A Common Setting for the Design of Iterative Learning and Repetitive Controllers with Experimental Verification

Previous work has shown that the structure of Repetitive Control (RC) and that of Iterative Learning Control (ILC) differ only in the location of an internal model of the disturbance. In this paper it is shown how this common setting permits derivation of controllers in one domain based on an existing controller in the other. This is illustrated using the following case studies: 1) an RC scheme is derived based on an existing ILC scheme which has the structure of a servo compensator (this is first extended to comprise both current-error feedback and previous-error feedforward implementations), and 2) an ILC scheme is developed based on an existing RC scheme which also has a servo compensator structure, but differs from (1) by containing only a single internal model representation. In this case the presence of a single internal model restricts the derived ILC structure to assume the form of a disturbance observer. All controllers are shown to have similar equivalent representations, with parameters derived by using linear quadratic regular analysis. This correspondence in structure enables comparison of the effect of the structure (ILC or RC, servo compensator or disturbance observer), number of internal models, and use of error (feedback or feedforward) on subsequent performance. This is undertaken using experimental results obtained using a gantry robot