A Design Method for Two-Degree-of-Freedom Multi-Period Repetitive Control Systems with the Specified Frequency Characteristic

Abstract

Multi-period repetitive controllers improve the disturbance attenuation characteristic of themodified repetitive control system that follows the periodic reference input with small steady stateerror. Recently, the parameterization of all stabilizing multi-period repetitive controllers was studied.However, when the parameterization of all stabilizing multi-period repetitive controllers is used, theinput-output characteristic and the feedback characteristic cannot be specified separately. From thepractical point of view, it is desirable to specify the input-output characteristic and the feedback characteristicseparately. In addition, the parameterization is useful to design stabilizing controllers. Fromthis view-point, the parameterization of all stabilizing two-degree-of-freedom multi-period repetitivecontrollers those can specify the input-output characteristic and the disturbance attenuation characteristicseparately was solved by Yamada et al. However, when we design a stabilizing two-degree-offreedommulti-period repetitive controllers using the parameterization proposed by Yamada et al, thefrequency characteristic of the control system cannot be settled so easily. From the practical point ofview, the frequency characteristic of the control systems are required to be easily settled. This problemcan be solved by obtaining the parameterization of all stabilizing two-degree-of-freedom multi-periodrepetitive controllers with the specified frequency characteristic. In this paper, we propose the parameterizationof all stabilizing two-degree-of-freedom multi-period repetitive controllers with thespecified frequency characteristic.