Analysis and synthesis of uncertain variable structure feedback systems with bounded controllers
Abstract
A class of feedback controllers capable of reducing parameter sensitivities and rejecting disturbances is investigated in this thesis. The methodology uses, in its idealized form, piecewise continuous bounded feedback controllers, resulting in sliding of the state trajectory along a switching manifold in an estimated region of the state space. A new decoupling state transformation is presented which makes the methodology easier to apply, both analytically and computationally. Continuous and discontinuous bounded feedback controls are developed which guarantee practical stability of all motions of a class of uncertain dynamical systems with norm-bounded uncertainties. The implementation of variable structure controllers in the case of bounded control inputs is discussed and different estimates of the domain of attraction for a class of multivariable uncertain linear time-invariant variable structure systems are obtained. New techniques to estimate domains of attraction for such systems are presented. Quadratic and norm-type Lyapunov functions for the decoupled subsystems are given and utilized in order to form a Lyapunov function for the overall system. The presented methodology also makes use of the comparison systems principle, the notion of combining different Lyapunov functions, and some parameter optimization techniques. Finally, the approach is applied to the attractivity region estimation problem for systems with relay-type controllers. Parametric estimates of the stability domain are given. An algorithm is presented to maximize the extent of the estimated regions. In order to demonstrate the applicability of the presented results, and to compare the obtained results with the existing ones, several illustrative examples along with computer simulations are presented. Also, the control of a two-joint planar robot manipulator with hard bounds on its torques is successfully addressed.
Degree
Ph.D.
Advisors
Zak, Purdue University.
Subject Area
Electrical engineering
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