Design of discrete-time repetitive control system for pole placement and application

In this paper, a new repetitive control system is proposed from the viewpoint of pole placement. The contributions are as follows. First, the proposed repetitive controller can assign all poles of the closed-loop system on a disk with a given radius and the center at the origin. As a result, faster convergence of the controlled error to zero than the previous ones is obtained. Secondly, the proposed controller is obtained explicitly, and the design method does not require an equation to be solved. The design effort is independent of the period of the repetitive signals to be tracked or rejected. In other words, the design effort is very small, even if the period is very large. Thirdly, the robustness of the control system is improved by introducing a low-pass finite-duration impulse-response filter in the controller. Finally, the proposed scheme is applied to a de servo motor system, and the effectiveness is demonstrated by both simulations and experiments.