperatures
on the performance of an electric machine used for traction is also described. A
detailed literature survey is presented for the existing estimators and controllers
that have been used in induction machine based electric drive in general and for
EVs and HEVs. The literature survey explains the past eorts of the researchers
to estimate and control the
ux, torque and speed of the induction machine based
electric drive for industrial and traction applications. Moreover, it has been argued
that estimating and managing of thermally derated torque in induction machine
based electric drive is rare. The development of control technique for the degrada-
tion control of traction induction machine in EVs and HEVs is limited to improve
the eciency, performance and loss of life time (aging). It is still an open research
task for a traction electric drive.
Chapter 3 is devoted to the development of a mathematical model of the In-
duction Machine which has been chosen as a propulsion machine as detailed in
chapter-2. This model will be used in propulsion drive needed for the hybrid and
electric vehicles. It provides the background details needed for better understand-
ing the induction machine from a dynamical system viewpoint. This model will be
subsequently used for observer and controller design. A two-phase representation
of a three-phase induction machine is described in this chapter. The voltage,
ux,
and current equations which are helpful in obtaining the induction machine model
in arbitrary rotating reference frame and stationary reference frame are presented.
The 5th order nonlinear model of induction machine, both in stationary reference

11
frame and arbitrary rotating reference frame is derived. This model is used to de-
rive the Linear Parameter Varying (LPV) model of an induction machine. Later
on, this model will be used for the design of robust controllers and observers which
are necessarily required for the ecient operation of eld-oriented control (FOC)
of 3induction machine drive for the application in hybrid and electric vehi-
cles. In the end, it is also simulated in MatlabR
/Simulink software to appreciate
its advantages from ecient operation viewpoint and model validation viewpoint
as well.
Chapter 4 deals with the estimation of thermally derated torque of an induc-
tion machine based electried powertrain. This estimation is based on the LPV
model presented in the preceding chapter. The estimation of thermally derated
torque is more critical for obtaining the precise control to manage the thermally
derated torque, improve the eciency and minimize the loss of life time (aging)
of an induction machine based electried powertrain. Along with the estimation
of thermally derated torque,
ux of an induction machine based electric drive is
also estimated. These objectives have been obtained by using a robust LPV based
estimation technique. The LPV observer operates on a highly nonlinear currents
and
ux dynamics. Initially, the proposed estimation technique has been success-
fully tested by creating a theoretical scenario. Later on, estimation technique is
investigated using shortened Federal Urban Driving Schedule (FUDS) test cycle
for Hybrid Electric Vehicle (HEV) electric powertrain.
Chapter 5 presents the Linear parameter varying based estimation scheme, dis-
cussed in Chapter 4 is used here to design linear parameter varying control tech-
nique to manage and compensate the thermally derated torque for an induction
machine based electried powertrain. The proposed scheme has the capability to
retain the nominal performance even in the face of severe rise in the operating and
surrounding temperatures. Due to the variations in ambient and operating tem-
peratures, reasons are discussed in Section 2.3, proposed linear parameter varying
control scheme reschedules its control signals to attain eective performance. The
ecacy of the proposed algorithm is demonstrated for an EV operating in Federal

12
Urban Driving Schedule (FUDS) with a dynamic temperature prole. The nonlin-
ear simulation results conrm the LPV observer capability to successfully estimate
the
ux and derated torque in an EV drive system. The proposed technique, after
validating in simulation environment, is veried experimentally on an Induction
Machine (IM) drive controlled by NI myRIO-1900.
Chapter 6 describes a degradation control technique that is proposed to mitigate
the electric machine based electried powertrain degradation while simultaneously
providing the desired closed loop performance. The performance of an electried
powertrain in extreme operating conditions is greatly compromised. This is due to
the fact that meeting the road loads, ensuring ecient powertrain operation and
minimizing the loss of lifetime (aging) of an electric machine are three essential but
con
icting targets. In this chapter, a multi-objective Linear Parameters Varying
(LPV) based Field-oriented Control (FOC) is proposed to address the problem of
con
icting objectives mentioned above. The eectiveness of the proposed control
framework is tested for a direct drive electried powertrain of a three-wheeled
vehicle commonly found in urban transportation for Asian countries. The urban
driving schedule based simulation results conrm that the lifetime of induction
machine can be enhanced by appropriate controller design without compromising
its performance.
Chapter 7 concludes the dissertation through outlining the main contributions
and list of directions that can be accomplished in the future research.

Chapter 2
Electric Machines in Hybrid and
Electric Vehicles
This chapter discusses the types of the propulsion machines, their pros and cons,
and their comparison based on the controllability, reliability, power density, techno-
logical maturity, eciency, availability, and cost. A study based on aforementioned
factors is done and concludes that induction machine is the excellent and decent
choice for the Electric Vehicles (EVs) and Hybrid Electric Vehicles (HEVs). This
chapter also describes the primary requirements of the electric traction drive for
EVs and HEVs. The eects of change in operating and surrounding temperatures
on the performance of an electric machine used for traction is also described. A
detailed literature survey is presented for the existing estimators and controllers
that have been used in induction machine based electric drive in general and for
EVs and HEVs. The literature survey explains the past eorts of the researchers
to estimate and control the
ux, torque and speed of the induction machine based
electric drive for industrial and traction applications. Moreover, it has been argued
that estimating and managing of thermally derated torque in induction machine
based electric drive is rare. The development of control technique for the degrada-
tion control of traction induction machine in EVs and HEVs is limited to improve
the eciency, performance and loss of life time (aging). It is still an open research
task for a traction electric drive.
13

14
2.1 Introduction
The propulsion electric machines and a ICE provides the traction power to the
hybrid electric vehicles as shown in Figure 2.1. The traction power is delivered
to the wheels through either the electrical power transmission path (EPTP) or
the mechanical power transmission path (MPTP) or the combination of two. The
vehicle electric machine drive subsystem must be capable of fullling the vehicle
requirements at nominal load as well as extreme load conditions during starting
and acceleration. The electric machine acts as motor and generator in either of
the hybrid topology presented in Figure 1.2. The propulsion electric machine is
the major component of an Electric Vehicle (EV). The schematic diagram of an
electried powertrain is shown in Figure 2.2. The traction motor can also recover
the regenerative energy whenever the vehicle's brakes are applied. Therefore, the
primary requirements of the electric traction drive for EVs and HEVs are the
following: [22{27]:
High torque density and power density
High starting torque
High Power
High eciency over wide torque and speed rang
Very wide speed ranges
Including constant torque and constant power regions
High intermittent overload capacity
Reasonable cost
Reliability
High eciency for regenerative braking

15
Fuel Engine
BatteryConverter Motor/GeneratorTransmission Vehicle
Friction
Brakes
Electrical Chemical Mechanical+
+
Figure 2.1: Parallel HEV Conguration.
/g3
Battery Converter Motor/Generator
Transmission
Mechanical Electrical
Figure 2.2: Schematic of an electric vehicle (EV) powertrain
The fuel eciency and utilization time of the internal combustion engine in hybrid
electric vehicle is based on precise and ecient utilization of electric machine. The
selection of electric machine is based on appropriate torque-speed characteristics
to deliver the demanded vehicle performance. The size of the electric machine is
another important factor to be needed because it is to be packed and mounted
inside the vehicle.
Figure 2.3 demonstrates the benchmark torque-speed curve of electric motor adopted
in EVs and HEVs [2]. The propulsive eort versus speed that is required at the
starting of vehicle from the electric motor is also shown in the Figure 2.3(b). It is
clear from the curve that motor transmitted the maximum torque to the wheels
upto the base speed where the maximum power condition of the motor is achieved.
After this motor is not able to provide the rated torque. Modern power electronics
circuits are used to operate the electric motor drive at any desired point inside the
envelope of the torque-speed characteristics curve. Transmission gears are adopted

16
Figure 2.3: Electric Traction Motor (a) Torque-Speed Curve (b) Propulsive
Eort Versus Speed [2].
to match the lower rotations of the wheels to higher rotations of the electric motor
in hybrid electric vehicles applications [28].
Figure 2.4 shows the the typical characteristics of an electric motor drive. High
speed range operation with constant power beyond the rated speed is achieved by

17

ux-weakening.
Figure 2.4: Motor Characteristics [2].
2.2 Propulsion Electric Machine Topologies
In recent vehicles, electric machines of more than 100 dierent types are used.
Electric machines can be grouped as AC and DC types. Before 1980's, DC ma-
chines had wide applications in industries as well as in vehicles. DC machines are
used in hybrid and electric vehicle technology because of variable torque-speed
control and wide range of operation [29]. DC machines provide ease of control but
they need commutator and brush maintenance, eciency is low and also power
to weight ratio is low. DC machines have been employed as for propulsion in
Peugeot Partner (1990), Honda EV Plus(1997), Berlingo (1995) [15] and PSA
Peugeot-Citreon (France) [2]. A prototype of plug-in type series hybrid electric
vehicle using DC machine is implemented in [30].
After 1980, AC machines have started to replace the DC machine due the disadvan-
tages of the later. At present, a great range of electric machines for use in vehicles

18
is commercially available. The possible candidate AC machines for HEVs and EVs
are induction machines, permanent magnet machines and switched-reluctance ma-
chines [15, 31], as shown in Figure 2.5. Figure 2.5 also presents the cross-sections
of the above mentioned machines. The next section will discuss these machines
brie
y.
Figure 2.5: Major traction and industrial machines.
2.2.1 Induction Machines
With much research and improvement activities over the last many decades, the
technology of induction machine has become mature [32, 33]. Present growth
in power electronics devices and digital signal processing chips, have made the
control of induction machine like the separately-excited DC machine without the
need of maintenance [34]. Induction machines are adopted in EVs, HEVs, and
industry due to its low cost, reliability, ruggedness, robustness, high torque during
starting and acceleration, high instant power, and wide range of speed of oper-
ation. Moreover, induction machines are inherently de-excited with respect to
inverter fault hence highly recommended to be used in automobile industries for
precautionary measures [35]. The power to weight ratio of induction machines
is much higher than the DC machines, therefore they are small in size as well.
The induction machines also belong to the rotor and commutator less topology.
Induction machines are of two kinds: wound-rotor and squirrel-cage. In wound-
rotor type induction machine, the windings on the rotor are taken outside with
the aid of slip rings. Due to this, external resistance can be added to change the

19
rotor resistance. In squirrel-cage induction machine, the windings on the rotor are
made of short-circuited aluminum or copper bars whose ends are welded to the
copper rings. Automotive researchers show high interest in squirrel-cage induc-
tion machine for hybrid and electric vehicles. Induction machines are extensively
used as a propulsion machine in hybrid and electric vehicles applications. Tesla
Model (2012), Honda Fit EV (2012), Toyota RAV4 EV (2012), Renault/Kangoo
(1998), BMW/X5 (Germany), Chevrolet (USA),Durango (USA), etc. [2, 15, 36].
In [37, 38], due to the simplicity, ruggedness, cheapness, low maintenance cost,
high dynamic performance, and availability of enough starting torque and ability
of acceleration, induction motor of squirrel-cage type is used as a propulsion mo-
tor in series HEVs. Chris Mi proposed induction machine of squirrel-cage type
as a propulsion machine in hybrid and electric vehicles due to its small size as
compared to DC machine, ease of fabrication, and high eciency [39, 40]. Wide
speed choice of operation can be achieved by
ux-weakening with invariable power.
Due to the occurrence of breakdown torque, the wide invariable power operation
of induction machine is limited. This can be overcome by the use of multi-phase
pole adjusting induction machines for the propulsion application [41, 42]. Tesla
Motors have adopted induction machines for almost all types of hybrid and electric
vehicles[13].
2.2.2 Permanent Magnet Machines
Permanent magnet machines are widely used in traction, industry, and commercial
applications. Permanent magnet machines are competing induction machine in the
hybrid and electric vehicle applications. Recently, permanent magnet machines are
used by famous automaker for their hybrid electric vehicles. Toyota and Honda
have adopted permanent magnet machines for more or less all types of hybrid and
electric vehicles [13]. These machines have a various advantages such as high power
density (for a known output power, there is a signicance reduction in complete
weight and volume), high eciency (low losses), range of speed operation is wide,
and compact size. It has small invariable power region. The primary dierence

20
between the permanent magnet machines and other kinds of rotating machine is
the way in which they are excited. In permanent magnet machines, permanent
magnets are used in the rotor as the eld stimulant circuit, which is responsible for
the production of air-gap magnetic
ux. Therefore, the permanent magnets give
the loss-less excitation without any external electric circuit. Conversely, because of
permanent presence of
ux from these permanent magnets, DC bus voltage method
is much dicult for these types of machines as compared to the induction machines.
The primary drawbacks of the PM machines are wrecked magnet chips and heating
due to the rotor eddy currents at very high speed reduces the magnetization of
the magnets [29].
Permanent magnet machine can be divided into two groups: permanent magnet
synchronous machine (PMSM) and permanent magnet brushless DC (PM BLDC)
machine. The major dierence between the two is the stator winding [43{45]. In
PMSM, sinusoidally distributed stator windings along the perimeter of the stator
is producing the back-emf of sinusoidal nature. In PM BLDC, stator windings
produce the back-emf of trapezoidal-shape. According to the shape and position
of rotor's permanent magnet, PMSM are of three kinds: surface mount permanent
magnet machine, interior permanent magnet machine, and unset permanent mag-
net machine. The only dierence between the three kinds of permanent magnet
synchronous machine is the placement of magnet into the rotor.
Permanent magnet machines are used as a propulsion machine in the hybrid and
electric vehicles by famous automakers due to small size, low losses, and less weight
in comparison to the induction machines [32, 33]. These have been used in Nis-
san Leaf (2010), Hyundai Blueon (2012), Mitsubishi iMiev (2009), Toyota Prius
(Japan), Nissan/Tino (Japan), Honda Insight (Japan) etc. [2, 15, 36]. The perma-
nent magnets are needed for the permanent magnet machines which make them
more costly as compare to the other types of the AC machines. At higher speed,
rotor eddy currents increase the magnet heating, which is the source of demag-
netization [29]. Placing the permanent magnet inside the rotor of the machine,
improves the high speed operation due to the
ux-weakening but cost will be
increased [46].

21
2.2.3 Switched Reluctance Machines
Another potential propulsion candidate for the hybrid and electric vehicles is the
switched reluctance machines. These machines have the advantages of simplicity,
ruggedness, reliability, inexpensive, fault-tolerant control and operation, and ex-
cellent torque-speed envelope and large invariable power range. Besides , there are
many disadvantages including acoustic noise, high torque ripples, electromagnetic
interference noise, and high bus current ripples. The above mentioned advantages
and disadvantages are much critical for traction applications. Suitable solution
to the aforementioned disadvantages are required to obtain a practicable switched
reluctance motor based HEVs [47, 48]. The switched-reluctance machine has not
yet been used in EVs and HEVs, but it is successfully expressed as prototype [49].
The switched reluctance motor has been adopted in the Holden/ECOmmodore
(Australia) hybrid electric vehicle for its traction system [2].
2.3 Traction Operation Versus Industrial Oper-
ation
Vehicle with electried powertrains exhibit degraded performance when operated
in harsh environments. Conventionally, electric machine acts as a prime mover
in EVs and HEVs as shown in Figure 2.1 and 2.2. It is one of the most reliable
and most rugged component in the entire electric powertrain whether it is the
powertrain of small car, delivery trucks, buses and vehicle used in construction as
shown in Figure 2.6.
In traction applications, machine has to be operate in dierent driving cycles,
dierent ambient (surrounding) temperatures, dierent pay loads and varying op-
erating temperatures as comparison to the industrial operation of a machine. In
addition to these, machine faces the rapid start/stop conditions and part load con-
ditions. The causes which eect the operation of electric powertrain of an hybrid
and electric vehicles are shown in Figure 2.7.

22

Toyota Prius 2017
/g3
Urban Delivery Trucks
100% Electric Truck (BYD USA)
Electric Passenger Bus (BYD USA)
/g3
Figure 2.6: Hybrid and electric vehicles.
Figure 2.7: Variations in (a) Drive cycle (b) Ambient temperature (c) Pay-
loads and (d) Operating temperature.
As a result, all these conditions aect the winding resistances, produce the im-
balance in the voltages and currents during the operation of traction machine for
an electric powertrain [50{53] as shown in Figure 2.8. Due to these eects, the
performance of a traction machine is deteriorated in following ways:

23
Torque of an electric powertrain is thermally derated.
Eciency of an electric powertrain is reduced.
Aging (loss of lifetime) of a traction machine is increased.

/g302004006008001000120013600.180.20.220.240.260.280.3
Time [s]Resistance [ Ω]

rR@ 200C
rR@ 400C
rR@ 600C
rS@ 200C
rS@ 400C
rS@ 600C
230230.2 230.4 230.6 230.8 231-200-150-100-50050100150200
Time [s]uS [V]
udS
uqS
00.20.40.60.811.2-40-30-20-1001020
Time [sec]idS [A]
Figure 2.8: (a) Rotor and stator resistance variations (b) Operating voltages
imbalances and (c) Operating currents imbalances.
2.4 Induction Machine for Traction System
In [2, 15], a complete comparison is accomplished among the induction machines,
switched reluctance machines, and permanent magnet machines. The comparison
is based on the following factors: controllability, reliability, power density, tech-
nological maturity, eciency, availability, and cost. The comparison has disclosed
that the induction machine is the best appropriate choice for the applications in
hybrid and electric vehicles although a hard competition exists with permanent
magnet machines. The main advantages of adopting induction machine for EVs

24
and HEVs are the availability of instant torque response only possible due the lit-
tle leakage inductances, and capable to function in hostile environment. Induction
machine has advantages of reliability, cheapness, ruggedness, and have an excel-
lent invariable power region. The DC bus voltage control method is much feasible
for the induction machines based propulsion drives as compared to the permanent
magnet machines where constant source of
ux is available to disturb this oper-
ation. Furthermore, it has very good eciency along the broad range of speed
operation. Table 2.1 provide the summary for the traction machines comparison.
In this table, '0' indicates minimum and '10' indicates maximum respectively in
the evaluating criteria.
Table 2.1: Electric Traction Systems Evaluation
Sr.
No.Characteristics Vs
Propulsion SystemsDC IM PM SRM
1 Power Density 5 7 10 7
2 Eciency 5 7 10 7
3 Controllability 10 10 8 6
4 Reliability 6 10 8 10
5 Technological maturity 10 10 8 8
6 Cost 8 10 6 8
7 Availability 8 10 8 5
Total 42 64 58 56
As a result, induction machines is an excellent and decent choice for the hybrid and
electric vehicles. Therefore, the primary objective of this research is to develop the
novel (robust and advanced) controllers for the ecient control of the induction
machine based propulsion drive for the applications in hybrid and electric vehicles
to achieve the high performance in the presence of conditions given in Section 2.3.
The others objectives are:
Design and implementation of a novel and robust observer for induction
machine to estimate the thermally derated torque to achieve the ecient
control of traction system.

25
Design and implementation of novel and robust controller based on the novel
and robust observer to manage the thermally derated torque (improve the
performance) of traction system for hybrid and electric vehicles.
Design and implementation of degradation control of an traction induction
machine for hybrid and electric vehicles.
2.5 Sizing of propulsion Machine
The sizing of the propulsion machine is an important step in a hybrid and electric
vehicles to increase fuel saving and improve dynamic performances. The hybridiza-
tion factor is the key point in HEVs and can be dened as a ratio between the
peak power of the traction machine ( PEM) and the power of internal combustion
engine (PICE).
HF =PEM
PEM+PICE=PEM
PHEV(2.1)
WherePHEV is the total peak propulsion power to push the hybrid electric vehi-
cle [54]. The tractive and traction torque needed for a vehicle can be computed
from equations (3.40)-(3.42) given later. The tractive torque can be dened as
the torque needed to overcome the resistive torque to drive the vehicle [28]. The
instantaneous tractive power can be given as
PTR(t) =L(t)v(t) (2.2)
Wherev(t) is the vehicle's instantaneous velocity.

26
2.6 Research Scope in Induction Machine Con-
trol
The traction machine is a necessary part of the drivetrain in the hybrid and electric
vehicles. In order to optimize the operation of an electric powertrain, major eorts
are in the direction of physical design of machine and improving its performance
by means of closed-loop controllers. High performance induction machine based
drive can be achieved by adopting the eld-oriented control (FOC) method. But,
the machine parameters needed for the implementation of eld-oriented controller
(FOC) should be exact and precise to obtain the good static and dynamic perfor-
mance from the induction machine drive for the applications in electric vehicles
and hybrid electric vehicles traction system. The IM parameters change as the
operating conditions change. Operating conditions for an EV and HEV propulsion
system change constantly. Trac situations, driving cycles etc., are the reasons
of variation in speed. Also temperature has the eect on parameters, which is
in
uenced by ambient season and loading etc as elaborated in Section 2.3. Due to
these eects, the
ux and torque of an electried powertrain is thermally derated
as compared to the industrial induction machines, where the variation in temper-
ature and payload is very little. The eects of rise in operating and surrounding
temperatures on the performance of induction machine drive has been studied in
this research. In addition, a novel control techniques has been developed by con-
sidering the eects of rise in operating and surrounding temperatures to manage
the thermally derated torque and to minimize the degradation on the performance
of electric drive.
2.6.1 Parameter Variations Eects
In direct or feedback eld-oriented control (DFOC) method, the exact and precise
measurement of rotor
ux components is most critical and necessary. The genera-
tion of unit vectors which ensures the decoupling between d-axis and q-axis current

27
components of the stator is dependent on these
ux components. The model equa-
tions (3.29)-(3.36) given later show that the exact and precise values of rotor
ux
components is deteriorated by the variations in the following parameters.
stator resistance
rotor resistance
wide variations in rotor speed
These variations are much sever for the operation of induction machine drive used
in electric vehicles and hybrid electric vehicles. Both the resistances (stator and
rotor) change due to the machine heating, skin eect, harmonics, and other non-
idealities. Temperature shows signicant eect on the stator resistance as well
as on the rotor resistance. There will be a 20% to 60% change in the resistance
when temperature changes from ambient temperature to the maximum operating
temperature. The change in operating temperature is upto 115 Cofor high power
induction machine [17, 18].
The conductor resistance temperature dependence is given as:
R=Rref(1 +(TTref)) (2.3)
where,Ris the conductor resistance at operating temperature, T(Co),Rrefis the
conductor resistance at ambient temperature, Tref(Co) andis the temperature
coecient. For copper conductor = 0:004041=Coand for aluminum conductor
= 0:004308=Co, both measured at an ambient temperature (20 Co).
The eects of rise in operating and ambient temperatures on the torque-speed
characteristic curves of induction machine are studied in [55]. At a high value
of rotor resistance due to the elevated temperature, the starting torque and the
slip of the motor is also quite high which results in the decrease in the amount of
power in air-gap that actually converts into mechanical form. This phenomenon
ultimately ends up with a lower eciency of induction machine. The simulation

28
050100150200250300350−400−2000200400600
Angular Velocity (rad/s)Torque (N.m)

@20 0C
@0 0C
@40 0C
300310320−1000100200
Figure 2.9: Eect of ambient and operating temperatures on the dynamic
torque-speed characteristic curve for unipolar load torque.
study for three dierent ambient temperatures presented in Figures 2.9 and 2.10.
In Figures 2.9 and 2.10, the zoomed portions of the plot represent the variation in
dynamic performance of induction machine by the change in ambient temperature
for unipolar and bipolar load torque.
050100150200250300350−400−2000200400600
Angular Velocity (rad/s)Toruqe (N.m)

@20 0C
@0 0C
@40 0C
300310320−1000100200
Figure 2.10: Eect of ambient and operating temperatures on the dynamic
torque-speed characteristic curve for bipolar load torque.

