Application of Sliding Mode Control in Induction Motor Drive VSB – Technical University of Ostrava

VSB – Technical University of Ostrava

Faculty of Electrical Engineering and Computer Science

Department of Electronics

Application of Sliding Mode Control in Induction Motor Drive

PHD THESIS

Ing. Chau Si Thien Dong

Supervisor: Prof. Ing. Pavel Brandstetter, CSc.

Ostrava, December 2017

i

Declaration

I hereby declare that this PhD thesis was written by myself. I have quoted all the references I have drawn upon.

ii

Acknowledgement

Firstly, I would like to express my deeply acknowledgement to Professor Pavel Brandstetter for Professor’s kindly support, encouragement, and inspired supply. I have learned so much from his rich knowledge and experience in power electronics and electrical drives. Without Professor Pavel Brandstetter, I cannot finish this research work.

I sincerely thank Dr. Duy Hoang Vo for providing me with materials and links that I could not possibly have discovered on my own, for his kind words and for introducing me to this PhD program.

It is my pleasure to work with him.

I am hugely indebted to Professor Petr Chlebis, Associate Professor Ivo Neborak, Associate Professor Petr Palacky, Dr. Martin Kuchar, who gave me plenty of valuable guidance and advices. I also thank Ing. Jiri Hajovsky and Dr. Ordrej Petrtyl, who supported me at the first steps in this work and have been always willing to help me. Moreover, I would like to thank all other Professors and colleagues in Department of Electronics, Faculty of Electrical Engineering and Computer Science, VSB – Technical University of Ostrava. All of them have warm heart and make me feel comfortable each time I went to Ostrava.

I am grateful to all colleagues in Faculty of Electrical and Electronics Engineering, Ton Duc Thang University. They are so kind when spending time to support me. Especially, I like to thank Dr.

Bach Hoang Dinh for reading and suggestions, Dr. Phuong Thanh Tran for supporting and kind help in my work during my PhD study. I am thankful to Dr. Van Van Huynh who gave me right advice at right time.

I am grateful Dr. Dao Phan for his kindly support during my study and stay in Czech Republic.

Finally, I must express my deeply appreciation to my parents and my husband for providing me with unfailing support and continuous encouragement throughout my years of study.

iii

Abstract

Induction motors, as well as electrical drives, are widely used in industry applications and consume a large number of electrical energy in the world. Energy saving, torque fast response and speed accuracy are main area in controlling induction motors. During last years, control methods have been developed to get these goals. Among these control methods, field - oriented control (FOC) is more and more popular because of high performance, energy saving, controlled acceleration, etc. However, in controlling AC machine drive by using FOC, the motor speed is required. Together with the development of semiconductor technologies and digital signal processing (DSP), software instruments have been used to estimate speed, reducing hardware complexity and cost of a mechanical speed sensor.

However, due to the nonlinearity, high order and multivariable properties of induction motor dynamics, the development of advanced induction motor control is still a challenging task.

In this research proposal, basic description of the torque and flux control, as well as the theory and application of sliding mode algorithms are reviewed in details. From that, a sliding mode control algorithms for speed control is proposed to implement the pulse width modulation with a constant switching frequency. In addition, the sliding mode observer for speed estimation is investigated. The parameter sensitivity of the observer and controller are analyzed. Furthermore, the robustness of control and observer algorithms are also proved by Lyapunov’s criterion. Simulation models and control structures in MATLAB – Simulink environment are developed to verify the performance of the proposed algorithms. Finally, the experimental work in an induction motor drive controlled by eZdsp^TMF28335 is presented to compare with theoretical assumptions and simulation results.

Key words: induction motor, sliding mode control, sliding mode observer, Lyapunov’s theory, vector control, rotor resistance estimation, rotor resistance estimation, sensorless control.

iv

Content

DECLARATION ... I ACKNOWLEDGEMENT ... II ABSTRACT ...III CONTENT ... IV GLOSSARY OF ABBREVIATION AND SYMBOLS ... VII LIST OF IMAGES AND CHARTS ... XIII LIST OF TABLES ... XXIII

