Nonlinear Optimal Tracking Control of a Piezoelectric Nanopositioning Stage

摘要

High performance nanopositioning stages, used in a variety of applications such as atomic force microscopy and three-dimensional nanometer- scale lithography, require stringent position control over relatively large displacements and a broad frequency range. Piezoelectric materials, which are typically employed in nanopositioning stages, provide excellent position control when driven at relatively low frequency and low field levels. However, in applications where the stage operates over a relatively large region (microns to millimeters) and broad frequency range (Hz - kHz), piezoelectric materials often exhibit nonlinear and rate-dependent hystereis which require control designs that can effectively accommodate such behavior. In this paper, a nonlinear, thermal-relaxation, piezoelectric constitutive law is incorporated into an open loop optimal tracking control design to accurately track a desired reference signal when nonlinearities, thermal relaxation and hysteresis are present. A comparison between linear optimal control and the nonlinear optimal control design is given to illustrate performance enhancements when the constitutive behavior is included in the control design.