Integral Manifold in System Design with Application to Flexible Link Robot Control
ILLINOIS UNIV AT URBANA DECISION AND CONTROL LAB
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The integral manifold concept is used in this thesis for controller design in various problems. A definition and the conditions for the existence of the integral manifold are given. Integral manifolds in linear systems are analyzed with special attention given to how the linear system possesses an input dependent manifold. Flexibility in flexible link robots is shown to be a cause for phase delay, which is reduced by a corrective controller based on the integral manifold concept. For a class of nonlinear systems with nonlinear output, the author designed a nonlinear PI controller that achieve asymptotic tracking and disturbance rejection of bounded signals which are not only unknown but also slowly varying. Finally, we showed the existence of a lower order optimal problem which is equivalent to a singularly perturbed optimal problem with initial conditions restricted to a manifold. Throughout this thesis, results obtained from the manifold approach are shown to be consistent with, and sometimes even extend, some established results in singularly perturbed systems. Keywords Manipulators Optimal control.