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.

Stick-slip piezoelectric actuators are promising because they enable both macroscale motion in stepping mode and nanoscale motion in scanning mode. However, when the scanning range and frequency are significant, the slip motion between their driving foot and end-effector is always possible, leading to the unwanted transition between scanning and stepping modes. Aiming to fully exploit the scanning capability of a stick-slip piezoelectric actuator, this article proposes a novel method for exploring the actuator’s scannable trajectory set. A dynamic model that cascades the actuator’s linear dynamics and the frictional relationship between its driving foot and the end-effector is established. Then, parameters are identified based on the actuator’s response. With these parameters, the scannable trajectory set of the actuator can be analytically obtained. The high consistency between the experimental results and the model predicted set validates the effectiveness of the proposed method. The exploration of the set paves the way for the high-throughput scanning of the stick-slip piezoelectric actuator. As a demonstration, a high throughput (scanning range × frequency) of 3000 μm × Hz is realized at arbitrary macro positions in the crossscale nanopositioning test, by a typical stick-slip actuator, improving 1–2 orders of magnitude over existing ones.

Rate-dependent hysteresis seriously deteriorates the positioning accuracy of the piezoelectric actuators, especially when tracking high-frequency signals. As a widely-used nonparametric Bayesian method, the Gaussian process (GP) has proven its effectiveness in nonlinear hysteresis modeling. In this paper, the dimension of the input to the GP model is extended to consider more dynamic features of the tracking signal so as to improve the rate-dependent hysteresis modeling accuracy. In contrast with the traditional training set containing only the position and speed information, the acceleration and jerk information, as well as their temporal distribution information, is also included in the input of the model. An inverse hysteresis compensator (IHC) is established in the same way, and open-loop and closed-loop controllers are developed by using the IHC. Experimental results on a PEA stage show that with the increase in the input dimension, the hysteresis modeling accuracy improves greatly and, thus, the controllers based on IHC can achieve a better tracking performance.