Linear Optimal Multi-periodic Repetitive Control - A Low Order Controller Scheme

This article proposes a new method for treating the computational problem in discrete timelinear multi-periodic repetitive control systems, where the reference signal includes several periodiccomponents with already known periods. As periods get large, the computational problem becomesprominent. This work thus investigates the frequency contents of reference signals, where the orderof original repetitive controller is lowered by considering only a reduced number of poles, namely, themost important contributors to the total energy of the multi-periodic reference signal. A lower ordermulti-periodic repetitive controller is designed which assures BIBO stability of the closed-loop system,and approximate tracking is achieved. Finally, experimental tests on a non-minimum phase springmass damper system demonstrate the effectiveness of this new controller