Saturation and Hysteresis Nonlinearity Modeling of Piezoelectric Actuators Based on Hybrid-PINN Model

Piezoelectric actuators are widely used in precision positioning systems. However, their inherent nonlinear behaviors, particularly hysteresis and output saturation, degrade modeling accuracy and limit control performance. Existing studies have generally used either black-box models or traditional physical models. The former typically lack physical interpretability, while the latter can exhibit limited accuracy when the actuator response includes coupled nonlinear effects. To address this issue, this paper proposes a hybrid physics-informed neural network (Hybrid-PINN) framework. An equivalent attenuation model, with a calibrated attenuation coefficient, is first established to describe output saturation and provide a nominal physical reference. A parallel neural network is then introduced to compensate for higher-order residuals not accounted for by the nominal physical model. By incorporating a physically constrained loss function, the proposed framework combines information from the physical mechanism with experimental data. A series of experiments was conducted on a stacked lever-amplified piezoelectric actuator. The results show that the proposed model captures the main hysteresis and saturation tendencies of the tested actuator, and that prediction accuracy is improved by more than 20% compared with the traditional physical model. A detailed comparison with a multilayer perceptron, a standard physics-informed neural network, and LSTM models was also performed. The proposed model achieves lower prediction errors in most of the tested cases and exhibits improved convergence under current experimental conditions. Overall, this work provides a physically interpretable modeling framework at the actuator level for piezoelectric actuators within their calibrated operating range.