Design of Sliding Mode Controller for Uncertain Multivariable Systems in the absence of Structure Matching Conditions

정합 조건이 만족되지 않는 불확실한 다변수 계통에 대한 슬라이딩 모드 제어기의 설계

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. In order to eliminate an influence over partial state variables due to unknown constant disturbances we perform the appropriate block-decomposition for a given system. Functional observers are introduced to estimate the unknown constant disturbances. The sliding mode controller is designed in such a way that the partial state variables in the state-space are directed towards switching surfaces and regulated to the origin asymptotically. Numerical examples are discussed as illustrations.