29
2.6.2 Review of Existing Estimators and Controllers
In the hybrid and electric vehicle applications, the key problem is the performance
of the electric traction system. The induction machine has been adopted for a
propulsion system due to ease of control, reliability, high power density, techno-
logically mature, high eciency, ruggedness, availability of instant torque response
during starting and acceleration, wide range of speed of operation, cost and inher-
ently de-excited with respect to inverter fault. The feedback eld-oriented control
of the induction machine is the most commonly adopted instantaneous speed/-
torque and
ux control method for the hybrid and electric vehicle's propulsion
system. The induction machine parameters change as the operating condition
changes. Operating conditions for HEV propulsion system will change continu-
ously. Trac situations, driving cycles, etc. are the reason of variation in speed.
Also temperature has the eect on parameters, which is in
uenced by ambient
season, loading, etc. The feedback eld-oriented control of induction machines
primarily depends upon the precise
ux estimation. However, an accurate estima-
tion of
ux is hard due to the deviations in the machine's electrical parameters.
Both the resistances (stator and rotor), which produces the imprecision in the
ux
estimation and in the generation of unit vectors (cos eand sine), increase linearly
with temperature, depending upon the temperature co-ecient of the resistance
of the material. The unit vectors are used to guarantee correct alignment of stator
direct-axis current with the
ux vector and stator quadrature-axis current per-
pendicular to it. This provides the decoupled control as in separately-excited DC
machines. Secondly, unit vectors are used for the purpose of control. Therefore,
the imprecision of the estimated
ux will degrade the performance of torque/speed
control.
Moreover, the HEV and EV electric machine torque generation capability is greatly
aected by the surrounding thermal conditions as the motor parameters get al-
tered [50]. Therefore, it is important to estimate the de-rated torque so that overall
performance of the electric drive in an HEV can be monitored and later on it can
be improved to meet the desired objectives.

30
Therefore, novel (robust and advance) observer-controller set is necessarily re-
quired for the ecient operation of induction machine based propulsion drive for
the use in EVs and HEVs. As a result, torque compensation and degradation
control of machine has been ensured.
2.6.2.1 Estimation Problem
An estimator (observer) is a supporting dynamical system which generates the
estimate of the process's states by taking the input and output signal of the pro-
cess. Then, this can be used to complete the closed loop control. Eective and
suitable control techniques of induction machine propulsion systems need torque,
speed and
ux estimates in the presence of the parameter variations due to the
change in surrounding and operating temperatures. In hybrid and electric vehi-
cles, to achieve high performance, eld-oriented control of induction motor drive
is adopted. To implement the eective eld-oriented control of induction motor
drive exact knowledge of rotor
ux, torque as well as speed is required. Rotor

ux, torque and speed are sensitive to the variation in rotor resistance, stator
resistance, and load torque. Therefore robust observer is required. There are sev-
eral methods available in the existing literature for the estimation of rotor
ux
and speed. The Luenberger and Kalman observers are the commonly adopted
types of the induction machine observers [56{58]. The Luenberger observer uses
the stationary reference frame equations of induction machine model to estimate
the the rotor
ux and stator currents. The Luenberger observer's gain matrix Lis
computed from the machine's model. Therefore, it does not work eciently due
to the large variations in parameters due to the change in temperature as well as
in measurements.
The current model
ux estimator [59]-[60]-[61] and voltage model
ux estima-
tor [62] are extensively used for the
ux estimation using the terminal quantities
of the induction machine. The performance of current model
ux estimator is
deteriorated at high speed and the performance of voltage model
ux observer is
deteriorated at low speed due to the variation in the rotor resistance and stator

31
resistance respectively. Because, the value of input signals are needed for voltage
model
ux observer which are very low at low speed and synthesis of rotor
ux
components with the help of speed and current signals are more easy at low speed.
A hybrid model
ux observer is suggested in [63], to use the current model
ux
estimator at low speed and voltage model
ux estimator at high speed to over-
come the problem of rotor and stator resistance variations. It does not completely
overcome the dependency of observer on stator and rotor resistance.
Model referencing adaptive techniques are suggested in [64]-[65]-[66], two
ux es-
timators are considered. One operates as a reference model, and other performs
as an adaptive observer. The exact estimation of
ux still remained as a problem.
Another technique for the
ux estimation is Extended Kalman lter as proposed
in [58, 67, 68], where only motor terminal quantities are used. However, this
technique has inherent problem of computation expense. Kubota, Matsuse and
Nankano [57], used the full-order adaptive Luenberger
ux observer to estimate
the stator currents and rotor
uxes with the help of fourth order part of the fth-
order induction machine model in stationary reference frame with constant rotor
speed. Estimation of speed is done through the proportional plus integral formula.
Sliding mode has advantages of robustness and parameter invariance and order
reduction [69] . Sliding mode observer of Derdiyok et al. [70] is used for the
ux
estimation with the same portion of induction machine model used in Kubota's
observer. Sliding mode observer proposed by Utkin, Guldner, and Shi [69] is also
used for the
ux and speed estimation of induction machine. Utkin's observer is
also based on the fourth order part of the fthe-order induction machine model in
stationary reference frame. In the sliding mode technique based observers, the gain
computation is tedious and trial basis. Sliding mode control technique has also
the problem of chattering. In order to overcome the problem of chattering, higher-
order sliding mode control (HOSM) techniques based observers are proposed and
presented in [71{73]. But, the HOSM control technique is not robust like FOSMC
method. For the implementation of HOSM control, pure dierentiator is needed
which is not practicable and chattering is also appeared due to un-modeled fast
dynamics sooner or later. In Verghese and Sander's
ux observer [59], only
ux

32
estimation is focused by the authors. A fth-order observer is also proposed in
[74], to overcome the parameter's variation due to the abrupt change in operating
conditions. In [75], the structure of the observer is inspired from the structure
of Zak [76]. This observer faces the sever problem whenever the change in rotor
speed is aggressive as in the case of hybrid and electric vehicles.
Another area of observer design in these days is the Linear Parameter Varying
(LPV) technique. The main objective of the LPV control (gain scheduling) tech-
nique is to control the plant over the predened operating range, but rather than
simply being robust to variations in the plant, the controller is allowed to schedule
itself based on some measurements. This is in opposite to the traditional Linear
Time Invariant control technique which relies on the localized linear characteristics
of the plant at a particular operating condition. The advantage of the LPV control
structures lies in their explicit exploitation of knowledge of the actual plant dy-
namics, based on measurement. In addition to the measurement signal, the LPV
control technique takes the advantage of exogenous plant information to update
its dynamics in real time. It is important to note that this information modies
not only the control signal, but also the way in which measurement signals are
processed through the LPV control technique. As a consequence, LPV control
technique can provide better robustness and performance properties than xed
controllers, which ignore the non-stationary nature of the plant. An LPV based
rotor
ux observer is presented in [77] but it only considered the rotor speed and
rotor resistance variations. It does not consider the stator resistance variation
in its observer design. In [78], LPV based observer for an induction machine is
proposed and implemented which only takes the rotor resistance and load torque
variations. In [79], only the stator resistance and rotor resistance variations have
been taken into account.
From the above discussion, it can be seen that a variety of observer design tech-
niques exist to address IM control in general. Some of them even consider limited
parameter variations but not in the context of traction motors
ux and torque
derating due to the change in operating and surrounding temperatures. It is
worthwhile to mention that the study on estimating the thermally derated torque

33
of an electried powertrain is rare to the best of authors knowledge. As a result,
in this research, a novel robust LPV based observer has been developed by taking
into account the rotor resistance, stator resistance, and speed variations for the
ecient control implementation of induction machine used in electric and hybrid
vehicles.
2.6.2.2 Control Problem
Direct eld-oriented control of an induction machine drive has two control loops:
inner current loop, and outer
ux and torque/speed control loops as shown in the
Figure 2.11.
Flux
command
Motor+
+n*
r
Speed
commandG2
G1de-qe
to
ds-qs2-phase
to
3-phaseVFI
Flux
estimationVd
ia
ib
ic-
-ids
iqsidss
iqss
nr
r^
r^
r
==
cosϴe sinϴeUnit vectorVR
Figure 2.11: Direct Field-oriented Control Block Diagram With Rotor Flux
Orientation [3].
To realize these controller, Conventional Field-Oriented Control (FOC) is com-
monly used to ensure ecient operation of an IM based electric drive [13, 80].
The performance of conventional FOC is highly dependent on IM rotor and stator
parameters. These parameters are adversely aected in extreme operating condi-
tions, part loads and variation in payloads. As a result, eciency and torque of
an electried powertrain is also aected. Feedback linearization concept is used
in [81{84] to compute the gains of the proportional plus integral controller for the

34

ux and speed regulator. The robustness and parameter variations are not con-
sidered in the computation of controllers. As a consequence, performance of the
control is deteriorated. Passivity based techniques [85{87], and First-order sliding
mode control approaches [13, 88, 89] have been all studied and investigated. SMC
technique is robust but it suers from chattering problem. Due to the chattering
in control, the optimal
ux and torque is dicult to ensure for traction applica-
tions. The Higher Order Sliding Mode (HOSM) control based FOC is one of the
possible solutions to minimize the chattering phenomenon and has been presented
in [71{73]. But, the HOSM control technique is not robust like FOSMC method.
For the implementation of HOSM control, pure dierentiator is needed which is
not practicable and chattering is also appeared due to un-modeled fast dynamics
sooner or later.
In [12], PI based eld-oriented controller is implemented for the
ux and torque
tracking for the hybrid electric vehicle's applications. The resulting controller is
robust against the rotor resistance variations only. Adaptive anti-windup tech-
nique is deployed in [40], to design the
ux and torque controller to implement
the FOC of an induction machine for a hybrid electric vehicle. Machine parameter
variations are not considered in the design process. Jalalifar, and Amir Farrokh
in [37] implemented a controller based on input-output feedback linearization with
the observer based on adaptive backstepping technique for the series hybrid elec-
tric vehicle. Field-oriented control based proportional plus integral controller has
been proposed in [90], for the sensorless operation of induction machine drive for
electric vehicle application. The output feedback controller is designed and val-
idated in [91]. It addresses the limited parameter variations. Sensorless control
techniques for electric vehicles are presented in [58, 68] for torque and
ux tracking.
In [77], linear parameter varying (LPV) feedback controller for the inner current
loop is designed by taking into account the mechanical speed and the rotor resis-
tance as the varying parameter. The outer
ux and speed regulators are based on
sliding mode control technique. In [78], linear parameter varying (LPV) feedback
controller for the inner current loop is designed by taking into account the rotor

35
speed as the varying parameter. The outer
ux and speed regulators are designed
classical linear techniques.
From the above discussion, it can be seen that a variety of control design tech-
niques exist to address IM control in general. To the author best knowledge, in the
current literature managing the thermally derated torque of an electried power-
train is rare. The development of control technique to cater for the degradation
(aging, eciency, performance) as a joint criteria is limited as well. As a result,
linear parameter varying (LPV) feedback controller for the inner current loop has
been designed by taking into account the rotor speed, rotor resistance, and stator
resistance as the varying parameters. The outer
ux and speed regulators has been
designed by solving the linear matrix inequalities. The development of advance,
novel, and robust observer-controller set has been addressed in this research to
cope with derated torque and powertrain degradation due to the rise in operating
and ambient temperatures.
2.7 Conclusion
To achieve the high performance of an electric drive in the presence of phenomenon
discussed in Section 2.3, selection of the electric machine for the electric propulsion
system of the EVs and HEVs is the most crucial step. Therefore, the selection
of induction machine for the electric propulsion system of EVs and HEVs has
been done on the basis of following parameters: controllability, reliability, power
density, technological maturity, eciency, availability, ruggedness and cost. Due
to the parameters variations, the static and dynamic performance of induction
machine, adopted as a propulsion machine in this research, is signicantly aected,
have been discussed. The existing techniques for the compensation of the eects
due to the parameters variations on induction machine also have been described.
From this, it has been concluded that opportunities are exist in control, design and
ecient use of induction machine drives in EVs and HEVs. As mentioned earlier,
this research focuses on the design and development of novel (robust and advance)

36
control techniques to estimating, managing the thermally derated torque, improv-
ing the eciency of an electric powertrain and to minimize the loss of lifetime
(aging) of an traction machine in the presence of adverse conditions presented in
Section 2.3.
In the coming chapter, control-oriented non-linear model of an induction machine
based drive will be formulated. An Linear Parameter Varying (LPV) model will
be developed and presented for an induction machine based electric drive. Later
on, LPV and non-linear models will be validated and analyzed for the parameters
variations.

Chapter 3
Mathematical Modeling of
Induction Machine
Things of this world cannot be made known without Mathematics.
Roger Bacon (1220-1292), Opus Majus, Transl. R. Burke 1928.
This chapter is devoted to the development of a mathematical model of the In-
duction Machine which has been chosen as a propulsion machine as detailed in
chapter-2. This model will be used in propulsion drive needed for the hybrid and
electric vehicles. It provides the background details needed for better understand-
ing the induction machine from a dynamical system viewpoint. This model will be
subsequently used for observer and controller design. A two-phase representation
of a three-phase induction machine is described in this chapter. The voltage,
ux,
and current equations which are helpful in obtaining the induction machine model
in arbitrary rotating reference frame and stationary reference frame are presented.
The 5th order nonlinear model of induction machine, both in stationary reference
frame and arbitrary rotating reference frame is derived. This model is used to de-
rive the Linear Parameter Varying (LPV) model of an induction machine. Later
on, this model will be used for the design of robust controllers and observers which
are necessarily required for the ecient operation of eld-oriented control (FOC)
37

38
of 3induction machine drive for the application in hybrid and electric vehi-
cles. In the end, it is also simulated in MatlabR
/Simulink software to appreciate
its advantages from ecient operation viewpoint and model validation viewpoint
as well.
3.1 Construction and Principle of Induction Ma-
chine
An induction machine consists of two physical parts: stator and rotor. An idealized
two pole, 3machine is shown in the Figure 3.1. The 3 windings which are
1200displaced by each other are wounded in the slots of the stator to produce the
three-phase sinusoidal rotating magnetomotive force waves.
Figure 3.1: Idealized two pole three-phase induction machine [4].
The rotor of the induction machine is of two types: squirrel cage rotor and wound
rotor. A cage rotor has a chain of conducting bars which are placed into the rotor
slots and shorting rings are used to short it at either end. A wound rotor has a

39
similar windings as of stator windings and rotor's shaft has slip rings which are used
to tie the ends of the three rotor windings. The brushes are used to short the three
phase rotor windings. If 3 voltages are supplied to the windings of the stator.
the three phase stator magnetomotive forces are developed and they produce the
stator magnetic eld. When the stator magnetic eld cut the rotor conductors,
it induces the voltage in the rotor side. The rotor currents will
ow due to the
induced voltages and as explained earlier rotor of the machine is short-circuited.
The rotor currents will interact with the eld of air-gap to induce the torque.
Due to the induced torque, rotor will begin rotating. The direction of rotation is
the same as that of the rotating eld. The dierence between synchronous speed
(stator
ux speed) and rotor speed is known as the slip speed. The slip, s, of the
machine can be given as:
s=nenr
ne(3.1)
whereneandnrare the synchronous speed and rotor speed respectively.
The rotating eld in the rotor circuit will be produced due to the induced currents
and it can be given as:
fr=sfe (3.2)
wherefrandfeis the rotor frequency and stator frequency respectively.
The induced torque due to the relative motion between the stator and rotor mag-
netic elds are given as:
ind=kBrBs (3.3)
whereBrandBsare rotor and stator magnetic
ux densities respectively. kis a
constant depending on the machine construction. The induced torque will be zero
when rotor is running at synchronous speed and in result the rotor slow down due
the frictional losses.

40
3.2 Induction Machine Modeling
Electromagnetic coupling exists between the stator and rotor circuits of the in-
duction machine. Therefore, the coupling coecient between the stator and rotor
phases changes continuously with the change of rotor position r. This coupling
eect can be removed by transferring/referring the stator and rotor variables to
a common reference frame which may rotate at any speed (arbitrary reference
frame) [3], [34]. For better graphical interpretation and simpler mathematical ma-
nipulation, a three-phase machine can be represented by an equivalent two-phase
machine as shown in Figures 3.2 and 3.3. The variables in the equivalent two
phase machine are: direct axis (d) and quadrature axis (q) variables as described
in Figure 3.3.
b
c
arϴr
Figure 3.2: Coupling eect in three-phase stator and rotor windings of the
machine.
In Figure 3.3, dsqscorrespond to stator direct and quadrature axes, and drqr
correspond to rotor direct and quadrature axes. In Figure 3.2, the axes a, b, c are
the stator abc reference frame and the rotor reference frame for the subscript of s
and r attached to these axes respectively. If the synchronous speed, ne, is zero, the
common reference frame is said to be non-rotating and it is known as stationary
reference frame (SRF) [3]. Similarly, if neis not zero, the common reference frame

41
is said to be a rotating and it is known as synchronously rotating reference frame
(SSRF) [3].
dsqs
drqr
ωr
ϴr
Figure 3.3: Equivalent two-phase machine.
The stator axes variables: a, b, c can be transformed to the dqaxes as shown
in Figure 3.3 by the following equations.
fqs=2
3[fascos +fbscos(1200) +fcscos(+ 1200)] (3.4)
fds=2
3[fassin +fbssin(1200) +fcssin(+ 1200)] (3.5)
Where the symbol frepresent the current, the voltage and
ux of the three-phase
and two-phase stator circuit. fqsis the stator quadrature axes voltage, current, or

ux,fdsis the stator direct axes voltage, current, or
ux, fasis the stator phase a
voltage, current, or
ux, fbsis the stator phase bvoltage, current, or
ux and fcs
is the stator phase cvoltage, current, or
ux.

42
Similarly, the stationary direct (d) and quadrature (q) axes quantities can be
converted to synchronously rotating direct (d) and quadrature (q) axes quantities
as shown in Figure 3.4 by the following equations.
fds=fs
qssine+fs
dscose (3.6)
fqs=fs
qscosefs
dssine (3.7)
The rotating reference frame quantities can be converted to synchronously rotating
reference frame by the following equations.
fs
ds=fqssine+fdscose (3.8)
fs
qs=fqscose+fdssine (3.9)
qs-axis
ds-axisasVasVbsbs
csVcsVdssVqss
ϴ
Figure 3.4: Stationary frame abctodsqsaxes transformation.

43
Figure 3.5: Location of rotating dqaxes relative to stationary dqaxes.
After the substitution of three-phase stator sinusoidal and balanced voltages in
the (3.4) and (3.5), following equations yields.
fs
qs=fmcos(!et+) (3.10)
fs
ds=fmsin(!et+) (3.11)
Again, substituting (3.3) and (3.4) in (3.7) and (3.8), yields
fs
qs=fmcos (3.12)
fs
ds=fmsin (3.13)
(3.10) and (3.11) show that fs
qsandfs
dsare balanced, two phase voltage or current
of equal peak values and the latter is at =2 angle phase lead with respect to the
other component. (3.12) and (3.13) show that the sinusoidal variables in sta-
tionary reference frame (SRF) appear as dc quantities in a synchronously rotating
reference frame (SRRF).
3.2.1 d-q Model of a Three-phase Induction Machine
The eld-oriented control (FOC) of induction machine adopted for the traction
applications depend upon the (3.10)- (3.13) shown in the last section. Therefore,

44
thedqmodel of the induction machine will be presented and described in the
following.
3.2.1.1 d-q Model of a Three-phase Induction Machine in Synchronously
Rotating Reference Frame
The equivalent circuit of daxis andqaxis of two-phase machine shown in Fig-
ure 3.3 for the three-phase induction machine referred to a synchronously rotating
reference frame (SRRF) at any arbitrary speed nas shown in Figure 3.6. The
d-axis and q-axis stator voltage equation can be described as:
Figure 3.6: Dynamicdqequivalent circuits of a 3 induction machine.
udS=rSidS+ddS
dtneqS (3.14)

45
uqS=rSiqS+dqS
dt+nedS (3.15)
where
qS=lSiqS+M(iqS+iqR) (3.16)
dS=lSidS+M(idS+idR) (3.17)
where all the variables are in rotating form. qsanddsare the q-axis and d-axis
stator
ux respectively. rS,ne,M, andlSare the stator resistance, synchronous
speed, magnetizing inductance, and stator leakage inductance respectively. udS
anduqSare the d-axis and q-axis stator voltages respectively as well as these are
the inputs of the system. idSandiqSare the d-axis and q-axis stator currents
respectively as well as these are the outputs of the system. idRandiqRare the
d-axis and q-axis rotor currents respectively.
Since the rotor of the machine is moving at the speed of ne, the rotor dqaxes
moves at the speed of nenrrelative to the arbitrary (synchronously) rotating
reference frame. So, the rotor equations are
udR=rRidR+ddR
dt(nenr)qR (3.18)
uqR=rRiqR+dqR
dt+ (nenr)dR (3.19)
where
qR=lRiqR+M(iqS+iqR) (3.20)
dR=lRidR+M(idS+idR) (3.21)
qRanddRare the q-axis and d-axis rotor
ux respectively. rR,ne,nr,M,
andlRare the rotor resistance, synchronous speed, rotor speed, magnetizing
inductance, and rotor leakage inductance respectively. udRanduqRare the d-axis
and q-axis rotor voltages respectively.

