Iterative control of dynamics-coupling effects in piezo-based nano-positioners for high-speed AFM

This article addresses the compensation of dynamics-coupling effects in piezo-actuators used for positioning in atomic force microscopes (AFMs). Piezo-actuators are used to position (or scan) the AFM probe (relative to the sample) both parallel to the sample surface (x-y-axes) and perpendicular to the sample surface (z-axis). During AFM operation, such as nanofabrication and imaging of soft biological samples, the probe-sample distance (in the z-axis) needs to be precisely controlled to maintain the probe-sample interaction at a desired value; otherwise, large variation of the probe-sample distance can result in distortions of the fabricated parts (in nanofabrication) and can cause sample damage (when imaging soft biological samples). In this article, we show that dynamics-coupling from the scan axes (x-y-axes) to the perpendicular z-axis can generate significant variations in the probe-sample distance during high-speed AFM operation, i.e., when the sample is scanned at high speed. We use an inversion-based iterative control approach to compensate for these dynamics-coupling effects. Convergence of the iterative approach is investigated and experimental results show that the coupling-caused errors can be reduced to the noise level using the proposed approach. Thus, the main contribution of this article is the development of an approach to substantially reduce the coupling-caused positioning errors and thereby, to enable high-speed AFM operation.