MODELING AND CONTROLLER DESIGN OF

PERMANENT MAGNET SYNCHRONIZING MOTOR (PMSM)

NORAN ZAHRINE ZAINAL

A project report submitted in partial fulfillment of the

requirements for the award of the degree of

Master of Engineering

(Electrical- Mechatronic and Automatic Control)

Faculty of Electrical Engineering

UniversitiTeknologiMalaysia

JUNE 2013

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Especially for:

My parent who offered me unconditional love, understanding and support throughout

my life

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ACKNOWLEDGEMENTS

In the name of Allah, first of all I would like to express gratitude to Allah for His

grace, gave me the pleasure of space, time and opportunity to complete the report of this

thesis.

I also would like to take this opportunity to thank all especially to my supervisor,

PROF. DR. MOHD FUA’AD RAHMAT as much help, encouragement, guidance,

advices and motivation.

Thank you also to my parents for their advice and support until I’ve reached up

to this level. To my wife and also my children,I’m very sorry for the hardest time and

thank you very much for giving me time and encouragement up to this point until this

thesis completed.

Also not to forget to my friends who often share their knowledge and opinion to

me to complete this thesis.

Thank you again.

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ABSTRACT

This dissertation describes design and simulation of permanent magnet

synchronizing motor (PMSM) using Proportional Integral (PI) controller & Fuzzy Logic

controller. The implementation of the speed control in the aircraft actuators system

required an accurate, stable and precise output response. A correct derivation of

mathematical model of permanent magnet synchronous motor (PMSM) vector

controlled is very important and as fundamental of all analysis. In order to design a

stable position loop, the fast and stable inner loop control need to be achieved first. Than

followed by the outer loop control position. In order to have low percent overshoot of

the response, the adjustment gain PI controller method is used. Implementing this

method, a good response with zero steady state error will be achieved. Analysis of the

output simulation response is performed to verify the quality of the design using PI &

Fuzzy Logic is present in this dissertation.

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ABSTRAK

Projek ini menerangkan rekabentuk dan simulasi magnet kekal motor segerak

(Permanent Magnet Synchronizing Motor, PMSM) menggunakan Proportional Integral

(PI) Controller & Fuzzy Logic Controller. Pelaksanaan kawalan kelajuan dalam sistem

penggerak pesawat yang tepat dan stabil diperlukan. Terbitan yang betul model

matematik magnet kekal motor segerak (PMSM) vektor kawalan adalah sangat penting

dan sebagai asas bagi semua analisis. Dalam usaha untuk reka bentuk gelung kedudukan

stabil, kawalan gelung dalaman yang cepat dan stabil perlu dicapai dahulu dan diikuti

dengan kedudukan motor. Dalam usaha untuk mempunyai peratus terlajak rendah

sambutan, keuntungan pelarasan nilai PI dan fuzzy logic controller digunakan.

Melaksanakan kaedah ini, sambutan yang baik dengan sifar ralat keadaan mantap akan

tercapai. Analisis simulasi pengeluaran dilakukan untuk mengesahkan kualiti reka

bentuk antara PI dan Fuzzy Logic Controller

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TABLE OF CONTENTS

CHAPTER TITLE PAGE

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENTS iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES ix

LIST OF FIGURES x

LIST OF SYMBOLS xii

LIST OF ABBREVIATIONS xiii

1 INTRODUCTION

1.1 Project Background 1

1.2 Objectives 3

1.3 Scope of Works 3

1.4 Methodology 4

1.5 Dissertation Overview 4

2 LITERATURE REVIEW

2.1 Literature Review of dissertation 6

2.2 Matrix Converter 10

2.2.1 Introduction 10

2.2.2 Matrix converter operation principle 12

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2.3 Electro Mechanical Actuator (EMA) 14

