PSZ 19: 16(Pind.1197)

Judul MODERN AND INTELLIGENT CONTROLLER FOR A MAGNETIC BEARING SYSTEM

SESIPENGAJL\N: ____ 2~ __ a_oo __ 7 __ _

Saya SHARATUL IZAH BINTI SAMSUDIN (IIURUF BESAR)

mengalru membenarkan tesis (PSM/Sarjana!Doktor Falsafah)* ini disimpan di Perpustakaan Universiti Teknologi Malaysia dengan syarat-syarat kegunaan seperti berikut:

l. Tesis adalah balanilik Universiti Teknologi Malaysia. 2. Perpustalcaan Universiti Teknologi Malaysia dibenarlcan membuat salinan untuk tujuan

pengajian sahaja. 3. Perpustak:aan dibenarkan membuat salinan tesis ini sebagai bahan pertukaran antara

institusi pengajian tinggi. 4. ••sua tandakan < 4 )

D SULIT D TERHAD II {II TIDAK TERHAD

/1

UJ/fj

(Mengandungi maldumat yang berdarjah keselamatan atau kepentingan Malaysia seperti yang termaktub di dalam

AKTA RAHSIA RASMI 1972)

(Mengandungi maldumat TERHAD yang telah ditentukan oleh organisasilbadan di mana peoyelidikan dijalankan)

(TANDA~GAN PENULIS) v

(TANDATANGAN PENYELIA)

Alamat Tetap:

NO.lO, JALAN DESA BAK.TI, TAMAN

DESA BARU, 75350 MELAKA. DR. SHAHRUM SHAH BIN ABDULLAH

Nama Penyelia

Tarikh: 23 NOVEMBER 2006 Tarikh: 23 NOVEMBER 2006

"I hereby declare that I have read this thesis and in

my opinion this thesis is sufficient in terms of scope and

quality for the award of the degree of Master of Engineering

(Electrical - Mechatronics & Automatic Control)"

S igrtature : ...................................................................... .

Name of Supervisor : DR. SHAHRUM SHAH BIN ABDULLAH

Date : 23 NOVEMBER 2006

MODERN AND INTELLIGENT CONTROLLER FOR A MAGNETIC BEARING SYSTEM

SHARATUL IZAH BINTI SAMSUDIN

A thesis submitted in fulfilment of the requirements for the award of the degree of

Master of Engineering (Electrical- Mechatronics & Automatic Control)

Faculty ofElectrical Engineering Universiti Teknologi Malaysia

NOVEMBER 2006

ii

I declare that this thesis entitled "Modern and Intelligent Controller for a Magnetic

Bearing System" is the result of my own research except as cited in the references.

The thesis has not been accepted for any degree and is not concurrently submitted in

candidature of any other degree .

..A

::= ~ ~~~~·~;;~·~~SUDIN Date : 23 NOVEMBER 2006

iii

To my dearest husband, parents and family for their encouragement and blessing

iv

ACKNOWLEDGEMENT

Alhamdulillah, I am grateful to ALLAH SWT on His blessing in completing

this project. I woUld like to take this opportunity to express my gratitude to the

supervisor of this project, Dr. Shahrum Shah Abdullah for his guidance and help. I

would have faced ,a great deal of difficulties in completing this project without his

professional knowledge and experience in related fields.

I would also like to express my appreciation to Kolej Universiti Teknikal

Kebangsaan Malaysia (KUTKM) for giving me ~ opportunity to study in Univer~iti

Teknologi Malaysia (UTM). This chance is too meaningful for me.

Finally, 1 would like to thank to my husband, Sani Irwan Bin Md. Salim, and my parents wlio always support and motivate constantly besides my friends and

everyone who have contributed and provided assistance directly or indirectly towards

the completioh of this thesis.

v

ABSTRACT

A magnetic bearing system is a device that uses electromagnetic forces to

support a rotor without mechanical contact. The focus of this project will be on the

stability and control of the MBC 500 system test bed constructed by Magnetic

Moments Incorporated. The MBC 500 system contains a stainless steel shaft or

rotor, which can be levitated using eight horseshoe electromagnets, four at each end

of the rotor. A controller, which is able to stabilize the position of the rotor by

varying the electromagnet force, tjJ produced by the electromagnets at the end of the

shaft, will be designed. For this purpose, the formulation of the mathematical

dynamic model of magnetic bearing system is derived initially and it was followed

by establishing the state space model of the system. Then, system model is

linearized at the equilibrium point using a Taylor Series and the shaft is assumed as a '

rigid body. In addition, a state feedback controller using a pole placement technique

and a fuzzy logic controller as an alternative control strategy are designed. This

project will be implemented using MATLAB 6.5.

vi

ABSTRAK

Sistem magnetik: bering adalah satu perkak:asan yang menggunakan daya

elektromagnetik: untuk menyokong rotor tanpa memerlukan aplik:asi mekanik:al.

