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

This article proposes a new method for treating the computational problem in discrete time linear multi-periodic repetitive control systems, where the reference signal includes several periodic components with already known periods.  As periods get large, the computational problem becomes prominent. This work thus investigates the frequency contents of reference signals, where the order of original repetitive controller is lowered by considering only a reduced number of poles, namely, the most important contributors to the total energy of the multi-periodic reference signal. A lower order multi-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 spring mass damper system demonstrate the effectiveness of this new controller.