Piezoelectric Hysteresis Modeling and Compensation Based on an Enhanced Rate-Dependent Prandtl-Ishlinskii Model

Piezoelectric actuators are widely used in ultra-precision micropositioning systems, but their inherent rate-dependent hysteresis nonlinearities severely degrade dynamic positioning accuracy. This paper proposes an enhanced rate-dependent generalized Prandtl–Ishlinskii (ERGPI) model that accurately captures rate-dependent hysteresis evolution and substantially improves the modeling of dynamic nonlinear responses. To efficiently obtain reliable model parameters, an improved dynamic adaptive differential evolution algorithm (ID-LSHADE) is developed, which accelerates convergence without sacrificing identification accuracy. The proposed ERGPI model achieves superior rate-dependent hysteresis modeling performance with negligible parameter overhead: the relative root-mean-square error and relative maximum error are up to 1.04% and 2.08%, respectively, outperforming the traditional GPI model over a wide frequency range. Based on the well-identified ERGPI model, a direct inverse feedforward compensation strategy is further constructed to suppress hysteresis-induced positioning errors. Experimental results demonstrate that the combined modeling and identification framework accurately characterizes the asymmetric and rate-dependent hysteresis of piezoelectric actuators with high efficiency and low parametric complexity. Broadband hysteresis compensation and trajectory tracking experiments further verify the effectiveness of the proposed feedforward scheme in mitigating hysteresis nonlinearities and improving dynamic positioning performance. This study provides an effective alternative for high-precision dynamic control of piezoelectric micropositioning systems.