Discrete-time repetitive control system with multiple periods

In this paper, a new approach to regulate any periodic signals with multiple periods is proposed and a useful discrete-time controller called multiple repetitive controller is presented. 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 not only can assure the stability of the closed loop system but also 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. The design effort is very small even if the periods are very large. Finally, the proposed scheme is applied to DC servo motor system, and the effectiveness is demonstrated by simulation.