Extension of a multi-rate control law independently of both reference and disturbance responses

This study discusses a design method for sampled-data multi-rate control systems, in which the sampling interval of the plant output is an integer multiple of the hold interval of the control input. In this study, a desired response in discrete time is assumed to be obtained using a multi-rate control law, and then the multi-rate control law is extended such that an existing discrete-time disturbance and reference responses are simultaneously maintained. In the proposed multi-rate control system, the intersample response can be improved independently of the discrete-time response. Finally, the effectiveness of the proposed method is shown through numerical examples.