1. INTRODUCTION ... 1

1.1 Review of Previous Studies ... 1

1.1.1 Vector Control of Induction Motor Drives ... 1

1.1.2 Sensorless Vector Control of Induction Motor Drives ... 2

1.1.3 Variable Speed Control of Induction Motor Drives ... 4

1.2 Objectives and Scope of this Study ... 5

1.3 Organization of this Dissertation ... 6

2. BACKGROUND AND LITERATURE REVIEW ... 8

2.1 Field - Oriented Control of Induction Motor Drives ... 8

2.1.1 Coordinate Transformation ... 8

2.1.2 Vector Control of Induction Motor Drives ... 10

2.2 Speed Sensorless Control Technology ... 18

2.3 Sliding Mode Theory ... 19

2.3.1 Sliding Mode Control ... 19

2.3.2 Sliding Mode Observer ... 23

3. SLIDING MODE OBSERVER IN CONTROL OF INDUCTION MOTOR DRIVES ... 25

v

3.1 Introduction ...25

3.2 Sliding Mode Observer ...25

3.3 Robust Sliding Mode Observer...32

3.4 Simulation Results ...36

3.4.1 Introduction ... 36

3.4.2 Speed Control of Induction Motor Drives ... 38

3.4.3 Sensorless Control of Induction Motor Drives ... 42

3.4.4 Parameter Sensitivity ... 46

3.4.5 Robust Sliding Mode Observer ... 52

3.5 Discussions and Conclusions ...61

4. SLIDING MODE CONTROL OF INDUCTION MOTOR DRIVES ... 62

4.1 Introduction ...62

4.2 Sliding Mode Controller Design ...63

4.3 Gain Adaptation Sliding Mode Controller ...67

4.4 Simulation Results ...69

4.4.1 Sliding Mode Control of Induction Motor Drives ... 69

4.4.2 Sensorless Sliding Mode Control of Induction Motor Drives ... 73

4.5 Discussions and Conclusions ...78

5. EXPERIMENTAL RESULTS ... 79

5.1 Introduction ...79

5.2 Experimental Results ...83

5.2.1 Speed Control of Induction Motor ... 84

5.2.2 Speed Control of Induction Motor with Load ... 89

vi

5.2.3 Sensorless Speed Control of Induction Motor ... 93

5.2.4 Sensorless Speed Control of Induction Motor with Load ... 98

5.2.5 Sliding Mode Control of Induction Motor ... 103

5.2.6 Sliding Mode Control of Induction Motor Drives with Load ... 105

5.2.7 Sensorless Sliding Mode Control of Induction Motor ... 107

5.2.8 Sensorless Sliding Mode Control of Induction Motor with Load ... 111

5.3 Discussion and Conclusions ... 114

6. SUMMARY AND FUTURE WORKS ... 116

6.1 Summary ... 116

6.2 Future Works... 117

REFERENCES ... 118

LIST OF OWN PUBLICATIONS ... 124

LIST OF PROJECTS ... 126

vii

Glossary of abbreviation and symbols

AC Alternating Current

ADC Analog – to – Digital Converter

ANN Artificial Neural Network

CCS Code Composer Studio

DC Direct Current

DFO Direct Field – Oriented Control

DSC Digital Signal Controller

DSP Digital Signal Processor

DTC Direct Torque and Flux Control

EKF Extended Kalman Filter

FLC Fuzzy Logic Control

FOC Field – Oriented Control

FSMC Fuzzy Sliding Mode Control

FTC Fault Tolerant Control

GA Genetic Algorithm

GPIO General Purpose Input/Output

HF High Frequency

IFO Indirect Field – Oriented Control

IM Induction Motor

ISMC Integral Sliding Mode Control

KF Kalman Filter

viii

LO Luenberger Observer

MRAS Model Reference Adaptive System

PI Proportional – Integral

PID Proportional – Integral – Derivative

PMSM Permanent Magnet Synchronous Motor

PWM Pulse-Width Modulator

RFO Rotor Field - Oriented Control

SCI Serial Communication Interface

SFO Stator Field – Oriented Control

SM Sliding Mode

SMC Sliding Mode Control

SMO Sliding Mode Observer

SVM Space Vector Modulation

VSC Variable Structure Control

VSS Variable Structure System

rpm revolutions per minute

im [A] magnitude of magnetizing current

*

im [A] reference magnitude of magnetizing current

md,mq

i i [A] magnetizing current vector components in coordinate system [ , ]d q

m ,m

i _ i _{ [A]} magnetizing current vector components in coordinate system [,]

, ,

Ra Rb Rc

i i i [A] rotor current of individual phases

ix

R ,R

i_ i _ [A] rotor current vector components in stator coordinate system [,]

Sa Sb Sc, ,

i i i [A] stator current of individual phases

Sq Sd i

i , [A] stator current vector components in rotor coordinate system [d,q]



 S S i

i , [A] stator current vector components in stator coordinate system [,]

Sx,Sy

i i [A] stator current vector components in oriented coordinate system [ , ]x y

* * Sx,Sy

i i [A] reference stator current vector components in [ , ]x y

kc [-] control constant of frequency converter

n [-] order of the system

p [-] number of poles

max

uC [V] maximum value of control voltage



 S

S u

u , [V] stator voltage vector components in stator coordinate system [,]

* *

S

,

S

u

_

u

_ [V] reference stator voltage vector components in [,]

Sx, Sy

u u _[V] stator voltage vector components in oriented coordinate system [x,y]

* *

Sx

,

Sy

u u

[V] reference stator voltage vector components in [x,y]

d, q

x x [-] components of a vector x^Rin rotor coordinate system [ , ]d q

x, y

x x [-] components of a vector x^Oin oriented coordinate system [x,y]

,

x x_{ } [-] components of a vector x^Sin stator coordinate system [ , ]

 [rad] electric rotor angle

 [rad] stator angle

x



[-] total leakage constant

R, S

  [-] rotor and stator leakage constant

m [rads^-1] mechanical angular speed

*



m [rads^-1] reference mechanical angular speed

R [rads^-1] rotor angular speed ˆ_R

 [rads^-1] estimated rotor angular speed

R [rads^-1] absolute error between the actual speed and estimated rotor speed

S [rads^-1] stator angular speed

sl S R

   [rads^-1] slip frequency

R, R

 

[Wb] rotor flux vector components in stator coordinate system [,]



R [Wb] rotor flux magnitude

R

im [A] magnetizing current phase vector in rotor coordinate system [d,q]

S

im [A] magnetizing current phase vector in stator coordinate system [,]

R

iR [A] rotor current phase vector in rotor coordinate system [d,q]

S

iR [A] rotor current phase vector in stator coordinate system [,]

R

iS [A] stator current phase vector in rotor coordinate system [d,q]

S

iS [A] stator current phase vector in stator coordinate system [,]

u [-] input vector

S

uS [V] stator voltage vector in stator coordinate system [ , ] 

xi

R

uR [V] rotor voltage vector in rotor coordinate system [ , ]d q

x [-] state vector

xO [-] a vector in oriented coordinate system [x,y] xR [-] a vector in rotor coordinate system [d,q] xS [-] a vector in stator coordinate system [,]

xˆ [-] estimated state vector

x [-] absolute state error vector

y [-] output vector

yˆ [-] estimated output vector

S

ψ

S [Wb] stator flux vector in stator coordinate system [ , ] 

R

ψ

R [Wb] rotor flux vector in rotor coordinate system [ , ]d q

S

ψ

R [Wb] rotor flux vector in stator coordinate system [ , ] 

J [kgm²] moment of inertia

K

M [-] transfer constant of frequency converter

L

m [H] magnetizing inductance

S R

L

L ,

[H] rotor and stator inductance

Rs

,

Ss

L L

[H] rotor and stator leakage inductance

S R

R

R ,

[] rotor and stator phase resistance ˆ_R,ˆ_S

R R [] estimated rotor and stator phase resistance

R, S

R R  _[] absolute rotor and stator phase resistance error

xii

T

e [N] electrical torque

T

sw [s] switching period of frequency converter

T

M [-] time constant of frequency converter

T

L [N] load torque

S R

T

T ,

[s] rotor and stator time constant

U

d [V] DC link voltage

V [-] Lyapunov function

A [-] state matrix

A [-] A k ΑG C

Aˆ [-] estimated state matrix

B [-] input matrix

C [-] output matrix

I [-] unit matrix

G [-] gain matrix of sliding mode observer

P [-] positive matrix

Q [-] positive matrix

S [-] sliding surface vector

xiii

List of images and charts

Figure 2-1. Stator current phase vector ... 8

Figure 2-2. Complex coordinate systems. ... 9

Figure 2-3. Vector diagram of the induction motor – principle of the vector control ... 11

