Synthesis and stability of a multirate repetitive learning controller

We introduce a multirate repetitive learning controller that can be used as an “add-on” module to further enhance the performance of a feedback control system. As a result of its multirate characteristic, the user can choose a sampling rate to achieve the required performance based on the trade-off between the accuracy and complexity of the controller. This controller learns the plant input based on the tracking error down-sampled using a weighted averaging filter. The learned input is subsequently passed to the plant through an arbitrary hold mechanism determined by the user. The paper extends the existing stability results for single-rate repetitive controllers to the proposed multirate controller. It also provides an explicit procedure for its design and stability analysis