Research on hysteresis compensation method of piezoelectric actuator for ultra-precision drive

Piezoelectric actuators are the core driving components for active resonance and low-frequency vibration suppression of cantilever beams. However, the inherent hysteresis and creep nonlinearities of piezoelectric ceramics severely restrict positioning accuracy and vibration control performance, causing relative displacement errors up to 25% under open-loop conditions, which directly undermines the stability and precision of cantilever beam active vibration control systems. The classical Prandtl-Ishlinskii (PI) model is limited by its symmetric hysteresis assumption, failing to accurately fit the dynamic asymmetric hysteresis characteristics under vibration suppression conditions; while the pure data-driven NARX neural network lacks physical prior constraints, resulting in poor generalization and insufficient long-term operational stability. To address these challenges, this paper proposes a hybrid PI-NARX neural network modeling method for high-precision piezoelectric hysteresis compensation. Three modeling strategies, including the PI model, NARX neural network, and PI-based NARX coupled model, are established and systematically compared. Combined with inverse model feedforward control, the proposed method is fully verified via simulation and experimental tests. This method provides an efficient and practical solution for high-precision, high-speed active vibration control of cantilever beam structures, with significant engineering application value.