Simplex-type variable structure controllers for stability and performance

Abstract

This thesis considers the problem of guaranteeing robust stability as well as performance for plants that can be modelled as linear systems which are perturbed by nonmatching disturbances and parametric uncertainties. The use of simplex-type variable structure controllers (simplex controllers) is analyzed and results are given for both the state feedback and dynamic output feedback cases.

In both of these cases, it is shown that the sliding mode dynamics associated with the variable structure control system (VSCS) can be completely parameterized in terms of a free parameter matrix. Having reduced the problem to one of selecting the free matrix, we show that this is actually equivalent to the problem of designing either an ${\cal H}\sb\infty$-norm bounding state feedback control or an ${\cal H}\sb\infty$-norm bounding output feedback control for a linear system. Design procedures are given, and it is shown how a reduced-order (less than the order of the plant) simplex controller can be designed to guarantee robust stability as well as a certain level of disturbance attenuation for the system in the sliding mode.