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  • AAllmmaa MMaatteerr SSttuuddiioorruumm –– UUnniivveerrssiittyy ooff BBoollooggnnaa    

    PhD School in

    Automatic Control Systems and Operational Research

    Christian Conficoni

    Nonlinear Constrained and Saturated Control of

    Power Electronics and Electromechanical Systems

    Phd Thesis

    PhD Coordinator: Advisor: Prof. Andrea Lodi Prof. Andrea Tilli

    Academic year 2012‐2013 

  •  

  • Abstract

    Power electronic converters are extensively adopted for the solution of timely issues, such

    as power quality improvement in industrial plants, energy management in hybrid electrical

    systems, and control of electrical generators for renewables. Beside nonlinearity, this sys-

    tems are typically characterized by hard constraints on the control inputs, and sometimes

    the state variables. In this respect, control laws able to handle input saturation are crucial

    to formally characterize the systems stability and performance properties. From a prac-

    tical viewpoint, a proper saturation management allows to extend the systems transient

    and steady-state operating ranges, improving their reliability and availability.

    The main topic of this thesis concern saturated control methodologies, based on mod-

    ern approaches, applied to power electronics and electromechanical systems. The pur-

    sued objective is to provide formal results under any saturation scenario, overcoming the

    drawbacks of the classic solution commonly applied to cope with saturation of power con-

    verters, and enhancing performance. For this purpose two main approaches are exploited

    and extended to deal with power electronic applications: modern anti-windup strategies,

    providing formal results and systematic design rules for the anti-windup compensator, de-

    voted to handle control saturation, and “one step” saturated feedback design techniques,

    relying on a suitable characterization of the saturation nonlinearity and less conservative

    extensions of standard absolute stability theory results.

    The first part of the thesis is devoted to present and develop a novel general anti-windup

    scheme, which is then specifically applied to a class of power converters adopted for power

    quality enhancement in industrial plants. In the second part a polytopic differential in-

    clusion representation of saturation nonlinearity is presented and extended to deal with a

    class of multiple input power converters, used to manage hybrid electrical energy sources.

    The third part regards adaptive observers design for robust estimation of the parameters

    required for high performance control of power systems.

  • ii

  • Acknowledgements

    At the end of these three years, I realize how much help, support and encouragement I

    received from so many people. First of all I would like to thank my parents; without their

    unconditioned moral (and economic) support, I would have never been able to accomplish

    my studies. A special thanks to my beloved twin sister Elisa, who has been always close

    to me, and a perfect neighbor. I’d like to thank all my family members in general, who

    always seem so proud of me.

    Much part of this thesis work has been inspired by the advices and the insightful consider-

    ations of my advisor prof. Andrea Tilli. I owe him my cultural growth during these years,

    both form a methodological and engineering viewpoint. Therefore I would like to thank

    him for the opportunity, and for his valuable help.

    My appreciation goes to prof. T. Hu who hosted me for six months at the University of

    Massachusetts, Lowell, giving me the possibility to work at timely interesting topics, along

    with is research team, formed by skilled and kind guys I’d like to thank too.

    Finally a great thanks to all my close friends, that I know since my college, or high school

    years. It is always a pleasure to hang out with such nice and smart people, often their

    accomplishment motivated me to try my best during these research period. Obviously a

    special though goes also to my “fellow travelers”, that is my PhD colleagues Giovanni,

    Matteo, and Raffaele, the dialogue with them made this experience even more profitable.