Figure 2-4. Structure of the current model ... 14

Figure 2-5. The control structure of the induction motor ... 16

Figure 2-6. A block diagram of the frequency converter with DC link voltage ... 16

Figure 2-7. Sensorless control structure of induction motor ... 19

Figure 3-1. Control structure of induction motor drive with SMO ... 32

Figure 3-2. Control structure with SMO and resistance estimation ... 35

Figure 3-3. Simulation result: The reference speed ... 38

Figure 3-4. Simulation result: The load torque ... 38

Figure 3-5. Simulation result: Speed control Stator current vector components i_S and i_S ... 39

Figure 3-6. Simulation result: Speed control Stator current vector components i_Sx and i_Sy ... 39

Figure 3-7. Simulation result: Speed control Rotor flux vector components



_R and



_R ... 40

Figure 3-8. Simulation result: Speed control Torque ... 40

Figure 3-9. Simulation result: Speed control Speed ... 41

Figure 3-10. Simulation result: Speed control with measurement noise Speed ... 42

Figure 3-11. Simulation result: Sensorless control with nominal values Stator current vector components iS_ and i_S ... 42

Figure 3-12. Simulation result: Sensorless control with nominal values Estimated stator current vector components ... 43

xiv

Figure 3-13. Simulation result: Sensorless control with nominal values Absolute stator current errors

... 43

Figure 3-14. Simulation result: Sensorless control with nominal values Rotor flux vector components R



and



_R ... 43

Figure 3-15. Simulation result: Sensorless control with nominal values Estimated rotor flux vector components ... 44

Figure 3-16. Simulation result: Sensorless control with nominal values Absolute rotor flux errors ... 44

Figure 3-17. Simulation result: Sensorless control with nominal values Torque ... 44

Figure 3-18. Simulation result: Sensorless control with nominal values Estimated speed ... 45

Figure 3-19. Simulation result: Sensorless control with nominal values Speed ... 45

Figure 3-20. Simulation result: Sensorless control with nominal values Absolute speed error ... 45

Figure 3-21. Simulation result: Sensorless control with increased stator resistance of 30% Speed ... 47

Figure 3-22. Simulation result: Sensorless control with increased stator resistance of 30% Estimated speed ... 47

Figure 3-23. Simulation result: Sensorless control with increased stator resistance of 30% Absolute speed error ... 47

Figure 3-24. Simulation result: Sensorless control with decreased stator resistance of 30% Speed ... 48

Figure 3-25. Simulation result: Sensorless control with decreased stator resistance of 30% Estimated speed ... 48

Figure 3-26. Simulation result: Sensorless control with decreased stator resistance of 30% Absolute speed error ... 48

Figure 3-27. Simulation result: Sensorless control with increased rotor resistance of 30% Speed ... 49

Figure 3-28. Simulation result: Sensorless control with increased rotor resistance of 30% Estimated speed ... 49

Figure 3-29. Simulation result: Sensorless control with increased rotor resistance of 30% Absolute speed error ... 50

Figure 3-30. Simulation result: Sensorless control with decreased rotor resistance of 30% Speed ... 50

xv

Figure 3-31. Simulation result: Sensorless control with decreased rotor resistance of 30% Estimated speed ... 50 Figure 3-32. Simulation result: Sensorless control with decreased rotor resistance of 30% Absolute speed error ... 51 Figure 3-33. Simulation result: Sensorless control with increased stator and rotor resistance of 30%

Speed ... 51 Figure 3-34. Simulation result: Sensorless control with increased stator and rotor resistance of 30%

Estimated speed ... 51 Figure 3-35. Simulation result: Sensorless control with decreased stator and rotor resistance of 30%

Speed ... 52 Figure 3-36. Simulation result: Sensorless control with decreased stator and rotor resistance of 30%

Estimated speed ... 52 Figure 3-37. Simulation result: Robust sensorless control with decreased resistances of 50% Stator current vector components i_S and i_S ... 53 Figure 3-38. Simulation result: Robust sensorless control with decreased resistances of 50% Estimated stator current vector components ... 53 Figure 3-39. Simulation result: Robust sensorless control with decreased resistances of 50% Absolute stator current errors ... 53 Figure 3-40. Simulation result: Robust sensorless control with decreased resistances of 50% Rotor flux vector components ... 54 Figure 3-41. Simulation result: Robust sensorless control with decreased resistances of 50% Estimated rotor flux vector components ... 54 Figure 3-42. Simulation result: Robust sensorless control with decreased resistances of 50% Absolute rotor flux errors ... 54 Figure 3-43. Simulation result: Robust sensorless control with decreased resistances of 50% Torque 55 Figure 3-44. Simulation result: Robust sensorless control with decreased resistances of 50% Speed . 55 Figure 3-45. Simulation result: Robust sensorless control with decreased resistances of 50% Estimated speed ... 55

xvi

Figure 3-46. Simulation result: Robust sensorless control with decreased resistances of 50% Absolute speed error ... 56 Figure 3-47. Simulation result: Robust sensorless control with decreased resistances of 50% Stator resistance ... 56 Figure 3-48. Simulation result: Robust sensorless control with decreased resistances of 50% Rotor resistance ... 56 Figure 3-49. Simulation result: Robust sensorless control with increased resistances of 50% Stator current vector components i_S and i_S ... 57 Figure 3-50. Simulation result: Robust sensorless control with increased resistances of 50% Estimated stator current vector components ... 57 Figure 3-51. Simulation result: Robust sensorless control with increased resistances of 50% Absolute stator current errors ... 58 Figure 3-52. Simulation result: Robust sensorless control with increased resistances of 50% Rotor flux vector components ... 58 Figure 3-53. Simulation result: Robust sensorless control with increased resistances of 50% Estimated rotor flux vector components ... 58 Figure 3-54. Simulation result: Robust sensorless control with increased resistances of 50% Absolute rotor flux errors ... 59 Figure 3-55. Simulation result: Robust sensorless control with increased resistances of 50% Speed .. 59 Figure 3-56. Simulation result: Robust sensorless control with increased resistances of 50% Estimated speed ... 59 Figure 3-57. Simulation result: Robust sensorless control with increased resistances of 50% Absolute speed error ... 60 Figure 3-58. Simulation result: Robust sensorless control with increased resistances of 50% Stator resistance ... 60 Figure 3-59. Simulation result: Robust sensorless control with increased resistances of 50% Rotor resistance ... 60 Figure 4-1. Sliding mode control structure ... 68

xvii

Figure 4-2. Simulation result: Sliding mode control with sign function Stator current vector components

iS_ and i_S ... 69

Figure 4-3. Simulation result: Sliding mode control with sign function Stator current vector components iSx and i_Sy ... 69

