NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...

Response in cm
4
3
2
1
0
−1
−2
−3
Passivity Based
Linearized Robust
−4
0 1 2 3 4 5
Time
6 7 8 9 10
Figure 4.8: Passivity Based Control vs. Linear Robust Control
increasing the amplitude of the rst oscillation after it was turned on (notice in Fig-
ure 4.9 how the rst oscillation after the loop was closed is greater than the open loop
response).
The unusually high rst state energy ( R x 2
1dt) number of the backstepping
control as shown in 4.1 is actually the direct result of this initial perturbation in the
beam's motion, and it is therefore misleading. It's strong attenuation of the beam's
oscillations, clearly seen in Figures 4.10 through 4.12, is a direct result from the
fact that this control design used more control energy than the other designs. This
became a weakness on the experimental testbed, however, because it's high input
signal requirements were too demanding on the electric motor, and it was unable to
e ectively regulate the FBS.
4.2.5 SGA: Nonlinear H 2 Optimal Control
The SGA technique performed reasonably well in simulation. It regulated the
NLBP faster than the linearized H1 and the PBC controller as seen in Figures 4.15
and 4.16, however it was not as e ective as the backstepping (Figure 4.17 or the
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