Tracking an unknown two-frequency reference using a frequency estimator-based servocompensator

In this work, we address the tracking problem for an unknown reference comprised of two sinusoids. We propose an adaptive servocompensator based on a pair of frequency estimators. Slow adaptation is used to create three time scales within the closed-loop system, corresponding to the controller and plant dynamics, fast frequency estimate, and slow frequency estimate. Stability of the boundary-layer system, comprised of the servocompensator and plant dynamics, is achieved with a stabilizing controller. Novel nonlinear analysis is then performed on the average system to show global asymptotic stability. The algorithm´s performance is verified by experiments conducted on a commercial nanopositioner, and its performance is shown to be comparable to that of iterative learning control.