The parameterization of all stabilizing two-degree-of-freedom multi-period repetitive controllers for multiple-input/multiple-output plants with specified frequency characteristic

In order to improve the disturbance attenuation characteristic of modified repetitive control systems, Gotou et al. proposed a Multi-period repetitive controller that follows the periodic reference input with small steady state error. Recently, there are studies on the parameterization of all stabilizing multi-period repetitive controllers. However, the input-output characteristic and the feedback characteristic cannot be specified separately as it is desirable from the practical point of view when the parameterization of all stabilizing multi-period repetitive controllers is used. Besides, the parameterization is useful to the design stabilizing controllers. Yamada et al. solved this problem by obtaining the parameterization of all stabilizing two-degree-of-freedom multi-period repetitive controllers. Chen et al. also proposed that for multiple-input/multiple-output plants. However, because the low-pass filter is related to four free parameters in the parameterization, using their method is not easy to specify the low-pass filter in the internal model for the periodic reference input of which the role is to specify the frequency characteristic. To specify the frequency characteristic with ease, this paper proposes the parameterization of all stabilizing two-degree-of-freedom multi-period repetitive controllers for multiple-input/multiple-output plants with specified frequency characteristic such that the low-pass filter can be specified in advance.