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

In this paper, we propose the parameterization of all robust stabilizing simple multi-period repetitive controllers for multiple-input/multiple-output (MIMO) plants with specified input-output frequency characteristic. Recently, Sakanushi et al. proposed the parameterization of all robust stabilizing simple multi-period repetitive controllers such that the controller works as a robust 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. However, using their method, it is complex to specify the low-pass filters in the internal model for the periodic reference input that specifies the input-output frequency characteristic, because the low-pass filters are related to more than three free parameters. Our proposed parameterization in this paper overcomes this problem by specifying the low-pass filters beforehand. That is, using our parameterization, we can design a control system which has desirable input-output frequency characteristic more easily than the method proposed by Sakanushi et al.