Design of robust repetitive control system for multiple periods

An approach to regulating quickly any periodic signals with multiple periods is proposed. The contributions are as follows. First, the proposed multiple repetitive controller not only can be implemented with much fewer memory elements than previous ones but also can provide much faster convergence of the controlled error to zero. Secondly, the proposed repetitive controller can assign all poles of the system on a disk with a given radius whose center is the origin. Thirdly, the proposed controller is obtained in an explicit form and the design method requires no equation to be solved. Fourthly, the robustness of the system is improved by introducing a low pass zero phase filter