Figure 4-4. Simulation result: Sliding mode control with sign function Rotor flux vector components R



and



_R ... 70

Figure 4-5. Simulation result: Sliding mode control with sign function Torque ... 70

Figure 4-6. Simulation result: Sliding mode control with sign function Speed ... 70

Figure 4-7. Simulation result: Sliding mode control with saturation function Speed ... 71

Figure 4-8. Simulation result: Sliding mode control with saturation function Stator current vector components i_S and i_S ... 71

Figure 4-9. Simulation result: Sliding mode control with saturation function Stator current vector components i_Sx and i_Sy ... 72

Figure 4-10. Simulation result: Sliding mode control with saturation function Rotor flux vector components



_R and



_R ... 72

Figure 4-11. Simulation result: Sliding mode control with saturation function Torque ... 72

Figure 4-12. Simulation result: Sliding mode control with saturation function Speed ... 73

Figure 4-13. Simulation result: Sensorless sliding mode control Stator current vector components i_S and i_S ... 74

Figure 4-14. Simulation result: Sensorless sliding mode control Estimated stator current vector components ... 74

Figure 4-15. Simulation result: Sensorless sliding mode control Absolute stator current errors ... 74

Figure 4-16. Simulation result: Sensorless sliding mode control Stator current vector components i_Sx and i_Sy ... 75

xviii

Figure 4-17. Simulation result: Sensorless sliding mode control Rotor flux vector components



_R and

R



... 75

Figure 4-18. Simulation result: Sensorless sliding mode control Estimated rotor flux vector components ... 75

Figure 4-19. Simulation result: Sensorless sliding mode control Absolute rotor flux vector errors ... 76

Figure 4-20. Simulation result: Sensorless sliding mode control Torque... 76

Figure 4-21. Simulation result: Sensorless sliding mode control Estimated speed ... 76

Figure 4-22. Simulation result: Sensorless sliding mode control Speed ... 77

Figure 4-23. Simulation result: Sensorless sliding mode control Absolute speed error ... 77

Figure 5-1. Experimental structure ... 79

Figure 5-2. Induction motor 1LA7106-4AA10 ... 80

Figure 5-3. Indirect Frequency Inverter ... 80

Figure 5-4. Control system with eZdsp^TMF28335 ... 80

Figure 5-5. Laboratory stand of induction motor ... 81

Figure 5-6. Flowchart of main program (a) main program (b) initialization program ... 82

Figure 5-7. Flowchart of ADC interrupt subroutine ... 83

Figure 5-8. Experimental result: Reference speed ... 84

Figure 5-9. Experimental result: Speed control Stator current vector components i_S and i_S ... 85

Figure 5-10. Experimental result: Speed control Stator current vector components i_Sx and i_Sy ... 85

Figure 5-11. Experimental result: Speed control Magnetizing current component

i

_Sx ... 86

Figure 5-12. Experimental result: Speed control Torque current component

i

_Sy ... 86

xix

Figure 5-13. Experimental result: Speed control Reference stator voltage vector components u_Sx and

uSy ... 87

Figure 5-14. Experimental result: Speed control Reference stator voltage vector components u_S and uS_... 87

Figure 5-15. Experimental result: Speed control Rotor flux vector components _R and _R ... 88

Figure 5-16. Experimental result: Speed control Torque ... 88

Figure 5-17. Experimental result: Speed control Speed ... 89

Figure 5-18. A LabVolt’s electrodynamometer ... 90

Figure 5-19. Experimental result: The load torque ... 90

Figure 5-20. Experimental result: Reference speed for load torque testing ... 90

Figure 5-21. Experimental result: Speed control with load Stator current vector components i_S and iS_ ... 91

Figure 5-22. Experimental result: Speed control with load Stator current vector components i_Sx and i_Sy ... 91

Figure 5-23. Experimental result: Speed control with load Rotor flux vector components _R and _R ... 92

Figure 5-24. Experimental result: Speed control with load Torque ... 92

Figure 5-25. Experimental result: Speed control with load Speed ... 92

Figure 5-26. Experimental result: Reference speed ... 93

Figure 5-27. Experimental result: Sensorless control Stator current vector components i_S and i_S . 94 Figure 5-28. Experimental result: Sensorless control Estimated stator current vector components .... 94

Figure 5-29. Experimental result: Sensorless control Absolute stator current errors ... 94

xx

Figure 5-30. Experimental result: Sensorless control Stator current vector component i_S ... 95 Figure 5-31. Experimental result: Sensorless control Stator current vector component i_S ... 95 Figure 5-32. Experimental result: Sensorless control Stator current vector components i_Sx and i_Sy ... 96

Figure 5-33. Experimental result: Sensorless control Rotor flux vector components _Rand _R .... 96 Figure 5-34. Experimental result: Sensorless control Estimated rotor flux vector components ... 97 Figure 5-35. Experimental result: Sensorless control Absolute rotor flux errors ... 97 Figure 5-36. Experimental result: Sensorless control Torque ... 97 Figure 5-37. Experimental result: Sensorless control Speed ... 98 Figure 5-38. Experimental result: Sensorless control with load Stator current vector components i_S and iS_ ... 99 Figure 5-39. Experimental result: Sensorless control with load Estimated stator current vector components ... 99 Figure 5-40. Experimental result: Sensorless control with load Absolute stator current errors ... 99 Figure 5-41. Experimental result: Sensorless control with load Stator current vector components i_Sx and iSy ... 100 Figure 5-42. Experimental result: Sensorless control with load Rotor flux vector components



_Rand

R

 ... 100 Figure 5-43. Experimental result: Sensorless control with load Estimated rotor flux vector components ... 101 Figure 5-44. Experimental result: Sensorless control with load Absolute rotor flux error... 101 Figure 5-45. Experimental result: Sensorless control with load Torque ... 102 Figure 5-46. Experimental result: Sensorless control with load Speed ... 102

xxi

Figure 5-47. Experimental result: Sliding mode control Stator current vector components i_Sand i_S ... 103 Figure 5-48. Experimental result: Sliding mode control Stator current vector components i_Sxand i_Sy ... 103 Figure 5-49. Experimental result: Sliding mode control Rotor flux vector components



