Discrete-Time Fractional-Order Terminal Sliding Mode Tracking Control

This chapter presents a practical discrete-time FO terminal sliding mode control strategy for high-precision tracking tasks based on linear motors. In particular, the practical parametric uncertainties involving sliding friction, uncertain payload, and disturbance in tracking tasks are considered in this work. Combining Grünwald-Letnikov FO definition and terminal sliding mode technique, the proposed method synthesizes a novel discrete-time FO terminal SMC law to drive the sliding mode dynamics into the stable region in finite steps theoretically even though the system is suffering from uncertainties and disturbances, and the motion on the surface can guarantee higher tracking precision than the conventional discrete-time terminal sliding surface by selecting suitable controller parameters. The theoretical analyses give out the guideline of parameter selection, and experiments are carried out on the linear-motor-based test platform to demonstrate that the proposed controller is easily implemented and can achieve high-precision tracking, fast response, and considerable robustness to uncertainties.