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 nanoposi-tioining 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 requires 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 hyteresis 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.