_Rand _R ... 104 Figure 5-50. Experimental result: Sliding mode control Torque ... 104 Figure 5-51. Experimental result: Sliding mode control Speed ... 104 Figure 5-52. Experimental result: Sliding mode control with load Stator current vector components i_S and i_S ... 105 Figure 5-53. Experimental result: Sliding mode control with load Stator current vector components i_Sx and i_Sy ... 105

Figure 5-54. Experimental result: Sliding mode control with load Rotor flux vector components



_R

and _R ... 106 Figure 5-55. Experimental result: Sliding mode control with load Torque ... 106 Figure 5-56. Experimental result: Sliding mode control with load Speed ... 106 Figure 5-57. Experimental result: Sensorless sliding mode control Stator current vector components i_S and i_S ... 107 Figure 5-58. Experimental result: Sensorless sliding mode control Estimated stator current vector components ... 107 Figure 5-59. Experimental result: Sensorless sliding mode control Absolute stator current errors .... 108 Figure 5-60. Experimental result: Sensorless sliding mode control Stator current vector components i_Sx and i_Sy ... 108

xxii

Figure 5-61. Experimental result: Sensorless sliding mode control Rotor flux vector components



_R

and _R ... 109 Figure 5-62. Experimental result: Sensorless sliding mode control Estimated rotor flux vector components ... 109 Figure 5-63. Experimental result: Sensorless sliding mode control Absolute rotor flux errors ... 109 Figure 5-64. Experimental result: Sensorless sliding mode control Torque ... 110 Figure 5-65. Experimental result: Sensorless sliding mode control Speed ... 110 Figure 5-66. Experimental result: Sensorless sliding mode control with load Stator current vector components i_Sand i_S ... 111 Figure 5-67. Experimental result: Sensorless sliding mode control Estimated stator current vector components ... 111 Figure 5-68. Experimental result: Sensorless sliding mode control Absolute stator current errors .... 111 Figure 5-69. Experimental result: Sensorless sliding mode control Stator current vector components i_Sx and i_Sy ... 112

Figure 5-70. Experimental result: Sensorless sliding mode control Rotor flux vector components



_R

and _R ... 112 Figure 5-71. Experimental result: Sensorless sliding mode control Estimated rotor flux vector components ... 112 Figure 5-72. Experimental result: Sensorless sliding mode control Absolute rotor flux errors ... 113 Figure 5-73. Experimental result: Sensorless sliding mode control Torque ... 113 Figure 5-74. Experimental result: Sensorless sliding mode control Speed ... 113

xxiii

List of tables

Table 3-1. Induction Motor Parameters ... 36 Table 5-1. Parameter of induction motor 1LA7106-4AA10 ... 79 Table 5-2. Actual parameter of induction motor 1LA7106-4AA10... 83

1

1. Introduction

Induction motors, which were firstly invented by Nikola Tesla in 1885, are a type of AC electrical drives. Induction motors can be made without any electrical connections to the rotor. They do not have brushes, slip rings and as a result, they are robust and sturdy and require low maintenance.

Because of their advantages, induction motors are widely used in industry such as pumps and fans, paper and textile mills, locomotive propulsion, electric vehicles, machine tools, heat pumps, rolling mills, wind generation systems, etc. [1] – [33], [73], [85]

However, induction motors have some disadvantages such as complex relationships between frequency and stator voltages, complex dynamics of AC machines, machine parameter variation, and a complex signal processing of feedback signals. As a result, controlling of induction motor drives is very complicated. Some of unexpected occasions in controlling induction motor drives can be listed as long response time, large settling speed error, or unstable operation, etc. Especially in a low speed range or in case of having external noise, these phenomenon are worse. Moreover, the response time of power electronic switching devices and their limited overload capacity eliminate usage of control methods in practice. In recent years, along with development of semiconductor technologies, signal processing, and digital microprocessors, researches for adjustable speed AC motor drives have been developed.

Advanced induction motor control methods, which give fast response, low settling error and no overshoot in a wide speed range, are still the challenge tasks. [1] – [33]

So in this chapter, some researches about controlling induction motor drives are reviewed. Then, the goals of this thesis are listed and the organization of the thesis is proposed.

1.1 Review of Previous Studies

1.1.1 Vector Control of Induction Motor Drives

In many decades, control methods have developed for induction machines such as scalar control [1], [18], field - oriented control (FOC) [2] – [6], [8] – [11], [14], [15], [19] – [25], [28] – [30], [34] – [39], [74], [78], [79], [81], [86] – [88], [92] and direct torque and flux control (DTC) [7], [12], [40] – [43], [75], [84], [91]. The first one, scalar control, is due to the magnitude variation of the control variables only and disregards the coupling effect [18]. Thus, scalar control is easy to implement but it has inferior performance, especially in low speed applications, and now it is almost diminished in real world [1], [18].

The second method, the field - oriented control (FOC) or the vector control, was originated in Germany at the end of 1960s [18]. In FOC, the stator or rotor currents are presented by vectors [2] – [6], [8] –[11], [14], [15], [19] – [25], [28] – [30], [34] – [39], [74], [78], [79], [81], [86] – [88], [92]. This control is based on projections which transform a three – phase time and speed dependent system into a two co-ordinate time invariant system. This projections lead to a structure similar to that of a DC machine. Because of advantages of FOC, FOC is applicable to both induction and synchronous motors.

FOC could be classified into two types as rotor field – oriented control (RFO) [1], [2] and stator field – oriented control (SFO) [1], [2], [9]. In rotor field – oriented control, the reference frame rotates with the rotor flux, while in stator field – oriented control, the reference frame rotates with the stator flux. The

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rotor field - oriented control of induction motor can also be classified as direct field - oriented control (DFO) [1], [2] and indirect field - oriented control (IFO) [1], [2]. In direct field - oriented control, estimation of rotor flux vector can be based on direct measurement of air gap flux and stator current.

