A Design Method for Simple Repetitive Controllers with Specified Input-output Characteristic

The simple repetitive control system proposed by Yamada et al. is a type of servomechanism for periodic reference input. Thus, the simple repetitive control system follows a periodic reference input with 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. However, when using the method of Yamada et al., it is complex to specify the low-pass filter in the internal model for the periodic reference input that specifies the input-output characteristic. To specify the input-output characteristic more easily, Murakami et al. examined the parameterization of all stabilizing simple repetitive controllers with the specified input-output characteristic such that the input-output characteristic can be specified beforehand. However, they omitted complete proof on account of space limitations. This paper gives a complete proof of the parameterization of all stabilizing simple repetitive controllers with the specified input-output characteristic of Murakami et al. and demonstrates the effectiveness of the parameterization of all stabilizing simple repetitive controllers with the specified input-output characteristic. Control characteristics of a simple repetitive control system are presented, as well as a design procedure for a simple repetitive controller with the specified input-output characteristic.