  • Contents

    Introduction vii

    I Anti-windup Solutions 1

    1 Modern Anti-Windup Strategies 2

    1.1 Modern anti-windup problem statement and objectives . . . . . . . . . . . . 2

    1.2 Direct Linear Anti-windup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

    1.3 Model Recovery Anti-windup . . . . . . . . . . . . . . . . . . . . . . . . . . 12

    1.4 Command Governor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

    1.5 Novel Anti-Windup strategy: general idea . . . . . . . . . . . . . . . . . . . 22

    2 Saturated Nonlinear Current Control of Shunt Active Filters 27

    2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

    2.1.1 SAF saturated control strategy motivation . . . . . . . . . . . . . . 28

    2.2 System model and control objectives . . . . . . . . . . . . . . . . . . . . . . 31

    2.2.1 State space model derivation . . . . . . . . . . . . . . . . . . . . . . 31

    2.2.2 Control objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

    2.3 Internal model-based current controller . . . . . . . . . . . . . . . . . . . . . 34

    2.4 Input saturation and current bound issues . . . . . . . . . . . . . . . . . . . 35

    2.5 Current control Anti-Windup scheme . . . . . . . . . . . . . . . . . . . . . . 39

    2.5.1 Improvements in the anti-windup strategy . . . . . . . . . . . . . . . 44

    2.6 Dealing with current and anti-windup unit limitations . . . . . . . . . . . . 46

    2.6.1 General problem formulation . . . . . . . . . . . . . . . . . . . . . . 47

    2.6.2 Reduced problem formulation . . . . . . . . . . . . . . . . . . . . . . 48

    2.7 Current saturation strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

    2.8 Numerical and simulation results . . . . . . . . . . . . . . . . . . . . . . . . 55

    2.8.1 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

    2.8.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

    2.9 Alternative SAF AW unit design . . . . . . . . . . . . . . . . . . . . . . . . 61

    3 On the control of DC-link voltage in Shunt Active Filters 64

    3.1 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

    iv

  • 3.2 Control oriented DC-Bus capacitor sizing . . . . . . . . . . . . . . . . . . . 66

    3.3 Robust integral control of voltage dynamics . . . . . . . . . . . . . . . . . . 67

    3.4 Averaged control solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

    II Explicit Saturated Control Design 75

    4 Control of Linear Saturated Systems 76

    4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

    4.2 Reducing conservatism in saturation nonlinearity characterization . . . . . . 77

    4.3 Saturated control design via LMI constrained optimization techniques . . . 80

    4.3.1 Domain of attraction maximization . . . . . . . . . . . . . . . . . . . 80

    4.3.2 Disturbance rejection with guaranteed stability region . . . . . . . . 82

    4.3.3 Convergence rate maximization . . . . . . . . . . . . . . . . . . . . . 85

    4.4 Improvements via non-quadratic Lyapunov functions . . . . . . . . . . . . . 88

    4.4.1 Piecewise quadratic Lyapunov functions . . . . . . . . . . . . . . . . 89

    4.4.2 Polyhedral Lyapunov functions . . . . . . . . . . . . . . . . . . . . . 91

    4.4.3 Composite quadratic Lyapunov functions . . . . . . . . . . . . . . . 94

    5 Control Design for Power Converters fed by Hybrid Energy Sources 99

    5.1 Introduction and motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

    5.2 State-space averaged model . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

    5.2.1 State space description for 4 operational modes . . . . . . . . . . . . 102

    5.2.2 Averaged model for the open loop system . . . . . . . . . . . . . . . 103

    5.3 Saturated controller design for robust output tracking . . . . . . . . . . . . 106

    5.3.1 Converting the tracking problem to a stabilization problem . . . . . 107

    5.3.2 State feedback law design via LMI optimization . . . . . . . . . . . . 108

    5.3.3 Numerical result for an experimental setup . . . . . . . . . . . . . . 110

    5.4 Stability and tracking domain analysis via piecewise quadratic Lyapunov

    functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

    5.4.1 Piecewice LDI description . . . . . . . . . . . . . . . . . . . . . . . . 112

    5.4.2 Piecewise quadratic Lyapunov function . . . . . . . . . . . . . . . . 115

    5.4.3 Invariance and set inclusion LMI conditions . . . . . . . . . . . . . . 117

    5.4.4 Stability region estimation via LMI optimization . . . . . . . . . . . 118

    5.5 Simulation and experimental results . . . . . . . . . . . . . . . . . . . . . . 119

    6 Saturated Speed Control of Medium Power Wind Turbines 123

    6.1 Introduction and moti