2.3.1 Introduction 14

2.3.2 EMA operation concept 15

3 RESEARCH METHODOLOGY

3.1 Introduction 18

3.2 Classification and advantages of PMSM 18

3.3 Structure design for the PMSM 20

3.4 Vector control theory 23

3.5 Mathematical model for PMSM 27

3.5.1 Dynamic Equation 27

3.5.2 Steady state equation 31

3.5.3 Power and Torque in terms of load angle 34

3.5.4 Maximum Torque Condition 36

3.5.5 Torque control loop 37

4 DESIGN, RESULTS AND ANALYSIS

4.1 Introduction 39

4.2 Direct Current id design 40

4.3 Quadrature Current iq design 43

4.4 Speed ωm loop design 45

4.5 Analysis on current and speed loop 46

4.6 Adjustment of the gain value for the id, iq 48

and speed loop

4.7 Fuzzy Logic Controller 51

5 CONCLUSION AND SUGGESTION

5.1 Conclusion and recommendation 56

5.2 Suggestion 57

REFERENCES 58

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LIST OF TABLES

TABLE NO. TITLE PAGE

4.1 Choice of sampling times 39

4.2 Comparison id result between theoretical and simulation 42

result

4.3 Comparison iq result between theoretical and simulation 44

result

4.4 Knowledge base for output single 51

4.5 Linguistic term 52

4.6 Comparison between Trimf & Gaussmf type in fuzzy logic 55

4.7 Comparison between PI controller & fuzzy logic 55

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LIST OF FIGURES

FIGURE NO. TITLE PAGE

2.1 Conventional current regulate torque control strategy

in the rotor reference frame 09

2.2 Basic matrix converter circuit 11

2.3 Simplified basic matrix converter circuit 13

3.2 Classification of AC motor 19

3.3 Structure of surface mounts PMSM 21

3.3(i) Configuration of rotor design in PMSM 22

3.4 Sum of the vector for three-phase to two phase 24

3.4(i) Three phase and stationary frame ( ) 25

3.4(ii) Stationary frame ( ) to field oriented frame (d-q) 26

3.5 Synchronous motor schematic and equivalent circuit 27

per phase

3.5(i) Two poles and two conductor’s synchronous motor 28

schematic

3.5(ii) Equivalent circuit per phase for quadrature axis 29

3.5(iii) Equivalent circuit per phase for quadrature axis 30

3.6 Per phase phasor diagram 32

3.7 Torque versus Load angle curve for non-salient machine 35

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3.8 Loci current id vsiq for non salient and salient machines 36