F okus utama projek ini adalah pada kestabilan dan pengawalan sistem MBC 500

yang dibina oleh Magntic Moments Incorporated. Sistem MBC 500 ini meliputi aci

tahan karat atau rotor, yang mana boleh diapungkan menggunakan Iapan ladam

elektromagnet, di mana terdapat empat ladam elektromagnet pada setiap hujung

rotor. Satu pengawal direkabentuk untuk menstabilkan kedudukan rotor dengan

mengubah daya electromagnet, ; yang dihasilkan pada hujung aci. Untuk tujuan ini,

model matematik: dinamik: bagi sistem magnetik: bering ini dirumuskan pada awalnya

dan kemudian disusuli dengan model keadaan-ruang bagi sistem ini. Seterusnya,

model sistem ini dilinearkan pada titik keseimbangan dengan menggunak:an Siri

Taylor sementara aci dianggap sebagai badan tegar. Selain daripada itu, satu

pengawal suapbnlik keadaan yang menggunak:an teknik "poie-placemeht" berserta

pengawal "fuzzy logic" sebagai pengawal altematif dfrekabentuk. Projek ini

dijalankan dengan menggunakan perisian MATLAB 6.5.

vii

TABLE OF CONTENTS

CHAPI'ER TITLE PAGE

ACKNOWLEDGEMENT iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES xii

LIST OF FIGURES xiii

LtST OF ABBREVIATIONS xvi

LIST OF SYMBOLS xvii

1 l:NTRODUCTION 1

1.1 Project Overview 1

1.2 Objectives ofProject 2

1.3 Scopes ofProject 3

1.4 Research Methodology 3

1.5 Literature Research 4

1.6 Layout Of Thesis 6

2

3

4

BACKGROUND ON MAGNETIC BEARING SYSTEM

2.1 Introduction MBC 500 Magnetic Bearing System

viii

7

7

2.1.1 Advantages and Disadvantages of a Magnetic Bearing

System 10

2.1.2 Analysis and System Modeling for Magnetic Bearing

System 10

POLE PLACEMENT CONTROLLER DESIGN APPROACH

3.1 Introduction of Designing a Control System

3.2 State-space Representation of Multi-Input-Multi-Output

(MIMO) Systems

3.3 Controllability and Observability of the System

3.4 Regulator Systems and Control System

3.5 Introduction of Pole Placement Method

3.6 Pole Placement Design Technique

3.7 Necessary Condition for Arbitrary Pole Placement

3.8 Choosing the Location of Desired Closed-Loop Poles

3.9 State Feedback Gain Selection

FUZZY LOGIC CONTROL DESIGN APPROACH

4.1 Introduction of Fuzzy Logic System

4.1.1 Fuzzy Sets and Fuzzy Operators

4.2 Fuzzy Logic Controller

22

22

23

24

25

25

26

29

31

31

33

33

33

35

4.2.1 Fuzzifier

4.2.1.1 Universe ofDiscourse:

4.2.1.2 Membership Function:

4.2.2 Knowledge Base

4.2.3 Inference Engine

4.2.4 Defuzzifier

4.2.4.1 Center Of Gravity Method

4.3 Ordinal Structure Fuzzy Logic

4.4 Design Procedure of the Fuzzy Logic Controller

4.5 Direct Fuzzy Logic Controller Scheme

SIMuLATION RESULTS

5.1

5.2

Model for a Magnetic Bearing System

Stability Test on Magnetic Bearing System

35

36

36

38

39

39

40

41

43

45

46

46

47

1X

5.3 Controllability and Observability Test on a Magnetic Bearing

System 48

5.4 Obtaining System Response to Initial Condition 49

5.5 Designing of a Pole Placement Controller 52

5.5.1 Linear Pole Placement Controller Design 52

5.5.2 Response of a Linear Pole Placement Controller 56

5.6

5.5.2.1 Response of a Pole Placement

Controller with Xo = 0.08m

andB = 0 °:

