A design method for two-degree-of-freedom simple repetitive control systems for multiple-input/multiple-output plants

The modified repetitive control system is a type of servomechanism for periodic reference inputs. That is, the modified repetitive control system follows the periodic reference input with a small steady state error, even if a periodic disturbance or uncertainty exists in the plant. Using previously proposed modified repetitive controllers, even if the plant does not include time-delay, transfer functions from the periodic reference input to the output and from the disturbance to the output have infinite numbers of poles. To specify the input-output and the disturbance attenuation characteristic easily, Yamada et al. proposed the concept of a simple repetitive control system such that the controller works as a modified 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, Yamada et al. clarified the parameterization of all stabilizing simple repetitive controllers. Recently, the parameterization of all stabilizing two-degree-of-freedom simple repetitive controllers those can specify the input-output characteristic and the disturbance attenuation characteristic separately was proposed. However, the parameterization of all stabilizing two-degree-of-freedom simple repetitive controllers for multiple-input/multiple-output plants has not ever been considered. The purpose of this paper is to clarify the parameterization of all stabilizing two-degree-of-freedom simple repetitive controllers for multiple-input/multiple-output plants.