Extended Disturbance Observer-Based Integral Sliding Mode Control for Nonlinear System via T-S Fuzzy Model

Abstract

In this paper, an extended disturbance observer-based integral sliding-mode control for a nonlinear system is proposed by the Takagi-Sugeno (T-S) fuzzy model approach. The proposed method focuses on two points: First, improving the design flexibility of integral fuzzy sliding-mode control (IFSMC) by transforming a conventional T-S fuzzy model structure into a novel form. Second, expanding a previous disturbance observer-based control (DOBC) concept by introducing a Fourier analysis to deal with the non-periodic form of disturbance. By using the modified form of the fuzzy model, a novel sliding surface combined with estimated disturbance through several fuzzy disturbance observers (FDOB) is suggested. Besides, a sufficient condition for guaranteeing asymptotic stability of the sliding dynamic with $H_\infty $ control performance is proposed by applying a proper Lyapunov function with the linear matrix inequality (LMI) concept. Furthermore, a reachability problem of the proposed sliding surface is also handled by introducing another Lyapunov function. Finally, the effectiveness of the proposed method is demonstrated by comparing previous studies, which focused on robust control techniques, based on the simulation results of an inverted-pendulum system.