A design method of robust stabilizing simple multi-period repetitive controllers

A multi-period repetitive control system is a type of servomechanism for a periodic reference input. Even if a plant does not include time-delay, the transfer function from the periodic reference input to the output and that from the disturbance to the output of the multi-period repetitive control system generally have an infinite number of poles. In order to specify the input-output characteristic and the disturbance attenuation characteristic easily, Yamada et al. propose the concept of simple multi-period repetitive control systems such that the controller works as a stabilizing multi-period repetitive controller and the transfer function from the periodic reference input to the output and that from the disturbance to the output have a finite number of poles. However, the method by Yamada et al. cannot apply for the plant with uncertainty. The purpose of this paper is to propose the concept of robust stabilizing simple multi-period repetitive controllers for the plant with uncertainty and to clarify the parametrization of all robust stabilizing simple multi-period repetitive controllers.