A Hybrid Adaptation Strategy for Repetitive Control of an Uncertain Delay Lagrangian System

In this work, we present a novel repetitive control (RC) strategy to achieve accurate position tracking of a 1-DOF Lagrangian system. Such controller is able to cope with model uncertainties and unknown transmission delays in the control architecture. The classic repetitive structure is augmented with an observer of the residual disturbance, to be compensated by means of the RC action. The repetitive unit is updated at hybrid instants so that the disturbance observer is close to its steady-state before anew repetitive correction is applied. In addition, communication delay is also estimated by the proposed control structure. This way, practical asymptotic stability of the overall system can be achieved with a simple proportional correction of the RC, also under perturbations of the steady-state estimate due to model uncertainties. In light of the aforementioned properties, the proposed RC-based controller is shown to be an easy-to-tune, robust solution capable of improving the tracking performance for the given case of study.