Minimax LQG controller design for nanopositioners

Abstract

A design and experimental implementation of a minimax linear-quadratic-Gaussian (LQG) controller to damp the resonant modes of a piezoelectric tube scanner (PTS) used in most commercial atomic force microscopes is presented in this paper. The controller design is presented to account two uncertainties in the system which arises due to (a) the spill over dynamics of the PTS at high frequencies and (b) changes in resonance frequency of the scanner which occur due to the various loads on the scanner or due to the environmental factors such as temperature and humidity. The effectiveness of the proposed controller is presented by experimental results and the experimental results show that, the proposed controller is able to flatten down the frequency response of the PTS by providing 18 dB damping of the first resonant mode of the scanner.