Hysteresis modeling of piezoelectric micro-positioning stage based on convolutional neural network

Abstract

The inherent hysteresis nonlinearity of piezoelectric actuator degrades the positioning accuracy of the micro-positioning stage. Prandtl–Ishlinskii model is widely used for piezoelectric hysteresis modeling, yet it is a rate-independent model with weak generalization ability. To overcome this problem, we proposed a convolutional neural network model based on the Prandtl–Ishlinskii model, which consists of a rate-dependent Prandtl–Ishlinskii model layer and convolutional network layer. The rate-dependent Prandtl–Ishlinskii model layer extends the traditional Prandtl–Ishlinskii model to describe the rate-dependent hysteresis behavior. The convolutional network layer with deep learning ability extracts the deep features of the input signal to improve the generalization ability of the hysteresis model. The experiment results indicate that the standard error of the proposed hysteresis model to predict displacement at unmodeled frequencies has been reduced by 18.74%–36.75% in comparison with the Prandtl–Ishlinskii model, which verifies that the proposed hysteresis model has not only higher accuracy but also stronger generalization ability.