Hysteresis Characterization Modeling and Control of Inchworm Piezoelectric Linear Motors Based on the Bouc–Wen Model

Abstract The inchworm piezoelectric linear motor (IWPELM) exhibits pronounced hysteresis nonlinearity, leading to a multivalued mapping between input voltage and output displacement. This significantly degrades positioning accuracy and limits practical applications. To address this issue, this paper develops an enhanced Bouc–Wen (EBW) hysteresis model together with a dedicated identification method. First, the hysteresis characteristics of the IWPELM are analyzed, and the classical Bouc–Wen (CBW) model is improved by introducing an asymmetric hysteresis representation and dynamic frequency‐dependent parameters, thereby enabling a more comprehensive description of the hysteresis behavior under practical operating conditions. In addition, a high‐order extended Kalman filter (HEKF) is designed to dynamically process the nonlinear terms, improving the fitting accuracy of the model with respect to the measured motion trajectories. Subsequently, a parameter identification algorithm that combines Double Q‐learning and particle swarm optimization (PSO) is developed. Compared with conventional PSO, the proposed algorithm reduces the root‐mean‐square error (RMSE) between the model output and the experimental data to 0.0070 μm, demonstrating superior identification performance. Finally, a feedforward compensation controller is constructed based on the inverse EBW model to explicitly compensate for hysteresis nonlinearity, while a fractional‐order super‐twisting sliding mode control (FOSTSMC) scheme is designed to suppress unmodeled dynamics and external disturbances. The resulting composite control strategy effectively mitigates the hysteresis effects in the IWPELM, achieving a maximum error of only 0.0039 μm between the compensated output and the desired trajectory, together with a linear fitting coefficient of 0.99998845. Compared with classical control schemes, the proposed approach significantly enhances positioning accuracy and system robustness, providing a solid theoretical foundation and practical support for the application of piezoelectric actuators in high‐precision scenarios.