Discrete-Time Design of Fractional Delay-Based Repetitive Controller with Sliding Mode Approach for Uncertain Linear Systems with Multiple Periodic Signals

In this paper, a discrete-time design of a fractional internal model-based repetitive controller with a sliding mode approach is presented for uncertain linear systems subject to repetitive trajectory and periodic disturbance. The proposed algorithm, named a fractional delay-based repetitive sliding mode controller (FD-RSMC), aims to enhance tracking accuracy, transient response, and robustness against parametric variations beyond what is offered by conventional repetitive controllers. First, a fractional delay-based repetitive controller (FD-RC) that allows the periodic delay steps to be noninteger is presented to improve the trajectory tracking accuracy and good disturbance compensation of multiple periodic signals. Second, a sliding mode control (SMC) with a discrete-time reaching law is systematically incorporated into FD-RC to improve transient response, especially during the learning period of FD-RC, and also to provide system robustness against model uncertainties. Finally, the stability proof of the closed-loop system with the proposed controller is assessed based on a delayed-sliding mode-reaching condition. Finally, comparative simulation studies are presented to demonstrate the superior performance of the proposed controller.