Adaptive Fuzzy Total Sliding-Mode Control of Unknown Nonlinear Systems

This paper proposes the adaptive fuzzy total sliding-mode control systems with integral (I-AFTSMC) and proportional-integral (PI-AFTSMC) learning algorithms for the unknown nonlinear systems. These AFTSMC systems are comprised of a fuzzy total sliding-mode controller and a robust controller. The fuzzy total sliding-mode controller is utilized to approximate an ideal controller and the robust controller is designed to cover the approximation error between the fuzzy total sliding-mode controller and the ideal controller. In these designs the fuzzy rules are on-line tuned by the derived learning algorithm in the sense of Lyapunov function, so that the stability of the system can be guaranteed. The proposed AFTSMC systems are applied to the fault accommodation control of a Van der Pol oscillator and trajectory tracking control of a linear piezoelectric ceramic motor. The simulation result of Van der Pol oscillator and the experimental result of linear piezoelectric ceramic motor demonstrate that the effectiveness of the proposed AFTSMC systems for achieving favorable tracking performance. Comparing to the integral learning algorithm, the proportional-integral learning algorithm can achieve faster convergence of the tracking error; this comparison is also illustrated by the simulations and experiments.