The Parameterization of All Stabilizing Two-Degree-of-Freedom Simple Multi-Period Repetitive Controllers with Specified Frequency Characteristic

The simple multi-period repetitive control system proposed by Yamada and Takenaga is a type of servomechanism for periodic reference inputs. This system follows a periodic reference input with a small steady-state error, even if there is periodic disturbance or uncertainty in the plant. In addition, simple multi-period 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 and Takenaga clarified the parameterization of all stabilizing simple multi-period repetitive controllers. Recently, Yamada et al. proposed the parameterization of all stabilizing two-degree-of-freedom(TDOF) simple multi-period repetitive controllers that can specify the input-output characteristic and the disturbance attenuation characteristic separately. However, when using the method or Yamada et al., it is complex to specify the low-pass filter in the internal model for the periodic reference input that specifies the frequency characteristic. This paper expands the result by Yamada et al. and proposes the parameterization or all stabilizing TDOF simple multi-period repetitive controllers with specified frequency characteristic such that the low-pass filter can be specified beforehand.