A Design Method for a Robust Stabilizing Multi-Period Repetitive Control System for Multiple-Input/Multiple-Output Plants with Specied Input-Output Frequency Characteristic Using the Parameterization

Abstract

The multi-period repetitive control system is a type of servomechanism for a periodic reference input. Recently, the parameterization of all robust stabilizing multi-period repetitive controllers for multipleinput/ multiple-output plants with uncertainty was obtained by Chen et al. However, using their method, it is complex to specify the low-pass filter in the internal model for the periodic reference input of which the role is to specify the input-output frequency characteristic. Because, the low-pass filter is related to four free parameters in the parameterization proposed by Chen et al. Chen et al. examined the parameterization of all robust stabilizing multi-period repetitive controllers for multiple-input/multiple-output plants with specified input-output frequency characteristic such that the input-output frequency characteristic can be specified beforehand. However, they omitted complete proof on account 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 robust stabilizing multi-period repetitive controller with specified input-output frequency characteristic. A numerical
example is presented to illustrate the effectiveness of the proposed method.