Model reference adaptive damping control for a nanopositioning stage with load uncertainties.

In this paper, a scheme of model reference adaptive integral resonant control (MRAIRC) is presented for adaptive precision motion control of a piezo-actuated nanopositioning platform. The major advantage of the proposed scheme lies in the adaptivity for dynamic changes resulting from load uncertainties. Existing standard integral resonant control (IRC) with constant controller gains is normally designed based on the identified system model under no external load. For the proposed MRAIRC, a standard IRC is first designed using an analytical approach, assuming that a second-order system model is obtained in advance. Afterwards, the designed closed-loop is utilized as a reference model for systems with model uncertainties. The adaptive laws of the controller gains are determined according to the well-known MIT rules. An offline trail-and-error operation is conducted for adaption gains' tuning. The stability of this adaptive control system is proved through Lyapunov stability analysis. Simulation and experimental studies demonstrate that the proposed MRAIRC is superior to the standard IRC in terms of the tracking errors for commonly used raster scanning signals at 5, 10, and 20 Hz with load variations of the platform ranging from 0 to 1000 g.