LAUSR

During the raster scanning of atomic force microscopes (AFMs), the coupling effect from the fast-axis to the slow-axis is extraordinarily pernicious, especially when the scanning rate is set high. Whilst great efforts have been made in the field of piezo-actuated stages, less attention is paid on control design to mitigate this coupling effect. In this paper, we propose a modified repetitive control based cross-coupling compensation (MRC-CCC) approach for high-speed and high-precision scanning motion control of a piezoelectric tube scanner in AFMs. Based on the experimental observations, we first describe this coupling effect as the periodic disturbance to the output of the slow-axis when the fast-axis is designed to track triangular trajectories. Then, the MRC-CCC controller is developed to remedy the periodic disturbances, which generates the compensation signals targeting the coupling effect. Therefore, the complicated modeling of the cross-coupling effect is avoided, which significantly reduces the complexity of usage. To ensure the high-precision tracking performance for the slow-axis in scanning, we further design a tracking controller that combines with the offline trained MRC-CCC controller. Finally, comparative experiments are conducted on an AFM piezoelectric tube scanner. Experimental results show that the developed MRC-CCC approach significantly compensates for the coupling effect, in which the root-mean-square tracking error is substantially reduced from 172.1 to $3.3\text{ nm}$ at the scanning rate of 40 Hz. We also perform high-speed scanning tests for AFM imaging to verify the effectiveness of the development.