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  • ROBUST CONTROL OF SYSTEMS SUBJECTED TO

    UNCERTAIN DISTURBANCES AND ACTUATOR

    DYNAMICS

    Rodolfo VILLAMIZAR MEJIA

    ISBN: 84-689-2579-9 Dipòsit legal: GI-633-2005

  • Universitat de Girona Departament d’Electrònica, Informàtica i Automàtica

    Robust Control of Systems

    Subjected to Uncertain Disturbances

    and Actuator Dynamics

    by

    Rodolfo Villamizar Mej́ıa

    Advisors

    Dr. Josep Veh́ı and Dr. Ningsu Luo

    DOCTORAL THESIS Girona, Spain March, 2005

  • Universitat de Girona Departament d’Electrònica, Informàtica i Automàtica

    Robust Control of Systems

    Subjected to Uncertain Disturbances

    and Actuator Dynamics

    by

    Rodolfo Villamizar Mej́ıa

    A dissertation presented to the Universitat de Girona in partial fulfillment of the requirements of the degree of DOCTOR OF PHILOSOPHY

    Advisors

    Dr. Josep Veh́ı

    Dr. Ningsu Luo

    Girona-Spain, March, 2005

  • Universitat de Girona Departament de Electrònica, Informàtica i Automàtica

    Abstract

    Robust Control of Systems Subjected to Uncertain Disturbances and Actuator Dynamics

    by Rodolfo Villamizar Mej́ıa

    Advisors: Dr. Josep Veh́ı and Dr. Ningsu Luo

    January, 2005 Girona, Spain

    This dissertation focuses on the design and validation of robust controllers that can effectively reduce vibrations in structures due to external disturbances such as earthquakes, strong winds or heavy dynamic loads. The design of the controllers is based on control theories traditionally used in structural control: Lyapunov stability theory, Sliding Mode Control and Clipped-Optimal Control, another recently introduced: Backstepping Control and one that had not been used before in this control area: Quantitative Feedback Theory. The main advantage by using these techniques is that some open structural problems such as actuator dynamics, uncertain distur- bances, uncertain parameters, measurement limitation and dynamic coupling can be treated. Numerical validation of the controllers proposed is performed on typical structural models. A 10-story base isolated structure, a truck-bridge structural platform and a two-span bridge are used. Their control scheme contains inherit one o more open structural control problems. Three experimental prototypes are used to implement the robust controllers proposed, in order to ex- perimentally verify their viability and effectiveness. The main contribution of the present thesis is obtaining robust structural controllers, numerically and experimentally verified, that account structural control problems such as actuator dynamics, uncertain parameters, dynamic coupling, measurement limitations and unknown disturbances and based on novel control techniques.

  • To whom give sense to my life: my family

    My parents Pedro Jesús and Ana Inés My wife Martha Cecilia

    My brothers Orlando and Jesús M My sisters Luz Marina, Rubiela, Gloria Carmen and Floralba

    All my nephews and brothers in law

  • Contents

    Contents ix

    List of Figures xi

    Acknowledgments xv

    1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 Objective of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.4 Structure of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

    2 Literature Review 3 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Structural Control Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

    2.2.1 Passive Control Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2.2 Active Control Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.3 Semi-active control devices . . . . . . . . . . . . . . . . . . . . . . . . . . 5

    2.3 Structural Control Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3.1 Optimal Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.2 Robust Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.3 Predictive Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

    3 Open Problems in Structural Control 15 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2 Unknown Disturbances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.3 Measurements Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.4 Dynamic Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.5 Actuator Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

    3.5.1 Hysteretic Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.5.2 Actuator Time Delay and Friction Force . . . . . . . . . . . . . . . . . . . 17

    3.6 Uncertain Structural Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.6.1 QFT LTI design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.6.2 QFT controller for uncertain structures . . . . . . . . . . . . . . . . . . . 23

    4 Structural Control Approaches 25 4.1 Structural System A: 10-story Base Isolated Structure . . . . . . . . . . . . . . . 25

    4.1.1 Control Configuration 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

    ix

  • x CONTENTS

    4.1.2 Control Configuration 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.1.3 Control Configuration 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

    4.2 Structural System B: Structure Uncertainly Excited by Temporary Coupling . . 40 4.2.1 Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.2.2 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

    4.3 Structural System C: Full Scale Two-Span Bridge . . . . . . . . . . . . . . . . . . 50 4.3.1 Control Configuration 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.3.2 Control Configuration 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

    5 Experimental Verification 63 5.1 Experimental Prototype A. 6-story test building semiactively controlled . . . . . 63

    5.1.1 Semiactive Control Devices . . . . . . . . . . . . . . . . . . . . . . . . . . 64 5.1.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 5.1.3 Identification of the System . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5.1.4 Identification of MR dampers . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.1.5 Semiactive Control Algorithms . . . . . . . . . . . . . . . . . . . . . . . . 70 5.1.6 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

    5.2 Experiment Prototype 2 : Pseudo-dynamic test sub-structure . . . . . . . . . . . 84 5.2.1 Controller design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.2.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5.2.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

    5.3 Experimental Prototype 3. 2-story Actively Controlled Test Building . . . . . . 92 5.3.1 Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.3.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

    6 Conclusions and Future Work 99

    Bibliography 101

    Vita 109

  • List of Figures

    2.1 Actively controlled Kiobashi Seiwa building. . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 AMD control device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Type of Active Tuned Liquid Column Damper (ATLCD) . . . . . . . . . . . . . . . . 5 2.4 Full-Scale Implementation of Structural Control in USA . . . . . . . . . . . . . . . . . 7 2.5 Full-scale 20T MR Fluid Damper . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.6 Basic block diagram for predictive control system (PCS) . . . . . . . . . . . . . . . . . 12 2.7 Overall block diagram of an adaptive predictive control system . . . . . . . . . . . . . 13

    3.1 Representative Mode Shapes of the Bridge Evaluation Model . . . . . . . . . . . . . . 19 3.2 LTI structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.3 Bounds allowed for M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.4 Plant templates at ω=10,30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.5 All bounds in the Nichols Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.6 Intersection of bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.7 A possible final loop LN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.8 Effect of including F (jω) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.9 LTI structure for structural control . . . . . . . . . . . . . . . . . . . . . . . . . . 24

    4.1 A 10-story base isolated building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.2 Absolute peak values a). Displacement, b). Velocity c). Acceleration . . . . . . . . . . 32 4.3 Absolute 1st floor displacement . . . . . . . . . . . . . . . . . . . . . . . . . . . .