However, the flux sensor is very expensive, and needs special installation and maintenance. In practice, the rotor flux is usually computed from the stator voltage and current [1], [2]. However, this method is difficult to operate at very low speed and depends on parameters such as stator and/or rotor resistances and inductances. The studies of parameter sensitivity show that the parameters can significant effect system performance such as stability, dynamic response, especially in low speed range [1], [2], [20], [23], [26], [38], [44]. Indirect field - oriented control is based on the slip relation. This control method is very sensitive to the rotor time constant T_R [1], [2], [10], [21], [45], [46]. Once the rotor time constant is not set correctly, the motor is detuned and the controller performance will become sluggish [1], [2], [10], [46]. The continuous on-line tuning of rotor time constant T_R is very complex. The extended Kalman filter (EKF), model reference adaptive system (MRAS) can be used to identify the rotor time constant [1], [60]. The stator flux orientation (SFO) has advantage that flux vector estimation accuracy is affected by the stator resistance variation only [1].

Clearly, vector control, compared to scalar control, is more complex, so the use of powerful microcomputers are required. Following the rapid development of control and semiconductor technologies, such as microcontrollers or DSP, control principles of AC drives have been developed.

Today, the vector control has been used widely in industry for high performance, especially in low speed applications. [38]

The last method or the DTC, known as an advanced scalar control method, is introduced firstly in the mid - 1980s [1], [7], [12], [40] – [43], in which an inverter voltage space vector through the look - up table. This technique was claimed to have nearly comparable performance with vector controlled drives and recently, the scheme was introduced in commercial products and created wide interest [1].

The DTC performs very well without speed sensors. However, the disadvantage of DTC is unstable at low speed because the error in the voltage measurement and stator resistance in integral become erroneous at low speed. Several modifications such as space vector modulate DTC, high accuracy of the torque and speed control can be maintained in the whole speed range [7], [12], [40] – [43], [75], [84], [91].

1.1.2 Sensorless Vector Control of Induction Motor Drives

In controlling induction machine drives, stator voltages, stator currents, rotor fluxes, as well as mechanical speed are required. However, sensors, including flux sensors and speed sensor, increase the complexity and high cost of hardware and decrease reliability of the system. In practice, rotor flux vector is estimated from stator current vector and voltage vectors by a current model or a voltage model.

Moreover, the rotor speed is estimated by an observer, called sensorless control of induction motor drives. [2], [3], [5] – [7], [9], [13], [17], [19] – [21], [23], [24], [26], [27], [35], [37] – [39], [42] – [48], [74], [75], [78] – [80], [83], [86], [89]

The main techniques which are used for the rotor speed estimation are signal injection [51], observers and soft computing methods [62]. There are many kinds of observers applied for nonlinear systems, such as the model reference adaptive system (MRAS) [27], [29], [36], [61], [63], [64], [75],

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[84], [89], Kalman filter (KF) or extended Kalman filter (EKF) [2], [36], [39], [65], Luenberger observer (LO) [66] – [68], sliding mode observer (SMO) [2], [5] – [8], [13], [17], [19] – [21], [23], [25] – [27], [32], [35], [36], [38], [42] – [47], [74], [86]. The soft computing methods are artificial neural network, fuzzy network, which are very complicated to apply in real world. However, with rapid development of micro – processing, soft computing methods such as fuzzy logic [9], [22], [33], [36], neural network [28], [30], [45], [50], genetic algorithm [11], [14], [31], are interested research field in future.

These observers require knowledge of an induction motor’s parameters and variations in these parameters lead to incorrect estimation and degrade motor performance [68], especially in low speed range [63], [69], [83]. In an induction motor, parameters change with temperature, frequency and saturation such as magnetizing inductance, stator resistance, rotor resistance, stator/rotor leakage inductance or transient stator inductance [62]. Thus, it is necessary to update parameter values during motor operation. Parameter variations have been studied in the pass and extensive discussions in many research, which can be listed as offline parameter identification methods and online parameter estimation methods. In offline identification techniques, parameters are identified by using complicated mathematical processing of the measurement results, machine’s magnetizing cure or series of no-load tests. The accuracy of parameters, which are determined in offline methods, depends on the sample rate selection, quantization errors, resolution and accuracy of sensors [62]. In contrast, together with development of micro-processing, online identification techniques have proposed such as adaptive stator resistance estimation in [6], [62], [63], [69], [82], rotor resistance estimation [62]. The error of stator and rotor resistance is 25% detuning [6], even up to 50% of their nominal values [64].

In MRAS, some state variables, which are from a reference model, are compared with the state variables, which are estimated by using an adaptive model. The difference between these state variables is then used in an adaptation mechanism, and the output adjusts the adaptive model until satisfactory performance is obtained [49]. Disadvantages of MRAS are sensitive to the noise and parameter variations. To improve the performance of the observer, some schemes, which are robust to stator and rotor resistances variation, are introduced. Some modifications of traditional MRAS are proposed such as MRAS^CC, which is based on the error between estimated and measured stator current and rotor flux [64], [65]. Another modification of MRAS is also proposed in [29]. Continuous adaptation methods of stator resistance with MRAS are presented in some research [63]. An artificial intelligence based MRAS method seems to offer satisfactory performance even at very low speed range [27] – [30], [36], [45], [75], [78], [83], [89].

Kalman filter was published between 1959 and 1961. The Kalman filter is an optimal estimation for linear system models with additive independent white noise in both the transition and the measurement systems. Unfortunately, most systems in practice are nonlinear. The EKF, which are extended from Kalman filter, is employed for nonlinear system or systems which are not well known or do not have inaccurate models. However, if the initial estimation of the state is wrong or the process is modeled incorrectly, the filter may quickly diverge. In some modification, the performance of EKF is improved by using H-infinity from robust control, or Riccati equation. [2], [36], [39]

In recent years, sliding mode observer (SMO) is more and more popular [2], [5] – [8], [13], [17], [19] – [21], [23], [25] – [27], [32], [35], [36], [38], [42] – [47], [74], [86]. Sliding mode technique was originally in 1970s by Utkin. However, the application of sliding mode methods appeared in the mid 1980s. Slotine et al. (1986) defined an observer strategy in which the output errors were fed back in both

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a linear and a discontinuous manner for nonlinear systems. In some contributions, the role of the magnitude of the discontinuous element is discussed, in which the discontinuous element may enhance robustness but also increase the sensitivity to the measurement noise. Recent development consider the extension of first order sliding mode observer, which is known as traditional sliding mode observer, to higher order sliding mode method [12], [25], [28], [35], [42], [49]. Another area of interest is the development of the robustness of a sliding mode observer, such as rotor and stator resistances estimation, rotor time constants estimation [40], [42], [43], [49], [50], [51], disturbance observer [36], [46], or combination between the methods [50].

