Design of a Discrete-time Repetitive Controller for Periodic Disturbances

Since digital implementation of repetitive controllers is simpler than analog in many industrial applications, some design criteria for a discrete-time repetitive controller to suppress periodic disturbances within a specified frequency range are presented. The small gain theorem is applied to perform the controller design for system stability. Upper and lower bounds of the discrete-time repetitive controller parameters that ensure the stability of the control system and the tracking performance are derived based on the shaping of the sensitivity functional. Therefore, the repetitive controller is designed by the parameters in between upper and lower bounds. The control performance of the presented method is evaluated in a turntable system which is exposed to periodic disturbances. Computer simulation is presented to illustrate the effectiveness of the proposed repetitive controller design.