Design of cascade fuzzy sliding-mode controller

In this paper, a new cascade fuzzy sliding-mode controller (CFSMC) for a class of uncertain underactuated systems is presented. Firstly, two states are chosen to construct the first-layer sliding-mode surface which can be considered as a general state variable. Then the first-level sliding surface and one of the left state variables are used to construct the second-layer sliding surface. This process continues till the last-level sliding surface is obtained. Considering there exists uncertainty in the system´s model, fuzzy logic is used as an approximator to identify the uncertainty. Using Lyapunov law, we derive the sliding-mode control law and the related parameters adaptive law of fuzzy logic. The CFSMC can guarantee the stability of all the sliding surfaces, and the simulation results show the validity of this method.