Point-to-Point Repetitive Control with Optimal Tracking Time

For systems that execute tasks repetitively, learning control strategies such as iterative learning control and repetitive control have proven to be useful tools for mitigating the effects of model uncertainty to improve system performance. While such strategies have been used to solve the point-to-point motion tracking problem, existing techniques require either that the reference positions are tracked at the same time within each iteration, or that the initial conditions are reset between each iteration of the task. This paper aims to relax these assumptions through the development of a two stage repetitive control framework that drives the system to periodically track a sequence of temporally-varying reference positions by using minimal control effort. Here, the first stage updates the control signal such that the system accurately tracks the reference positions, while the second stage modifies the tracking time requirements of the reference positions to minimize the applied control effort. The effectiveness of the control strategy is demonstrated via simulated application of the algorithm on a mass-spring-damper system.