Model Reference Adaptive Control With Perturbation Estimation for a Micropositioning System

This brief presents a scheme of model reference adaptive control with perturbation estimation (MRACPE) for precise motion control of a piezoelectric actuation micropositioning system. One advantage of the proposed scheme lies in the fact that the size of tracking error can be predesigned, which is desirable in practice. A second-order nominal system is assumed, and the unmodeled dynamics and nonlinearity effect are treated as a lumped perturbation, which is approximated by a perturbation estimation technique. A dead-zone modification of the adaptive rules is introduced to mitigate the parameter drifts and to speed up the parameter convergence. Moreover, the proposed MRACPE scheme employs the desired displacement trajectory rather than the voltage signal as the reference input. The stability of the closed-loop control system is proved through Lyapunov stability analysis. Experimental studies show that the MRACPE is superior to conventional proportional-integral-derivative control in terms of positioning accuracy for both set-point and sinusoidal positioning tasks, which is enabled by a significantly enlarged control bandwidth.