The Parameterization of All Stabilizing Two-degrees-of-freedom Simple Repetitive Controllers and Its Application

The simple repetitive control system proposed by Yamada et al. is a type of servomechanism for periodic reference inputs. This system follows a periodic reference input with a small steady-state error, even if there is periodic disturbance or uncertainty in the plant. In addition, simple repetitive control systems ensure that transfer functions from the periodic reference input to the output and from the disturbance to the output have finite numbers of poles. Yamada et al. clarified the parameterization of all stabilizing simple repetitive controllers. Recently, Yamada et al. proposed the parameterization of all stabilizing two-degrees-of-freedom simple repetitive controllers that can specify the input-output characteristic and the disturbance attenuation characteristic separately. However, they omitted the complete proof because of space limitations. This paper gives the complete proof and demonstrates the effectiveness of the parameterization. The control characteristics of the system are presented, along with a design procedure for a two-degrees-of-freedom simple repetitive controller. A numerical example and an application for a motor control experiment are presented to illustrate the effectiveness of the proposed method.