Understanding Inertia and Saturation in Operational Hysteresis Through a Physics-Based Piezo Model

High-tech systems require precise motion control in the subnanometer position error range. With no magnetic interference and low mass, piezoelectric actuators are ideal for sensitive and high-speed environments. The proposed piezoelectric actuator, a multi-layer piezo stack made of lead zirconate titanate (PZT) material, is affected by non-linearities (e.g., hysteresis, dielectric relaxation). Therefore, to deliver high accuracy, precise mathematical modelling is essential to enable control. Current mathematical models often fail to capture all static and dynamic effects related to charge and voltage prediction. This paper introduces a comprehensive physics-based model that holistically integrates key physical phenomena, including inertia and saturation in the operational hysteresis. In this work, the model's parameters are identified and its performance is validated against experimental data across a range of operating conditions. The results demonstrate that the proposed model achieves a superior prediction accuracy, improving performance significantly, as compared to established methods. This outcome confirms the model's ability to reliably predict actuator behaviour.