Design of distance-based fuzzy sliding mode controller with adaptive fuzzy rule insertion

An adaptive distance-based fuzzy sliding mode controller is developed. In the process of designing the proposed fuzzy controller, we firstly calculate the distance between the actual state (s,s˙) and the sliding line in the s-s˙ plane, and then define a new variable called the signed distance. Then we adopt the signed distance as the unique input variable for the fuzzy controller, which is called a distance-based fuzzy sliding-mode controller (D-FSMC). Hence, both the number of fuzzy rules and the complexity of the D-FSMC are greatly reduced compared to those of in the conventional FSMC. We can show that the stability of the control system is guaranteed under the Lyapunov sense. Finally, an adaptive process is employed to systematically develop the effective fuzzy rules for the D-FSMC. Computer simulations are given to verify the validity of the proposed adaptive D-FSMC