ADAPTIVE BACKSTEPPING CONTROL OF ACTIVE MAGNETIC damping control effort while the utilization of a single

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  • ADAPTIVE BACKSTEPPING CONTROL OF ACTIVE MAGNETIC BEARINGS

    SILU YOU

    Bachelor of Electrical Engineering

    Huazhong University of Science and Technology

    July, 2007

    submitted in partial fulfillment of requirements for the degree

    MASTER OF SCIENCE IN ELECTRICAL ENGINEERING

    at the

    CLEVELAND STATE UNIVERSITY

    April, 2010

  • ii

    This thesis has been approved

    by the Department of Electrical and Computer Engineering

    and the College of Graduate Studies by

    ________________________________________________

    Thesis Committee Chairperson, Dr. Lili Dong

    ________________________________

    Department/Date

    ________________________________________________

    Committee Member, Dr. Daniel Simon

    ________________________________

    Department/Date

    ________________________________________________

    Committee Member, Dr. Wenbing Zhao

    ________________________________

    Department/Date

  • iii

    ACKNOWLEDGEMENTS

    By the end of my graduate study at Cleveland State University, there are some

    people I really want to say thanks to.

    First of all, I would like to thank my supervisor, Dr. Lili Dong, for her patience

    and directions that help me overcome lots of difficulties. Also, my sincere gratitude goes

    to other professors: Dr. Daniel Simon, Dr. Wenbing Zhao and Dr. Zhiqiang, Gao. They

    taught me not only academic knowledge but also how to be a professional person.

    I would like to thank my friends Kai Zhang, Honglei Zhang, Yao Zhang and

    Shuang Wu. We have created a life-long friendship that I will never forget.

    At last, I want to give my deepest thankfulness to my parents, for their selfless

    love and support in my life.

  • iv

    NOMENCLATURE .......................................................................................................... vi

    LIST OF TABLES............................................................................................................ vii

    LIST OF FIGURES......................................................................................................... viii

    ABSTRACT........................................................................................................................ 1

    CHAPTER I INTRODUCTION........................................................................................ 2

    I. 1 Background......................................................................................................... 2

    I. 2 Adaptive Backstepping ....................................................................................... 5

    I. 3 Contributions of the thesis................................................................................... 7

    I. 4 Thesis outline...................................................................................................... 8

    CHAPTER II MODELING OF ACTIVE MAGNETIC BEARING.............................. 12

    II. 1 Principles......................................................................................................... 12

    II. 2 Nonlinear model of AMB and its linearization................................................. 15

    II. 3 Summary of the chapter ................................................................................... 19

    CHAPTER III ADAPTIVE BACKSTEPPING CONTROL WITH FULL-STATE

    FEEDBACK...................................................................................................................... 20

    III. 1 Control objective and strategy ........................................................................ 20

    III. 2 Model transformation ..................................................................................... 22

    III. 3 Design procedure............................................................................................ 23

    III. 4 Simulation result ............................................................................................ 27

    III. 5 Robustness of ABC ........................................................................................ 37

  • v

    III. 6 Comparison with PID control ......................................................................... 40

    III. 7 Summary of the chapter.................................................................................. 43

    CHAPTER IV ADAPTIVE OBSERVER-BASED BACKSTEPPING CONTROL...... 44

    IV. 1 Control objective and strategy ........................................................................ 44

    IV. 2 Model transformation..................................................................................... 46

    IV. 3 Observer design ............................................................................................. 47

    IV. 4 Design procedure of the control law ............................................................... 49

    IV. 5 Simulation results and analysis....................................................................... 53

    IV. 6 Robustness of AOBC ..................................................................................... 57

    IV. 7 Comparison with PID..................................................................................... 59

    IV. 8 Summary of the chapter ................................................................................. 60

    CHAPTER V SUMMARY AND FUTURE RESEARCH .............................................. 62

    V. 1 Summary......................................................................................................... 62

    V. 2 Future work..................................................................................................... 64

    REFERENCES ................................................................................................................. 66

  • vi

    NOMENCLATURE

    ABC: Adaptive backstepping control

    AC: Lyapunov adaptive coefficients

    AMB: Active magnetic bearing

    AOBC: Adaptive observer-based backstepping control

    EMF: Electromotive force

    CLF: Control Lyapunov function

    DOF: Degree of freedom

    GA: Genetic algorithm

    LC: Lyapunov adaptive coefficients

    LQR: Linear quadratic regulator

    MIMO: Multiple-input multiple-output

    PI: Proportional-integral

    PID: Proportional-integral-derivative

    SISO: Single-input single-output

  • vii

    LIST OF TABLES

    TABLE PAGE

    Table 1: Parameter configurations .................................................................................19

    Table 2: Position of AMB with four parameters at a floating rate of 20000%.................39

    Table 3: Maximum factors by which system parameter can increase before the onset of

    instability.......................................................................................................................39

    Table 4: Optimized PID gains........................................................................................40

    Table 5: Disturbance response characteristics in position with different Lyapunov

    coefficients ....................................................................................................................57

  • viii

    LIST OF FIGURES

    FIGURE PAGE

    Figure 1:Magnetic actuator ........................................................................................13

    Figure 2: AMB model ....................................................................................................15

    Figure 3: Block diagram of open-loop AMB plant .........................................................18

    Figure 4: Model of ABC of AMB ....................................................................................22

    Figure 5: The closed-loop adaptive system ....................................................................28

    Figure 6: SIMULINK model of ABC ..............................................................................29

    Figure 7: Control results of the three states with different LC........................................30

    Figure 8: Disturbance (θ ) estimates when 1 2 3 500c c c= = = ........................................31

    Figure 9: Disturbance and estimates when 1 2 33000, 1000, 500c c c= = = .......................31

    Figure 10: Control effort (voltage) with different LC .....................................................32

    Figure 11: Control efforts with step disturbance and ramp disturbance when

    1 2 3 1 23000, 1000, 500, 1, 1c c c γ γ= = = = = .....................................................................33

    Figure 12: Control result with different AC ...................................................................34

    Figure 13: Disturbance and its estimates when 1 210, 1γ γ= = ......................................34

    Figure 14: Disturbance and its estimates when 1 22000, 0.1γ γ= = ................................35

    Figure 15: Control efforts with different AC .....................................................