Chun-Xia Li

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 higher. Whilst great efforts have been made in the field of piezo-actuated stages, less attentions are 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 disturbances 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 at 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 a 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 172.1nm to 3.3nm at the scanning rate of 40-Hz. We also perform high-speed scanning tests for AFM imaging to verify the effectiveness of the development.

This paper presents a modified rate-dependent Prandtl–Ishlinskii (MRPI) model for the description and compensation of the rate-dependent asymmetric hysteresis in piezoelectric actuators. Different from the commonly used approach with dynamic weights or dynamic thresholds, the MRPI model is formulated by employing dynamic envelope functions into the play operators, while the weights and thresholds of the play operators are still static. By this way, the developed MRPI model has a relatively simple mathematic format with fewer parameters and easier parameter identification process. The benefit for the developed MRPI model also lies in the fact that the existing control approaches can be directly adopted with the MRPI model for hysteresis compensation in real-time applications. To validate the proposed model, an open-loop tracking controller and a closed-loop tracking controller are developed based on a dynamic hysteresis compensator, which is directly constructed with the MRPI model. Comparative experiments are carried out on a piezo-actuated nanopositioning stage. The experimental results demonstrate the effectiveness and superiority of the controllers based on the developed MRPI model compared to the controllers based on the rate-independent P–I model and the rate-dependent P–I model with dynamic weighting functions.