Robust Internal Model-based Control for Linear-Time-Invariant Systems in Discrete-time Domain

This paper introduces a new strategy for robustly controlling linear discrete-time systems that experience both periodic disturbances modeled by an uncertain exosystem and bounded matched disturbances. The strategy, called internal model-based sliding mode control, combines the robustness of sliding mode control with the precise tracking capabilities of internal model-based control. This new approach, inspired by implicitly discretized first order sliding mode control, offers superior performance with reduced chattering compared to explicit methods while maintaining simplicity. By effectively suppressing chattering and leveraging the exosystem model incorporated in the internal model-based controller, the proposed method achieves superior disturbance rejection compared with feedback loops relying either on internal model-based control or sliding mode control only. The presented simulation example illustrates the application of the proposed controller and the obtained results show that significant disturbance rejection improvement is achieved.