5.5.2.2 Response of a Pole Placement

Controller with Xo = Om and

5.5.2.3 Response of a Pole Placement

Controller with Xo = 0.08m

56

58

5.5.3 Nonlinear Pole Placement Controller Design 62

5.5.4 Response of a Nonlinear Pole Placement Controller63

Designing a Fuzzy Logic Controller 65

5.6.1 Direct Fuzzy Logic Corttroller Design Technique 66

5.6.2 Fuzzy logic controller with error ofXl_out and error

of X2 _out as inputs 67

5.6.2.1 Membership function 67

5.6.2.2 Rule base 68

5.6.3 Fuzzy logic controller with error and derivative of

X I_ out; error and derivative ofX2_out as inputs 69

5.6.3.1 Membership function 70

5.6.3.2 Rule base 71

X

6

5.6.4 Fuzzy Logic Controller with error of controlled states

variables as inputs 75

5.6.4.1 Membership function

5.6.4.2 Rule base

5.6.5 Response of Fuzzy Logic Controller

CONCLUSION AND FUTURE WORK

6.1 Conclusion

6.2 Recommendation for Future Work

REFERENCES

APPENDIX A

75

76

77

82

82

83

85

88

Fuzzy Logic Controller using Fuzzy Logic Toolbox in MATLAB

88

xi

xii

LIST OF TABLES

TABLE NO TITLE PAGE

Table 2-1 : System variables 12

Table 2-2 : System parameters 12

Table 5-l : Range of state feedback gain, k for the nonlinear plant 68

Table 5-2: Fuzzy inference rules oficontrol_1 and icontrol_2 71

Table 5-3: Fuzzy inference rules oricontrol_l 73

Table 5-4: Fuzzy inference rules oficontrol_2 73

xiii

LIST OF FIGURES

Figure 2.1 : MBC 500 Magnetic Bearing System 8

Figure 2.2 : Magnetic bearing 8

Figure 2.3 : Attractive force exerted by electromagnet 9

Figure 2.4: MBC500 system configuration 11

Figure 2.5 : Rotor configuration 13

Figure 2.6 : Force I moment relation 14

Figure 3.1 : Closed-loop control system with u=-kx 28

Figure 4.1 :Block of fuzzy controller 35

Figure 4.2 : Examples of membership functions 37

Figure 4.3 : The centroid method of defuzzification 40

Figure 4.4: Structure of the ordinal fuzzy logic model 42

Figure 5.1 : Linear plant for a magnetic bearing system 46

Figure 5.2: Nonlinear plant for a magnetic bearing system 47

Figure 5.3 : Root location of a magnetic bearing system 48

Figure 5.4 : Response to initial condition for uncontrolled system 50

Figure 5.5 : Response to initial condition for center of mass of the rotor 50

Figure 5.6 : Response to initial condition for angle between rotor and z-axis

Figure 5.7: Block diagram of pole placement controller design

Figure 5.8: Pole placement controller

51

54

54

Figure 5.9: State feedback gain

Figure 5.10 : Response oflinear controlled signals with :xo = 0.08m and

(} = 0 0

Figure 5.11 :Response oflinear controlled state variables with Xo = 0.08m

and(}= 0 °

xiv

54

56

57

Figure 5.12: Response oflinear controlled output plant with :xo= 0.08m and

57

Figure 5.13: Response of linear controlled signals with x0 =Om and(}= 10 o

58

Figure 5.14: Response oflinear controlled state variables with xo =Om and

(} = 10 ° 58

Figure 5.15: Response of linear controlled output plant with :xo =Om and

(} = 10 ° 59

Figure 5.16: Response of linear controlled signals with :xo = 0.08m and

0=10° 60

Figure 5.17: Response of linear controlled state variables with xo = 0.08m

and (} = 10 ° 60

Figure 5.18: Response oflinear controlled output plant with xo = 0.08m and

(} = 10 °

Figure 5.19: Response of nonlinear controlled state variables

Figure 5.20: Response of nonlinear controlled output plant

61

63

64

XV

Figure 5.21 : Block diagram of fuzzy logic controller with exl and ex2 as

inputs 67

Figure 5.22 : Fuzzy inference rules of icontrol_l and icontrol_2 using Matlab

69

Figure 5.23 : Block diagram of fuzzy logic controller with exl, delta exl , ex2

and delta ex2 output controlled as inputs 69

• Figure 5.24: Fuzzy inference rules of icontro1_1 using Matlab 72

Figure 5.25 : Fuzzy inference rules of icontrol_2 using Matlab 74