respectively

3.9 Maximum torque per current id and iq 37

3.10 Diagram of general arrangement of Torque control 38

4.1 Model for open loop transfer function of id 40

4.2 Model for close loop transfer function of id 41

4.3 Response of the direct current id loop 43

4.4 Model for close loop transfer function of iq 44

4.5 Response of the quadrature current iq loop 44

4.6 Model for close loop transfer function of speed, ωm 45

4.7 Response of the speed ωm loop. 46

4.8 Model for speed loop with PMSM (PI Controller) 47

4.9 Response of the current id, iq and ωm 48

4.10 Response of the current id, iq and ωm with the new k values. 50

4.11 Model for speed loop with PMSM (Fuzzy Logic) 52

4.12(i) Response of the current id 53

4.12(ii) Response of the current iq 53

4.12(iii) Response of the speed ωm 54

4.13(i) Response of the current id 54

4.13(ii) Response of the current iq 54

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LIST OF SYMBOLS

Lq - Quadrature inductance

Ld - Direct inductance

θ - Angle of the pendulum with respect to vertical axis

TL - External load torque

J - Motor shaft inertia

D - Damping coefficient of viscous friction

ωn - Natural frequency

- Damping ratio

Ki - Controller gain

ai - Controller zero

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LIST OF ABBREVIATIONS

PMSM - Permanent Magnet Synchronous Motor

EMA - Electro Mechanical Actuator

DC - Direct Current

FLC - Fuzzy Logic Controller

PI - Proportional Integral

AC - Alternating Current

RFO - Rotor Flux Oriented

PWM - Pulse Width Modulation

SPVM - Space Vector Modulation

EMF - Electromagnetic Force

EHA - Electro-Hydrostatic Actuator

VSI - Voltage Source Inverter

IGBT - Isolate Gate Bi-polar Transistor

SVM - Space Vector Modulation

MEA - More Electric Aircraft

CSE - Ground Support Equipment

IM - Induction Motor

PM - Permanent Magnet

CHAPTER 1

INTRODUCTION

1.1 Project Background

In this project a thorough analysis on design and simulation of a Matrix

Converter fed Permanence Magnet Synchronous Motor (PMSM) for an Electro

Mechanical Actuator (EMA) for Aircraft will be delivered. A 20kW at 4950 rpm

PMSM is used, with an aircraft power supply of three-phase, 115V line to neutral, 400

Hz supplied to the Matrix Converter. The matrix converter supplies the motor with

three-phase variable frequency and variable voltage ranging to a maximum of 150V at

300Hz. First, the model structure of PMSM is designed, followed by the overall control

system in order to control the EMA position. All the parameters for the mechanical part

of the actuator are included.

The flux vector control technique is the most popular method used in motor

control nowadays. It offers a precise control method for all types of motor. In this

project, the PMSM flux vector equations are derived and analysis for transient and

steady state condition will be presented. Vector control can simplify analysis of PMSM

by imitating the concept of the direct current (DC) motor. With the vector control

method, the efficiency and dynamic performance can be maximized. In addition, the

vector control for PMSM helps in improving the stability of the response. This model,

the appropriate control method is applied for direct axis current (id), quadrature axis

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current (iq), speed of the motor and position actuator arm, including the implementation

of the mechanical gearing of the EMA. Finally, the control parameters providing the

optimum results are chosen.

In this research, the major task is the controlling of the PMSM to give the

required result. Discussion on the theory regarding the design of the permanent magnet

in order to produce required Ld and Lq used in this simulation is included. Only minor

explanation of the matrix converter operation and EMA system is provide. However,

the design of this vector control depends on the matrix converter and EMA application.

The matrix converter is used to feed the stator currents. Transformations from

three-phase stator quantities to two-axis d-q quantities method are applied to link the

matrix converter and PMSM control strategy. The matrix converter can yield a superior

current waveform, with low current harmonics and high power factor when compared to

a conventional rectifier fed, dc link and constant voltage converter.

The EMA system may be used for actuating the rudder, ailerons, tail plane

horizontal stabilizer, flaps and slats on the aircraft system. The output of the EMA

system is a controlled position of this flight surface. Nowadays application, they are

more commonly found on the secondary flight surface such as flap and slats. The rotary

movement of the motor is connected to drive a lead screw through a gearbox and finally

producing linear output movement. The mechanisms of these mechanical parts are

considered the EMA system.

This research also can be used in other applications, which have similar

specifications and requirements. In this project the theoretical analysis, design and

simulation are on a realistic operation system can be applied to practical equipment.

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1.2 Objectives

The purpose of this project is to control the position of the aircraft EMA by

using PMSM and Matrix Converter. The objectives of this research are

To gain an understanding of PMSM, Matrix Converter and EMA for

aircraft system, operation and overall controlling system.

Modeling Derivation of the PMSM system

To design a model of PMSM base on vector control approached.

To design stable id and iq current loops and speed loops for the

system.

Controller design using proportional integral (PI) controller and

Fuzzy Logic

To simulate and analyze the resultsof the system by using Simulink

Matlab.

1.3 Scope of Works

The particular literature reviews have been studied to make the decision on how

to solve and what is the scope to be covered.

So, to accomplishing this research, a few scopes of works have been determined.

The first scope of work is to design the PMSM controller, based on the mathematical

model obtained, using Simulink.The controller design approach is using proportional

integral (PI) controller and Fuzzy Logic.Then the results should be analyzed to make a

comparison between PI andFuzzy Logic controller.

