Gated recurrent unit based frequency-dependent hysteresis modeling and end-to-end compensation

As the kernel part in such precise instruments as an atomic force microscopy, a piezoelectric actuator achieves nano-scale displacement resolution with fast response. However, the inherent hysteresis of a piezoelectric actuator badly limits its position accuracy and further results in image distortion of an atomic force microscopy. Hysteresis occurs with three coupled characteristics, respectively, nonlinearity, memory, and frequency-dependence, thereby increasing the difficulty of hysteresis modeling. Aiming at this problem, this paper sets up a gated recurrent unit based frequency-dependent hysteresis model and then proposes an end-to-end compensation method to correct image distortion. To be specific, a gated recurrent unit layer is designed to accurately describe the nonlinearity and memory of hysteresis, based on which, a modified back propagation neural network is constructed by introducing the frequency of input voltage to simulate the frequency-dependence characteristic, finally yielding a very accurate hysteresis model with strong generalization ability. Based on the constructed model, a novel piecewise Hermitian interpolation method is then proposed to deal with the uncompensated AFM images, obtained in both forward and backward scanning directions, so as to implement end-to-end compensation for hysteresis to generate a high-quality image. Experimental and application results are presented to demonstrate the satisfactory performance of the proposed modeling and compensation methods.