压电叠堆作动器率相关迟滞非线性建模研究

针对压电叠堆作动器的率相关迟滞非线性特性，该文提出了一种基于asymmetric unilateral backlash(aubacklash)算子的BP神经网络率相关迟滞建模方法。首先提出了改进的aubacklash算子，改善了Prandtl-Ishlinskii(PI)模型backlash算子在原点处残余位移及严格中心对称的问题；其次分析了压电叠堆作动器迟滞的率相关记忆特性，提出了率相关BP神经网络迟滞模型；最后搭建了迟滞建模精度评估系统，采用Levenberg-Marquardt(L-M)算法辨识aubacklash算子模型参数，确定了BP神经网络模型最优结构参数。实验结果表明，在高、低单一频率及混合频率下，BP神经网络模型较PI模型均方误差降低了70.90%～89.98%,相对误差降低了70.69%～89.84%,验证了该模型的精度与频率适应性。

Modeling on Rate-Dependent Hysteresis Nonlinear Characteristics ofPiezoelectric Stack Actuators

Aiming at the nonlinear characteristics of rate-dependent hysteresis of piezoelectric stack actuators, a BP neural network rate-dependent hysteresis modeling method based on the Asymmetric unilateral backlash (aubacklash) operator is proposed in this paper. Firstly, an improved aubacklash operator is proposed to improve the residual displacement at the origin and strict center-symmetry of the backlash operator of Prandtl-Ishlinskii (PI) model. Secondly, the rate-dependent memory characteristics of hysteresis of piezoelectric stack actuator are analyzed, and a rate-dependent BP neural network hysteresis model is proposed. Finally, the accuracy evaluation system of hysterectomy modeling is set up, the parameters of aubacklash operator model are identified by Levenberg-Marquardt(L-M) algorithm, and the optimal structural parameters of BP neural network model are determined. The experimental results show that the mean square error of BP neural network model is reduced by 70.90%~89.98% and the relative error is reduced by 70.69%~89.84% compared with the traditional PI model at high and low single frequency and mixed frequency, which verifies the accuracy and frequency adaptability of the model.