A Design Method for Simple Multi-Period Repetitive Controllers for Multiple-Input/Multiple-Output Plants

The multi-period repetitive control system is a type of servomechanism for a periodic reference input. Even if a plant does not include time-delays, using multi-period repetitive controllers, 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 infinite numbers of poles. To specify the input-output characteristic and the disturbance attenuation characteristic easily, Yamada and Takenaga proposed the concept of simple multi-period repetitive control systems, such that the controller works as a stabilizing multi-period repetitive controller and transfer functions from the periodic reference input to the output and from the disturbance to the output have finite numbers of poles. In addition, the parameterization of all stabilizing simple multi-period repetitive controllers was clari¯ed. However, Yamada and Takenaga did not clarify the parameterization of all stabilizing simple multi-period repetitive controllers for multiple-input/multiple-output plants. The purpose of this paper is to propose the parameterization of all stabilizing simple multi-period repetitive controllers for multiple-input/multiple-output plants.