A novel fuzzy second-order sliding mode observer-controller for a T-S fuzzy system with an application for robot control

This paper investigates an algorithm for the tracking performance of a Takagi-Sugeno (T-S) fuzzy system using the second-order sliding mode observer/controller technique. First, the original second-order nonlinear system is represented by a T-S fuzzy model, in which most of the parameters can be computed offline. A novel fuzzy second-order sliding mode observer (FSOSMO), which combines the T-S fuzzy model and the second-order sliding mode observer (SOSMO), is then designed to estimate the velocity. Also, a new fuzzy second-order sliding mode control (FSOSMC), which combines the T-S fuzzy model and the second-order sliding mode control (SOSMC), is proposed to stabilize and guarantee the exact motion tracking for the T-S fuzzy system. By integrating the T-S fuzzy model with SOSMO/C, the resulting observer/controller scheme preserves the advantages of both techniques, such as the low online computational burden of the T-S fuzzy model, and low chattering, fast response, and finite time convergence of the SOSMO/C. Moreover, the stability and convergence of the proposed closed loop observer-based controller strategy is theoretically proven by the Lyapunov method. Finally, the simulation results of a two-link robot manipulator are presented to demonstrate the effectiveness of the proposed approach.