Adaptive Optimal Parameter Estimation and Control of Servo Mechanisms: Theory and Experiments

Most of classical adaptive laws used in adaptive control have been developed based on the gradient descent algorithm to minimize the control error. Hence, the sluggish convergence of tracking error may affect the online learning, making accurate parameter estimation difficult. The aim of this article is to present a new adaptive law to achieve optimal parameter estimation, and then to showcase its application to adaptive control for a benchmark servo system to retain simultaneous convergence of both the estimation error and tracking error. For this purpose, an auxiliary filter is introduced to extract the estimation error, which is used to drive the adaptive law with a time-varying gain to minimize a cost function of the estimation error to achieve fast, accurate parameter estimation. Finally, this new adaptation is incorporated into an adaptive nonsingular terminal sliding-mode control for the considered servo system to obtain tracking control and parameter estimation simultaneously. The effectiveness of the developed method is validated by means of comparative simulations and experiments.