Adaptive Output Regulation of a Flexible Arm

Abstract

A self-tuned version of a controller for asymptotic trajectory tracking of the end point of a two-link flexible robot arm is presented. The bounded solution to the inverse system, which is used in the control law, is tuned by the estimates of the unknown robot parameters, generated by a least square identification scheme. Soundness of the state of the adaptive controller is achieved by a stabilizing linear feedback from the output error, with fixed gains and robust with respect to variations of the parameters. This guarantees the total stability of the system, which is the main ingredient used in the proof of the controller properties, through a Lyapunov-like approach. The controller performance is finally illustrated by numerically simulating the tracking of an end point ramp under payload mass variations.