46
The d-q representation presented above is used to derive the induction machine
model in synchronously rotating reference frame. The denitions of control vari-
ables and states are presented in Table 3.1. The denitions of parameters that are
used in the induction machine modeling equations are presented in Table 3.2.
Table 3.1: State Variables Used in the Modeling of The Induction Machine
Symbol Description Units
nr Rotor angular speed r=s
dS Rotor
ux of direct (d)-axis Wb
qR Rotor
ux of quadrature (q)-axis Wb
iS
dS Stator current of direct (d)-axis
(state and output)A
iS
qS Stator current of quadrature (q)-
axis (state and output)A
uS
qS Stator voltage of quadrature (q)-
axis (input)V
uS
dS Stator voltage of direct (d)-axis (in-
put)V
Table 3.2: Model's Parameters Description Used in Induction Machine Mod-
eling
Symbol Description
(2
MrR+2
RrS)
S2
R

M
SR
rR
R
 12
M
SR
3
2(P
2)M
R
With the help of (3.16)- (3.21) and manipulation of these equations for the state
(control) variable yields the following fourth-order electrical dynamics of the ma-
chine.
de
dR
dt=rR
Re
dR+np(nenr)e
qR+MrR
Rie
dS (3.22)
de
qR
dt=rR
Re
qRnp(nenr)e
dR+MrR
Rie
qS (3.23)
die
dS
dt=(2
MrR+2
RrS)
S2
Rie
dS+neie
qS+MrR
S2
Re
dR+npMnr
SRe
qR+1
sue
dS(3.24)
die
qS
dt=(2
MrR+2
RrS)
S2
Rie
qSneie
dS+MrR
S2
Re
qR+npMnr
SRe
dR+1
Sue
qS(3.25)

47
The subscript ein (3.22)- (3.25) means that all the quantities are in SRRF. The
(3.22)- (3.23) are the rotor
ux and (3.24)- (3.25) are stator currents of d-axis
and q-axis in the SRRF.
3.2.1.2 d-q Model of a Three-phase Induction Machine in Stationary
Reference Frame
The dynamic model of a three-phase machine in stationary reference frame (SRF)
can be obtained by simply putting the ne= 0 in the equations obtained for
the three-phase machine moving in a arbitrary (synchronously) rotating reference
frame. The model in SRF is required to implement the novel observer-controller set
for the ecient operation of induction machine based propulsion drive. Therefore,
corresponding stationary reference frame equations at stator can be represented
as
uS
dS=rSiS
dS+dS
dS
dt(3.26)
uS
qS=rSiS
qS+dS
qS
dt(3.27)
where
S
qR=lRiS
qR+MiS
qS (3.28)
S
dR=lRiS
dR+M(iS
dS (3.29)
At rotor:
0 =rRiS
dR+dS
dR
dt+nrS
qR (3.30)
0 =rRiS
qR+dS
qR
dtnrS
dR (3.31)
where the voltage of the rotor are, udR=uqR= 0, for squirrel cage induction
machine.
Now, d-q representation presented above is used to derive the induction machine
model in stationary reference frame. This model will be used for the eld-oriented

48
control (FOC) of three-phase induction machine drive for the application in hybrid
and electric vehicles. The denition of control variables and states are presented
in Table 3.1. The denition of parameters that are used in the induction machine
modeling equations are presented in Table 3.2.
Eliminating is
dRfrom (3.26) with the aid of (3.25) gives
Rotor
ux equations:
dS
dR
dt=rR
MS
dRnpnrS
qR+MrR
RiS
dS (3.32)
Similarly, eliminating is
qRfrom (3.24) with the aid of (3.21) gives
ds
qR
dt=rR
Rs
qR+npnrs
dR+MrR
Ris
qS (3.33)
To obtain the stator current equations, substituting the (3.24)- (3.25) and (3.28)-
(3.29) in (3.22)- (3.23) respectively gives
Stator current equations:
dis
dS
dt=(2
MrR+R2rS)
S2
Ris
dS+MrR
S2
Rs
dR+npMnr
SRs
qR+1
Sus
ds (3.34)
dis
qS
dt=(2
MrR+2
RrS)
S2
Ris
qS+MrR
S2
Rs
qR+npMnr
SRs
dR+1
Sus
qS (3.35)
Mechanical Equations:
The speed, nr, in (3.28)- (3.31) can not be generally treated as a invariable. It is
related to the torque of the machine as [3], [75]
e=L+Jdnm
dt+Bnr (3.36)

49
and
nm=2
npJdnr
dt(3.37)
Therefore, by substituting (3.37) in (3.36) yields
dnr
dt=np
2J(eLBnr) (3.38)
In (3.38), the electromagnetic generated torque ( e) is given as
e=3
2(np
2)M
r(s
dRis
qSs
qRis
dR) (3.39)
where,e,L,J,B,nmis the electromagnetic generated torque, load torque, rotor
inertia, rotor damping, and rotor mechanical speed respectively.
The (3.32)- (3.35) represent the fourth order nonlinear electrical dynamics of the
three-phase induction machine in stationary d-q reference frame. The (3.38) repre-
sent the mechanical dynamics of the the machine. Therefore, nonlinear dynamical
model of the three-phase induction machine is of fth-order.
3.2.1.3 The Complete Dynamics of an Induction Machine
The complete model at one place can be given as:
Electrical Equations:
dS
dR
dt=rR
MS
dRnpnrS
qR+MrR
RiS
dS (3.40)
ds
qR
dt=rR
Rs
qR+npnrs
dR+MrR
Ris
qS (3.41)
dis
dS
dt=(2
MrR+R2rS)
S2
Ris
dS+MrR
S2
Rs
dR+npMnr
SRs
qR+1
Sus
ds (3.42)

50
dis
qS
dt=(2
MrR+2
RrS)
S2
Ris
qS+MrR
S2
Rs
qR+npMnr
SRs
dR+1
Sus
qS (3.43)
Mechanical equation:
dnr
dt=np
2J(eLBnr) (3.44)
e=3
2(np
2)M
r(s
dRis
qSs
qRis
dR) (3.45)
3.3 Hybrid Electric Vehicle Drive System and
Control
A hybrid electric vehicle drive system consists of several major components in-
cluding the propulsion (traction) machine. The components are sensors, power
electronics converter, observers (estimators) to measure unknown parameters and
states, controllers and any dedicated processor. The current sensors measure the
two phase currents and from this information current of third phase is computed.
These currents are fed back to the controller. Speed sensor (encoder) may or may
not be used to measure the angular position of the rotor. In some cases rotor

uxes and angular position of the rotor are estimated and used for the control of
drive system. The controllers process the sensor and estimated data and control
the power electronics converter for the desired ecient operation.
In hybrid and electric vehicle, control methodology can be speed control or torque
control and
ux control as shown in the Figure 3.7. In this work, there are two
control loops. The outer loop is the
ux control loop and speed control loop with
indirect torque control loop i.e torque of the drive will be controlled indirectly.
The inner control loop is the current loop. In this work, the actual speed and the
actual
ux of the machine is compared with the reference values to produce the
reference currents of dandqaxes. These currents are compared with the actual
currents of dandqaxes to generate the pulses for the pulse width modulation

51
signals. In this research, eld-oriented control of three-phase induction machine
drive structure is used for the propulsion of hybrid and electric vehicles.
3.3.1 Field-oriented Or Vector Control of a Three-phase
Induction Machine Drive
This section explains the eld-oriented control of a three-phase induction machine
for the applications in EVs and HEVs. In vector or Field-oriented Control (FOC)
both the magnitude and phase alignment of the vector or control variables are
controlled. dqtransformation is employed in eld-oriented control to make the
control easier and simpler. dqtransformation also decouples the two phases of the
machine and machine behaves like a separately-excited DC machine in which eld
current vector, If, is used to control the
ux of the machine and armature current
vector,Ia, is used to control the torque of the DC machine respectively without
disturbing control of each other. Similarly, by employing the dqtransformation,
d-axis current of the machine's stator is used to control the
ux of the three-phase
machine and q-axis current of the machine's stator is used to control the torque of
the three-phase machine. Therefore, FOC is an attractive technique and provides
better static and dynamic performance of induction machine drive for EVs and
HEVs. The eld-oriented control can be represented in both in any arbitrary
rotating reference frame ( narbitrary ) and in stationary reference frame. The dq
transformation, equivalent circuits, and model are detailed in previous sections.
Field-oriented or vector control is of two types: (1) direct or feedback method, (2)
indirect or feed forward method. The dierence between the two method is how
the unit vectors ( coseandsine) are generated to accomplish the control.
3.3.1.1 Direct or Feedback Field-oriented Control
Direct or feedback eld-oriented control is used for the control of three-phase
induction machine. The feedback (direct) eld-oriented (vector) control is the

52
most commonly adopted instantaneous speed/torque control method for the hy-
brid and electric vehicle's drive system. The proposed block diagram of the direct
or feedback eld-oriented control (DFOC) of the induction machine drive for the
application in hybrid and electric vehicles is presented in Figure 3.7. The currents
components, i
ds, andi
qsare the principle vector control parameters which are dc
values in synchronously rotating reference frame (SRRF). These are converted to
stationary reference frame (SRF) with the aid of unit vectors ( coseandsine).
These unit vectors are generated from the rotor
ux vector components s
drand
s
qr. The resulting dandqaxis voltage signals are converted to phase voltages
reference for the voltage fed inverter with the help of 2 to 3transformation
block. The
ux components s
drands
qrare generated from the machine terminal
voltages and currents with the aid of robust observer, which will be elaborated
later. To achieve the precision control in
ux, a
ux control loop has been added.
The control of torque is achieved indirectly in the outer speed loop. The torque
is directly proportional to iqs. It can be of positive and negative polarity. Field-
weakening mode can be achieved by adjusting the
ux command as a function of
speed so that the inverter keeps itself in the PWM mode.
The key and crucial point in the eld-oriented control is that the daxis current
idsmust be aligned in the direction of rotor
ux brand theqaxis current iqs
orthogonal to it. Figure 3.8 explains this alignment with the aid of the rotor
ux
components s
drands
qrin stationary reference frame.The stator dsqsaxes are
xed while the deqeaxes are rotating at synchronous angular speed ne. The
angular position eis dierence between deaxis andqeaxis at any time, where
e=net. Figure 3.8 is showing the correct alignment of rotor
ux signals and
gives the following useful equations for direct eld-oriented control.
cose=s
dr
br(3.46)
sine=s
qr
br(3.47)

53
/g301*
R
n*
rRobust
Flux
Regulatorde-qe
to
ds-qs2-phase
to
3-phase
Transfor
-mationVFI
Robust
Observer+
–
+-i*
ds
i*
qsuds
uqs
nr
nrΦ^
r
/g2244eVR
Φerr
Robust
Speed
Regulatornerrids-err udss
uqssHEV
Battery
ua
ub
uc
2- Φ
to
3- Φia
ibds-qs
to
de-qeids
iqs+
–
-+
3-phase
Induction Machine
nrus
dqsΦ^
rTorque component
of stator currentiqs-errRobust
Current
Controller
Figure 3.7: Proposed Induction Machine Drive Structure with Direct or Feed-
back Field-oriented Control.
and
br=q
s2
dr+s2
qr (3.48)
Therefore, exact and precise rotor
ux is required to ensure that the daxis stator
current component and qaxis stator current component are perpendicular to each
other. In result, ecient operation of propulsion drive for the hybrid and electric
vehicles is guaranteed. The fth-order nonlinear mathematical model of induction
machine in stationary reference frame that is presented in (3.40)- (3.45) has been
used in this hybrid and electric drive structure and control.
3.4 Load Torque Prole
The load torque prole depends upon the parameters of the vehicle for which
propulsion system is designed. The size of the propulsion machine is dependent
on the load torque prole. Therefore, the initial step in measuring the performance

54
qsqe
de
dsiqs=i*qs
^qr=0
drs
cosθe-iqsθeids=i*
ds
^r=dr
neqrssinθe
Figure 3.8: Phasor Diagram for Direct Field-oriented Control in Syn-
chronously Rotating Reference Frame (SRRF)[3].
modeling is to come with an equation for the electric forces. This force is neces-
sarily required to propel the vehicle forward. This force (torque) must overcome
the resistance provided by the road and move the vehicle forward as shown in the
Figure 3.9. The aerodynamic force is because of the damping of the body of the
vehicle moving through the air and given as [37]:
Figure 3.9: Aerodynamic drag force, Rolling resistance force, Road grade force
on a Vehicle
.
fad=1
2airCdAfv2(3.49)

55
Whereairis the air mass density, Cdis the aerodynamic drag coecient, Afis
the frontal surface area of the vehicle, and vis the velocity of the vehicle.
The rolling resistance is because of the damping of the vehicle tires on the road
and given as:
froll=mgCrcosg (3.50)
Wheremis the mass of the vehicle, gis the gravity acceleration, Cris the rolling
resistance coecient, and gis the grade angle.
The force due to the slope of the road is known as road grade force and is given
as:
fgrade =mgsing (3.51)
Therefore, load torque can be modeled by taking in account the rolling resistance
force, road grade force and aerodynamic drag force and is given as:
L=Rtire
Rf[1
2airCdAfv2+mgCrcosg+mgsing] (3.52)
WhereRtireis the radius of the tire, and Rfis the total ratio between the motor
shaft and dierential axle of the vehicle.
3.5 Model Based Analysis and Simulation
In this section, the developed model and FOC based drive structure of three-
phase induction machine presented in section 3.2.1.2 and section 3.2.2.2 for the
applications in hybrid and electric vehicles has been implemented and veried
through the MatlabR
/Simulink software.

56
3.5.1 Model Simulation and Discussion
The analysis of the developed model for the three-phase induction machine is
performed with the parameters of 30 KW, 4-pole, 280 line to line voltage, and
50Hzelectrical frequency. Table 3.3 gives the parameters values for three-phase
induction machine. The simulation model has been developed for the machine to
analyze its dierent characteristics such as phase currents,
uxes, phase voltages,
speed and torque under dierent load conditions.
Table 3.3: Induction Machine Specications
Symbol Description Value/Units
P Power 30 KW
np Number of pole pair 2
fe Electrical frequency 50 Hz
VL Line to line voltage 280 V
rR Rotor resistance 0.228
R Rotor inductance 0.8 mH
rS Stator resistance 0.087
S Stator inductance 0.8 mH
M Mutual inductance 34.7 mH
J Inertia 1.662 kg:m2
B Damping 0.01 N:m:sec:rad1
To validate the presented dynamic model of the three-phase induction machine,
two cases are considered.
3.5.1.1 Positive Load Torque-Motoring Operation
In this case a positive load torque of 40 N:m is applied at t= 1msand it becomes
again zero at t= 1:5msto simulate the presented dynamic model of induction
machine to observe its motoring behavior. The prole of the applied load torque
is shown in the Figure 3.10. Three phase supply voltages which are 1200apart from
each other is applied as the input In the case of hybrid and electric vehicle, these
three phase voltages come from the inverter output whose input is the battery
bank voltages. Behavior of the electromagnetic generate torque, motor speed is
vivid from the Figure 3.11 when a load torque is applied. At time t= 1ms,

57
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8-5051015202530354045
Time (s)Load Torque TL (N.m)
Figure 3.10: Load Torque.
the electromagnetic generated torque is e>(L+Bnm). Figure 3.12 gives the
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-300-200-1000100200300400
Time (s)TL,Te (N.m) and Wr (rad/s)1.45 1.5 1.55312314316318Wr Rising Edge
0.95 11.05308310312314Wr Falling EdgeTe
Wr
TL
Figure 3.11: Induction machine load torque, electromagnetic generated
torque, rotor speed.
induction machine current in SRF. It is clear from the Figure 3.12 that as the
demanded electromagnetic generated torque from the motor at t= 1ms, the q-
axis current component increases to meet the requirement of the demanded torque
from the machine. Therefore, it is basically the torque component of the induction
machine drive. Figure 3.12 shows the dynamic behavior of the d-axis and q-axis
currents components in SRF and eect of the load torque is evident from the plots.
Three phase currents of induction machine are presented in Figure 3.12 to show
the load torque eects.

58
0 0.5 1 1.5 2 2.5 3-400-300-200-1000100200300400
Time (s)ia,ib and ic (A)ia
ib
ic
1 1.2 1.4 1.6-20020
ia
Figure 3.12: Induction machine three phase current for the unipolar load
torque.
The dynamic behavior of the machine can also observed by plotting the eversus
nras shown in Figure 3.13. The motoring behavior of the machine is also clear
from this plot. Zoomed version of this plot shows that rst steady state point
occurs when load torque is zero and second steady state point occurs when load
torque is 40 N.m. Again the motor settles at rst steady state point as the load
torque is removed.
050100150200250300350−300−200−1000100200300400
Angular Velocity (rad/s)Torque (N.m)

nr Vs Te
300310320−1000100200
Figure 3.13: Dynamic behavior of induction machine: Torque-speed curve.

59
3.5.1.2 Positive and Negative Load Torque-Motoring and Generating
Operation
In this case a positive load torque of 40N.m is applied at t= 1ms , it becomes
again zero at t= 1:5ms , its value is 40N.m at 2ms and it becomes again
zero att= 2:5ms to simulate the presented dynamic model of induction machine
to observe its motoring and generating behavior. The prole of the applied load
torque is shown in the Figure 3.14. Figure 3.15 presents the plot of the three-phase
0 0.5 1 1.5 2 2.5 3-40-30-20-10010203040
Time (s)Bipolar Load Torque (N.m)
Figure 3.14: Bipolar load torque.
stator current with application of load torque of Figure 3.14. Zoomed version of the
stator currents is given in Figure 3.15 to show the variation in these currents during
the motoring and generating operation of the machine. Figure 3.16 is plot for the
electromagnetic generate torque, machine's speed and the load torque. Dynamic
behavior of this machine as a generator and as a motor is evident from the plot
betweeneandnras shown in the Figure 3.17. Zoomed version of this plot shows
that rst steady state point occurs when load torque is zero and second steady
state point occurs when load torque is 40 N.m. This is the motoring behavior of
the machine. Again the motor settles at rst steady state point as the load torque
is zero att= 1:5 ms. A third steady state point occurs when the load torque
is40 N.m. This is the generating behavior of the machine. Again the machine
settles at rst steady state point as the load torque is zero at t= 2:5 ms.

60
0 0.5 1 1.5 2 2.5 3-400-300-200-1000100200300400
Time (s)ia,ib and ic (A)ia
ib
ic
0.6 0.8 1-20020ia2 2.2 2.4 2.6-20020ia
Figure 3.15: Induction machine phase currents for bipolar torque.
0 1 2 3 4−300−200−1000100200300400
Time (s)TL,Te (N.m) and nr (rad/s)

nr
TL
Te
0.450.50.55308310312314
0.9511.05312314316318
1.9522.05315320
2.452.52.55310315
Figure 3.16: Induction machine load torque, electromagnetic generated
torque, rotor speed for bipolar torque.
3.6 LPV Modeling of Induction Machine
In this section, LPV modeling of induction machine is presented. The general
representation of the group of LPV system in which state space matrices depend

61
050100150200250300350−300−200−1000100200300400
Angular Velocity (rad/s)Toruqe (N.m)

nr Vs Te
300310320−1000100200
Figure 3.17: Dynamic behavior of induction machine: Torque-speed curve.
on the parameter vector is described by
dx(t)
dt=A((t))x(t) +B((t))u(t) (3.53)
y=C((t))x(t) +Du(t) (3.54)
where,
x2Rnare the system state vector.
2Rsare the time varying parameter vector.
u2Rm2are the system input vector.
y2Rp2are the system output vector.
The matrices A(:),B(:),C(:) andD(:) are continuous matrix valued functions
of appropriate dimensions of the time varying parameter vector . In (3.53)
and (3.54), the system matrix, input matrix and output matrix can be written

62
as:
A((t)) =A0+i=NX
i=1i(t)Ai (3.55)
and
B((t)) =B0+i=NX
i=1i(t)Bi (3.56)
C((t)) =C0+i=NX
i=1i(t)Ci (3.57)
The time varying parameter vector, (t) can be expressed in the form given as
(t) = (1;2;:::;m)T; iii;i= 1;2;:::;m (3.58)
In order to develop the LPV model for the induction machine; in [77]- [79] only
the rotor speed and rotor resistance variations are modeled. In [78], only rotor
resistance are considered to obtain LPV model. In this work, the rotor resistance,
rR, the stator resistance, rS, and the rotor speed, nrare taken as linear varying
parameters. The state vector, x(t), derivative of the state vector,dx(t)
dt, input
vector,u(t) and output vector, y(t) for the induction machine LPV model of
(3.53) and (3.54) can be given as:
x(t) =h
is
dSis
qSs
dRs
qRiT
(3.59)
_x(t) =h
_is
dS_is
qS_s
dR_s
qRiT
(3.60)
u(t) =h
us
dSus
qSiT
(3.61)
y(t) =h
is
dSis
qSiT
(3.62)
The state space matrices A(),B(),C(), andDfor the induction machine LPV
model of (3.53) and (3.54) can be given as:
A((t)) =A0+i=3X
i=1i(t)Ai (3.63)

63
where
[1;:::; 3] := [rR;rS;nr] (3.64)
The LPV system matrix is given by
A() =2
6666664a11() 0a13()a14()
0a22()a23()a24()
a31() 0a33()a34()
0a42()a43()a44()3
7777775(3.65)
where 8
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>><
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>:a11() =L2
m1+Lr2
LsL2r
a13() =Lm1
LsL2r
a14() =PLm3
LsLr
a22() =L2
m1+Lr2
LsL2r
a23() =PLm3
LsLr
a24() =Lm1
LsL2r
a31() =L2
m1
Lr
a33() =1
Lr
a34() =np3
a42() =L2
m1
Lr
a43() =P3
a44() =1
Lr(3.66)
8
>>>>>><
>>>>>>:B=2
4I
O3
5
C=h
I Oi
D=h
Oi(3.67)
where,
=1
Ls(3.68)
In (3.67), Iis 22 identity matrix, and Ois 22 zero matrix.
In this LPV model of induction machine, is the time varying parameter vector

64
andP0is a convex polytopes with vertices, i;i= 1;2;:::;N: , and can be dened
as:
P0=Cofv1;v2;:::;vLg (3.69)
where,viare the vertices, i= 1;2;:::;L .L= 2are the number of vertices. Co
is a convex hull,i.e, the set of all convex combinations of vi(all points inside and
on the boundary of the polytopes).
The convex form of time varying parameter vector in the case of FOC of 3 
induction machine drive for the applications in EVs and HEVs becomes
(t) =i=8X
i=1ii (3.70)
8
>>><
>>>:1=rR
2=rS
3=nR(3.71)
The matrix A() depends upon the linear time varying parameters and matrices,
B,C, andDare constant. The matrix A() can be given as
A((t)) =A0+A11+A22+A33 (3.72)
and
A(rR;rS;nr) =A0+A1rR+A2rS+A3nr (3.73)
The time varying parameters 1,2and3are assumed to vary in the ranges
rR2[0:5rR;1:5rR] (3.74)
rS2[0:5rS;1:5rS] (3.75)
nR2[160;160] (3.76)

65
3.6.1 LPV Model Validation
Figure 3.18 shows the open-loop step responses for the developed LPV model
for the various values of nR,rRandrS. It is vivid from the responses that the
00.050.10.15Input-1: uds(V)ids(A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.800.050.10.15iqs(A)Input-2: uqs(V)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Open-loop Time Response of Affine LPV Model of Indu ction Machine
Time (seconds)Stator Currents
Figure 3.18: Open-loop time response of an LPV model. Unit step demand
inus
dS;for 10 equally spaced values of nR;rR;rS.
induction machine exhibits the prominent cross-coupling and badly damped poles
whose frequencies vary considerably with the rotor resistance, stator resistances
and rotor speed.
The obtained LPV model is validated in closed-loop against the original nonlinear
model presented in (3.40)- (3.44). Two input signal us
dSandus
qSare generated
with the sucient amplitude to energize the closed-loop system as reference signals
and are given by:
us
dS=umcos (3.77)

66
us
qS=umsin (3.78)
The reference voltage signals and load torque are shown in Figures 3.19 and 3.20.
The scheduling parameter nRis considered as an internal signal. The value of
0 0.05 0.1 0.15 0.2−400−300−200−1000100200300400
Time (s)Voltage (V)

udSs
uqSs
Figure 3.19: Input voltages us
dSandus
qSto validate the nonlinear model and
LPV model
0 0.5 1 1.50510152025303540
Time (s)TL(N.m)
Figure 3.20: Load torque input TLto validate the nonlinear model and LPV
model

67
therRandrSis kept constant. The validation plots for the output signals and
states signal are shown in Figure 3.21 and Figure 3.22 respectively. Plots show
that the LPV model connes the dynamics of nonlinear model well within the
required range of operation.
00.20.40.60.8 11.2−40−20020idS (A)
Non−linear model
LPV model
00.20.40.60.8 11.2−20020
Time (sec)iqS (A)
Non−linear model
LPV model0.85 0.9 0.95−505
Figure 3.21: Validation plots of output currents is
dSandis
qSof the original
nonlinear model and the LPV model.
Root Mean Square Error (RMSE) and Normalized Root Mean Square Error (NRMSE)
are used as performance indices to measure the validity of the LPV model against
the nonlinear model. Table 3.4 gives RMSE and NRMSE values of LPV model
and nonlinear model.
Table 3.4: Accuracy of the LPV model in comparison to the nonlinear model
Model states Cost Function
RMSE NRMSE
idS 1.9375e-004 0.9998
iqS 1.8993e-004 0.9998
dR 9.6877e-005 0.9999
qR 9.4966e-005 0.9999

68
00.20.40.60.8 11.2−1−0.500.5φdS (A)
Non−linear model
LPV model
00.20.40.60.8 11.2−0.500.5
Time (sec)φqS (A)
Non−linear model
LPV model0.85 0.9 0.95−0.100.1
Figure 3.22: Validation plots of states s
dRands
qRof the original nonlinear
model and the LPV model.
3.7 Conclusion
The mathematical modeling of an induction machine has been presented which
will be used in the propulsion system of hybrid and electric vehicles. The LPV
derivation of the non-linear model is also presented. This model will be subse-
quently used in the design of novel (robust and advance) control techniques to
estimate and manage the thermally derated torque in induction machine based
electric powertrain for EVs and HEVs. This model will be also used in designing
a control technique to improve the performance, eciency and loss of life time
(aging) of an electric powertrain. A direct eld-oriented control based structure
of induction machine propulsion drive has been proposed. Load torque prole has
been discussed which is useful for the determination of size of electric machine. At
the end, model based analysis and simulation of both an induction machine and an
induction machine based propulsion drive has been given. The results present the
motoring and generating behavior which is needed in hybrid and electric vehicles.
The RMSE and NRMSE are used as performance indices to show the eectiveness

69
of LPV model with non-linear model.
In the coming chapter, an LPV based estimator will be formulated and designed for
the estimation of thermally derated torque in EVs and HEVs electric powertrain.

