Open-Closed-Loop PD Iterative Learning Control Corrected with the Angular Relationship of Output Vectors for a Flexible Manipulator

A new iterative learning control (ILC) approach combined with an open-closed-loop PD scheme is presented for a flexible manipulator with a repeatable motion task in the case that only the endpoint pose of the flexible link is measurable. This approach takes advantage of the fact that the ILC performance is independent of the model used, thereby overcoming the drawback of the heavy reliance of PD controllers on the modeling accuracy. The open-closed-loop PD controller is mainly used to simultaneously reduce the effects of the modeling error and disturbances to enhance the controller's robustness. Meanwhile, an angular correction term is introduced by using the angular relationship of the system outputs to reward or penalize the ILC law. Specifically, when the current output tends toward the expected trajectory, the ILC law is enhanced accordingly; otherwise, it is penalized. The convergence conditions for the proposed approach are obtained through theoretical analysis, and experiments using a real flexible manipulator are presented. The results show that the proposed ILC scheme can overcome the impact of the endpoint error caused by link flexibility and has a good control effect.