Optimal Model Matching Design for High Bandwidth, High Resolution Positioning in AFM

Abstract

This paper introduces a two degree of freedom control design for achieving robust high resolution, high bandwidth positioning systems. Feedback designs have demonstrated a significant improvement in the performance of the flexure-stage based positioning systems in atomic force microscopes (AFM) that provide large travels with high resolution. In this paper, an optimal model matching framework, where both the feedback and feedforward controllers form the decision variables, is presented which facilitates achieving better performance in terms of the resolution bandwidth and robustness to modeling uncertainties in the closed-loop device. Feedback-only designs, which significantly diminish nonlinear effects of piezoactuation and other modeling uncertainties, are restricted by practical and fundamental limitations such as the control saturation and the Bode integral law. These limitations, which become even more prominent due to non-minimum phase zeros in the context of flexure stages with non-collocated actuators and sensors, typically lead to trade-off between resolution, bandwidth and the robustness of the positioning system. A two degree of freedom controller, achieves a better trade-off by exploiting feedforward designs that are not subject to some limitations that constrain the feedback-only designs. We show that our 2DOF design achieves performance objectives that are impossible for feedback-only designs. Experiments on positioning stages on a AFM show bandwidth improvements as large as 300% over existing feedback base designs.