Figure 5.26: Block diagram of fuzzy logic controller with ex1, ex2, ex3 and

ex4 controlled as inputs 75

Figure 5.27 : Fuzzy inference rules oficontrol_1 and icontrol_2 using Matlab

76

Figure 5.28 : Response of controlled state variables, x~, x2, x3 and X4 77

Pigure 5.29: Response ofcontrohed output plant, X1_out and X2_out 77

Figure 5.30 : Response of cohtrolled state variables, Xt, x2, x3 add X4 78 I ,

Figure 5.31 : Response of cotttrolled output plant, X 1_ out and Xi_ out 78

tigure 5.32 : Response of cortttolled state variables, x1, x2, x3 and X4 79

Figure 5.33 : Response of controlled output plant, Xl_out and X2_out 79

AMB

APACA

COG

FLC

LMS

MBC

LIST OF ABBREVIATIONS

Active Magnetic Bearing

Amplitude Phase Adaptive Control Algorithm

Center of Gravity

Fuzzy Logic Controller

Least Mean Square

Magnetic Bearing System

xvi

X;

Xi

xi Xi out

icontrol_i

Xo

e

m

a

a Cr

Or p(x)

LIST OF SYMBOLS

The displacement of center of mass of rotor

The state variables

The displacement of rotor at Hall Effect Sensor

The output variables

The controlled current

The center of mass of the rotor

The angle between rotor and z-axis

The forces exerted on the rotor

Total length ofthe rotor

Distance bearing to the end of rotor

Distance Hall Effect Sensor to the end of rotor

Moment inersia of the rotor with respect to rotation

Mass of the rotor

Force balance equation

Mass balance equation

xvii

Summation of all external forces applied to the system

Summation of all moments applied externally

Rotational moment of inertia of the system

Acceleration of the center of the gravity for the system

Angl.llar acceleration of the system

Controllability matrix

Observability matrix

Membership function of x

CHAPTERl

INTRODUCTION

1.1 Project Overview

Magnetic bearing is a device that uses electromagnetic forces to support a

rotor without mechanical contact. Magnetic bearings can be divided into two

categories which are passive and active magnetic bearing. Passive magnetic bearings

typically use permanent magnets in conjunction with electromagnets. With

permanent magnets, the force exerted on the rotor can be either attractive or

repulsive. A repulsive force results in a system that is stable without a controller.

However, the force exerted by the permanent magnets cannot be controlled and it is

limited by the strength of the magnets. On the other hand, for active magnetic

bearing, the force on the rotor can be controlled by changing the current flow in the

magnet coils [9]. The problem of using an active magnetic bearing is that it can only

exert an attractive force and make the system inherently unstable [14] and requiring

the use of a controller.

2

Many attempts have been made to conventional and modern controller other

than artificial controller as to overcome the stability problem since the application of

magnetic bearing system is widely used.

Active magnetic bearings have been used in a rapidly growing number of

applications such as jet engines, compressors, pumps, and flywheel systems that are

required to meet high speed, low vibration, zero frictional wear, and clean

environment specifications [2].

1.2 Objectives of Project

This thesis is expected to achieve four goals:

1.

2.

j.

To prove the mathematical dynamic model of the magnetic bearing

system.

To establish the state s~ace model of a magnetic bearing system. . ;

To design a mod~rli c8ntr~lier capable df cbntrolling ahd stabilizing the

position of the rotor for a rrtagnetic bearing system.

4. To design an intelligent controller as an alternative cortttol strategy for a

magnetic bearing syshHn.

3

1.3 Scopes of Project

This project presents a study of designing a controller for magnetic bearing

system based on the following:

1. Formulation and proving the mathematical dynamic model of magnetic

bearing system.

