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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
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"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
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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
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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
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iii
To my dearest husband, parents and family for their encouragement and blessing
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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.
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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.
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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.
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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
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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
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26
29
31
31
33
33
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35
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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
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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
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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
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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
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76
77
82
82
83
85
88
Fuzzy Logic Controller using Fuzzy Logic Toolbox in MATLAB
88
xi
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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
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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
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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
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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
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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
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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
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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.
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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.
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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.
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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
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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.
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