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1.4 Methodology

The research works are undertaken in the following five (5) development stages.

The first thing first is to implement the mathematical model for the IPC System.

Secondly it has to be modelled in the Simulink. Then it comes to the study on how to

apply the controller based on FLC algorithm in the Simulink. Here is the part that

needs to determine the input and output for the system and develop a fuzzy rule based

and its fuzzy set of membership function.All these things need to be simulating using

some sort of software such as MATLABSimulink. After that the simulation using PID

controller also need to be performed as a benchmarking for the FLC.Finally, both FLC

and PID simulation results will be compared to meet the objectives.

1.5 Dissertation Overview

This report has a compilation of many chapters that will elaborate in stages the

research work that have been carried out. As in general this report mainly consistsof six

main chapters which arean introduction, literature review, theory of PMSM, simulation

using PI and Fuzzy Logic Controller in MATLAB software, design of PMSM

controlresults analysis and conclusion& recommendation.

Chapter 1

This chapter discusses the important aspect of the research work such as project

background, objectives, scope of work, methodologyas well as the thesis outlineitself.

Chapter 2

This chapter will provide the Literature Review which discusses some papers of

the related area in controlling of PMSM, Matrix Converter and EMA. This chapter also

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discusses the advantages of the three main devices above and some general operation of

Matrix converter and EMA actuators.

Chapter 3

This chapter will be explaining the research methodology the required theory of

the PMSM machine structure and operation. Mathematical Model of the dynamic

equation used in the simulation is derived and developed. Further analysis on the power

and torque of state condition also had been discussed.

Chapter 4

This chapter presents the design of PMSM Control using Proportional Integral

(PI) & Fuzzy Logic controller. In PI controller design, simulation and analysis of the

Mathematical Model designed the current control and speed control will be shown. The

approached of the inner and outer loop control is used the proportion integral (PI)

control method and optimization.. Process of developing the PMSM model structure

using Matlab is clearly discussed. Verification on this structure also being done by

comparing simulation results with calculations method.

In Fuzzy Logic controller design stated the logic membership function and rules

are also been discussed. Comparisons between 2 types of fuzzy logic are used to see the

good response between these 2 types.

Chapter 5

This chapter concludes the dissertation and includes recommendation for future

research and study.

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REFERENCES

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synchronous motors”, Magnetics, IEEE Transactions on Volume 22, Issue 5, Sep 1986.

[2] Pillay, P., Krishnan, R., “Modeling of permanent magnet motor drives,” Industrial

Electronics, IEEE Transactions on Volume 35, Issue 4, Nov. 1988.

[3] Bennett, N., Wang, J., Shimmin, D.W., Binns, K.J, “A new vector control scheme

for an adjustable speed AC drive system utilizing a high field permanent magnet

synchronous machine” Electrical Machines and Drives, 1993. Sixth International

Conference on 8-10 Sep 1993.

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International

Volume 3, 14-16 Aug. 2004

[5] Spiteri S.C., Cilia J., Micallef B., Apap M., “Sensorless vector control of a surface

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Drives, 2002. International Conference on 4-7 June 2002.

[6] M. F. Rahman, L. Zhong, W. Y.Hu, K. W. Lim, “An Investigation of Direct and

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Drive Systems, 1997.

[7] Dr P W Wheeler, Dr J C Clare, M Apap, Dr L Empringham, and Dr K J Bradley, “A

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Aircraft Actuator” IEEE Industrial Elects. Society, Volume 3, 2-6 Nov. 2003.

59

[8] Wheeler, P.W., Clare, J.C., Empringham, L., “A vector controlled MCT matrix

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waveform quality” IEEE Industry Applications Conference, 2002.

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IEEE Power Engineering Journal Volume 16, Issue 6, Dec. 2002

[10] Oyama, J., Higuchi, T., Yamada, E., Koga, T., Lipo, T., “New control strategy for

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[17] Keith Bradley, “Module of Special Drive H5DSPD”, University of Nottingham.

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