2. The design of modem controller which is able to stabilize the position of

the rotor during operation. For this task, the state feedback control using

pole placement technique is applied.

3. The design of intelligent controller as to maintain the stability ofthe rotor

of a magnetic bearing system.

This project will be focused on designing a controller for MBC 500 magnetic

bearing system.

1.4 Research Methodology

The research work is undertaken in the following eight developmental stages:

1. Prove the mathematical dynamic model of a magnetic bearing system.

2. Establish the state space model of a magnetic bearing system.

3. Linearization: Nonlinear equations of a magnetic bearing system are

linearized at the equilibrium point using a Taylor Series.

4. Check the controllability and observability of a magnetic bearing system.

5. Design a state feedback controller using the pole placement technique.

6. Design an intelligent controller as an alternative control strategy.

4

7. Verify and analyse the controller design of a magnetic bearing system

simulated on MA TLAB-SIMULINK.

8. Evaluate the results as to compare the performance of both controller

stated.

1.5 Literature Research

The research on stabilizing and controlling a rotor of a magnetic bearing

system has gained momentum over the last decade. This is due to the nonlinear and

inherently unstable dynamics of the system. As the applications for active magnetic

bearing can be found widely, the importance for designing the appropriate and

efficient controller to monitor the magnetic bearings becomes vital. The following

paragraphs briefly discuss on several researches that have been done by researchers.

MBC 500 magnetic bearing system has been identified in designing a

classical controller and this was done by J. Shi and J. Revell (2002). MATLAB p-

Analysis and Synthesis toolbox was applied in system identification. Hewlett

Packard 3562A Dynamic Signal Analyzer is used to collect the experimental data

from the MBC 500 magnetic bearing system. Specifically, signal analyzer's swept

sine function is applied experimentally to determine the transfer function of a single

input single output (SISO) path through the magnetic bearing system. Next, lead

compensator is designed in real time as to stabilize the operation of the system.

P. Barney et all. (2003) introduced an active control of a magnetically

levitated spindle. In this study, an unbalanced spindle was actively centered using an

Active Magnetic Bearing (AMB). To perform this task, modeling, simulation and

test program was implemented to design the Adaptive Least Mean Square (LMS)

controller. This study involves the implementation ofLMS digital control algorithm

to maintain concentricity of an intentionally unbalanced spindle. The LMS

5

controller was implemented on an AMB system using a programmable digital signal

processor (DSP). The LMS system model utilized the validated SIMULINK model

as a basis with the addition of an imbalance forcing function and LMS feed forward

algorithm. Finally, the LMS controller was implemented on the MBC 500

significantly improved the concentricity of the unbalanced shaft.

P. Rebecca and P. Gordon (2003) from Michigan Technological University

did a research based on disturbance rejection control of an electromagnetic bearing

spindle. Adaptive control algorithm is applied to MBC 500 magnetic bearing

system. Adaptive control is an appealing approach for the system because the

controller can tune itself to account for an unknown periodic disturbance, such as

cutting or grinding forces, injected into the system. An adaptive controller called the

Amplitude-Phase Adaptive Control Algorithm (APACA) was designed to augment

the lead-filter compensator. The purpose of APACA is to predict and compensate

for the external disturbance. This paper proved that an adaptive control algorithm

can be applied to an Active Magnetic Bearing (AMB) system with a periodic

disturbance applied to the rotor and resulting in minimal motion of the spindle. By

then, the position of the rotor can be stabilized.

It was followed by the research of Y. H. John (1995). He introduced a fuzzy

logic approaches to improve on dual acting magnetic bearing. The idea is to adjust the

linear controller signal in such a way that nonlinear effects are better compensated. The

relationships of attractive force to the electromagnet currents and air gap are described

and compensated using fuzzy principles. The fuzzy controller described in this section

was designed in two steps. First, fuzzy descriptions of the various operating points

which describe the antecedents and possible control adjustments as the consequents in

the fuzzy control rules are computed. Second, a set of rules for control adjustments was

derived. The fuzzy rule outputs are composed using the max-min composition, and a

crisp value of an adjustment parameter was derived using the centroid method. The

design objective was to cancel the relationship of attractive force with respect to air gap

dimension. Finally, a fuzzy controller which is able to adjust a winding current and

controlling a magnetic bearing system is designed successfully.