A Fast and Precise Piezoelectric-Stage Positioning Scheme Using a Novel Modified Lemniscate Scanning Trajectory With Shunt-Based Model Predictive Control and Long Short-Term Memory

Piezoelectric stages are widely used in the field of high-precision measurement where controllers are designed for the stages to track reference trajectories. Most existing scanning trajectories tend to trigger mechanical vibrations or yield distorted images resulting in mapping errors. In addition, the performance of many existing controllers in tackling nonlinearities are, to a large extent, not satisfactory. To improve the situation, this paper aims to develop a modified lemniscate scanning trajectory combined with a shunt-based model predictive control and long short-term memory neural network to alleviate mechanical vibrations yielding a higher scanning rate and tracking accuracy. Experimental results are presented to validate the design and verify its effectiveness in which the proposed scheme outperforms the proportional-integral-derivative and model predictive control in terms of significant tracking error reductions. Quantitatively, vibration improvement of the modified lemniscate waveform over the raster’s triangular waveform in power spectrum analysis in terms of average decibel level is reduced from −49.67dB to −73.18dB. Percentage wise, performance improvement of the proposed controller over MPC in the same trajectory tracking at 10Hz the root-mean-square errors are reduced from 9.217% and 9.362% to 8.064% and 8.395% in X-axis and reduced from 7.431% and 7.153% to 5.557% and 4.694% in Y-axis, respectively. The root-mean-square errors at 50Hz are reduced from 43.015% and 46.071% to 35.394% and 37.746% in X-axis and reduced from 35.659% and 35.215% to 33.497% and 30.252% in Y-axis, respectively. Note to Practitioners—This paper was motivated by the problem of scanning speed and accuracy of piezoelectric stage-type measurement systems, such as atomic force microscopy. First, a novel modified lemniscate trajectory is presented to replace conventional trajectories that can minimize the image distortion thanks to reduction of the mapping errors of scanning paths as well as alleviation of mechanical oscillations of high-frequency resonances. Furthermore, the paper develops a model predictive control combined with a long short-term memory neural network that can efficiently deal with the nonlinear behavior of the piezoelectric stage to reduce unwanted path tracking errors. Experiments are conducted to validate the method and assess the effectiveness of the proposed trajectory and the control scheme. The preliminary results support the feasibility of the proposed approach, but since the proposed trajectory uses two curved lines at corners, it does require a more extended stroke stage.