A Spectrum-based Filter Design for Periodic Control of Systems with Time Delay

In this paper, we propose a completely analytical controller design that can address the periodic control problem for a stable minimum-phase linear system with arbitrary order that suffers from input/output time delays. Compared to repetitive control and other paradigms based on the Internal Model Principle, which are traditionally used in such cases, the proposed approach gives rise to finite-dimensional control laws. The effectiveness of the design stems from utilizing a filter structure derived from a reference desired sensitivity, which is shown to correspond to the control system that stabilizes the signal model. The proposed control design is experimentally validated on a physical system where the goal is to reject periodic disturbance acting on a mass-spring-damper setup where the sensor and the actuator are non-collocated.