Design of a sliding mode controller with fuzzy sliding surfaces

The authors suggest a sliding mode controller, using a linear time-varying sliding surface instead of the fixed sliding surface, which has robustness against parameter variations and extraneous disturbances during the reaching phase to the final sliding surface. By applying the Takagi-Sugeno (TS) fuzzy algorithm to the regulation of the linear time-varying sliding surface: the reaching time of the system trajectory is shorter than in the fixed method. This proposed scheme has better performance than the conventional method in reaching time, parameter variation and extraneous disturbance. To demonstrate its performance, the proposed control algorithm is applied to a rotational inverted pendulum