NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...

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Response in cm 4 3 2 1 0 −1 −2 −3 Linearized Robust Linearized Optimal −4 0 1 2 3 4 5 Time 6 7 8 9 10 Figure 4.5: Linear H1 vs. Linearized Optimal than this approach in the simulations. Figures 4.7 and 4.8 show that the linearized designs attenuated the vibrations faster. A possible explanation for the strange envelope of the rst state's oscillations, is that the dynamics in the feedback loop act as an energy shaping block. It is possible that, similar to the way the energy in two coupled pendulums is transfered back and forth before damping out, energy is being coupled back and forth between the control and the system dynamics, while being steadily absorbed by the controller's virtual damping e ect. 4.2.4 Backstepping Algorithm The backstepping control design performed very well { it seemed to damp the oscillations quicker than any of the other designs in simulation. Figures 4.10 through 4.12 show that it attenuated the vibrations faster than the other control designs. There were, however, two anomalies associated with this controller: it ex- pended a great deal more control e ort than the previous designs, and it began by 34
Response in cm Response in cm 4 3 2 1 0 −1 −2 −3 Passivity Based Open Loop Response −4 0 1 2 3 4 5 Time 6 7 8 9 10 4 3 2 1 0 −1 −2 −3 Figure 4.6: Passivity Based Control vs. Open Loop Response Passivity Based Linearized Optimal −4 0 1 2 3 4 5 Time 6 7 8 9 10 Figure 4.7: Passivity Based Control vs. Linear Optimal Control 35
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 and 8: 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: Response in cm 4 3 2 1 0 −1 −2
Page 49 and 50: Response in cm Response in cm 5 4 3
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 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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