Chapter 4
Estimation of Thermally de-rated
Torque of an Electried
Powertrain
This chapter deals with the estimation of thermally derated torque of an induc-
tion machine based electried powertrain. This estimation is based on the LPV
model presented in the preceding chapter. The estimation of thermally derated
torque is more critical for obtaining the precise control to manage the thermally
derated torque, improve the eciency and minimize the loss of life time (aging)
of an induction machine based electried powertrain. Along with the estimation
of thermally derated torque,
ux of an induction machine based electric drive is
also estimated. These objectives have been obtained by using a robust LPV based
estimation technique. The LPV observer operates on a highly nonlinear currents
and
ux dynamics. Initially, the proposed estimation technique has been success-
fully tested by creating a theoretical scenario. Later on, estimation technique is
investigated using shortened Federal Urban Driving Schedule (FUDS) test cycle
for Hybrid Electric Vehicle (HEV) electric powertrain.
70

71
4.1 Benets of Thermally Derated Torque Esti-
mation
The torque performance of an induction machine based electried powertrain de-
teriorates under the vast uncertainties in rotor and stator resistance due to the
temperature variations during the HEV operation. Similar worsening of the re-
sponse is expected due to the wide variations in rotor speed in HEV application.
These problems can be resolved by employing state-of-art estimation techniques.
The signicant benets of the thermally derated torque estimation are:
Ecient torque compensation control can be accomplished by the estimation
of thermally derated torque.
Meeting the road loads, ensuring ecient powertrain operation and minimiz-
ing the loss of lifetime (aging) of an electric machine are three essential but
con
icting targets. Con
icting objectives control technique can be developed
by estimating the thermally derated torque.
Instead of installing another sensor, virtual sensors can be developed to sense
a phenomena in parallel to real sensors (A cheaper solution). This reduces
dependence on a single sensor and can also help in sensor health monitoring
4.2 Advantage of LPV Control Technique
The main objective of the LPV control (gain scheduling) technique is to control the
plant over the predened operating range, but rather than simply being robust
to variations in the plant, the controller is allowed to schedule itself based on
some measurements. This is in opposite to the traditional Linear Time Invariant
control technique which relies on the localized linear characteristics of the plant at
a particular operating condition. The advantage of the LPV control structures lies
in their explicit exploitation of knowledge of the actual plant dynamics, based on

72
measurement. In addition to the measurement signal, the LPV control technique
takes the advantage of exogenous plant information to update its dynamics in real
time. It is important to note that this information modies not only the control
signal, but also the way in which measurement signals are processed through the
LPV control technique.
Several benets from employing the LPV methodology are immediately apparent.
As mentioned above, LPV control technique provides additional freedom to
achieve the performance and robustness objectives.
The classical approach to gain scheduling employs point wise interpolation
or heuristically based switching strategies. These techniques are potentially
hazardous, since they obliterate the time-varying nature of the plant and
lack systematic theoretical guarantees on performance.
LPV control techniques are direct extension of well-known LTI synthesis
techniques, so some engineering insight is preserved.
Some LPV plant are not stabilizable via xed controller hence the practical
need of gain scheduling.
As a consequence, LPV control technique can provide better robustness and per-
formance properties than xed controllers, which ignore the non-stationary nature
of the plant.
4.3 Linear Parameter Varying Observer for Elec-
tried Powertrain
Keeping in view the importance for estimation of thermally derated torque dis-
cussed in Section 4.1 and the potential attributes of the LPV control technique dis-
cussed in Section 4.2, an LPV based observer is designed to estimate the thermally
derated torque in an electried powertrain. The proposed estimation strategy is

73
Figure 4.1: Overall scheme
shown in Figure 4.1. In this scheme, it is assumed that the currents and rotor
speed measurements are available from the current and speed sensors respectively.
The machine terminal voltages are available at the output of voltage sensor for use.
Based upon these measurements, rotor
ux and torque de-rating are estimated to
enhance the performance of hybrid and electric vehicle drive.
The LPV observer based estimation technique is not only computationally cheap
but also has the potential for on-line implementation (See Chapter 5). Now we
will design the LPV observer for the estimation of
ux and thermally derated
torque of an electric drive using the stator current dynamics ( (3.42)- (3.43))
and rotor
ux dynamics ( (3.40)- (3.41)) of the induction machine model given in
Section 3.2.1.3. The induction machine model presented in Section 3.2.1.3 is stable
but has the prominent cross-coupling and badly damped poles whose frequencies
vary considerably with the rotor resistance, stator resistances and rotor speed as
shown in Figure 3.18.

74
4.4 Current and Flux Dynamics
The validated stator current and rotor
ux dynamics can be written as:
2
4_is
S
_s
R3
5=2
4As
11As
12
As
21As
223
5:2
4is
S
s
R3
5+2
4U1
U23
5us
S (4.1)
In (4.1),is
S,s
R, andus
Sare the stator current, rotor
ux, and stator voltage vectors
in stationary reference frame respectively.
is
S=2
4is
dS
is
qS3
5;s
R=2
4s
dR
s
qR3
5;us
S=2
4us
dS
us
qS3
5 (4.2)
As
11=2
42
MrR+2
RrS
S2
R0
02
MrR+2
RrS
S2
R3
5 (4.3)
As
22=2
4rR
Rnpnr
npnrrR
R3
5 (4.4)
As
21=2
4MrR
R0
0MR
R3
5 (4.5)
As
12=2
4MrR
S2
RnpMnr
S2
R
npMnr
S2
RMrR
S2
R3
5 (4.6)
U1=2
41
S0
01
S3
5 (4.7)
U2=2
40 0
0 03
5 (4.8)
whereneis the stator supply frequency, nris the rotor speed, npis the number of
pole pairs, rSis the stator resistance, rRis the rotor resistance, Sis the stator
inductance, Ris the rotor inductance, Mis the mutual inductance between
stator and rotor and = 12
M
SR, is the leakage factor.

75
The denition of rotor speed, electromagnetic generated torque and load torque
are given in (3.44), (3.45) and (3.52) respectively.
4.4.1 Linear Parameter Varying Dynamics
The LPV model of the current and
ux dynamics is required for the design of
LPV observer. The LPV dynamics are given in Section 3.6 by taking the rotor
resistance, stator resistance and rotor speed as time varying parameters. The
ranges of the variations of these parameters are given in (3.74)- (3.76).
4.4.2 LPV Robust Observer
After presenting the current and
ux dynamics and their corresponding LPV dy-
namics, an observer based on [92] is proposed to estimate the
ux and thermally
derated torque.
4.4.2.1 Structure of Robust LPV Observer
The observer written here for the system in presented in Section 3.6 is:
2
4_^is
S
_^s
R3
5=A()2
4^is
S
^s
R3
5+B()us
S+L()(is
S^is
S) (4.9)
^is
S=C()2
4^is
S
^s
R3
5 (4.10)
2
4_^is
S
_^s
R3
5=A()2
4^is
S
^s
R3
5+B()us
S+L()(is
SC()2
4^is
S
^s
R3
5) (4.11)
For performing the computation for the observer gain, the observer error is dened
as:
e=2
4is
S
s
R3
52
4^is
S
^s
R3
5 (4.12)

76
The state space equation of the error, eis then given as:
_e= (A()L()C())e (4.13)
4.4.2.2 Observer Stability
To ensure the stability of the observer error (4.13), the following theorem is pro-
posed.
Theorem 1: The system (4.11) is an observer for (3.53) and (3.54) , if there
exist appropriate matrices P, and Q such that
AT
iPCT
iQT
i+PAiQiCi0;i= 1;:::;2(4.14)
and consequently2
4^is
S
^s
R3
5will converge to2
4is
S
s
R3
5.
Proof: Consider the Lyapunov function V(e(t)) =eT(t)Pe(t) withP=PT,
where, (:)Tdenotes the transpose of the matrix. The derivative of the Lyapunov
function with respect to time along the system states (4.13) is:
dV(e(t))
dt=_eT(t)Pe(t) +eT(t)P_e(t) (4.15)
Putting error dynamics of (4.13) in (4.15), we have
dV(e(t))
dt= (A()L()C())TPe(t) +eT(t)P(A()L()C()) (4.16)
dV(e(t))
dt= (AT()PCT()LT())e(t) +eT(t)(PA()PL()C()) (4.17)
dV(e(t))
dt=eT(t)(PA()PL()C() +AT()PCT()LT())e(t) (4.18)

77
Quadratic stability is guaranteed if_V(e(t))0;8(t)6= 0 [93]. This condition is
veried if
((AT()PCT()LT()PT) + (PA()PL()C()))0 (4.19)
The (4.19) is the bilinear matrix inequality (BMI) and it can be converted to the
LMI by considering Q() =PL().
The (4.19) becomes:
AT()PCT()Q()T+PA()Q()C()0 (4.20)
(4.20) is an innite LMI condition. However, the dependence on the is ane,
(4.20) can be converted to a nite LMI problem by solving only at the vertices of
the polytopes.
Denition1: The polytopic system (A();P), with2P=Co(1;2;:::; 2)is
quadratically stable i there exists common Lyapunov matrix P=PTsuch that
AT
iPCT
iQT
i+PAiQiCi0;i= 1;:::;2(4.21)
Finally, if there exist appropriate matrices P, and Q, then it is obvious that (4.21)
holds and consequently the system in (4.11) is ane quadratically stable.
4.4.2.3 Observer Construction
Ifis measurable, at each vertex, design of local observer is possible. Then, the
linear combination of local observer gives the design of an LPV observer. Following
equation gives the gain of local observer.
Li=P1Qi (4.22)

78
LPV observer is computed as:
L=i=2X
i=1ciLi (4.23)
where,ci(t)0, and
i=2X
i=1ci= 1 (4.24)
4.4.2.4 Synthesizing the Robust LPV Flux Observer
Denition 2: If the time varying parameter vector, , contains the measurable and
immeasurable components. The immeasurable components are taken as parameters
uncertainties and only the range of their variations are known. The parameter
vector,, is dened as:h
T
mT
umi
(4.25)
wheremis a vector which contains measurable components and umis a vector
which contains immeasurable components.
Theorem 2: Ifm
i,i= 1;:::;Nmare the vertices that dene the polytope of the
measurable components and um
j,j= 1;:::;Numare the vertices that dene the
polytopic of the immeasurable components. Then, the robust LPV
ux observer
can be synthesized as:
AT
ijPCT
ijQT
ij+PAijQijCij0;i= 1;:::;Nm;j= 1;:::;Num (4.26)
where,P=PT0.
The gain of robust polytopic observer is computed as described in (4.22) and (4.24).
Theorem 3: If the
ux estimation is exact and precise, and the
ux error2
4s
dS
s
qR3
5
-2
4^s
dS
^s
qR3
5. converges towards zero then the estimation of torque de-rating will also

79
be exact and precise and torque de-rating errorh
e^ei
will also converge towards
zero.
The estimated torque is given as:
^e=3
2(np)M
R(^s
dRis
qS^s
qRis
dS) (4.27)
4.4.2.5 Selection of Observer Gain
We selected the observer gains using (4.22)- (4.24) which were computed by solving
the LMI in (4.21). The LMI optimization delivered a LPV observer with 8 vertices,
each vertex being an LTI regulator with four states.
The observer gains at each vertex are given in Appendix-C.
4.5 Evaluation of Estimation Scheme
The simulation of the proposed and designed robust LPV observer for the estima-
tion of thermal torque de-rating in HEV drive has been tested in two ways. The
values of dierent parameters are given in Table 4.1.
Table 4.1: Parameters Values
np 2
rS 0.8
rR 4
S0.47 H
R0.47 H
M0.44 H
B 0.04 N.m.sec.rad1
J 0.06 kg.m2

80
4.5.1 Theoretical Scenario
In this case, the input voltages us
dSandus
qS( (3.77) and (3.78) ) to the plant
and observer are generated from mathematical relations. Then the designed ro-
bust LPV observer is simulated for dierent initial conditions, and for ambient
temperature of200C, 200C, and 400Cto verify its convergence and estimation
performance. Simulation results show excellent performance of the designed ro-
bust LPV observer in the presence of vast variations in rotor resistance, stator
resistance, and rotor speed which are severe in HEV application. The de-rated
torque due to thermal eects has been estimated as seen in Figure 4.2(bottom).
0 0.1 0.2 0.3 0.4 0.5-101LPV Observer estimated ResultsD-Axis Flux [Wb]
0 0.1 0.2 0.3 0.4 0.5-101Q-Axis Flux [Wb]
0 0.1 0.2 0.3 0.4 0.5-20020
Time [sec]Torque [Nm]-20C
20C
40C
Figure 4.2: Robust LPV observer estimated results of : D-axis
ux(Top), Q-
axis
ux(Middle), and Torque de-ration(Bottom) at 200C, 200C, and 400C.
De-rated torque scenario due to thermal eects is more vivid at 0.01 seconds. It
is clear from the Figure 4.3, the convergence time of the robust LPV observer is
0.16 seconds. As a result, precise and exact estimation of
ux is available for the
ecient estimation of machine's electromagnetic generated torque and operation
of HEV's drive system. From Figure 4.2, it is clear that the estimation of
ux and
torque de-rating is guaranteed at dierent ambient temperature. The three-phase

81
input anddqvoltages to the electric drive system are given in Figure 4.4. These
results also proved the stability of proposed robust LPV observer. Hence, the
robust LPV observer proves to be a useful tool to estimate the de-rated torque.
0 0.1 0.2 0.3 0.4 0.5-101LPV Observer Convergence ResultsD-Axis Flux [Wb]Actual
Estimated
0 0.1 0.2 0.3 0.4 0.5-101Q-Axis Flux [Wb]
0 0.1 0.2 0.3 0.4 0.5-20020Torque [Nm]
Figure 4.3: Robust LPV observer convergence results of actual and estimated:
D-axis
ux(Top), Q-axis
ux(Middle), and Torque de-ration(Bottom).
4.5.2 HEV Powertrain
In this case, the input voltages us
dSandus
qSto the plant and observer has been
extracted from HEV electric power-train. It is for shortened FUDS test cycle.
Then, for dierent initial conditions and for ambient temperature of 200C, 200C,
and 400C, the designed robust LPV observer is simulated to verify its convergence
and estimation performance. Simulation results show excellent performance of the
designed robust LPV observer for the shortened FUDS test cycle for HEV electric
power-train in the presence of vast variations in rotor resistance, stator resistance,
and rotor speed. The de-rated torque due to thermal eects has been estimated
as seen in Figure 4.5(bottom).

82
0 0.1 0.2 0.3 0.4 0.5−2000200
(a)Time [s]IM Voltages [Volts]
Phase−a voltage
Phase−b voltage
Phase−c voltage
0 0.1 0.2 0.3 0.4 0.5−2000200
(b)Time [s]IM Voltages [Volts]
d−axis voltage
q−axis voltage
Figure 4.4: (a) 3-phase Input voltages to the electric drive system. (b) Vdand
Vqfor the electric drive system.
0 0.1 0.2 0.3 0.4 0.5-101LPV Observer estimated Results for Shortened FUDS T est CycleD-Axis Flux [Wb]
0 0.1 0.2 0.3 0.4 0.5-101Q-Axis Flux [Wb]
0 0.1 0.2 0.3 0.4 0.5-20020
Time [sec]Torque [Nm]-20C
20C
40C
Figure 4.5: Robust LPV observer estimated results for shortened FUDS test
cycle of : D-axis
ux(Top), Q-axis
ux(Middle), and Torque de-ration(Bottom)
at200C, 200C, and 400C.

83
De-rated torque scenario due to thermal eects is more vivid at 0.01 seconds. It
is clear from the Figure 4.6, the convergence time of the robust LPV observer is
0.18 seconds. As a result, precise and exact estimation of
ux is available for the
ecient estimation of machine's electromagnetic generated torque and operation
of HEV's drive system. From Figure 4.5, it is clear that the estimation of
ux and
torque de-rating is guaranteed at dierent ambient temperature. The three-phase
input anddqvoltages to the electric drive system for shortened FUDS driving
cycle are shown in Figure 4.7. These results also proved the stability of proposed
robust LPV observer in the practical scenario. Hence, the robust LPV observer
proves to be a useful tool to estimate the de-rated torque in the HEV electric
power-train.
0 0.1 0.2 0.3 0.4 0.5-101LPV Observer Convergence Results for Shortened FUDS Test CycleD-Axis Flux [Wb]Actual
Estimated
0 0.1 0.2 0.3 0.4 0.5-101Q-Axis Flux [Wb]
0 0.1 0.2 0.3 0.4 0.5-20020Torque [Nm]
Figure 4.6: Robust LPV observer convergence results for shortened FUDS
test cycle of actual and estimated: D-axis
ux(Top), Q-axis
ux(Middle), and
Torque de-ration(Bottom).
4.5.3 Thermally de-rated torque estimation
Figure 4.8 shows the performance of the proposed and designed observer in esti-
mating the thermally de-rated torque due to the the change in operating temper-
ature. It can be seen that the torque delivering capability is adversely aected

84
0 0.1 0.2 0.3 0.4 0.5−2000200
(a)Time [s]IM Voltages [Volts]
Phase−a voltage
Phase−b voltage
Phase−c voltage
0 0.1 0.2 0.3 0.4 0.5−5000500
(b)Time [s]IM Voltages [Volts]
d−axis voltage
q−axis voltage
Figure 4.7: (a) 3-phase Input voltages to the electric drive system. (b) Vdand
Vqfor the electric drive system.
by the temperature and operating speed. Moreover, the estimation results also
exhibit the torque de-rates nonlinearly with respect to temperature.
25 30 35 40 45 50 55 6080859095100105LPV Observer Estimated Torque De-rating for Shorten ed FUDS Test Cycle
Ambient Temperature [oC]Torque De-rating [%]
Torque Derating at High Speed
Torque Derating at Low Speed
Figure 4.8: Robust LPV observer estimated torque de-rating under dierent
operating conditions.

85
4.6 Conclusion
An LPV based robust observer has been proposed and designed to estimate the
rotor
ux and torque de-rating by utilizing the measurements of the stator currents
and the rotor speed. Ecient and exact rotor
ux and torque de-rating is necessary
for the implementation of FOC HEV drive. Simulation study is carried out to
investigate the performance of the designed robust LPV observer in theoretical
scenario and practical scenario for shortened FUDS test cycle for HEV electric
power-train, demonstrating the ecacy of the observer.
In the coming chapter this observer will be used to design a robust control tech-
nique for managing the thermally derated torque in EVs and HEVs electric pow-
ertrain.

Chapter 5
Managing Thermally Derated
Torque of an Electried
Powertrain
Linear parameter varying based estimation scheme, discussed in Chapter 4 is used
here to design linear parameter varying control technique to manage and com-
pensate the thermally derated torque for an induction machine based electried
powertrain. The proposed scheme has the capability to retain the nominal per-
formance even in the face of severe rise in the operating and surrounding tem-
peratures. Due to the variations in ambient and operating temperatures, reasons
are discussed in Section 2.3, proposed linear parameter varying control scheme
reschedules its control signals to attain eective performance. The ecacy of the
proposed algorithm is demonstrated for an EV operating in Federal Urban Driving
Schedule (FUDS) with a dynamic temperature prole. The nonlinear simulation
results conrm the LPV observer capability to successfully estimate the
ux and
derated torque in an EV drive system. The proposed technique, after validating in
simulation environment, is veried experimentally on an Induction Machine (IM)
drive controlled by NI myRIO-1900.
86

87
5.1 Introduction
In order to achieve fuel eciency and reduce emissions into the atmosphere, the
automobile manufacturers have decided to escalate modern technologies such as
EV and Hybrid Electric Vehicle (HEV) [94]. HEV has Atkinson cycle engine
based traction system and EM propulsion system [95, 96]. In order to achieve
fuel economy and emission reduction, only EM propulsion provides the traction
force for EV and HEV. Among the available EMs, Induction Machine (IM) has
been used for the traction system of EV and HEV because of the advantages
including reasonable cost, simpler control, enhanced power density and eciency,
consistent operation over wide speed range, elevated initial torque, technological
development and universal availability. IMs are also very robust, have rugged
construction and require little maintenance [97, 98]. Moreover, IMs are inherently
de-excited with respect to inverter fault hence highly recommended to be used in
automobile industries for precautionary measures [35]. Production level vehicles
have IM as an electric traction system [99].
In EV and HEV applications, where accurate and precise tracking is needed, a
major problem is the operation of the electric traction system. FOC technique
used for torque and
ux control of IM is sensitive to parameter variations. The IM
parameters change as the operating conditions change. Operating conditions for
an EV and HEV propulsion system change constantly. Trac situations, driving
cycles etc., are the reasons of variation in speed. Also temperature has the eect on
parameters, which is in
uenced by ambient season and loading etc. Due to these
eects, the
ux and torque of an electried powertrain is thermally derated as
compared to the industrial induction machines, where the variation in temperature
and payload is very little [50{53]. Flux and torque tracking performance of a
conventional FOC is deteriorated. Therefore, to attain high performance in EVs
and HEVs, eective implementation of FOC for an EV and HEV electric traction
system requires accurate and precise knowledge of thermally derated torque and

ux.

88
The primary requirement for the FOC technique is a robust and accurate estima-
tion of
ux and torque in presence of extreme variations in the parameters. In
order to meet the requirement, a robust LPV based observer has been developed
and discussed by authors in [100] to estimate the thermal
ux and torque derating
by taking into account the rotor resistance, stator resistance, and speed variations
for ecient control implementation of an EV and HEV electric traction system.
Mostly conventional Field-Oriented Control (FOC) is used to ensure ecient op-
eration of an IM based electric drive [80]. The performance of conventional FOC
is highly dependent on IM rotor and stator parameters. These parameters are
adversely aected in extreme operating conditions, part loads and variation in
payloads. As a result,
ux and torque of an electried powertrain is also af-
fected. To overcome the problem of parameter variations on the torque and
ux
performance of an electried powertrain, a robust controller based on LPV gain
scheduling technique for the estimation and control of thermal
ux and torque
derating in an electried powertrain and its evaluation under Standard Driving
Cycle (SDC) has been proposed. This technique addresses the problem of
ux and
torque derating due to the change in operating and surrounding temperatures of
an electried powertrain. The performance of the proposed LPV based controller
has been evaluated for a light duty electric vehicle against Federal Urban Driving
Schedule (FUDS) operating at various ambient temperatures, which is a common
controller evaluation approach adapted by automotive community [101] and [102].
Experiments are carried out on an IM drive, realized by the NI myRIO-1900, us-
ing FUDS driving cycle to investigate that the proposed technique is eective and
delivers robust performance.
The rest of the chapter is structured as follows: Section 5.2 brie
y describes the
vehicle dynamics and nonlinear mathematical modeling of IM. EV performance
constraints and IM parameters (rotor and stator resistance) estimation is pre-
sented in Section 5.3. Section 5.4 elaborates the control structure which includes
the robust LPV current controller, robust
ux and torque controllers derivation
and its stability. Optimal
ux calculation and reference current calculation are
presented also in Section 5.4. Comparison of the proposed LPV control strategy

89
with Sliding Mode Control (SMC) technique is established in Section 5.5. The
evaluation of proposed controller based on SDC is presented in Section 6.8 fol-
lowed by experimental verication in Section 5.7. The concluding comments are
presented in Section 5.8.
5.2 Vehicle Dynamics and IM Modeling
5.2.1 Vehicle Modeling and Dynamics
The proposed observer-controller pair strategy takes into consideration the EV
aerodynamics and is not applied to the induction motor alone. The vehicle model
is based on mechanics and aerodynamics principles [58].
The load torque ( L) of a vehicle is given by
L= (Fa+Fg+Fr+Fw|{z}
Ft)Rw (5.1)
where,Fais the aerodynamic resistance force, Fgis the grade resistance force, Fr
is the rolling resistance force, Fwis the acceleration resistance force, Ftis the total
road load, and Rwis the wheel radius.
The following speed dynamics in the motor referential is used to describe the wheel
drive:
dnM
dt=np
J(eLbnM) (5.2)
where,nMis the motor mechanical speed, eis the motor generated torque, np
is the number of pole-pair, Jis the total inertia (rotor and load), and bis the
friction.
Moreover, the EV speed ( vw) is proportional to the IM speed ( !M), which can be
expressed in term of wheel radius Rw, and the gear box ratio ( GR) as follows:
vw=Rw
GR!M (5.3)

90
and the vehicle torque ( w) is given by
w=eGRt (5.4)
where,tis the transmission eciency.
5.2.2 Dynamics of IM
Induction machine dynamics, presented in Section 3.2.1.3 based on d-qaxis coor-
dinate can be written as [55, 100, 103]:
8
>>>>>><
>>>>>>:_idS=k1idS+k2dR+k3nRqR+k4udS
_iqS=k1iqS+k2qRk3nRdR+k4uqS
_dR=k5dRnpnRqR+k6idS
_qR=k5qR+npnRdR+k6iqS(5.5)
where,dandqstand for direct and quadrature axis respectively and
8
>>>>>>>>>>>>>>>>>>>>><
>>>>>>>>>>>>>>>>>>>>>:k1=(2
MrR+2
RrS)
S2
R
k2=MrR
S2
R
k3=npM
SR,k4=1
S
k4=1
S
k5=rR
R
k6=MrR
R
k7=b
J
k8=np
J
= 12
M
SR(5.6)
where= 12
M
SRis the leakage factor. nR,rR,rS,R,S,Mandnpare
the synchronous speed ( r=m), rotor speed ( r=m), rotor and stator resistances (
),
rotor and stator inductances ( H), mutual inductance ( H) and the number of pole
pairs respectively.