Another disadvantage of sliding mode is the chattering. There are many different ways to reduce the chattering phenomenon such as low pass filter [5], gain adaptation, HF injection [42]. Saturation and sigmoid function are used to reduce the chattering [5]. There is no difference in operation of these two functions however the choice of the slope parameter becomes an interesting issue. Another method is gain adaptation for sliding mode observer. If the gain is set too high, the system becomes unstable. In contrast, oscillation level can be increased if the gain is small. By using gain adaptation, gain is adjusted on the parameter variations and external noise so the chattering is eliminate [5]. A sliding observer, which is combined with HF injection, is proposed in [42].

Generally, EKF, LO and SMO observers give high accuracy in a wide speed range, especially in high speed range, about 0.2 % at speed of 1500 rpm. However, the convergence rate of EKF is lower compared to LO and SMO. Moreover, MRAS [27], [29], [36] and EKF observer [2], [36], [39] are are suitable for applications with a medium speed. In contrast, the Luenberger observer and sliding mode observer are robust to parameter variation and noise and can work well at low speed and very low speed ranges [2], [7], [8], [13], [17], [19] – [21], [23], [25] – [27], [32], [35], [36], [42], [44] – [47].

1.1.3 Variable Speed Control of Induction Motor Drives

In FOC control, classic PI controllers are normally used in control loops. However, the control performance depends on the induction motor parameters and unknown disturbances and controller parameters are chosen by “trial and error” [2], [36]. Once motor parameter and speed reference change, the performance is not good [20], [21], [23], [25] – [27], [32], [44] – [46], [77]. As a result, PI controllers cannot satisfy the requirements for different speed commands. To improve the control performance, many advanced control methods have been developed, such as back – stepping control, neural network [30], [45], [50], [51], fuzzy logic control [9], [22], [33], [36], sliding mode control [2] – [4], [8], [9], [14], [15], [22], [25], [26], [28], [30], [31], [33] – [35], [38], [39], [45], [50], [52] – [59], [79], [88].

Sliding mode control was introduced in 1977 by Utkin, which overcomes some disadvantages of PI controllers. In the years after, the sliding mode research community expanded rapidly and the number of publications grew corresponding because of its robustness to the noise and parameter variations and easy to design [2] – [4], [14] – [16], [34], [38], [44], [47], [52] – [55], [57] – [60], [79], [88]. To ensure the robustness of the sliding mode control, high gain is required. However, high gain is the main reason of a chattering phenomenon. This is unwanted phenomenon which causes low accuracy and high heat loss [2] – [4], [8], [9], [14], [15], [22], [25], [26], [28], [30], [31], [33] – [35], [38], [39], [45], [50], [52] – [59]. Many studies have been developed to reduce this phenomenon, which include sliding surface such as super – twisting [57], second order structure [16], [20], [26], [55], [56], [59],

5

integral sliding mode observer [8], [70], [79]. In the similar way, the sign function or tagmoid or hyperpol sigznal is chosen instead of sign function. One of controller parameters is the gain of the sliding mode controller. This gain must be chosen to overcome the noise and the paramter variations. If this gain adaptive sliding mode control is too large, the chattering problem becomes serious. In contrast, the algorithm cannot be converged and the system could be become instability. So chosing appropriate gain is very important. Some research focused on choosing the gain according to noise and parameters [13], [17], [22], [25], [38], [44].

Moreover, the sliding mode controller can be combined with other intelligent control methods, for example fuzzy logic [9], [22], [33], [36], [80], [91], neural network [28], [30], [45], [50], genetic algorithm [11], [14], [31], [76], [81], [92] adaptive control [14], [15], [25], [35], [38], [39], [56], [57], [59], [79], [90] that can give more robust and better transient response controllers. However, these methods have disadvantages such as torque ripple, acoustic noise, and require amount of computation time and microcomputer memory etc. In contrast, in methods based on the mathematical model, the minimum operating speed is restricted. So, some of the hybrid control methods combining the mathematical model and signal injection are developed.

From above reviews, the sliding mode control and sliding mode observer prove an advantage over the other control methods and observer, especially in parameter variation and external noises. So, in this thesis, a sliding mode control with sliding mode observer for an induction motor is investigated in a wide range of speed, espcially in low speed range. Moreover, to overcome the disadvantages of sliding mode theory, an integral sliding mode control with saturarion function is proposed. In addition, an online estimation for stator and rotor resistances at the same time is developed to increase the robust of the proposed sliding mode control and observer.

1.2 Objectives and Scope of this Study

The primary goal of this study is to develop a robust controller for induction motors in a wide range of speed, which involves a sliding mode controller and a robust sliding mode observer. The control algorithms are tested on the laboratory stand with an induction motor drive. To achieve the work objectives, the following specific tasks are determined:

- Theoretical analysis of the sliding mode control.

- Choice of suitable methods for the speed estimation and speed control of the AC drive with induction motor. In this thesis, the sliding mode observer is chosen to estimate speed of the induction motor. The stator and rotor resistances are also estimated. This makes the system more robust, insensitivity with parameter variations. In this thesis, suppose that the variations of parameter is changed up to 50% of their nominal values. The sliding mode control is also chosen, too because of its simplicity and robustness. The speed control has to get good performance characteristics, such as the settling time is smaller than 1 s, the absolute settling error is smaller than 5 rpm in a wide range of speed.

- Creation of simulation models and the simulation of the control structures in the MATLAB/Simulink software environment.

- Choice of the proper control microcomputer system with a digital signal processor. Among a various types of digital signal processor, family of TMS320F28335 are chosen because of

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their highly integrated and high performance solutions such as real math calculation support, as well as high speed counter, PWM and high interrupt response and processing.

- Development and realization of a sliding mode control algorithm. The robustness of the proposed algorithm is proved by using the Lyapunov’s stability criterion.

- Design of a laboratory stand with the induction motor drive for the experimental verification of the chosen control algorithms. The laboratory stand includes an induction motor of Siemens, an indirect frequency converter with DC link voltage. The induction motor operates at the desired speed under the external load torque. Experimental measurements and evaluation of laboratory model properties are compared with theoretical assumptions.

