Modified adaptive fuzzy sliding mode controller for uncertain nonlinear systems

In this paper, a modified adaptive fuzzy sliding mode controller for a certain class of uncertain nonlinear systems is presented. We incorporate the fuzzy sliding mode control technique with a modified adaptive fuzzy control technique to design a modified adaptive fuzzy sliding mode controller so that the proposed controller is robust against the un-modeled dynamics and the approximation errors. Firstly, we establish a fuzzy model to describe the dynamic characteristics of the given uncertain nonlinear system. Then, based on the fuzzy model, a fuzzy sliding mode controller is designed. By considering both the information of tracking error and modeling error, the modified adaptive laws for tuning the adjustable parameters of the fuzzy model are derived based on the Lyapunov synthesis approach. Since the modified adaptive laws contain both the tracking error and the modeling error, it implies that the fuzzy model parameters would continuously converge until both the tracking error and modeling error converges to zero. An inverted pendulum control system is simulated to demonstrate the control performance by using the proposed method.