A novel piezoelectric hysteresis modeling method combining LSTM and NARX neural networks

In order to study the hysteresis nonlinear characteristics of piezoelectric actuators, a novel hybrid modeling method based on Long-Short-Term Memory (LSTM) and Nonlinear autoregressive with external input (NARX) neural networks is proposed. First, the input-output curve between the applied voltage and the produced angle of a piezoelectric tip/tilt mirror is measured. Second, two hysteresis models named LSTM and NARX neural networks were, respectively, established mathematically, and then were tested and verified experimentally. Third, a novel adaptive weighted hybrid hysteresis model which combines LSTM and NARX neural networks was proposed through analyzing and comparing the unique characteristics of the above two hysteresis models. The proposed hybrid model combines LSTM's ability to approximate nonlinear static hysteresis and NARX's high dynamic-fitting ability. Experimental results show that the RMS errors of the hybrid model are smaller than those of LSTM model and NARX model. That is to say, the proposed hybrid model has a relatively high accuracy. Compared with the traditional differential equation-based and operator-based hysteresis models, the presented hybrid neural network method has higher flexibility and accuracy in modeling performance, and is a more promising method for modeling piezoelectric hysteresis.