NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...

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4 Simulation Results 29 4.1 The Simulated Testbed . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.2 Evaluation of the Plots in Simulation . . . . . . . . . . . . . . . . . . 31 4.2.1 Linearized Optimal H 2 . . . . . . . . . . . . . . . . . . . . . . 31 4.2.2 Linearized H1 . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.2.3 Passivity Based Control . . . . . . . . . . . . . . . . . . . . . 33 4.2.4 Backstepping Algorithm . . . . . . . . . . . . . . . . . . . . . 34 4.2.5 SGA: Nonlinear H 2 Optimal Control . . . . . . . . . . . . . . 36 4.2.6 SGA: Nonlinear H1 Control . . . . . . . . . . . . . . . . . . . 39 4.3 Tabulated Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.4 Tuning and Ease of Implementation . . . . . . . . . . . . . . . . . . . 45 4.5 Robustness Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 5 Experimental Results 49 5.1 Testbed and Open Loop Response . . . . . . . . . . . . . . . . . . . . 49 5.2 Linearized Optimal and Robust Controls . . . . . . . . . . . . . . . . 49 5.3 Passivity Based Control . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.4 Successive Galerkin Approximations . . . . . . . . . . . . . . . . . . . 52 5.5 Tabulated Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 6 Conclusion and Future Work 61 6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 6.2 Extensions to this Research . . . . . . . . . . . . . . . . . . . . . . . 62 Bibliography 66
List of Tables 4.1 Tabular Comparison of Simulated Results . . . . . . . . . . . . . . . 45 4.2 Tabular Comparison of Simulated Robustness . . . . . . . . . . . . . 47 5.1 Tabular Comparison of Experimental Results . . . . . . . . . . . . . . 59 ix
Page 1 and 2: NONLINEAR CONTROLLER COMPARISON ON
Page 3 and 4: BRIGHAM YOUNG UNIVERSITY GRADUATE C
Page 5 and 6: ABSTRACT NONLINEAR CONTROLLER COMPA
Page 7: Contents Acknowledgments vi List of
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
Page 59:
all of the physical parameters exce
Page 62 and 63:
Response in m 0.05 0.04 0.03 0.02 0
Page 64 and 65:
Response in m 0.05 0.04 0.03 0.02 0
Page 66 and 67:
Response in m Response in m 0.05 0.
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
control was that it requires only t
Page 74 and 75:
to the Galerkin approximation techn
Page 77 and 78:
Bibliography [1] P. Kokotovic M. Ja
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NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...

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