Amplitude-adaptive asymmetric Prandtl–Ishlinskii modeling for nonlinear hysteresis in piezoelectric actuators

Accurate modeling of nonlinear hysteresis in piezoelectric ceramic actuators (PCAs) is essential for high-precision active vibration control, particularly under conditions involving significant variations in drive amplitude. Conventional Prandtl–Ishlinskii (PI) models exhibit limited accuracy when describing amplitude-dependent hysteresis, motivating the development of a more robust approach. This study introduces an amplitude-adaptive asymmetric PI (AAAPI) model, specifically designed to capture asymmetric hysteresis behavior of PCAs across a wide range of input amplitudes. The proposed model incorporates minor-loop extremum-dependent terms into the asymmetric PI framework, enhancing its generality for diverse amplitude-variation patterns. To ensure accurate parameter identification, an adaptive differential evolution algorithm is employed. Experimental validation demonstrates that, within a 2–10 V excitation range, the AAAPI model achieves a substantial improvement in accuracy, reducing normalized root-mean-square error from 4.54% (classical PI) to 0.67%, and decreasing maximum hysteresis error by 85.2%. The proposed AAAPI framework, integrating amplitude-related terms and adaptive optimization, significantly advances hysteresis modeling for piezoelectric actuators by achieving superior accuracy (RMSE 0.28%, max error 0.67%) across wide amplitude and frequency ranges, thereby offering a robust solution for precision control under varying operating conditions. These results confirm the superior capability of the AAAPI model to characterize amplitude-dependent hysteresis across varying operating frequencies, offering a significant advancement for precision control in piezoelectric actuator applications.