NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...
NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...
NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...
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Response in m<br />
0.05<br />
0.04<br />
0.03<br />
0.02<br />
0.01<br />
0<br />
−0.01<br />
−0.02<br />
Linear Robust<br />
Linear Optimal<br />
−0.03<br />
0 1 2 3 4 5 6 7<br />
Time<br />
Figure 5.4: Linear Robust vs. Linear Optimal<br />
though Figures 5.6 and 5.7 show that the linearized controllers' attenuation was more<br />
uniform.<br />
Since its performance increases with respect to the linearized designs in going<br />
from simulation to the hardware testbed, the passivity based control design is justi ed.<br />
Its robustness is also apparent from its portability between simulation and hardware.<br />
5.4 Successive Galerkin Approximations<br />
The successive Galerkin approximations yields the best results in hardware.<br />
Both the HJB solution and the HJI solution outperform the linearized controlsaswell<br />
as the passivity based control, as shown in Figures 5.9, 5.10, and 5.11. Figure 5.16<br />
shows that the nonlinear robust approximation slightly outperforms the HJB solution,<br />
perhaps because its design emphasizes robustness with respect to the unmodelled<br />
e ects of the exible beam.<br />
The SGA method succeeds in outperforming standard linear approaches as<br />
well as a passivity based design. Its implementation is straightforward, and it is eas-<br />
ily tuned to optimize its performance. Its excellent performance in hardware speaks<br />
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