Proposal for Simple Repetitive Controllers

Abstract

The modified repetitive control system is a type of servomechanism for periodic reference input. Even if the plant does not include a time delay, the transfer functions from both the reference input and the disturbance of the output of the modi¯ed repetitive control system generally have an in¯nite number of poles, and for this reason it is di±cult to settle the input-output and the disturbance attenuation characteristics of a modi¯ed repetitive control system. From a practical point of view, the input{output and the disturbance attenuation characteristics of a control system need to be settled easily, and thus, it is desirable that the transfer functions from both the reference input and the disturbance to the output have a finite number of poles. In order to easily specify the input-output and the disturbance attenuation characteristics, we propose the concept of a simple repetitive control system in which the controller works as a stabilizing modi¯ed repetitive controller and the transfer functions to the output from both the reference input and the disturbance have a ¯nite number of poles. In addition, the parametrization of all stabilizing simple repetitive controllers is clarified. A simple design procedure for a stabilizing simple repetitive controller is presented.