91
The electromagnetic generated torque, rotor speed and rotor
ux can be expressed
as 8
>>><
>>>:e=3
2npM
R(dRiqSqRidS)
nR=npnM
R=q
2
dR+2
qR(5.7)
where,nRis the rotor electrical speed and Ris the rotor
ux.
5.2.3 LPV Modeling of Induction Machine
The design of a robust LPV control technique for the IM based EV drive is based
on an LPV state space model of the form
8
<
:dx(t)
dt=A((t))x(t) +B((t))u(t)
y=C((t))x(t) +D((t))u(t)(5.8)
wherex2Rn,2Rs,u2Rm2andy2Rp2are state, time varying parameter,
input and output vectors respectively. The matrices A(:),B(:),C(:) andD(:) are
continuous matrix valued functions of appropriate dimensions of the time varying
parameter vector . The validated LPV dynamics and denition of matrices are
given in Section 3.6. In this model, rR,rSandnRare taken as scheduling signals.
5.3 EV Performance Constraints and IM Param-
eter Estimation
5.3.1 Performance Criteria
To have a smooth EV performance, the following criteria need to be observed:

92
The (5.9) that describes the vehicle must track the speed prole of the driving
cycle.
min
ids;iqs;nekv(t)vcycle(t)k (5.9)
where,v(t) andvcycle(t) are the actual vehicle speed and desired vehicle speed
respectively.
The (5.10) that describes the torque requirement must be exact and precise
for the smooth operation of EVs.
min
ids;iqs;neke(t)eref(t)k (5.10)
wheree(t) anderef(t) are the actual and reference torque of IM over the
entire range of operation.
The (5.11) describes that the IM drive system must track the reference
ux
to reduce the fuel consumption in EVs.
min
ids;iqs;nekR(t)Rref(t)k (5.11)
whereR(t) andRref(t) are the actual and reference
ux of IM over the
entire range of operation.
5.3.2 IM Performance Curve
Induction motor performance curve is generated by rapidly loading the motor from
the no-load condition to the locked rotor condition using xed terminal voltages.
Figure 5.1 represents the motor performance curve (plot of the motor shaft speed
as a function of torque of the motor) at room temperature (250C) which is used as a
baseline. This is very useful information for EV application that needs intermittent
function with a lengthy rest interval between every duty cycle. In this experiment,
the rotor slip is 1.548 percent at rated voltage.

93
040801201602002402803203604000255075102
nR [rad/sec]τe [N.m]

250C
400C
20821021221421644464850
Figure 5.1: Induction motor (used in this work) performance curve at 250C
and 400C(Torque derating at 400Cis vivid).
In EV and HEV applications, frequent starts and stops of high inertial loads exist.
Due to this, EM temperature increases and the rotor and stator resistances also
increase. This means that the motor performance curve at room temperature is
inadequate. Figure 5.1 also shows the EM performance curve at high temperature
(400C). It is clear that torque of EM is derated due to the change in one or both
temperatures. Therefore, an LPV control technique is proposed in this work to
minimize the torque derating problem due to the temperature eects.
5.3.3 Rotor and Stator Resistance Estimation
The estimation of rotor and stator resistance are required for the design of the
proposed observer-controller pair strategy. To estimate the rotor resistance, model
based approach has been adopted from [104, 105]. It is further assumed that rotor
speed, stator voltages and currents measurements are available for use from the

94
speed, voltage and current sensors respectively.
rR=vuutn2
slR"
ne2
M
Q
I2
S+neSR#
(5.12)
where
nslis the slip frequency and given as:
nsl=nenR (5.13)
Qis the reactive power and can be calculated as:
Q=udSiqSuqSidS (5.14)
The estimation of stator resistance is given by [104]:
rS=krR (5.15)
k=rSn
rRn(5.16)
where,rRn,rSnare the nominal values of rotor and stator resistance, respectively.
The temperature dependence of rotor and stator resistance is given by [55]:
r=r0[1 +
T] (5.17)
where,r0is the resistance at reference temperature ( T0= 25oC),is the temper-
ature coecient of resistance, and
Tis the temperature increase.
5.4 Control Design
In this section, the design of robust LPV current controllers for inner feedback
loop is presented. Robust
ux and torque controllers are designed and presented

95
Reference
TrajectoriesTorque and
Flux
ControlReference
Currents
CalculationCurrents
ControlInduction
Machine
Dynamics
Observer/g306e
/g1152R
/g306e
/g1152R^v1
v2iSref USe
eiS
iSnR
nRnRInner loop
++
+–
e
Outer loop^
Figure 5.2: Inner and outer loop strategy in induction machine.
for outer feedback loop. It is designed using the LPV dynamics of IM presented
in Section 5.2.3.
5.4.1 Controller Structure
The overall control structure considered in this work is presented in Figure 6.1. It
consists of four components. Each component is designed individually. Currents
control block is a stator current feedback controller which tracks the desired current
set pointiSref. It is a robust LPV output feedback controller. Its inputs are the
two stator currents available from measurement. It is scheduled with the rotor
speednR, rotor resistance rRand stator resistance rS. Currents control block
ensures good tracking over the entire operating range. LMIs are formulated for
the computation of this controller. It permits to take the advantage of LPV
formulation of the machine to design the robust LPV
ux observer and stator
current controller. The construction of observer and controller is simple and easy
to implement. This structure also gives the robust controllers for outer
ux and
torque loop which is another advantage of this structure. A robust LPV observer
is designed to estimate the thermal
ux and derated torque and it is presented in
Chapter 4. Input Output Feedback Linearization (IOFL) is used to generate the
reference current vector and to linearize and decouple the rotor
ux and torque as
shown in Figure 6.1 [93]. Finally, the diagonal gains for torque and
ux control
are designed by formulating an LMI using the concept of Robust Input Output
Feedback Linearization (RIOFL). These controllers ensure the robust tracking of
the rotor
ux and EM torque.

96
The major advantage of this control structure is that overall control problem is
subdivided into four independent sub-control problems. The closed-loop stability
of each independent sub-control problem is proved. Reference torque trajectory
is generated by the driver and powertrain controller blocks as described in Sec-
tion 5.6.1. The
ux request is calculated from the torque request to achieve the
fuel economy and its derivation is given in Section 5.4.6.
5.4.2 Robust LPV Current Controller
In this section, an LPV current feedback controller is synthesized for an LPV
model of IM presented in Section 5.2.3. This LPV current control design technique
is practically valid. LPV control is an extended form of H1optimal control to
nonlinear or time varying systems that can be represented in LPV framework [106].
Actuator constraints, disturbance rejection, and reference tracking are the design
specications on the control system. These are the control sensitivity function,
complementary sensitivity function and sensitivity function to shape the design
specications. H1norm can be adopted to ensure these specications. L2-gain of
the closed-loop system is an alternate to H1norm in the LPV framework. The
idea of `generalized plant' is commonly adopted in LPV control to express design
specications.
Consider an LPV plant with state space representation:
8
>>><
>>>:_x=A()x+B1()w+B2()u
z=C1()x+D11()w+D12()u
y=C2()x+D2()w(5.18)
wherewandzare the external input and controlled output vectors, respec-
tively. The time varying parameter (t) can be expressed in the form (t) =
(1;2;:::;L)Tand the range of each parameter iis given as
i(t)2
i;i
(5.19)

97
Pis a convex polytopes with vertices, i;i= 1;2;:::;N: , and can be dened as
P=Cofv1;v2;:::;vLg (5.20)
whereviare the vertices, i= 1;2;:::;L .L= 2are the number of vertices. Cois
a convex hull ,i.e, the set of all convex combinations of vi(all points inside and
on the boundary of the polytopes).
The objective is to design the gain schedule LPV output feedback control. The
state space representation of the dynamic controller is:
8
<
:_xK=AK()xK+BK()y
u=CK()xK+DK()y(5.21)
which ensures the internal stability and a guaranteed L2-gain bound
for the
closed-loop operator ((5.18) and (5.21)) from the disturbance signal wto the error
signalz, that isZT
0zTzd
2Z0
TwTwd;8T0 (5.22)
Next, LPV controller with guaranteed L2-gain performance is presented in the
following theorem:
Theorem 3. Consider the LPV plant ((5.18)) with parameter trajectories con-
strained as in (6.20). There exist an LPV output feedback controller ((5.21))
enforcing closed-loop stability and an upper bound
> 0 on theL2-gain of the
closed-loop system ((5.18) and (5.21)) from wtoz, if there exist parameter depen-
dent symmetric matrices X() andY() and a parameter dependent quadruple of
state space data ( ~AK();~BK();~CK();~DK()) such that
2
6666664AY+B2~CK+   
~AT
K+A ATX+~BKC2+  
B1 XB 1+~BKD2
I
C1Y+ (D12~CK)TC1D11
I3
7777775<0 (5.23)

98
2
4X I
I Y3
5>0 (5.24)
whererepresents the terms required to achieve symmetry in matrix and is
dropped for simplicity.
Proof. See [107].
Based on the above theorem, the LPV controller synthesis problem can be solved
by solving the optimization problem
min
X();Y();~AK();~BK();~CK()
(5.25)
such that (6.60) and (6.61) hold 82P and the controller of the form (5.21) can
be computed by adopting the following two step scheme:
1) SolveRandSfrom the singular value decomposition of IXY
8
<
:IXY=UVT
)R=Up
;ST=p
VT(5.26)
2) Compute AK,BKandCKwith
8
>>>>>><
>>>>>>:CK= (~CKDKC2Y)(ST)1
BK= (R)1(~BKXB 2DK)
AK= (R)1(~AKRBKC2YXB 2CKST
X(A+B2DKC2)Y)(ST)1(5.27)
DKis zero for the output feedback control. Now, the scheduling parameter is given
by (6.20) and the LPV model is ane, the constraints ((6.60) and (6.61)) constitute
an LMI system. Hence, the construction of LPV controller with guaranteed L2-
gain performance can be reduced to an LMI problem and is numerically tractable.

99
So, the controller can be constructed as
2
4AK()BK()
CK()DK()3
5=i=2X
i=1ci2
4AK(i)BK(i)
CK(i)DK(i)3
5 (5.28)
5.4.3 Design Methodology
Depending on the results described in Section 6.7.2, an LPV output feedback
controller is designed for the IM presented in Section 5.2.3. The objectives of this
design are: (1) to achieve stability of the plant over the wide range of operation,
(2) to get fast tracking with disturbance and noise rejection capability with little
or no overshoot and (3) taking into account the control actuator constraints.
A mixed sensitivity loop shaping technique is adopted to meet the design objec-
tives. Where WTandWSare the weighting gains which shape the output com-
plementary sensitivity T() and sensitivity S() functions. WKis the weighting
gain used to express the upper bound on the control sensitivity K()S() function.
The generalized plant is shown in Figure 6.2.
r
zS
zT
zKG( /g545) Ws
WT
WK
K( /g545)u y e
–
Figure 5.3: Constraints on S;T,andKSin term of a generalized plant.

100
These weighting gains are tuned iteratively until the design objectives are met
satisfactorily. The values of these gains are
WS=2
4s+1:05
0:45s+5450
0s+1:05
0:45s+5453
5 (5.29)
WT=2
40:6 0
0 0:63
5 (5.30)
WKS=2
40:05 0
0 0:053
5 (5.31)
In this design, win (5.18) describes the desired input r, which is the reference
stator current iSref. Whereas zin (5.18) is a vectorh
zSzTzKiT
, that has the
output of the weighting matrices WS,WTandWK. These are used to shape the
sensitivity (from rtoe), complementary sensitivity (from rtoy) and the control
sensitivity (from rtou) respectively.
Now, the LMI problem of (6.60) and (6.61) with the weighting functions given
in (6.68), (5.65) and (5.31) is solved to achieve the LPV output feedback controller.
LPV controller has six states (four come from the plant and two from WS). The
achieved optimal value of
is 1.023. The resultant controller is comparatively
simple and easy to implement.
The performance and stability of the nonlinear system (original) presented in
Section 5.2.2 are discussed with the designed LPV controller. It is observed in
controller evaluation, Section 5.6.2, that better performance and stability are ob-
tained for the closed-loop nonlinear system in the whole range of operation. Hence,
this technique proves to provide the practical solution for the control of a highly
nonlinear system (Section 5.2.2).

101
5.4.4 Robust Torque and Flux Controller
To design a nonlinear control for tracking of torque and
ux, the concept of Input
Output Linearization (IOL) is adopted. The IOL gives linear dierential relation-
ship between output and input which is direct and simple [93]. For the control
of IM, the relative degree and zero dynamics are well dened and are stable re-
spectively [108]. Thus IOL can be adopted and performed. The input and output
vectors for RIOL are
iS=h
idSiqSiT
(5.32)
y=h
eRiT
(5.33)
To ensure the decouple operation of FOC for IM
qR= 0 (5.34)
To perform the RIOL, dierentiating e, andRrelations from (6.22) and putting (6.10)
(only the two
uxes equations), it yields
_R=dR_dR+qR_qR
R(5.35)
Now, by taking the two
uxes from ((6.10)) and using the denition:
nenR=rRM
RiqS
^dR(5.36)
It yields:
_dR=rR
RdR+rRM
RidS+rRM
RiqS
dRqR (5.37)
and
_qR=rR
RqR (5.38)

102
Now (5.35) yields
_R=rR
RR+rRM=R(idS^dR+iqS^qR)
R(5.39)
Time-derivative of the electromagnetic generated torque, ein (6.22) is
_e=3
2npM
R(dR_iqS+iqS_dRqR_idSidS_qR) (5.40)
Putting (5.39) and (5.40) in matrix form
2
4_e
_R3
5=G+H2
4idS
iqS3
5 (5.41)
where
G=2
4L
Jb
JnR
rR
RR3
5;H=2
403
2npM
JR^dR
rRM
RR^dR 03
5
The estimation of rotor
ux is aected by the variations in the rotor resistance,
stator resistance and rotor speed. Therefore, uncertainty in
ux estimation is
considered to achieve the robust
ux and torque controllers for the outer feedback
loop in FOC of the electried powertrain. Thus, by replacing ^dRwith ^dR+
dR, (5.41) can be rearranged as
2
4_e
_R3
5=^G+^H2
4idS
iqS3
5+2
43
2npM
JRdRiqS
rR
RdR3
5 (5.42)
where
^G=2
4^L
Jb
JnR
rR
R^dR3
5;^H=2
403
2npM
JR^dR
rRM
R03
5
and Considering the following control law:
2
4idS
iqS3
5=G
H+1
H2
4udS
uqS3
5 (5.43)

103
Putting (5.43) into (5.42), yields
2
4_e
_R3
5=2
4udS
uqS3
5+2
43
2npM
JRdRiqS
rR
RdR3
5:2
4dRiqS
dR3
5 (5.44)
Let the desired output vector be
yd=h
edRdiT
(5.45)
whereedis the desired torque and Rdis the desired rotor
ux.
The torque and rotor
ux tracking errors are
ee=eed (5.46)
and
eR=RRd (5.47)
From (5.44), the torque and
ux controllers are
udS=K1ee+ _Rd (5.48)
uqS=K2eR+_Rd (5.49)
The closed-loop error dynamics becomes
2
4_ee
_eR3
5=Ke2
4udS
uqS3
5+Be2
4iqS
dR3
5 (5.50)
where
Ke=2
4K10
0K23
5;Be=2
43
2np
JM
R0
0rRM
R3
5

104
To convert the closed-loop error dynamics into an LMI, the denition of bounded
real lemma is used [107] which is given as
2
6664ATP+PA PB CT
BTP
I DT
C D
I3
77750 (5.51)
wherePis a positive denite matrix, P=PTand
is greater than zero.
Putting closed loop error dynamics matrices from (5.50) into (5.51), yields
2
6664KT
eP+PKePBeI2
BT
eP
I2 0
I2 0
I23
77750 (5.52)
This is a Bilinear Matrix Inequality (BMI). To deal with BMI, considering N=
PKe, the resultant LMI is
2
6664NT+N PBeI2
BT
eP
I2 0
I2 0
I23
77750 (5.53)
The solution of (5.53) gives the NandP. From these, the gains of the torque and

ux controllers can be constructed as:
Ke=P1N (5.54)
The gains of torque and
ux controllers are diag( 300;230).

105
5.4.5 Reference Current Calculation
The reference currents are calculated by dierentiating the torque eand rotor

uxRequations,
_R=rR
R2
dR+MrR
RdRidRrR
R2
qR+MrR
RqRiqR
R(5.55)
Let the rst derivative of the torque eisv1and the rst derivative of the rotor

uxRisv2, it yields.
v1=3
2npM
R(dR_iqS+iqS_dRqR_idSidS_qR) (5.56)
v2=rR
R2
dR+MrR
RdRidRrR
R2
qR+MrR
RqRiqR
R(5.57)
(5.56) and (5.57) can be re-written as
M2
4idS
iqS3
5=N (5.58)
where
M=2
4MrR
RdRMrR
RqR
npM
RJqRnpM
RJdR3
5 (5.59)
and
N=2
4R(v2+rR
RR)
v1+b
JnR+1
JL3
5 (5.60)
From (5.58), the reference currents command can be calculated as
iSref=2
4idSref
iqSref3
5=1
jMj2
R[M]1[N] (5.61)

106
5.4.6 Reference Flux Calculation
The IM functions at dierent speeds and torques based on the operating conditions
of the vehicle. Therefore, this section presents the reference
ux calculation to
optimize the electrical energy consumption. It is not possible to achieve the energy
optimization with standard reference of
ux. The standard
ux reference is not
adopted for the EVs and HEVs. In reality, for small torque demand, it is not
useful to keep the
ux reference at high level when a small
ux reference can
provide the same torque. Higher levels of
ux demand the use of more current
and therefore, more energy. In order to minimize the energy utilization, reference

ux is computed using the torque reference. The machine steady-state losses on
the stator and rotor sides are given by [12]:
PLoss=3
2rS(i2
dS+i2
qS)
|{z}
Stator losses+3
2M
R(nenR)RiqS
|{z}
Rotor losses(5.62)
Putting the steady state values of idS,iqSandnenRtaken from (6.10), in (5.62)
gives
PLoss=3
2"
rSR
M2
+
rS+M
R2
rR!e
TkR#
(5.63)
where,Tk=3
2npM
R. Optimal
ux reference, to minimize the energy consumption,
can be obtained by minimizing (5.63)
8
>><
>>:Rref=optq
jTerefj
opt=
M
Tk
1 +
M
R2rR
rS1=2!1=2(5.64)
Moreover, the constraints on the stator voltages and currents are not considered
in the analysis worked out here. Indeed, the stator voltages and currents cannot
increase from their maximum physical values which is described by the weakening
region in the standard
ux reference selection. To solve the voltage and current
constraints, the standard
ux reference prole is used as a maximum value. The

107
standard
ux reference signal is written as
m=8
<
:0 ifjnRjnb
nb
jnRj0ifjnRj>nb(5.65)
where0is the maximum value of the
ux without saturation and nbis the base
speed of IM.
To meet the constraints on the stator voltage and current, the optimum reference

ux signal ((6.68)) does not exceed the standard reference
ux signal ((5.65))
during the entire operation of the EV.
5.5 Comparison With Sliding Mode Control
In order to validate the eectiveness and robustness of proposed LPV control
scheme, another technique is used for comparison. The technique is called \FOC
HOSMC" in this paper and originally presented in [72]. It discusses the perfor-
mance of IM by taking into account the rotor and stator resistances variations (one
parameter variation at a time) by utilizing the concept of Higher Order Sliding
Mode (HOSMC) technique.
In order to evaluate the closed loop performance of the LPV control scheme with
FOC-HOSMC scheme, two cases are studied. The rst case is under similar load
torque and velocity signal references are generated and utilized as in [72, 109] to
observe the eectiveness of the LPV control scheme. The accuracy of both scheme
is quantitatively assessed by considering the chattering in the output velocity
prole. The LPV control technique has chattering of 0 :0009 rad/sec as compared
to 0:36 rad/sec chattering of the FOC-HOSMC scheme. Simulation result of actual
and reference velocity signal is plotted together in Figure 5.4.
The second case is under the variations of stator and rotor resistances. The percent
tracking error in the rotor velocity (
z1) and the increment of the optimal rotor

ux modulus (
R) with respect to steady state value obtained without motor

108
0510152025300246τL [N.m]
(a)
0 10 20 300102030τe [N.m]
(b) Time [sec]24252629.9229.9429.9629.9830
Figure 5.4: Simulation result for closed loop rotor velocity performance. ( a)
Load torque taken in closed loop simulation. ( b) Rotor velocity tracking: refer-
ence (red) and actual (blue).
parameter variations are used as performance indices. The simulation results are
presented and summarized in Tables 6.3 and 6.4. From Tables 6.3 and 6.4, one
Table 5.1: Performance comparison of FOC-HOSMC and FOC-LPV to stator
resistance variations
FOC-HOSMC FOC-LPV

rS
z1
R
rS
z1
R
20%0:12% 62% 20%0:10% 59:4%
40%0:2% 139% 40%0:17% 135:6%
60%0:3% 216% 60%0:23% 210%
80% 80%0:27% 230%
can examine that LPV control scheme performs well in the tracking of the rotor
velocity in the presence of variations in stator and/or rotor resistance. On the
other hand, the increase in the optimal rotor
ux reference signal is signicantly
less in the presence of such variations. The proposed LPV control technique is

109
Table 5.2: Performance comparison of FOC-HOSMC and FOC-LPV to rotor
resistance variations
FOC-HOSMC FOC-LPV

rR
z1
R
rR
z1
R
20%0:03% 7:82% 20%0:009% 6:2%
40%0:042% 17:33% 40%0:022% 11:42%
60%3:5% 1590% 60%0:40% 590%
80% 80%0:53% 729%
also tested for more rotor and stator resistance variations ( 80%) and result are
summarized in Tables 6.3 and 6.4.
5.6 Standard Driving Cycle Analysis
This section describes the eectiveness of the designed observer controller pair for a
standard driving cycle. It is evaluated on a high delity EV simulator constructed
in MATLAB/SIMULINK for an actual electric vehicle shown in Figure 5.5, as
commonly exercised by automotive community to evaluate their control frame-
works [110] and [111]. The evaluation is conducted at 200C, 400Cand 600Cam-
bient temperatures to show the eectiveness of the proposed control framework.
5.6.1 EV Specications and Simulation Detail
The vehicle architecture considered in this article is shown in Figure 5.5. The
specications of a light duty EV and cage induction machine are given in Table 6.1.
The electric powertrain consists of powertrain controller, EM with transmission,
battery and vehicle brakes. The
ow of energy is from the battery and EM to the
drive shaft and vice versa. The powertrain controller (1) drives the desired torque
signal to the EM control unit; and (2) perform the transmission to the vehicle. The

110
Vehicle SpeedDesired vehicle
speed
DriverPowertrain
ControllerElectric
MachineTrans-
missionVehicle
DynamicAccelerator
BrakeTorque
RequestTorque
EM Vehicle
BrakesTorque
Out
Brake RequestTractive
ForceElectric Powertrain
Converter Battery
Figure 5.5: Vehicle level system architecture.
Table 5.3: Specications of an induction machine and a light duty electric
vehicle
Induction Machine
npNo. of pole pairs 2rS Stator resistance 0.22
rRRotor resistance 0.209
SStator inductance 0.425H
RRotor inductance 0.043HMMutual inductance 0.04H
J Inertia 0.124Kg.m2
b Damping 0.013N.m.s.rad1
Light duty Electric Vehicle
M Mass 350Kg
r Radius of wheel 0.205m
Af Frontal area 2.1m2
CrRoll coecient 0.013
CdDrag coecient 0.42
aim of the driver block is to simulate the decision of the driver on the braking pedal
and the accelerator positions depending on the actual and desired vehicle speed
and slope of the road. The desired vehicle speed is considered to be known by the
particular driving cycle, FUDS in case of this work. A classical proportional plus
integral controller has been adopted with proportional gain, kp= 0:25 and integral
gain,ki= 0:01 to reproduce the reaction of driver regarding the tracking of the
vehicle speed. The driver block takes the error between the actual and desired
vehicle speeds as an input, and the output is a pedal signal with a saturated scale
from1 to 1. It is interpreted as a brake-pedal position and accelerator-pedal
position when it is negative and positive respectively. In powertrain controller,
the requested EM torque can be decided on the accelerator pedal position or the

111
brake pedal position. The EM is supposed to deliver the requested torque through
transmission to the vehicle eciently. This study mainly focuses on managing
of thermally derated torque of the electried powertrain. The compensation of
thermally de-rated torque of EM (electric powertrain) mainly . How to eciently
compensate the thermally de-rated torque in EM (electric powertrain) on the basis
of the vehicle operating conditions and the powertrain operating condition is the
main concern in this work and has been addressed through LPV control.
5.6.2 Control Evaluation
A predened city driving cycle FUDS which has several starts and stops is used
for evaluating the performance of proposed LPV control strategy regarding the
managing of thermally derated torque of an electried powertrain via a change
prole of temperature. A validation temperature prole is shown in Figure 5.6.
0200400600800100012001360306090120150
Time [s]Temperature [0C]

@ 200C
@ 400C
@ 600C
Figure 5.6: Simulation results: Temperature prole for the controller observer
pair evaluation at dierent ambient temperatures.

