NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...

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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
Page 1 and 2: NONLINEAR CONTROLLER COMPARISON ON
Page 3 and 4: BRIGHAM YOUNG UNIVERSITY GRADUATE C
Page 5: ABSTRACT NONLINEAR CONTROLLER COMPA
Page 9: List of Tables 4.1 Tabular Comparis
Page 12 and 13: 4.19 SGA: Nonlinear H1 vs. Linear O
Page 14 and 15: Figure 1.1: TORA System One of the
Page 16 and 17: 1.3 Literature Review In surveying
Page 19 and 20: Chapter 2 Plant Speci cations and M
Page 21 and 22: Figure 2.2: Mechanical Model of Fle
Page 23 and 24: Figure 2.4: Translational Oscillati
Page 25 and 26: 2.3 Software Set-up All of the cont
Page 27 and 28: Chapter 3 Overview of Control Strat
Page 29 and 30: The optimal gain matrix was given b
Page 31 and 32: 3.3 Passivity-Based Control Certain
Page 33 and 34: limitations, k 1 and k 2 are tuning
Page 35 and 36: Now we regard as the control variab
Page 37 and 38: where V satis es the well known Ham
Page 39 and 40: ecause one can quickly adjust the Q
Page 41 and 42: Chapter 4 Simulation Results 4.1 Th
Page 43 and 44: disturbances, whereas the hardware
Page 45 and 46: Response in cm 4 3 2 1 0 −1 −2
Page 47 and 48: Response in cm Response in cm 4 3 2
Page 51 and 52: Response in cm 4 3 2 1 0 −1 −2
Page 57 and 58:
It is seen in Figure 4.23 that the
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all of the physical parameters exce
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Response in m 0.05 0.04 0.03 0.02 0
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Response in m 0.05 0.04 0.03 0.02 0
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Response in m Response in m 0.05 0.
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Page 70 and 71:
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control was that it requires only t
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to the Galerkin approximation techn
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Bibliography [1] P. Kokotovic M. Ja
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NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...

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