NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...
NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ... NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...
control was that it requires only the angle as an input (no state estimation), though perhaps this explains why it is not very e cient in its use of control e ort. 60
Chapter 6 Conclusion and Future Work 6.1 Overview The exible beam system is a nonlinear system subject to the higher-order dynamics of the beam's motion, as well as to the non-linearity caused by the coupling between the rotational actuator and the quasi-linear motion of the mass at the end of the beam. Despite all of these nonlinearities and despite all of the unmodelled dynamics, the linearized approaches work adequately and damp the beam's vibration. It was gratifying to note, however, that the full nonlinear approaches did prove tobe better controllers when implemented in hardware. The successive Galerkin approximations to the HJB and HJI equations pro- duce control algorithms that e ciently regulate the non-linear benchmark problem. The performance of these algorithms as implemented on the FBS is superior to the performance of standard linearized controllers as well as a passivity-based design and a backstepping design. All of the control strategies studied produce robust, stabi- lizing designs, though the passivity based approach is very sensitive to its feedback parameters. In implementing this broad sample of nonlinear control algorithms, the similar- ities and di erences of the studied approaches become more apparent. The standard linearized optimal and robust approaches are simply ways of computing the appro- priate state-feedback gains so that the system is optimally regulated and robust with respect to a given cost function. This approach is thus dependent on an expert fa- miliar with the system to choose an appropriate cost function. This is very similar 61
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Chapter 6<br />
Conclusion and Future Work<br />
6.1 Overview<br />
The exible beam system is a nonlinear system subject to the higher-order<br />
dynamics of the beam's motion, as well as to the non-linearity caused by the coupling<br />
between the rotational actuator and the quasi-linear motion of the mass at the end<br />
of the beam. Despite all of these nonlinearities and despite all of the unmodelled<br />
dynamics, the linearized approaches work adequately and damp the beam's vibration.<br />
It was gratifying to note, however, that the full nonlinear approaches did prove tobe<br />
better controllers when implemented in hardware.<br />
The successive Galerkin approximations to the HJB and HJI equations pro-<br />
duce control algorithms that e ciently regulate the non-linear benchmark problem.<br />
The performance of these algorithms as implemented on the FBS is superior to the<br />
performance of standard linearized controllers as well as a passivity-based design and<br />
a backstepping design. All of the control strategies studied produce robust, stabi-<br />
lizing designs, though the passivity based approach is very sensitive to its feedback<br />
parameters.<br />
In implementing this broad sample of nonlinear control algorithms, the similar-<br />
ities and di erences of the studied approaches become more apparent. The standard<br />
linearized optimal and robust approaches are simply ways of computing the appro-<br />
priate state-feedback gains so that the system is optimally regulated and robust with<br />
respect to a given cost function. This approach is thus dependent on an expert fa-<br />
miliar with the system to choose an appropriate cost function. This is very similar<br />
61