Design of robust repetitive control system for multiple periods

In this paper, a new approach to regulate 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 less memory elements than the 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 to solve no equation. Fourthly, the robustness of the system is improved by introducing a low pass zero phase filter.