정합조건이 만족되지 않는 불확실한 다변수 계통에 대한 슬라이딩 모드 제어기의 설계

Design of sliding mode controller for uncertain multivariable systems in the absence of matching conditions

All models of dynamical systems invariably have some measure of uncertainties associated with some of their dynamics. The recent approaches to establish robustness of stabilizing feedback control against the possible uncertainties have a serious limitation, that is their applicability only to the systems that satisfy the matching conditions. Such conditions are rarely met in general applications. If a particular system satisfies the matching conditions, the addition of an actuator will destroy the satisfaction of such conditions. In this paper, we develop robust control algorithm for uncertain multivariable systems in which the matching conditions are not necessarily met. We empoly Lyapunov's second method to derive robust stabilizing controllers which guarantee asymptotic stability against prescribed uncertainties. The derivation consists of transforming the original uncertain system to controllable canonical form and constructing a constant switching surface by designing the closed-loop characteristics as a function of the uncertainties. Numerical examples are discussed as illustrations.