NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...

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Response in m 0.05 0.04 0.03 0.02 0.01 0 −0.01 −0.02 Open Loop Response −0.03 0 1 2 3 4 5 6 7 Time Figure 5.1: Open Loop Response of the FBS H 2 control did not even stabilize the system until its gains were recomputed, and its nal gains were substantially lower (Kc =[;45 11:3 1:8:32]) than those used in the simulations. Figure 5.4 shows that the linearized H1 controller outperformed the H 2 design by a small margin. Clearly the unmodelled dynamics and disturbances in the system are enough to give the robust design an advantage when applied to a real, physical plant. 5.3 Passivity Based Control The passivity-based algorithm's results in hardware are very similar to its simulated response. It displays the same unusual rebound behavior: it damps the vibration rmly in the rst seconds, then the amplitude of the vibrations increases before nally dying out (see Figure 5.5). This phenomenon, though not a serious e ect in this experiment, could be a serious liability in situations where a monotonically decreasing response envelope is required. The passivity-based design yields better performance than the linearized controls as measured by the energy in the rst state, 50
Response in m Response in m 0.05 0.04 0.03 0.02 0.01 0 −0.01 −0.02 Linear Optimal Open Loop Response −0.03 0 1 2 3 4 5 6 7 Time 0.05 0.04 0.03 0.02 0.01 0 −0.01 −0.02 Figure 5.2: Linear Optimal vs. Open Loop Linear Robust Open Loop Response −0.03 0 1 2 3 4 5 6 7 Time Figure 5.3: Linear Robust vs. Open Loop 51
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NONLINEAR CONTROLLER COMPARISON ON
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BRIGHAM YOUNG UNIVERSITY GRADUATE C
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ABSTRACT NONLINEAR CONTROLLER COMPA
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Contents Acknowledgments vi List of
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
Page 59: all of the physical parameters exce
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 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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