NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...

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
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