112
It has a duration of 1360 s and exhibits the operating performance under very
fast temperature, very low temperature and constant temperature. Very fast tem-
perature, very low temperature and constant temperature operations can also be
examined between 0-180, 900-1200 and 600-900 s, respectively. The temperature
prole is realized from the stator voltages and currents, motor speed and power uti-
lized over the entire driving cycle. Figure 5.7 gives the results for traction system.
Figure 5.7 represents the vehicle speed tracking performance of the LPV control
method via a change prole of temperature and shows clearly the dierent phases
of constant speed, acceleration and deceleration. As the result signify, LPV con-
trol method accomplishes the vehicle speed tracking performance conditions well
over the entire temperature prole (low, high and constant temperatures).
02004006008001000120013600102027
Time [s]EV speed [Km/hr]

Desired speed
EV speed
Figure 5.7: Tracking of vehicle speed prole via a change prole of tempera-
ture (at ambient temperature of 400C) with LPV controller observer pair.
The rotational speed of IM is given in Figure 5.8.
The change in the IM drive system parameters (rotor and stator resistances at
dierent ambient temperatures) for the light duty electric vehicle operated in a
complete FUDS cycle are shown in Figure 5.9.

113
02004006008001000120013600200040006000800010000
Time [s]IM speed [rpm]
Figure 5.8: Induction machine speed.
02004006008001000120013600.180.20.220.240.260.28
Time [s]Resistance [ Ω]

rR@ 200C
rR@ 400C
rR@ 600C
rS@ 200C
rS@ 400C
rS@ 600C
Figure 5.9: Simulation results: Rotor and stator resistance variations over the
entire period of operation at dierent ambient temperatures.
The major component of the electric powertrain is an EM. To measure its perfor-
mance the requested torque prole that is generated by the powertrain controller
depending upon the accelerator and brake pedal position is supposed to be tracked

114
by the EM at all operating (temperature) conditions. Figure 5.10 gives the re-
quested torque tracking with LPV control method via a change prole of temper-
ature (in the presence of vast uncertainties in the stator and rotor resistances). As
0200400600800100012001360−15015304555
Time [s]EM torque [N.m]

Torque request
EM torque with LPV control
2022042062088910
Figure 5.10: Simulation results: Tracking of torque request prole via a
change prole of temperature (at ambient temperature of 400C) with LPV con-
troller observer pair.
can be seen, torque tracking is excellent at all operating conditions in the presence
of rapid changes in requested torque signal. These rapid changes are due to the
high trac situations in FUDS route. Consequently, a smoother operation of the
vehicle is guaranteed. This also shows the accuracy of the estimation of thermally
derated torque through LPV observer.
The optimal
ux request for the EM is generated from the torque request signal as
explained in Section 5.4.6. To achieve better eciency from the electric powertrain,
an EM is assumed to track the optimal
ux request over the entire period of
operation via a change prole of temperature. Figure 5.11 represents requested

ux tracking. It is clear that the performance of an EM based on the requested

ux tracking is more accurate and precise with the LPV control method at all
temperature conditions. It is clear also from Figure 5.10 that the requested
ux is
less than the rated
ux (0.55 Wb) over the entire driving cycle. It reduces the fuel

115
020040060080010001200136000.20.40.6
Time [s]EM flux [Wb]

Flux request
EM flux with LPV control
EM rated flux
1921941961980.120.140.16
Figure 5.11: Simulation results: Tracking of
ux request prole via a change
prole of temperature (at ambient temperature of 400C) with LPV controller
observer pair.
consumption in EVs. Figures. 5.7, 5.10 and 5.11 also illustrate the performance
of the proposed LPV observer during the operation of EV.
It is worth notice also that stator voltages and currents never attained their upper
limit during simulation because of the upper limit set on the
ux reference in (6.68).
A close up view in short time frame of stator voltages and currents in the IM is
given in Figure 5.12. Therefore, improved performance of electric powertrain with
respect to the compensation of thermally derated torque of an EM is ensured.
The performance of proposed LPV control method via a change prole of temper-
ature is presented in Table 5.4 for three dierent ambient temperatures. RMSE
and NRMSE are used as performance indices.
Table 5.4: Performance indices comparison for proposed LPV based FOC
control framework at dierent ambient temperature
Vehicle Level Machine Level
Speed prole tracking Torque tracking Flux tracking
Performance indices Temperature
200C 400C 600C 200C 400C 600C 200C 400C 600C
RMSE 0.1551 0.1536 0.1451 0.1950 0.1956 0.1965 0.0099 0.00982 0.0097
NRMSE 0.8449 0.8464 0.8549 0.8050 0.8044 0.8035 0.9901 0.99018 0.9903

116
230 230.2 230.4 230.6 230.8 231−505
(a)Time [s]iS [A]

idS
iqS
230 230.2 230.4 230.6 230.8 231−2000200
(b)Time [s]uS [V]

udS
uqS
Figure 5.12: Simulation results: Induction machine direct and quadrature
axis (a) stator currents. (b) stator voltages: corresponding to the operation of
electried powertrain at 400C.
5.7 Experimental Verication
In the previous Sections it has been amply demonstrated that the proposed LPV
scheme fully obviates the torque derating eects arising from the motor resistance
variations arising from temperature changes. However, there is still a need to
put this LPV controller to test on a hardware rig. For this purpose, a hardware
test set-up consisting of an IM, a Controller Board and a Torque Measurement
arrangement is employed to validate the controller test results. The current Sec-
tion is essentially divided into four sub-sections. The rst sub-section 5.7.1 de-
scribes the test set-up formed. The remaining three sections are dedicated to
the hardware results of the three experiments performed. Practical observation
of the open loop thermal torque eects (the rst experiment) is discussed in the
second sub-section 5.7.2. The third sub-section 5.7.3 addresses the excellent per-
formance on the test bed of the LPV controller for a step demand on the torque,
in contrast to the sliding mode based results reported in the literature [13], this
experiment is performed on the raised temperature prole. The third and nal

117
experiment, aimed at validating controller for the harsh environment faced by an
electried powertrain in a challenging urban environment, is addressed in the last
sub-section 5.7.4 of this Section. For this purpose the speed demand prole was
generated from FUDS.
5.7.1 Experimental Setup
This section elaborates the experimental setup used for the validation of proposed
estimation and control technique for an electried powertrain. Figure 5.13 shows
the experimental setup devised. The control algorithm was implemented on a
control board based on NI myRIO-1900 from National Instruments. The setup also
included the inverter to control the IM, sensors (voltage, current and speed), torque
measurement, autotransformer and electric brake to generate the load torque. The
NI myRIO-1900 was interfaced to a PC. The data logging, downloading and data
communication functions are performed by the microprocessor.
Inverter
Autotransformer Oscilloscope
PC (NI LabVIEW Installed)
NI myRIO-1900 Voltage and current sensors IM
Speed sensor
Load Torque and speed measurement
Figure 5.13: Experimental setup of an IM drive system.

118
The braking mechanism is realized by the magnetic powder brake (DL 1019 P)
of DE LORENZO group which consists on load cell (DL 2006 E) with 150 N
range. The powder brake is controlled by brake control unit (DL 1054 TT) of same
company. It allows measuring the rotating speed and the torque generated by an
electric machine. It also provides the excitation voltage to the brake.
The electric machine drive system shown in Figure 5.13 is equipped with state
of the art sensors. These sensors are heavily relied upon to monitor each of the
electric machine drive subsystem precisely. Among number of sensors in machine
test setup, the optical transducer (DL 2031 M) for measuring the rotation speed
through a slotted optical switch with encoder disc. The current of machine is
sensed due to change in magnetic eld using a hall eect sensor ( ACS724 ).
5.7.2 Open Loop Torque Derating Conrmation
In EV and HEV applications, frequent starts and stops of high inertial loads exist.
Due to this, EM temperature increases and the rotor and stator resistances also
increase. This means that the motor performance curve at room temperature is
inadequate. Figure 5.14 also shows the measured EM performance curve at high
temperature (400C). It is clear that torque of EM is derated due to the change in
one or both temperatures.
5.7.3 Comparison with Sliding Mode Controller
In order to validate the eectiveness and robustness of proposed LPV control
scheme, another technique is used for comparison and is originally presented in [13]
and is named \FOC SMC" in this paper. It addresses the control,
ux and torque
estimation of IM based on rst order Sliding Mode Control (SMC) technique.
To compare the LPV control technique, presented in this paper, torque reference
similar to the prole used in [13] is generated. The resistance reference similar to
prole used in [13] is used in controller computation. The accuracy of the proposed
LPV control technique has quantitatively been assessed and is about 99 :1% as

119
040801201602002402803203604000255075102
nR [rad/sec]τe [N.m]

400C(Simulated)
400C(Experimental)
208210212214216444648
Figure 5.14: Experimental result: Induction motor (used in this work) per-
formance curve at 400C(Torque derating at 400Cis vivid).
compared to 97% accuracy of the FOC-SMC scheme. Experimental results of the
actual and estimated quantities are plotted together in Fig. 5.15. The proposed
LPV control technique is also tested for more rotor and stator resistance variations
(80%). In a result, an accurate torque estimation and control is demonstrated.
This can be concluded that the proposed LPV control technique is more robust to
rSandrRvariations. The currents required to generate the reference torque are
also less. Furthermore, chattering behavior of SMC is overcome by LPV, which
leads to smaller
ux and torque estimation error as well as better control stability.
Consequently, the proposed LPV technique can give more accurate estimation and
control, even when the rotor and stator resistance are bound to change.
5.7.4 Torque Derating Compensation against FUDS Cycle
In the third experiment, FUDS driving cycle based speed demand was presented
to the LPV Controller under the elevated temperature of 400C. Figures. 5.16, 5.17

120
0 1 2 3 4 5−10010τe [N.m]
(a)
0 1 2 3 4 500.51Rs [Ω]
(b)
0 1 2 3 4 5−505idS [A]
(c)
0 1 2 3 4 5−0.200.2φdR [Wb]
(d) Time [sec]
Figure 5.15: Actual (blue) and estimated (red) experimental results for a ref-
erence (trapezoidal-wave) of 10 Nm. (a) Torque tracking. ( b) Stator resistance
variation. ( c) Stator current. ( d) Rotor
ux.
and 5.18 show the experimental results for the dynamic performances of the pro-
posed LPV technique for traction induction machine at the raised temperature
of 400C. Figure 5.16 presents the IM speed tracking performance over the entire
driving cycle. It is clear from Figure 5.16 that LPV control algorithm provides
better performance in the presence of high inertial loads and frequent starts and
stops, despite the raised temperature is way above the nominal design tempera-
ture. The values for the RMSE and NRMSE are 0 :1569 and 0:8431 respectively.
The IM torque and
ux tracking performance is presented in Figures 5.17 and 5.18.
It is clear that the torque and
ux demands are met more precisely in the presence
of above mentioned conditions. The RMSE values between the torque and
ux
tracking of the reference value are 0 :2041 and 0:00994 respectively. This also shows
the accuracy of the estimation of thermally derated torque through LPV observer.

121
020040060080010001200136003006009001200
Time [s]IM speed [rad/s]

Desired IM speed
Actual IM speed
4004200200400
Figure 5.16: Experimental result: Tracking of induction machine speed prole
via a change prole of temperature (at ambient temperature of 400C) with LPV
controller observer pair.
0200400600800100012001360−15015304555
Time [s]EM torque [N.m]

Torque request
EM torque with LPV control
20220420620878910
Figure 5.17: Experimental results: Tracking of torque request prole via
a change prole of temperature (at ambient temperature of 400C) with LPV
controller observer pair.
The RMSE and NRMSE values of the induction machine speed, torque and
ux
tracking are shown in Figure 5.19. The experimental results (obtained) prove the
eectiveness of the proposed LPV technique.

122
020040060080010001200136000.20.40.6
Time [s]EM flux [Wb]

Flux request
EM flux with LPV control
1921941961980.120.130.14
Figure 5.18: Experimental results: Tracking of
ux request prole via a
change prole of temperature (at ambient temperature of 400C) with LPV con-
troller observer pair.
/g1004 /g856 /g1005 /g1009 /g1010 /g1013/g1004 /g856 /g1006 /g1004 /g1008 /g1005
/g1004 /g856 /g1004 /g1004 /g1013 /g1013/g1004 /g856 /g1012 /g1008 /g1007 /g1005/g1004 /g856 /g1011 /g1013 /g1009 /g1013/g1004 /g856 /g1013 /g1013
/g1004/g1004 /g856 /g1006/g1004 /g856 /g1008/g1004 /g856 /g1010/g1004 /g856 /g1012/g1005/g1005 /g856 /g1006
/g47 /g68/g3/g94/g393/g286 /g286 /g282 /g47 /g68 /g3 /g100 /g381/g396 /g395/g437/g286 /g47 /g68 /g3 /g38/g367/g437/g454/g90 /g68/g94 /g28
/g69 /g90/g68 /g94/g28
Figure 5.19: Experimental results: RMSE and NRMSE values of induction
machine: (a) Speed tracking (b) Torque tracking (c) Flux tracking.

123
5.8 Conclusion
An LPV observer and controller based robust FOC has been designed and vali-
dated for an IM based electried powertrain in this chapter. The stability of whole
LPV scheme is also established. Its ecacy is tested for an electried powertrain
operated in FUDS driving cycle with a dynamic temperature prole. The non-
linear simulations conrm the capability of (1) estimating the derated torque and

ux and (2) tracking the torque and
ux demands for the entire operation of the
electried powertrain. The performance of the proposed controller out performs
its SMC counterpart and is experimentally veried on an IM drive controlled by NI
myRIO-1900, using the current prole corresponding to FUDS driving cycle. The
experimental results conrm that the proposed technique is eective and deliv-
ers robust performance. The RMSE and NRMSE values are used as performance
indices to visualize the eectiveness of the LPV control scheme theoretically and
practically at dierent ambient temperatures.
In the coming chapter an LPV based degradation control scheme will be formulated
and discussed for EVs and HEVs electric powertrain.

Chapter 6
Degradation Control for an
Induction Machine based
Electried Powertrain
In this chapter a degradation control technique is proposed to mitigate the electric
machine based electried powertrain degradation while simultaneously providing
the desired closed loop performance. The performance of an electried powertrain
in extreme operating conditions is greatly compromised. This is due to the fact
that meeting the road loads, ensuring ecient powertrain operation and mini-
mizing the loss of lifetime (aging) of an electric machine are three essential but
con
icting targets. In this chapter, a multi-objective Linear Parameters Varying
(LPV) based Field-oriented Control (FOC) is proposed to address the problem of
con
icting objectives mentioned above. The eectiveness of the proposed control
framework is tested for a direct drive electried powertrain of a three-wheeled
vehicle commonly found in urban transportation for Asian countries. The urban
driving schedule based simulation results conrm that the lifetime of induction
machine can be enhanced by appropriate controller design without compromising
its performance.
124

125
6.1 Introduction
The real world problems oer targets that are often con
icting in nature. In
many practical control problems, energy consumption and meeting the desired
performance are typical con
icting objectives. For example, a semi-active suspen-
sion control oers good separation from road roughness and simultaneously keeps
permissible road holding performances, which are two con
icting but essential
performance objectives [112].
The automotive industry is rolling out energy-ecient electried powertrains due
to limited energy resources and increasing energy demands,. One of the integral
part of electried powertrain is traction motor, which has considerable impact
on the cost and performance of the vehicle. Induction machines (IMs), Perma-
nent Magnet Synchronous Machines (PMSMs) and Switched Reluctance Machines
(SRMs) are three possible candidates for traction applications. Among these, IMs
are robust, mature, require little maintenance and are inherently de-excited with
respect to inverter fault [35] and have been used for electric traction systems, such
as Tesla Roadster [80]. In an electried powertrain, meeting the road torque de-
mands, ensuring the ecient operations and minimizing the aging (loss of lifetime)
of traction motor are the desired objectives. However, variation in road loads is
met at the cost of motor eciency and life. Therefore these goals are important
to meet but con
icting in nature and make the control problem more challenging.
In an electried powertrain, Induction Machine (IM) is responsible to meet the
road loads in all operating conditions. However, due to part load operations and
variation in operating temperatures, the rotor and stator resistances change. As a
result, torque delivering capability of the motor de-rates [113], [114], [115], [116],
unlike an industrial drive which operates at constant loads and temperatures.
Under these conditions, IM has to supply the desired torque requested by the
driver, thus forcing the IM to operate in in-ecient regions. Similarly, the aging
of an IM is accelerated by several stress factors, which include high ambient tem-
peratures, variation in vehicle duty cycle and change in payloads. These stress

126
factors will create voltage and current imbalance and increase winding tempera-
tures during the IM operation for an electried powertrain, unlike an industrial
drive [117], [118], [119]. This will result in loss of
ux generation capability of
the windings, thus eecting the torque producing capability of IM. In order to
maximize the motor eciency or to reduce the power loss, the major eorts are
seen in better physical design of the motor [120], [101], [121] and improving its
performance by means of closed-loop controllers [68]. For a controller design of
an on-board motor to be used in an electried powertrain, the prime concern is
eciency. In fact, main argument behind the use of electric motors in energy
ecient vehicles is to take advantage of the high eciency ratings of an electric
motor as compared to that of internal combustion engines. If, in the pursuit of
high performance, the controller drives the motor to a low eciency operating
region, the whole design philosophy of electried powertrain will be jeopardized
and thus driving range of the vehicle will be compromised. Therefore, an ecient
IM drive, to be used for traction in an electried powertrain, must address the
issues highlighted above.
Conventional Field-Oriented Control (FOC) is commonly used to ensure ecient
operation of an IM based electric drive [80]. The performance of conventional
FOC is highly dependent on IM rotor and stator parameters. These parameters
are adversely aected in extreme operating conditions, part loads and variation
in payloads. As a result, eciency and torque of an electried powertrain is also
aected. This problem has been addressed by [68], [13] and [72] using Sliding-
Mode Control (SMC) based FOC. SMC technique is robust but it suers from
chattering problem. Due to the chattering in control, the optimal eciency is
dicult to ensure for traction applications. The LPV control design technique is
an ecient tool for the performance improvement of a closed-loop control system
in pre-dened operating range. However, it allows the controller to schedule itself
based on some measurements in addition to robustness. The key step of the
LPV control design technique is the selection of weighting functions. However, in
many practical problems, this is not always an easy task to achieve with the help
of optimally combined improvement of more than one objective (multi-objective

127
design). An LPV based control for industrial IM drive has been presented in
[78], [77] and [79], where the variation in motor parameters is not signicant during
the entire operation.
From the above discussion, it is clear that there is a true need of a control scheme
to address the con
icting features of an electried powertrain. In this chapter, an
LPV based FOC is proposed for traction IM. The outer loop in FOC generates the
desired currents from the torque and
ux controllers synthesized using LMIs. The
optimal
ux is estimated using LPV observer to ensure ecient IM operation [100].
The inner loop of FOC is formulated with the help of a multi-objective LPV con-
troller. The multi objective cost function is proposed based on con
icting goals in
an electried powertrain which are i) meeting the road torque demands, ii) ensur-
ing the IM ecient operations and iii) minimizing the IM aging (loss of lifetime).
The optimal weighting functions, which help to maximize the con
icting cost, are
selected using LMI based convex optimization approach [122] and are derived from
maximum static conditions on the motor voltage inputs and torque. The perfor-
mance of the proposed control framework is evaluated for a three-wheeled vehicle
against Federal Urban Driving Schedule (FUDS), a common controller evaluation
approach adapted by automotive community [101], [102]. The results are compared
with an LPV based FOC, which does not consider IM aging in the formulation of
the cost function. It is observed in the results that the aging of the traction IM is
signicantly reduced without compromising the overall performance.
This chapter advances as follows. A theoretical background of model based multi-
objective control problem is brie
y described in Section 6.2 followed by a brief in-
troduction to the proposed control framework in Section 6.3. Section 6.4 presents
the vehicle modeling, IM model and its LPV variant. The calculations for the
upper limit on the stator voltages are also conducted in Section 6.5. Section 6.6
describes the con
icting cost functions for electried powertrain. MOC design is
conducted and described in Section 6.7 by keeping in view the requirements of
three-wheeled vehicle. Section 6.7 also includes the
ux and torque estimation.
Section 6.8 describes the vehicle specications, details of simulations, controller

128
evaluation and result discussion. Summary and concluding comments are pre-
sented in Section 6.9.
6.2 Brief Theoretical Background of Multi-objective
Control Problem
In this section, the abstract form of the multi-objective control problem is pre-
sented. Let the plant to be controlled is represented by the state space model
8
<
:_x(t) =f(x(t);u(t);t)
y(t) =Cx(t)(6.1)
wherex(t)2Rndesignates the plant states, y(t)2Rnandu(t)2Rmare the
control outputs and inputs, subject to constraints ku(t)k1a. The purpose of
the control is to achieve y(t)jt!1!y.
The LPV state space representation of (6.1) is
8
<
:_x(t) =A((t))x(t) +B((t))u(t)
y(t) =C((t))x(t) +D((t))u(t)(6.2)
where(t)2Rsis the time varying parameter.
Considering two objectives as an example, this work aim to design the multi-
objective LPV controller
8
<
:_(t) =AK((t))(t) +BK((t))v(t)
u(t) =CK((t))(t) +DK((t))v(t)(6.3)
and to minimize the two con
icting objectives: control error, 1, and control energy
consumption 2, describes as
8
<
:1=RT
t0(y(t)y)T(y(t)y)dt
2=RT
t0(u(t))T(u(t))dt(6.4)

129
Then the multi-objective control problem (6.2)- (6.4) can be converted into the
con
icting cost function, Jand can be written as
J= min (1(x(t))) + min (2(x(t))) (6.5)
s.t.
1. The control in (6.3) exists.
2.ku(t)k1a
3.1L
1
4.2L
2
In practical control problem, energy consumption and performance error always
lie within an acceptable range and are designate by L
1andL
2. The maximum
acceptable values are called the practical objective constraint condition L. It is
notable that L
1andL
2are only the worst acceptable values and not the control
objectives. We will use similar approach to design the inner loop of FOC in the
subsequent sections.
6.3 Proposed LPV based FOC Framework for
Traction Induction Machine
In this section, the concepts of MOC have been adopted for LPV based FOC
to track the desired currents in the inner loop, issued by the torque and
ux
controllers residing in the outer loop. Fig. 6.1 shows the control framework for
the traction IM in an electric vehicle. The traction and braking requests are
issued by driver via accelerator ( ) or brake ( ) pedal in order to follow the
driving cycle. The supervisory controller translates the pedal signals into a torque
command ( command =e), which is then translated to a current reference, iqref.
In an electried powertrain, it is unusual to operate the electric machine at rated

ux due to the change in the road loads. Therefore, the
ux command ( ) is

130
vcommand
ud idref/g306e e /g306eTorque
Controller
Flux
ControllerMultiobjective
LPV Controller
Multiobjective
LPV ControllerIM
Dynamics
LPV Observer
/g2213^
d /g2213^
q i^
di^
q /g306^
eOptimal
Flux-+
-+-+
-+uq
/g550m
idiq
2iqref
/g306^
e
/g2213^/g2213
/g306^
ee /g2213 eideiqSupervisory Control
IM Drive System TransmissionVehicle
BrakesVehicle Duty Cycle
DriverSpeed Sensorvw
Break request/g536, /g543, /g306er
/g306command
/g306e/g550m /g306^
e /g2213^idiq
/g306LFtrac /g306e/g306w
uduq/g302, /g533
Figure 6.1: Proposed LPV based FOC control framework for a traction in-
duction machine.
obtained from the torque command to minimize the energy consumption, which
is then translated to a current reference, idref. The IM is controlled to deliver the
demanded torque, enhance the eciency and minimize the loss of life using LPV
based FOC technique. The IM drive system takes the speed, torque,
ux, current
and voltage signals which are then used to ensure the torque demand, ecient IM
operations and enhance the IM life. A gearbox is employed to amplify the IM
torque in order to drive the vehicle. The vehicle and IM dynamics necessary for
the synthesis of MOC, are given in the subsequent Sections.
6.4 Modeling of Electried Powertrain
This section describes the vehicle, drivetrain and IM dynamics followed by the
LPV variant of IM model.

