Backstepping quasi-continuous high-order sliding mode control for a Takagi–Sugeno fuzzy system with an application for a two-link robot control

A new control scheme is proposed for motion tracking of a Takagi–Sugeno fuzzy system using the backstepping quasi-continuous high-order sliding mode (HOSM) control technique. First, a Takagi–Sugeno fuzzy model is used to represent the original second-order nonlinear system; most of the parameters for this model can be computed offline. Next, a conventional backstepping sliding mode control (BSMC) is designed to stabilize and guarantee the exact motion tracking for the Takagi–Sugeno fuzzy system. However, use of the conventional sliding mode control generates significant chattering. Therefore, a quasi-continuous second-order sliding mode (QC2S) control is employed to reduce chattering and obtain higher tracking precision, resulting in a backstepping quasi-continuous second-order sliding mode (BQC2S) control law. Combining the Takagi–Sugeno fuzzy model with the BQC2S controller results in a controller scheme that preserves the advantages of both techniques, such as the low online computational burden of the Takagi–Sugeno fuzzy model, and the low chattering, robustness, and fast transient response of the BQC2S controller. Finally, the proposed controller is used to control a two-link robot manipulator and is compared with the existing approaches. Simulation results are presented to demonstrate the effectiveness of the proposed methodology.