NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...

Response in cm
4
3
2
1
0
−1
−2
−3
Linearized Optimal
Open Loop Response
−4
0 1 2 3 4 5
Time
6 7 8 9 10
Figure 4.3: Linearized Optimal vs. Open Loop Response
solutions to plants that are di cult to regulate using the standard linear approaches.
Figure 4.3 shows the LQR design's performance plotted against the open loop re-
sponse.
This linearized H 2 approach gave almost the best performance in simulations.
This is reasonable since the initial disturbance was small, and the system stayed within
a region where linearization yields a good estimate of the true system dynamics.
It should be said, though, that this control relied on relatively high gains (Kc =
[;658 69:8 26 3:7]), and it was later discovered that such gains resulted in actuator
dysfunction and instability on the hardware system. This really highlights the goal
of nonlinear control design research: to nd control laws that will e ectively regulate
systems when they operate in the presence of real-world nonlinearities or when they
operate well beyond their linear region.
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