131
6.4.1 Vehicle Dynamics and Drivetrain Modeling
The proposed MOC strategy takes into consideration the vehicle dynamics, which
act as a load torque for IM. The vehicle model is based on mechanics and aerody-
namics principles [58].
The load torque ( L) of a vehicle is given by
L= (Fa+Fg+Fr+Fw|{z}
Ft)Rw (6.6)
where,Fais the aerodynamic resistance force, Fgis the grade resistance force, Fr
is the rolling resistance force, Fwis the acceleration resistance force, Ftis the total
road load, and Rwis the wheel radius.
The following speed dynamics in the motor referential is used to describe the wheel
drive:
d!m
dt=np
J(eLb!m) (6.7)
where,!mis the motor mechanical speed, eis the motor generated torque, np
is the number of pole-pair, Jis the total inertia (rotor and load), and bis the
friction.
Moreover, the vehicle speed ( vw) is proportional to the IM speed ( !m), which can
be expressed in term of wheel radius Rw, and the gear box ratio ( NR) as follows:
vw=Rw
NR!m (6.8)
and the vehicle torque ( w) is given by
w=eNRt (6.9)
where,tis the transmission eciency.

132
6.4.2 Mathematical Model of IM
A three-phase IM in synchronously rotating reference frame can be expressed by
the mathematical equations, presented in Section 3.2.1.3, as follows, [100]:
8
>>>>>><
>>>>>>:_id=k1id+!eiq+k2d+k3!q+k4ud
_iq=k1iq!eid+k2qk3!d+k4uq
_d=k5d+np(!e!)q+k6id
_q=k5qnp(!e!)d+k6iq(6.10)
where 8
>>>>>>>>>>>>>>><
>>>>>>>>>>>>>>>:k1=(L2
mRr+L2
rRs)
LsL2r
k2=LmRr
LsL2r
k3=npLm
LsLr
k4=1
Ls
k5=Rr
Lr
k6=LmRr
Lr
= 1L2
m
LsLr(6.11)
id,iqandud,uqare the d-axis and q-axis stator currents and voltages respectively,
!is the electrical rotor speed, !eis the rotating reference frame velocity, dand
qare the d-axis and q-axis rotor
uxes, Ls,LrandLmare the stator, rotor and
mutual inductances respectively, RsandRrare the stator and rotor resistances
respectively.
The
ux and electromagnetic generated torque are calculated as follows:
8
>>>>>>>>><
>>>>>>>>>:!=np!m
e=k9(diqqid)
=q
2
d+2
q
iS=q
i2
d+i2
q
uS=q
u2
d+u2
q(6.12)

133
where
k9=3
2npLm
Lr(6.13)
is the rotor
ux, iSis the stator current and uSis the stator voltage.
Since the model is highly nonlinear and it needs to be converted into an LPV one
to design a multi-objective LPV controller. Based on Eq. (6.10), an LPV model
is obtained by taking Rr,Rsand!as varying parameters and !e= 0 [3]. The
continuous time state-space LPV model can be expressed as follows:
8
>><
>>:_x= (Ac+A

1+A

2+A

3|{z}
A())x+Bcu
y=Ccx(6.14)
whereAc,Bc,Ccare the nominal state-space matrices and A

1,A

2,A

3are
the varying parameter depended matrices. The denition of these matrices are
given as
A() =2
6666664a11() 0a13()a14()
0a22()a23()a24()
a31() 0a33()a34()
0a42()a43()a44()3
7777775(6.15)
where 8
>>>>>>>>>>>>>>>>>>>>>>>><
>>>>>>>>>>>>>>>>>>>>>>>>:a11() =a22() =L2
m1+L2
r2
LsL2r
a13() =Lm1
LsL2r
a14() =npLm3
LsL2r
a23() =npLm3
LsL2r
a31() =Lm1
Lr
a24() =Lm1
LsL2r
a42() =Lm1
Lr
a33() =1
Lra34() =np3
a43() =np3
a44() =1
Lr(6.16)
Bc=k4h
I OiT
;Cc=h
I Oi
(6.17)

134
In (6.17), Iis 22 identity matrix and Ois 22 zero matrix. The state, time
varying signal, input and output vectors of the achieved LPV model are
8
>>>>>>><
>>>>>>>:x(t) =h
idiqdqiT
y(t) =h
idiqiT
u(t) =h
uduqiT
(t) =h
RrRs!iT(6.18)
The time varying parameter
can be expressed as

= (
1;
2;:::;
L)T(6.19)
and the range of each parameter
iis given as

i(t)2

i
i
(6.20)
Pis a convex polytopes with vertices,
i;i= 1;2;:::;N: , and can be dened as
P=Cof
v1;
v2;:::;
vLg (6.21)
where
viare the vertices, i= 1;2;:::;L .L= 2are the number of vertices. Cois
a convex hull, i.e, the set of all convex combinations of
vi(all points inside and
on the boundary of the polytopes). The following expression denes the range of

1,
2and
3.8
>>><
>>>:
1(Rr)2[0:2Rr1:8Rr]

2(Rs)2[0:2Rs1:8Rs]

3(!)2[180 180](6.22)

135
6.5 Calculations for the Upper Limits on Stator
Voltages
The selection of weighting functions is the core for the design of proposed MOC.
The weighting functions, in this article, are computed by dening the upper limits
on stator voltages. In steady-state, the following relationships for d-axis and q-axis
stator currents can be dened from (6.10) and (6.12)
8
<
:id=d
Lm
iq=2
3e
pd(6.23)
The machine steady-state losses on the stator and rotor sides are given by
PLoss=3
2Rs(i2
d+i2
q)
|{z}
Stator losses+3
2Lm
Lr(!e!)diq
|{z}
Rotor losses(6.24)
The slip-speed characteristics of the machine can be obtained from the (6.10), (6.12)
and (6.23)
!=
32
dpp
94
dp216L2
re
Rr
4L2
re(6.25)
The speed of reference coordinate system !ecan be obtained from (6.10)
!e=Rrd+ 2Lriq!+q
R2
r2
d+ 4L2
ri2
qR2
r
2L2
riq(6.26)
The voltage limits can be expressed by assuming that the supplying source has a
certain maximum limit where the source is not able to deliver enough voltage to
increase the machine's torque. Substitution of (6.23), (6.25) and (6.26) into (6.24)
ud=Rs
dq
2
d4L2
ri2
q+ 2L2
ri2
q2
d
Lr
dq
2
d4L2
ri2
q +Rsd
Ls(6.27)
and
uq=
!e+(32
dnpp12)Rr
3
d+Rsiq (6.28)

136
where
1= 94
dn2
p (6.29)
2= 36n2
pL2
r2
di2
q (6.30)
3= 6npL2
rdiq (6.31)
6.6 The Multi-objective Functions
The ecient operation of a traction IM can be ensured by selecting the objective
function that addresses economic or performance features. Consequently, following
three con
icting objectives that can aect the operation of IM in an electried
powertrain have chosen.
1. To minimize the traction torque error;
2. To maximize the operating eciency of electried powertrain;
3. To minimize the loss of lifetime (aging) of an IM;
However, a right compromise among the dierent objective functions is required
to ensure the good design and this kind of problem is only solvable with multi-
objective approach. Therefore, following cost functions formulations have consid-
ered in this article:
6.6.1 Case-1
In this case, two con
icting objectives, meeting torque demands and ensuring the
ecient IM operations are considered in the formulation of con
icting cost function
to achieve the optimal performance of electried powertrain, without taking any
bound on the aging (loss of lifetime) of IM objective. The formulation is
J1= max ((id;iq)) + max1
er(id;iq)
(6.32)

137
6.6.2 Case-2
In this case, optimal performance of an electried powertrain is obtained by con-
sidering the all three above mentioned con
icting objectives in the formulation of
con
icting cost function. The formulation is
J2= max ((id;iq)) + max1
(id;iq)
+ max1
er(id;iq)
(6.33)
where,is the eciency of electried powertrain, is the loss of lifetime of IM
anderis the torque error.
Remark: Case 1 is discussed for the sake of comparison with proposed Case-2 in
Section 6.8 to highlight the benets of proposed framework.
6.6.3 Constraints
The constraints are imposed on the con
icting multi-objective control problem to
ensure the performance requirements of an IM based electried powertrain. These
constraints are dened as the cost function requirements:
iL
didiM
d (6.34)
iL
qiqiM
q (6.35)
uL
duduM
d (6.36)
uL
duduM
d (6.37)
where, the superscripts LandMstand for the minimum and maximum values
respectively.

138
6.6.4 Eciency of Electried Powertrain
The eciency of electried powertrain can be given as
=wvw
3
2(udid+uqiq)(6.38)
6.6.5 Road Load Error
The torque error can be written as
er=eeref (6.39)
The Root Mean Square Error (RMSE) value of the torque error eris computed
that is mostly used to evaluate practical implementations.
erRMSE =s
1
t2t1Zt2
t1[er(t)]2dt (6.40)
where, (t1;t2) is the vehicle operating interval.
6.6.6 Aging
The aect on IM winding due to thermal aging is an essential lifetime parameter.
Its aging rate, a derived formulation of Arrhenius [119], [123], can be calculated
as
(Tx) =02(TcTx)=HIC(6.41)
where,0is the reference lifetime in h and generally set to 20 ;000h [123], is
the lifetime in h at Tx,Tcis the reference temperature in0C(temperature in the
hottest point of the insulation system in the nominal work conditions), Txis the
reference temperature in0C(temperature in the hottest point of the insulation
system in the real work conditions) and HIC is the halving interval index0C(14,
11, 9:3, 8 and 10 for insulation class A,B,F,HandH0respectively) [119].

139
For the dynamic operation as in the case of electric vehicle, the percentage aging
factor is dened as
p(t1;t2) =1
0Zt2
t12(TxTc)=HICdt (6.42)
Then, the lifetime loss of the excess temperature time interval ( t1;t2) can be cal-
culated by
1;2=p(t1;t2):(Tx) (6.43)
6.6.7 Temperature Measurement
The temperature Txcan be estimated from the measurement of rotor and stator
resistance and is given as
R=R0[1 +(TxTc)] (6.44)
where,R0is the rotor and stator resistance at nominal work conditions ( T0=
25oC) andis the temperature coecient of resistance.
The rotor resistance can be estimated as
Rr=vuut!2
slLr"
!eL2
m
Q
I2s+!eLsLr#
(6.45)
where,!slis the slip frequency, and Qis the reactive power.
The estimation of stator resistance is given by [104]:
8
<
:Rs=kRr
k=Rs0
Rr0(6.46)
where,Rr0,Rs0are the nominal values of rotor and stator resistance, respectively.

140
6.7 LPV based FOC Control Design
In this section, we will expand on the control framework shown in Fig. 6.1.
6.7.1 Torque and Flux Estimation
The core requirement for the ecient operation of an IM based electric drive in
an electried powertrain is an accurate estimation of de-rated torque and
ux.
Therefore, a robust LPV observer [100] is designed to overcome the eects of un-
certainties in rotor resistance, stator resistance, and rotor speed. It is further
assumed that currents and speed measurements are available for use. The math-
ematics of the robust LPV estimator is devised as
8
>>>>>><
>>>>>>:2
4_^iS
_^3
5=A()2
4^iS
^3
5+BcuS+L()(iS^iS)
iS=Cc2
4iS
3
5;^iS=Cc2
4^iS
^3
5(6.47)
Eq. (6.47) can be rewritten as:
2
4_^iS
_^3
5=A()2
4^iS
^3
5+BcuS+L()Cc0
@2
4iS
3
52
4^iS
^3
51
A (6.48)
For carrying out the calculation for the estimator gain, the estimation error is
dened as:
e=2
4iS
3
52
4^iS
^3
5 (6.49)
The equation (state-space) of the estimation error, e, (subtracting the Eq. (6.48)
from Eq. (6.14)) is then specied as:
_e= (A()L()Cc)e (6.50)

141
The stability of the estimator error achieved in Eq. (6.50) and formula for com-
putation of estimator gains is outlined in [100]. The gain of the robust polytopic
estimator is obtained by solving LMIs formulated as follows:
8
<
:AT
iPCT
iQT
i+PAiQiCi0;i= 1;:::;2
P=PT0(6.51)
The computation of estimated torque is done as
^e=k9(^diq^qid) (6.52)
6.7.2 Multi-objective LPV Controller Synthesis
A multi-objective LPV current feedback controller is synthesized for an LPV model
of IM presented in Section 6.4.2. LPV control design is a comprehensive form of
H1optimal control to time-varying or nonlinear systems that can be formulated
in LPV form [106]. The design specications are dened by actuator constraints,
disturbance rejection, and reference tracking. These are the control sensitivity
function (to ensure ecient operations), complementary sensitivity function and
sensitivity function (to meet the torque demands) to shape the design specica-
tions.H1norm can be selected to guarantee these requirements. L2-gain of the
closed-loop system is an alternate to H1norm in the LPV structure. The idea
of `augmented plant' is commonly used in LPV control to formulate the design
specications. The closed-loop continuous time system architecture is shown in
Fig. 6.2, where P() is the state-space model given in (6.14); K() is the multi-
objective LPV output feedback controller. There are two inputs for the system
(plant): one is the feedback control u(from the multi-objective LPV controller),
other is the reference r. The reference input ris a vector of idandiqcurrents and
formulated as 2
4idref
iqref3
5=1
jMj2[M]1[N] (6.53)

142
r
z1
z2
z3P( /g545) We
WI
Wu
K( /g545)u y e
–
Figure 6.2: Closed loop system block diagram
where
M=2
4k6dk6q
k5k8qk5k8d3
5;N=2
4(v2+k5)
v1+k7!+1
JL3
5
For multi-objective LPV control design, the weighting function Wuis selected to
meet the actuator constraints without signicant degradation of performance. In
the drive system of an electried powertrain, the supplying source (battery) has a
certain maximum limit beyond which the source has no ability to supply sucient
voltage to increase electric machine's torque and this limit can be expressed as
(from (6.28))

!e+(32
dnpp12)Rr
3
dRsiq+uq= 0 (6.54)
where1= 94
dn2
p,2= 36n2
pL2
r2
di2
q,3= 6npL2
rdiq
Keeping in view the maximum voltage limit ((6.54)), Wuis selected as a high-pass
lter and formulated as
Wu=c
as+!u
s+c!u(6.55)
where,!u= 103rad/s, coecient cis a large number to place the pole of Wuat
very high frequency, it is 103and coecient ais selected as a design constant and
is tuned during the design process to meet the condition ((6.54)).
To meet the performance objective (robustness and tracking), WeandWIare
selected and ltering frequency is optimized to maintain high bandwidth of the

143
control system for satisfactory performance. The weighting function Weis formu-
lated as a high gain low-pass lter.
We=s+!eA
as+!e(6.56)
where,!e= 570 rad/sec, A= 0:002 and coecient ais selected as a design
constant.
The weighting function WIis also selected as design constant and a(We) andWI
both are optimized during control design by considering the following maximum
torque limit.
emax =3np2
d
4Lr(6.57)
The continuous time polytopic time-varying system is formulated by
2
6664_x
z
y3
7775=2
6664A()B1()B2()
C1()D11()D12()
C2()D21() 03
77752
6664x
w
u3
7775(6.58)
wherewandzare the external input and controlled output vectors, respectively.
The objective is to design the gain schedule LPV output feedback control which
will maximize the cost function described in (6.32) in case-1 and (6.33) in case-2.
The state-space representation of the dynamic controller is:
2
4_xK
u3
5=2
4AK()BK()
CK()DK()3
52
4xK
y3
5 (6.59)
which guarantees L2-gain bound
for the closed loop system ( (6.58) and (6.59))
and ensures the internal stability.
The LMI convex optimization approach is adopted to compute the multi-objective
gain scheduling LPV controller and presented in theorem 1.
Theorem: Consider the LPV system ((6.58)) with parameter trajectories con-
strained as in (6.20). There exists a gain scheduling multi-objective LPV output

144
feedback controller ((6.59)) imposing closed-loop stability and an upper bound

>0 on theL2-gain of the closed-loop system ((6.58) and (6.59)) from wtoz,
if there exist parameter dependent symmetric matrices V() andW() and a pa-
rameter dependent quadruple of state-space data ( ~AK();~BK();~CK();~DK())
such that([107])
2
6666664AW+B2~CK+   
~AT
K+A ATV+~BKC2+  
B1 VB 1+~BKD2
I
C1W+ (D12~CK)TC1D11
I3
7777775<0 (6.60)
2
4V I
I W3
5>0 (6.61)
wheresignies the terms needed to obtain symmetry in matrix and is omitted
for simplicity.
The multi-objective gain scheduling LPV output feedback controller
K() =i=LX
i=1ci2
4AK(i)BK(i)
CK(i)DK(i)3
5 (6.62)
is obtained by solving following optimization problem
min
V();W();~AK();~BK();~CK()
(6.63)
where 8
>>>>>>>>><
>>>>>>>>>:DK= 0
CK= (~CKDKC2W)(ST)1
BK= (R)1(~BKVB 2DK)
AK= (R)1(~AKRBKC2WVB 2CKST
V(A+B2DKC2)W)(ST)1(6.64)
In (6.64), the denition of RandSis
RST=InVW (6.65)

145
which can be solved by a singular value decomposition.
6.7.3 Robust Flux and Torque Controller
The concept of input-output linearization [93] is used to obtain the nonlinear
torque and
ux controller. For the control of IM, the relative degree and zero
dynamics are well dened and are stable respectively [69]. Thus input-output
linearization can be used and evaluated.
The complete derivation and construction of
ux and torque controllers are given
in Chapter 5 (Section 5.4.4).
6.7.4 Calculation for Reference Flux
The IM for an electried powertrain operates at dierent torques and speeds over
the entire driving cycle. Hence, it is unusual to operate the IM under the rated

ux. In this fashion, it is not possible to minimize the energy utilization. In order
to consume less energy, reference
ux is computed using the stator direct-axis
current reference in [68]. However, in this work, torque is the reference instead of
stator current. Therefore, in this work a new optimal
ux reference is computed
by taking into account the steady-state copper and iron losses of the machine on
the rotor and stator sides and formulated as [68]:
Ploss=k10
i2
d+i2
q

|{z}
Stator loss+k11i2
q|{z}
Rotor loss+k12
L2
mi2
d+k13i2
q

|{z}
stator iron loss(6.66)
where,8
>>>>>><
>>>>>>:k10=3
2Rs
k11=3
2Rr
Lm
Lr2
k12=1
Rc!2
e
k13=
L2
mLmLr
Lr2(6.67)

146
Applying the steady-state value of idandiqobtained from (6.10) in (6.66) and
minimizing the losses by dierentiating the total losses with respect to rotor
ux.
8
>>>><
>>>>:ref=Koptq
jerefj
Kopt=k140
B@(Rs+!2
eL2
m)
Rs+
RrL2m
L2r
+ (!2e(L2mLsL2r)2)
(RcL2r)!!1
CA1=2
(6.68)
where
k14=2
3Lm
np(6.69)
6.8 Performance Evaluation
This section will elaborate the vehicle specications, details of simulation scenarios
and simulation results.
6.8.1 Vehicle specications and simulation detail
The numerical simulations are a
exible and critical tool to comprehensively eval-
uate the electried powertrain under dierent driving cycles and loads. The de-
signed multi-objective LPV controller is also validated in simulations using the
nonlinear electried powertrain model constructed in MATLAB/SIMULINK for
an actual electric vehicle shown in Figure 6.1, as commonly exercised by automo-
tive community to evaluate their control frameworks [124], [111] and [110].
The simulations are based on an IM drive system used for traction in a three-
wheeled vehicle commonly found in urban transportation of Asian countries. The
simulator can evaluate an IM with LPV based FOC technique. FOC current
commands for IM control are generated by using the (6.53). A 4 :75KW induction
machine with class F insulation is used. The parameters of the IM and test vehicle
used in simulations are given in Tables 6.1 and 6.2.

147
Table 6.1: Specications of the three-wheeled vehicle induction machine
Parameter Value Parameter Value
np 2 Rs 0:22
Rr 0:209
Ls 0:0425 H
Lr 0:043 H Lm 0:04 H
J 0:124 Kg.m2b 0:06 N.m.s.rad1
Table 6.2: Specications of a three-wheeled vehicle used in urban transporta-
tion for Asian countries
Parameter Value Parameter Value
M 350KgRw 0:205m
Af 2:1m2Cr 0:013
Cd 0:42NR 8:32
Two cases are studied for the IM based electried powertrain in this work: (1)
under the cost function ((6.32)) which maximizes the eciency and meets torque
demands of an electried powertrain, (2) under the cost function ((6.33)) which
maximizes the eciency, meets the torque demands and minimizes the loss of life-
time of IM for an electried powertrain. The optimal
ux operation for minimum
losses on the rotor copper losses, stator copper and iron losses are implemented in
simulator for the both cases. For the IM under LPV-FOC technique, the optimal

ux calculations are given in Section 6.7.4.
The eectiveness of the multi-objective controller for an electried powertrain is
evaluated in two ways. Firstly, simulations are done for one complete driving cycle
to measure the eciency, torque error of an electried powertrain and the loss of
lifetime for an IM. In the second phase of evaluation, the slow aging process is taken
care of by conducting simulations for relatively long time. These simulations are
performed by considering the driving cycle prole of 75 minutes. It consists on a
complete driving cycle of 22 :6 minutes, then there is a rest time of 5 minutes and
same driving cycle is repeated twice (45 :2 minutes).

148
6.8.2 Simulation Results
A predened urban driving cycle FUDS, which has number of starts and stops, is
used for assessing the performance of proposed multi-objective LPV control strat-
egy. In order to achieve the con
icting goals, a multi-objective LPV controller is
obtained by selecting the optimal values of the weighting matrices Wu(parameter
a),We(parameter a) and WIfor the both cases. Table 6.3 gives the optimal
weighting matrices.
Table 6.3: Optimal Value of Weighting Matrices coecients
Case-1 Case-2
a(Wu)a(We)WIa(Wu)a(We)WI
0:22 2 0:90:19 2 0:75
The change in the IM drive system parameters (rotor and stator resistances) and
the winding temperature for a one complete cycle for the three-wheeled vehicle
are shown in Figure 6.3.
0200400600800100012000.210.220.230.240.250.260.270.280.29
Time [s]Resistance [ Ω]

020040060080010001200405060708090100110120
Temperature Tx [0C]
Rotor resistance
Stator resistance
Temperature
Figure 6.3: IM winding temperature and resistance over the entire period of
operation.

