Synthesis, Stability Analysis, and Experimental Implementation of a Multirate Repetitive Learning Controller

Abstract

This paper describes a multirate repetitive learning controller with an adjustable sampling rate that may be used as an “add-on” module to enhance the tracking performance of a feedback control system. The sampling rate of the multirate controller is slower than the remainder of the control system, and is selected by the user to achieve the required system performance based on a trade-off between the accuracy and the complexity of the controller. The multirate controller learns the system control input based on the tracking error down-sampled using a weighted averaging filter. The output of the multirate controller is up-sampled through an arbitrary hold mechanism determined by the user. This paper extends the existing stability results for single-rate repetitive learning controllers to the proposed multirate scheme. It provides an explicit procedure for its design and stability analysis. In addition, the proposed multirate repetitive learning controller is implemented on a mechanical system performing a non-colocated control task, where its effectiveness in reducing tracking errors while following periodic reference trajectories is shown experimentally.