Discrete sliding mode control with optimal generalized sliding function for non-minimum phase system

Abstract

Discrete sliding mode control with classical sliding function for the input–output representation is not applicable in non-minimum phase systems, due to the presence of unstable zero. In fact, the presence of the unstable zero risks deteriorating or saturating the control law. In order to surmount this problem, a new discrete generalized sliding mode controller for non-minimum phase systems is proposed with a new sliding function called discrete generalized sliding function. Here, the determination of optimal coefficients of the discrete generalized sliding function is proposed in terms of linear matrix inequalities. Using the proposed method, a discrete generalized sliding mode control for non-minimum phase systems with input–output model is presented and compared with the discrete generalized sliding mode controller using the pole placement method. An illustrative example verifies the effectiveness of the proposed technique.