High-Bandwidth Hysteresis Modeling of Piezoelectric Actuators Based on Modified NARX Neural Network

Piezoelectric actuators (PEAs), widely used in high-precision positioning applications, exhibit rate-dependent hysteretic nonlinearity, which seriously deteriorates the tracking performance. An accurate model is essential in the study of the PEA's hysteresis. In this paper, a modified nonlinear autoregressive with external input (NARX) neural network is proposed to predict the output of PEAs. Different from the traditional NARX neural network, the input rate is integrated into the neural network as an additional input. This modification helps to account for the rate-dependence of the PEA's hysteresis. Experiments are carried out on a commercial PEA, where a 1–100 Hz swept sinusoidal signal is utilized in the parameter identifications. Further, a sinusoidal signal with descending amplitude and a 1–300 Hz swept sinusoidal signal are used to verify the effectiveness of the proposed model in modeling the PEA's hysteresis. Experimental results show that both the RMS and maximum errors of modified NARX neural network are smaller than traditional NARX network, especially for high-frequency signals and amplitude-varying signals. The proposed modified NARX neural network achieves higher flexibility and accuracy in the bandwidth of 300 Hz, and thus is a promising hysteresis model for PEAs.