A design method for robust stabilizing multi-period repetitive controllers for multiple-input/multiple-output plants with specified input-output frequency characteristic

The multi-period repetitive control system is a type of servomechanism for a periodic reference input. When multi-period repetitive control design methods are applied to real systems, the influence of uncertainties in the plant must be considered. In some cases, uncertainties in the plant make the multi-period repetitive control system unstable, even though the controller was designed to stabilize the nominal plant. Recently, the parameterization of all robust stabilizing multi-period repetitive controllers for multiple-input/multiple-output plants was obtained by Chen et al. However, using their method, it is complex to specify the low-pass filter in the internal model for the periodic reference input of which the role is to specify the input-output frequency characteristic. Because, the low-pass filter is related to four free parameters in the parameterization proposed by Chen et al. This paper proposes the parameterization of all robust stabilizing multi-period repetitive controllers for multiple-input/multiple-output plants with specified input-output frequency characteristic such that the input-output frequency characteristic can be specified beforehand.