NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...
NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ... NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...
ACKNOWLEDGMENTS I would like to acknowledge my advisor Dr. Beard for all of his assistance and guidance in the direction of the research that culminated in the thesis. He has been a wonderful mentor, always willing to help me understand the intricacies of the mathematics and the subtleties of the eld of robust control. He has always been supportive of my ideas and a useful source of knowledge and experience. I would also like toacknowledge the encouragement I received from my other committee members Dr. Mclain and Dr. Stirling, and for their support of my en- deavors. I thank my family and friends wholeheartedly: I'm lucky to have a kind and patient family, and I'm indebted to them for their love and support, and for their quiet encouragement of my studies. Thanks to my friends also, for your fellowship. Especially, I'd like to thank Miguel Apeztegia for his friendship and support, and his aide in preparing this thesis.
Contents Acknowledgments vi List of Tables ix List of Figures xii 1 Introduction 1 1.1 Motivation and Problem Description . . . . . . . . . . . . . . . . . . 1 1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Plant Speci cations and Model 7 2.1 Hardware Set-up and Speci cations . . . . . . . . . . . . . . . . . . . 7 2.2 Derivation of the Mathematical Model . . . . . . . . . . . . . . . . . 8 2.3 Software Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3 Overview of Control Strategies Implemented on the Flexible Beam System 15 3.1 Linear Quadratic Regulation . . . . . . . . . . . . . . . . . . . . . . . 15 3.2 Linear H1 Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.3 Passivity-Based Control . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.4 Backstepping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.5 Successive Galerkin Approximations . . . . . . . . . . . . . . . . . . . 24 3.5.1 The H 2 Problem . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.5.2 The H1 Problem . . . . . . . . . . . . . . . . . . . . . . . . . 27 vii
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- Page 3 and 4: BRIGHAM YOUNG UNIVERSITY GRADUATE C
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- Page 12 and 13: 4.19 SGA: Nonlinear H1 vs. Linear O
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- Page 37 and 38: where V satis es the well known Ham
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- Page 41 and 42: Chapter 4 Simulation Results 4.1 Th
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- Page 47 and 48: Response in cm Response in cm 4 3 2
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Contents<br />
Acknowledgments vi<br />
List of Tables ix<br />
List of Figures xii<br />
1 Introduction 1<br />
1.1 Motivation and Problem Description . . . . . . . . . . . . . . . . . . 1<br />
1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3<br />
1.3 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4<br />
2 Plant Speci cations and Model 7<br />
2.1 Hardware Set-up and Speci cations . . . . . . . . . . . . . . . . . . . 7<br />
2.2 Derivation of the Mathematical Model . . . . . . . . . . . . . . . . . 8<br />
2.3 Software Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13<br />
3 Overview of Control Strategies Implemented on the Flexible Beam<br />
System 15<br />
3.1 Linear Quadratic Regulation . . . . . . . . . . . . . . . . . . . . . . . 15<br />
3.2 Linear H1 Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17<br />
3.3 Passivity-Based Control . . . . . . . . . . . . . . . . . . . . . . . . . 19<br />
3.4 Backstepping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21<br />
3.5 Successive Galerkin Approximations . . . . . . . . . . . . . . . . . . . 24<br />
3.5.1 The H 2 Problem . . . . . . . . . . . . . . . . . . . . . . . . . 24<br />
3.5.2 The H1 Problem . . . . . . . . . . . . . . . . . . . . . . . . . 27<br />
vii
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