Disturbance Observer-Based Integral Sliding Mode Control for Singularly Perturbed Systems With Mismatched Disturbances

Abstract

This paper presents a disturbance observer-based integral sliding mode control (ISMC) for singularly perturbed systems (SPSs) with mismatched disturbances. First, a linear state feedback control law for the slow subsystem of the SPS is designed, and the fast subsystem is established. Second, a disturbance observer and an ISMC incorporating the disturbance estimate are constructed. The gain of ISMC is obtained by applying the ${H_\infty }$ control theory, and the resulting ISMC can effectively attenuate the mismatched disturbances. Finally, the proposed method is applied to an electric system, which illustrates the effectiveness and feasibility. The proposed design methods are based on the reduced-order subsystems and thus free of the high dimensionality and possible numerical ill-conditioned problems.