NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...

More documents

Recommendations

Info

Response in m Response in m 0.05 0.04 0.03 0.02 0.01 0 −0.01 −0.02 SGA: Nonlinear Robust Passivity Based −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 5.15: SGA: Nonlinear H1 vs. Passivity Based SGA: Nonlinear Robust SGA: Nonlinear Optimal −0.03 0 1 2 3 4 5 6 7 Time Figure 5.16: SGA: Nonlinear H1 vs. SGA: Nonlinear H 2 58
for its true robustness, and its only drawback is the care with which one must choose appropriate basis functions for the approximation and an appropriate region of sta- bility, . 5.5 Tabulated Results Table 5.1 summarizes the performance of the control strategies implemented on the FBS. The rst row compares the e ective exponential decay rates { these values were computed by doing a least-square t of the rst three local maxima of the response curves. The PBC control shows an unusual perturbation in its response envelope, and its decay number is therefore not meaningful. The second row shows the integral of the total energy in the linear position state, y, from the time the control is turned on till the steady-state is reached at about 6 seconds. The third row compares the control e ort by giving the integral of the control signal from 2 to 6 seconds. (In the hardware tests steady-state error is non-existent due to the natural damping of the system, therefore the integrator is only run to t =6seconds.) Table 5.1: Tabular Comparison of Experimental Results Linear Optimal Linear H1 Passivity HJB HJI : e ; t 1.88 1.88 1.89 1.90 1.91 R y(t) 2 dt 1.71 1.71 1.63 1.41 1.1 R u(t) 2 dt .23 .33 1.35 .3 .44 Clearly the best control is the non-linear H1 (SGA/HJI) solution. It outperforms the other control laws without using as much control e ort as the PBC control. The next best control is the non-linear H 2 (SGA/HJB) solution. It does not attenuate the disturbance as fast as the HJI solution, but it also uses less control e ort. These two SGA-based controllers produced nonlinear feedback control laws that were noticeably superior to the linearized controllers. PBC performs better than both of the linearized controls, but it uses an unusual amount of control e ort. An advantage of the PBC 59
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 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: 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
show all

NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...

Create successful ePaper yourself

Delete template?

Save as template?