Adaptive Fuzzy Sliding Mode Control for Decoupled Uncertain Underactuated Systems

In this work, a decoupled adaptive fuzzy sliding mode control method for a class of underactuated systems with unknown terms is proposed. Firstly, the underactuated system is decoupled into two second-order subsystems, which are referred to the actuated and the underactuated parts, and the sliding manifold of the underactuated subsystem is implemented into the actuated subsystem through an inverse-tangent saturation function. Secondly, a sliding mode controller by decoupled method is designed. Then an adaptive fuzzy algorithm is presented to estimate the unknown terms of the system, moreover, the estimated upper bound of the fuzzy modeling error are solved by the adaptive algorithm. Finally, the stability analysis of the closed-loop system is verified by the Lyapunov stability theory. Simulation results on the overhead crane system are given to show the effectiveness of the proposed method.