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.

Hysteresis modeling is interesting yet challenging for piezoelectric actuated systems, which are often used in micro/nano scale measurement and manufacturing equipments. However, due to its complexity, few efforts have been devoted to characterizing cross-coupling hysteresis effect of multi-axis piezoelectric micropositioning stages. To this end, a distributed Hammerstein model, composed of a cascaded connection of a static nonlinearity and a dynamic linearity, is proposed in this paper to approximate the nonlinear spatial/temporal cross-coupling effect. This model outperforms conventional piezo models such as the Preisach model. Meanwhile, theoretical analysis is provided to guarantee the convergence of the proposed Hammerstein model. Finally, extensive experiments are conducted to verify the superiority of the proposed modeling method.

In this paper, an intelligent feedforward prediction and compensation scheme to combine with a dual-loop high-bandwidth controller is proposed for high-speed and high-precision tracking control of a nanopositioning stage. Firstly, the dual-loop controller (DLC) consisting of an inner-loop damping and an outer-loop tracking controller is developed with all the parameters optimized simultaneously, which could provide a control bandwidth over the first resonant frequency of the stage. Next, the Gaussian process (GP) machine learning model is employed to capture the dynamic characteristics of the tracking error of the dual-loop controlled plant. Then, a feedforward compensator is constructed to add a compensation term to the initial reference trajectory. Experimental investigations on a self-made piezoelectric-actuated stage validate the effectiveness of the intelligent tracking error prediction method and the excellent performance of the control strategy for high-precision tracking of high-frequency reference trajectories.

An electromagnetic-piezoelectric hybrid actuated nanopositioner for atomic force microscopy (AFM) is proposed. Applying the hybrid serial-parallel-kinetic design, the parallel xy -stage is actuated by the normal-stressed electromagnetic actuators to conduct planar scanning in a large scope. The z -axis is serially carried by the xy -stage and is actuated by a piezoelectric actuator (PEA) to track the sample’s topography with high speed. Moreover, a novel flexure mechanism is proposed for motion guidance and decoupling of the xy -stage, featuring the higher resonant frequency along the x -axis to satisfy the requirement of a faster planar axis in AFM imaging. The analytical model of the nanopositioner is established to optimally determine the parameters, and the results are verified by finite-element analysis. A prototype is fabricated and tested. Experimental results demonstrate that the triaxial strokes of 94.4 μm (x-axis), 102.8 μm ( y -axis), and 5.22 μm ( z -axis) are achieved, and the resonant frequencies are identified as 735 Hz ( x -axis), 650 Hz ( y -axis), and 6340 Hz ( z -axis), respectively. The implemented feedback controllers ensure the accuracy of high-speed trajectory tracking. Finally, the AFM imaging based on the proposed nanopositioner is conducted, confirming its effectiveness for large-scope and high-rate AFM imaging.