149
It is clear that the drive system parameters and winding temperature are greatly
in
uenced by the road load conditions and ambient temperature. To overcome the
eects of these changes on the performance of an electried powertrain, a multi-
objective controller is computed using LMI convex optimization approach for two
dierent cases (Section 6.6). The performance evaluation plots are shown through
Figure 6.4 through Figure 6.12.
0200400600800100012001360051015202530354045
Time [s]Vehicle speed [Km/h]

Desired speed
EV speed under Case−1
EV speed under Case−2
72074076078024681012
2202402602802122232425
Figure 6.4: Vehicle speed prole for the validation of multi-objective LPV con-
troller with and without aging compensation during the operation of electried
powertrain.
As seen in Figure 6.4 that the supervisory controller enables the vehicle to meet the
speed demands. The vehicle speed tracking performance is better for the case of
without aging compensation at the expense of more energy consumption as shown
in Figure 6.4 and the Root Mean Square Error (RMSE) for Case-1 is 0 :1451 and
for Case-2 is 0 :1522. The IM speed in this driving cycle is shown in Figure 6.5.
The torque of an IM based electried powertrain is greatly eected by the op-
erating temperature and parameter variations, as highlighted in [100] by the
term\thermally de-rated torque". The wheel torque is shown in Figure 6.6.

150
0200400600800100012001360020004000600080001000012000
Time [s]IM speed [rpm]

Desired IM speed
IM speed under Case−1
IM speed under Case−2
72074076078024681012
2202402602802224
Figure 6.5: IM speed under the validation driving schedule with and without
aging compensation.
0200400600800100012001360−15−5051525354555
Time [s]Wheel torque [N.m]

Torque demand
Wheel torque under Case−1
Wheel torque under Case−2
720740760780−10010
2202402602804681012
Figure 6.6: Vehicle torques with multi-objective LPV controller: without and
with aging compensation.
It is clear that the torque demands are met more precisely when the aging objective
is not formulated in the cost function. Again, it is possible only at the expense
of more current and voltage (more battery utilization and IM aging). The RMSE

151
values between the torque tracking of the reference value are 0 :195 and 0:231
for the case-1 and case-2 respectively. The multi-objective LPV controller also
overcomes the de-rating in the torque as vivid in Figure 6.6.
Dynamic eciency (the instantaneous eciency value at each sampling instant
in a driving cycle) approach is adopted instead of steady-state point eciency.
The power eciency characteristics of the IM based drive system under the both
cases with multi-objective LPV controller is presented in Figure 6.7. The average
power eciency under the both cases, with aging compensation and without aging
compensation are 76 :4% and 75:3% respectively.
0200400600800100012001360020406080100
Time [s]η [%]

Case−1
Case−2
Figure 6.7: Power eciency for an electried powertrain after the compensa-
tion of change in operating conditions with multi-objective LPV controller.
In the second case, (6.33) is considered in the computation of the controller and
simulated to measure the ecacy of the proposed controller. The vehicle speed
demand and IM torque tracking are within acceptable range when the aging was
considered in the cost function and it is clear from Figures 6.4 and 6.6. As a
result, the eciency and life of the electried powertrain is enhanced as shown
in the Figures 6.7 and 6.12. The IM voltages and currents for the both cases are

152
shown in the Figures 6.8 and 6.9. It can be observed that the current and voltage
demands are higher in Case 1 as compared to Case 2.
229 229.5 230 230.5 231−20−1001020Stator currents and voltages with aging compensation
Time [s]
(a)is [A]

id
iq
229 229.5 230 230.5 231−2200220
Time [s]
(b)us [V]

ud
uq
Figure 6.8: Induction machine direct and quadrature axis (a) stator currents.
(b) stator voltages with aging.
However, IM supply voltages, duty cycles, ambient temperature and parameters
change during the operation. Due to these changes, the IM temperature varies.
Therefore, IM life is eected, depending on the magnitude of the temperature.
IM life scenarios are explained next, to illustrate how IM life is aected when the
temperature changes with the time. Figures. 6.10 and 6.11 depicts the result of
the simulations that are performed for the evaluation of loss of lifetime of IM. It is
evident from the results that the entire driving period is of 75min and subsequent
cooling phase is of 3 :2h. Due to the motor losses, the winding temperature rose
up to the point when the last driving cycles ends. Then, when the vehicle is sta-
tionary, the IM emanates its heat to ambiance and winding temperature decreases
exponentially according to the adopted thermal laws.
The IM in an electried powertrain is operated for the entire period of driving
cycle of span 75 minutes and ambient temperature for this operation was 400C

153
229 229.5 230 230.5 231−20−1001020Stator currents and voltages without aging compensation
Time [s]
(a)is [A]

id
iq
229 229.5 230 230.5 231−2200220
Time [s]
(b)us [V]

ud
uq
Figure 6.9: Induction machine direct and quadrature axis (a) stator currents.
(b) stator voltages without aging.
010203040506070406080100120140160180
Time [min]Temperature Tx [0C]

010203040506070−5051015202530
Vehicle speed [Km/hr]Case−1: Temperature
Case−2: Temperature
Driving cycle
Figure 6.10: IM winding temperature: simulation of driving cycle.
which is the nominal temperature during the entire summer. The deterioration
rate is given (1) =((Tx)) = (1)=
0:2(TcTx)=HIC

, where(Tx) is the expected life

154
00.511.522.533.5406080100120140160180
Time [hr]Temperature Tx [0C]

00.511.522.533.5−5051015202530
Vehicle speed [Km/hr]Case−1: Temperature
Case−2: Temperature
Driving cycle
Figure 6.11: IM winding temperature: simulation of driving cycle with cooling
phase.
at a particular operating temperature Tx,HIC = 9:3,0is the rated life at rated
temperature Tc.
Assume the rated IM life span is 0= 20;000 h [123]. To nd the loss of lifetime
for entire driving cycle (43min) in the case-1, the rate of deterioration is 1 =(Tx) =
1=31746:5540 = 0:000031499(1/h). The product of the deterioration rate, period
of driving cycle and rated life gives the loss of lifetime 1;2, which in this case is
(0:0000314990:716620000) = 0 :412h. In case-2, the rate of deterioration is
1=(Tx) = 1=39114:4044 = 0:000025566(1/h). The product of the deterioration
rate, period of driving cycle and rated life gives the loss of lifetime 1;2, which in
this case is (0 :0011430:716620000) = 0:366h.
Similarly, loss of lifetime of the IM operated in an electried powertrain is also
evaluated at 200Cand results are summarized in Table 6.4. The dierence in loss
of lifetime for the both cases is due to the maximum peak temperature for a short
period in time.

155
Table 6.4: Loss of lifetime of IM at ambient temperature of 400Cand 200C
Case-1 Case-2
@400C@200C@400C@200C
0:412h 0:389h 0:336h 0:324h
Figure 6.12: (a) Average eciency of an electried powertrain. (b) RMSE
values of vehicle torque. (c) loss of lifetime of an IM.
Consequently, the number of peak temperature overshoots during vehicle operation
and short-term part loads are the critical aspects in loss of lifetime of a traction
motor due to thermal activity. Therefore, multi-objective LPV controller optimally
manages the current limits in order to avoid the further insulation deterioration.
Figure 6.12 shows the comparison of performance in both cases considered in this
article. It is clear from the above discussion that multi-objective LPV controller
provides better performance to achieve the con
icting objectives (in meeting the
torque demands, ensuring ecient electried powertrain operations and minimiz-
ing the loss of lifetime (aging) of an EM over the entire driving cycle). Hence,
it was conrmed in this paper that the lifetime of an EM can be enhanced by
appropriate controller design without compromising the performance signicantly.

156
6.9 Conclusion
A systematic approach based on LPV control technique for enhancing the perfor-
mance of an electried powertrain has been proposed in the chapter. A realistic
con
icting cost function was formulated by taking into account the torque de-
mands, ecient operation of an electried powertrain and loss of an IM lifetime
(aging) as three essential but con
icting objectives, which were used to develop
a multi-objective LPV-FOC controller. The optimal weighting lters were se-
lected based upon the upper bounds on the supply voltage (battery) and torque.
The ecacy of the proposed controller is evaluated for a three-wheeled vehicle
driven under the normal and extreme operating conditions. The simulation re-
sults conrmed that the aging of the IM was reduced without compromising the
performance of the IM drive.

Chapter 7
Conclusion and Future Directions
This chapter builds some concluding comments and then opinions for the contin-
uation/expansion of this work will be presented.
7.1 Conclusions
The summary of the thesis is disclosed as follow: Chapter 3 explains the LPV
modeling of induction machine and its validation. The comparison of the output
signals and state signals with non-linear model is done. Root Mean Square Error
(RMSE), which is less than 1 :93104for all states and then Normalized Root
Mean Square Error (NRMSE), which is less than 0.9998 for all states are also
investigated. This model is necessarily required for the development of novel con-
trol techniques to address the EVs and HEVs problems elaborated in Section 2.3
and Section 2.6.1: namely the ambient and operating temperatures eects on the
torque performance, eciency and the degradation of traction machine winding
for EVs and HEVs powertrain.
Chapter 4 explains the thermal derating of torque for an electried powertrain.
A novel and robust LPV based observer is designed for estimating the thermally
derated torque and its capability to estimate the thermally derated torque is in-
vestigated for HEV powertrain under dierent ambient temperature.
157

158
Chapter 5 describes the design of novel and robust LPV based controller to man-
age and compensate the thermally derated torque of an induction machine based
electried powertrain. The estimation technique presented in Chapter 4 is used to
accomplish it. The performance of designed observer-controller pair is investigat-
ing for the EV operating in standard driving cycle (FUDS) under. The proposed
control technique ensures good tracking performance in meeting the road loads
demands by keeping the the actuator constraints within the desired limits in the
presence of rise in operating and surrounding temperatures. The optimal
ux
calculations using the rotor and stator sides losses are also presented to achieve
the ecient operation of traction induction machine under the above mentioned
operating conditions.
The ecacy of the proposed control scheme is also investigated using a hardware
test set-up consisting of an IM, a Controller Board and a Torque Measurement
arrangement. Firstly, practical observation of the open loop thermal torque eects
is done using experimental set-up. Secondly, the excellent performance on the test
bed of the LPV controller for a step demand on the torque, in contrast to the
sliding mode based controller is addressed and this experiment is performed on
the raised temperature prole. The third and nal experiment, aimed at validat-
ing controller for the harsh environment faced by an electried powertrain in a
challenging urban environment, is addressed. For this purpose the speed demand
prole was generated from FUDS.
The LPV control method is selected. The main objective of an LPV control (gain
scheduling) technique is to control the plant over a predened operating range.
However, it allows the controller to schedule itself based on some measurements
in addition to robustness.
Chapter 6 explains the degradation control technique, proposed to mitigate the
eects of rise in ambient and operating temperatures on the life time of an traction
induction machine for EVs and HEVs while simultaneously providing the desired
closed-loop performance. In the synthesis of the degradation controller, meeting
the road loads, ensuring ecient powertrain operation and minimizing the loss

159
of lifetime (aging) of a traction machine are taken as three essential but con
ict-
ing targets. The eectiveness of the proposed control framework is tested for a
direct drive electried powertrain of a three-wheeled vehicle commonly found in
urban transportation for Asian countries. The urban driving schedule based sim-
ulation results conrm that the lifetime of induction machine can be enhanced by
appropriate controller design without compromising its performance.
7.2 Contributions
After going through a brief discussion on the presented work, the main contribu-
tions of the thesis can be enumerated as follows:
1. Development and validation of LPV model of an induction machine by taking
rotor resistance, stator resistance and rotor speed as scheduling signals.
2. Estimation of
(a) Thermally derated torque of an electried powertrain
(b) Flux of a traction induction machine
from the developed LPV dynamics of a traction induction machine under
the rise in operating and surrounding temperatures. These dynamics is used
to develop the estimation technique from linear parameter varying control
theory. The presented technique needed measurement from voltage sensors,
current sensors and speed sensors. These sensors are the compulsory part of
traction drive.
3. Development of open loop torque derating conrmation method for a trac-
tion machine in an electried powertrain due to the change in one or both
temperatures. This task is accomplished using the developed estimation
technique.

160
4. Design, development and evaluation of a robust LPV control framework for
the electried powertrain in managing the thermally derated torque of an
electried powertrain perspective.
5. Formulation of a con
icting cost functions by considering the following ob-
jectives
(a) To minimize the traction torque error
(b) To maximize the operating eciency of electried powertrain
(c) To minimize the loss of lifetime (aging) of an IM
6. Design, development and evaluation of a robust multi-objective LPV based
eld-oriented control framework in mitigating the electric machine based
electried powertrain degradation while simultaneously providing the desired
closed loop performance perspective.
7.3 Future Directions
The presented research work in this document can be expanded in several direc-
tions.
The following future tasks are suggested for estimating and managing the ther-
mally derated torque's control scheme.
1. In this manuscript, electrical equations of a traction induction machine are
used to develop the estimation and compensation control techniques for the
thermally derated torque of an electried powertrain. In future, thermal
dynamics of a traction induction machine can be developed to make the
estimation and control techniques more robust.
2. The proposed estimation and compensation control techniques are evaluated
using the developed EV simulator and induction machine based electric drive.
These scheme will also be evaluated using the hardware in the loop (HIL)
powertrain setup.

161
3. The operating temperature, in the proposed schemes, is computed from the
estimation of induction machine winding's rotor and stator resistances. This
can also be computed by development of induction machine thermal dynam-
ics. This will make the estimation and control schemes more simple and
robust.
The suggested future tasks for the proposed degradation control for an induction
machine based electried powertrain are;
1. The developed EV simulator is used to investigate the ecacy of degradation
control scheme. This control scheme will also be investigated using the
hardware in the loop (HIL) powertrain setup.
2. The gains of weighting lters in the design of degradation control scheme are
tunned by hit and trial method keeping in view the upper stator voltages
and currents bounds. The o line optimization technique can be used to
tunned the gains of weighting lters to make the design process simple and
less time consuming.
3. The performance of this technique in aging perspective should be evaluated
by on road testing on actual electric vehicle.
4. The both control schemes are tested and evaluated for the light duty vehicle
and three-wheeled electric vehicles used in urban transportation of Asian
countries. The high power traction induction machine used in transit buses
system faces more temperature eects as compared to medium power trac-
tion induction machine. Therefore, the both control schemes should be tested
for the high power traction induction machine to evaluate the ecacy of the
proposed techniques.

Chapter 8
Appendices
8.1 Appendix A
8.1.1 Close-loop stability and synthesis of controller
The generalized plant and closed-loop system are shown in Figures 8.1 and 8.2.
/g3Twz
Ku
Figure 8.1: Generalized plant diagram.
/g3T w z
Figure 8.2: Closed-loop system.
162

163
The state-space representation can be given as:
8
>>><
>>>:_x(t) =Ax(t) +Bw(t)
z(t) =Cx(t) +Dw(t)
x(0) = 0(8.1)
Assume that T(s) is stable and the H1norm of the closed-loop system is given as
kTk2
1=maxR1
0zT(t)z(t)dtR1
0wT(t)w(t)dt; w6= 0 (8.2)
It is clear from (8.2) that kTk1<
is equivalent to
Z1
0(zT(t)z(t)
2wT(t)w(t))dt< 0 (8.3)
Assuming a Lyapunov function,
V(x) =xTPx; P =PT>0 (8.4)
Sincex(0) =x(1) = 0,kTk1<
is enforced by the existence of P=PT>0
such that
_V(x) +1

zT(t)z(t)
wT(t)w(t)<0;8x(t);w(t) (8.5)
To convert (8.5) in to LMI, putting (8.6) and (8.7) into (8.5)
_V(x) =xT(ATP+PA)x+xTPBw +wTBTPx (8.6)
Z=Cx+Dw (8.7)
It yields
h
xTwTi2
4ATP+PA+1

CTC PB +1

CTD
BTP+1

DTC
I+1

DTD3
52
4x
w3
5<0 (8.8)

164
ForkTk1<
the (8.8) must hold for all xandw. The (8.8) can be rewritten as
2
4ATP+PA PB
BTP
I3
5+1

2
4CT
DT3
5h
C Di
<0 (8.9)
The existence of solution to LMI in (8.9) is necessary condition for kTk1<
.
Using Schur complement, the (8.9) can also be written as
2
6664ATP+PA PB CT
BTP
I DT
C D
I3
7775<0 (8.10)
From Figure 8.1, the state-space representation of closed-loop system is given as
8
<
:_xc(t) =Acxc(t) +Bcwc(t)
z(t) =Ccxc(t) +Dcwc(t)(8.11)
where
Ac=2
4A+BuCkCvBuCk
BkCvAk3
5 (8.12)
Bc=2
4Bw+BuDkDvw
BkDvw3
5 (8.13)
Cc=h
Cz+DzuDkDvDzuCki
(8.14)
Dc=h
Dzw+DzuDkDvwi
(8.15)
The closed-loop transfer function T(s) is given as
Ts=2
4AcBc
CcDc3
5=Cc(sIAc)1Bc+Dc (8.16)
Further solving for H1output feedback control results in two LMIs.
2
666664AY+YAT+Bu~Ck+ (Bu~Ck)T ~Ak+A+Bu~DkCvBw+Bu~DkDvw (CzY+Dzu~Ck)T
 ATX+XA+~BkCv+ (Bk~Cv)TXBw+~BkDvw (Cz+Dzu~DkCv)T
 
I (Dzw+Dzu~DkDvw)T
  
I3
777775<0
(8.17)

165
2
4Y I
I X3
5<0 (8.18)
8.2 Appendix B
8.2.1 Induced L-2 norm of LPV systems
The LPV system in state-space form can be given as:
G:8
<
:dx(t)
dt=A((t))x(t) +B((t))w(t)
z(t) =C((t))x(t) +D((t))w(t)(8.19)
where the system matrices are the continuous function of the parameter . In
addition,(:) is a piecewise continuous function of time, :R+!Rm, that is
assumed to satisfy the known bounds
i(t)2
i;i
; i= 1;2;:::;m (8.20)
The set of parameter vectors 2Rmsatisfying the magnitude constraints in (8.20)
is denoted by Pand the set of admissible trajectories. The performance of Gcan be
specied in term of its L2gain from input wto outputzassumingx(0) = 0 [125].
kGk=sup 06=w2L2(Rp);(:)2Akzk
kwk(8.21)
8.3 Appendix C
8.3.1 Thermally derated torque's observer gains
The observer gains are selected using (4.22)- (4.24) which were computed by solv-
ing the LMI in (4.21). The LMI optimization delivered a LPV observer with 8
vertices, each vertex being an LTI regulator with four states.

166
The observer gains at each vertex are
@ vertex-1
L1=2
666666445:93 0
0 45:93
4 51:9
51:9 43
7777775
@ vertex-2
L2=2
666666449:91 0
0 49:91
551:9
51:9 53
7777775
@ vertex-3
L3=2
666666449:91 0
0 49:91
5 51:9
51:9 53
7777775
@ vertex-4
L4=2
666666450:09 0
0 50:09
451:9
51:9 43
7777775

167
@ vertex-5
L5=2
666666450:09 0
0 50:09
4 51:9
51:9 43
7777775
@ vertex-6
L6=2
666666449:89 0
0 49:89
551:9
51:9 43
7777775
@ vertex-7
L7=2
666666449:91 0
0 49:91
551:9
51:9 53
7777775
@ vertex-8
L8=2
666666445:93 0
0 45:93
451:9
51:9 43
7777775

168
8.4 Appendix D
8.4.1 LPV current controllers gains
The LPV controller Klpvwas computed by solving the optimization problem
of (5.25) such that (6.60) and (6.61) hold. With the weighting functions dened
in (5.31),the LMI optimization gave a LPV controller with eight vertices, each
vertex being an LTI controller with six states. Four states come from the plant
and two from WS: The achieved optimal value of performance index
is 1.023.
The controller gains at each vertex are
@ vertex-1
AK(1) = 1106:2
66666666666640:00340:00010:00030:0060 1:20857:2151
0:00010:00330:0069 0:0003 5:1533 1:7220
0:0000 0:00000:00000:00020:00090:0007
0:0000 0:0000 0:00020:00000:0004 0:0032
0:0004 0:0014 0:0031 0:00042:36580:0131
0:0021 0:0004 0:00070:00380:01314:64563
7777777777775
BK(1) =2
66666666666640:64020:4883
0:49340:6538
0:8040 0:3800
0:2492 0:7760
219:2878495:4651
707:6236 313:23843
7777777777775
CK(1) = 1105:2
40:00150:00110:0032 0:0011 1:2318 3:9566
0:0012 0:0015 0:0015 0:00292:8186 1:71063
5

169
DK(1) =2
40 0
0 03
5
The plant matrices BandCare not time varying. Therefore, the controller
matricesBK(:),CK(:) andDK(:) remain same at each vertex. The controller
matrixAK(:) is only varied and given below.
@ vertex-2
AK(2) = 1106:2
66666666666640:00350:0001 0:00590:0027 1:20857:2151
0:00010:00340:00360:0059 5:1533 1:7220
0:0000 0:00000:0000 0:00020:00090:0007
0:0000 0:00000:00020:00000:0004 0:0032
0:0004 0:0015 0:0009 0:00292:36580:0131
0:0021 0:0005 0:00420:00070:01314:64563
7777777777775
@ vertex-3
AK(3) = 1106:2
66666666666640:00350:00010:00030:0059 1:20857:2151
0:00010:00340:0068 0:0003 5:1533 1:7220
0:0000 0:00000:00000:00020:00090:0007
0:0000 0:0000 0:00020:00000:0004 0:0032
0:0004 0:0015 0:0031 0:00042:36580:0131
0:0021 0:0005 0:00070:00370:01314:64563
7777777777775
@ vertex-4
AK(4) = 1106:2
66666666666640:00350:0001 0:00590:0027 1:20857:2151
0:00010:00330:00360:0059 5:1533 1:7220
0:0000 0:00000:0000 0:00020:00090:0007
0:0000 0:00000:00020:00000:0004 0:0032
0:0004 0:0015 0:0009 0:00292:36580:0131
0:0021 0:0005 0:00420:00070:01314:64563
7777777777775

170
@ vertex-5
AK(5) = 1106:2
66666666666640:00350:00010:00030:0060 1:20857:2151
0:00010:00330:0069 0:0003 5:1533 1:7220
0:0000 0:00000:00000:00020:00090:0007
0:0000 0:0000 0:00020:00000:0004 0:0032
0:0004 0:0015 0:0031 0:00042:36580:0131
0:0021 0:0004 0:00070:00380:01314:64563
7777777777775
@ vertex-6
AK(6) = 1106:2
66666666666640:00340:0001 0:00590:0027 1:20857:2151
0:00010:00330:00360:0059 5:1533 1:7220
0:0000 0:00000:0000 0:00020:00090:0007
0:0000 0:00000:00020:00000:0004 0:0032
0:0004 0:0014 0:0009 0:00292:36580:0131
0:0021 0:0004 0:00420:00070:01314:64563
7777777777775
@ vertex-7
AK(7) = 1106:2
66666666666640:00350:00010:00030:0059 1:20857:2151
0:00010:00330:0068 0:0003 5:1533 1:7220
0:0000 0:00000:00000:00020:00090:0007
0:0000 0:0000 0:00020:00000:0004 0:0032
0:0004 0:0014 0:0031 0:00042:36580:0131
0:0021 0:0004 0:00070:00370:01314:64563
7777777777775

171
@ vertex-8
AK(8) = 1106:2
66666666666640:00340:0001 0:00590:0027 1:20857:2151
0:00010:00330:00360:0059 5:1533 1:7220
0:0000 0:00000:0000 0:00020:00090:0007
0:0000 0:00000:00020:00000:0004 0:0032
0:0004 0:0014 0:0009 0:00292:36580:0131
0:0021 0:0004 0:00420:00070:01314:64563
7777777777775
8.4.2 Torque and
ux controllers gains
The torque and
ux controllers were computed by solving the linear matrix in-
equality in (5.53) and Equation (5.54) gives us the gains of controllers.
The gains of torque and
ux controllers are diag ( 300;230).

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