Improving Tracking Accuracy for Repetitive Learning Systems by High-Order Extended State Observers

For systems executing repetitive tasks, how to realize the perfect tracking objective is generally desirable, for which an effective method called ``iterative learning control (ILC)'' emerges thanks to the incorporation of the repetitive execution of systems into an ILC design framework. However, nonrepetitive (iteration-varying) uncertainties are often inevitable in practice and greatly degrade the tracking accuracy of ILC, which has not been treated well, regardless of considerable robust ILC results. This motivates this article to develop a new design method to improve the tracking accuracy of ILC by adopting a high-order extended state observer (ESO) to address ill effects of nonrepetitive uncertainties and uncertain system models. With the designed ESO-based ILC, the robust tracking of any desired trajectory can be achieved such that the tracking error can be decreased to vary in a small bound depending continuously on the bounds of high-order variations of nonrepetitive uncertainties with respect to the iteration. It makes the tracking accuracy of ILC possible to be regulated through the design of ESO, of which the validity is demonstrated by including a simulation example.