1.3 Organization of this Dissertation

This dissertation is organized into six chapters. The first one reviews the existing works of an induction motor control and efficiency improvements. From that, objectives of the dissertation and scopes of this study are pointed out. The final section of this chapter is the organization of this thesis.

In the second chapter, all needed literatures are reviewed. The basic of the thesis depends on the vector control. Because the vector control is based on space vectors of stator currents and voltages so firstly, the coordinate transformation equations are introduced. After that, the vector control equations, an induction motor mathematical model, as well as the structure of vector control are developed.

Moreover, backgrounds of the sliding mode control and the sliding mode observer are also presented.

All these theories are necessary to develop control algorithms in next chapters. Finally, the structure of sensorless control of induction motor is also developed and explained.

In this thesis, one of the most important parts is design of a sliding mode observer. So, the third chapter develops a sliding mode speed observer in controlling induction motor drives. Firstly, the sliding mode observer is developed in detail. The structure of sliding mode observer, choosing the parameters are presented step by step. The stability of proposed algorithms is proved by using Lyapunov’s criterion.

From that, the rotor speed is estimated online. Because the observer is very sensitivity to the noise and parameter variation, rotor and stator resistances are also estimated to increase robustness of the observer in the next section of this chapter. Finally, the simulation model in MATLAB – Simulink environment is created to prove the operation of the sliding mode observer. At first, PI control of induction motor using an encoder is tested under the nominal condition, with and without load. The effect of external noises, including load torque and measurement noise, is also tested. Next, PI control using sliding mode observer is derived. The robustness of sliding mode observer is checked by changing rotor and stator resistances. The last part of simulation is PI control using sliding mode observer in case of having stator and rotor resistance estimation. The simulation results are compared together to prove the exactness of the theoretical assumption.

After developing a sliding mode observer, the next important work is to develop a sliding mode control of an induction motor. Similar to the third chapter, in chapter 4, firstly, an integral sliding mode controller is developed. The reference torque current component and the reference flux current component are derived step by step. Choosing parameter for controllers is also presented. After that, simulations are also done. In this part, sliding mode control is tested with encoder and with sliding mode

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observer. The results are used to compare with the ones of conventional PI controllers and ones of conventional sliding mode controllers.

The fifth chapter shows experimental results. A laboratory of an induction motor is created to verify the performance of proposed algorithms. In this laboratory, an induction motor of Siemens is used together with an indirect frequency converter with DC link voltage, which is designed at the Department of Electronics, VSB – Technical University of Ostrava. All algorithms are developed by using a digital signal processing eZdsp^TMF28335. This DSP is strong enough to develop and run the proposed algorithms. Experimental results are compared to the simulation results to check the realizable of control algorithms. In this section, experiments are just focus on PI control and sliding mode control using an encoder and a sliding mode observer, with and without load. Firstly, the PI control with no load is done using an encoder. The same situation as in 1^st section is repeated with load. The results of PI control using a sliding mode observer with and without load are presented in the 3^rd and the 4^th section in this chapter, respectively. Next four sections are similar to the four previous section, in which PI controllers are replaced by sliding mode controllers in the speed control loop and the flux control loop.

Finally, all conclusions and suggested future works are discussed in the sixth chapter. The advantages and disadvantages of algorithms are pointed out in this chapter. All theory assumptions, which are presented in the previous chapter and are not tested in experiments, will be focused in next plan

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2. Background and Literature review

2.1 Field - Oriented Control of Induction Motor Drives

A field - oriented control (FOC) or a vector control is a very popular method for controlling induction motors in practice because of a better dynamic behavior, a full motor torque capability at low speed, and a decoupled control of torque and flux. Vector control of electrical drives is based on the control of both magnitude and phase of each phase current and voltage, represented by machine current and voltage space vectors. [2] – [6], [8] – [11], [14], [15], [19] – [25], [28] – [30], [34] – [39], [74], [78], [79], [81], [86] – [88], [92]

Definitions of space vector and coordinate transformations are introduced in the first subsection.

Additionally, vector control and a structure of vector control of induction motors are presented in the subsection 2.1.2.

2.1.1 Coordinate Transformation

In practice, there is very common to use a space vector to describe a model of three-phase electrical drives, which the three – phase system is analyzed at the same time instead of looking at each phase separately. Moreover, a simplified mathematical description of an AC motor, including an induction motor, may be achieved by defining a complex space vector. [1], [2]

Figure 2-1. Stator current phase vector

AC motors, including induction motors, with 3 phase stator and rotor windings are fed by three phase stator currents i i_{Sa Sb}, and i_Sc, which are measured by current sensors. In the vector control, these 3 phase stator currents are represented by a rotating vector i^S_S in the stator coordinate system [,] [1], [2]



²



2 3

S

S   iSa iSb a iSca iS_  jiS_

i (2.1)

Similarly, the rotor current space vector i^S_Rin stator coordinate system [,] is given in Equation (2.2) [1], [2]

9



²



2 3

S

R   iRa iRb a iRca iR_  j iR_

i (2.2)

where i_S and i_S are stator current vector components, i_R and i_R are rotor current vector components in the stator coordinate system [,]; ae^{j2 /3} , i i i_Sa, ,_{Sb Sc} are instantaneous values of the stator three-phase currents, and i_Ra,i_Rb,i_Rcare respectively instantaneous values of the rotor current of individual phases and the currents in three phases for winding without a connected node, which must satisfy condition following [1], [2]

Sa Sb Sc 0

i i i  (2.3)

Ra Rb Rc 0

i i i  (2.4)

Thus, the transformation from the three-phase system



^{a b c, ,}



to the stator coordinate system ]

,

[  (known as Clark transformation) is defined as follow [1], [2]

1 0

1 2

3 3

S Sa

S Sb

i i

i i





 

   

     

   

(2.5)

The reverse transformation is expressed in Equation (2.6) [1], [2]

1 0

1 3

2 2

Sa S Sb S

i i i i





 

 

    

   

     

(2.6)

Moreover, to describe the mathematical model of the induction motor with three phase stator and rotor windings, three coordinate systems are used, including the stator coordinate system [,], the rotor coordinate system [d,q] rotating at the electric angular rotor speed _R, and the oriented coordinate system [x,y] rotating at the stator angular speed _S (Figure 2-2) [1], [2]

Figure 2-2. Complex coordinate systems.