自适应光学系统中的倾斜镜、变形镜通常是应用压电陶瓷驱动器来进行精密位移控制，但压电陶瓷驱动器都有较大的非线性迟滞效应，对系统定位性能造成了一定的影响。为了补偿迟滞现象，需要对迟滞效应进行建模。本文通过引入迟滞算子，使用贝叶斯正则化训练算法训练BP 神经网络来构建压电陶瓷驱动器迟滞模型，以中国科学院光电技术研究所自主研制的压电陶瓷驱动器为对象开展了实验研究。实验结果表明，通过BP 神经网络构建的压电陶瓷驱动器迟滞模型具有较准确的辨识能力，其中正模型的相对误差为0.0127，逆模型的相对误差为0.014。利用所建立的模型，压电陶瓷驱动器的非线性度从14.6%降低到了1.43%。

The tilt mirrors and deformable mirrors in adaptive optics system are usually using piezoelectric ceramic actuators for precise displacement, however, piezoelectric ceramic actuators own obviously nonlinear hysteresis effect which affects the positioning performance of the system. In order to compensate the hysteresis, there is a need to model hysteresis effects. In this paper, hysteresis operator is introduced and using Bayesian regularization training algorithm to train BP neural network to construct hysteresis model of piezoelectric ceramic actuator, an experimental study was conducted on a piezoelectric actuator developed by Institute of Optics and Electronics, Chinese Academy of Sciences. The final experimental results show that the hysteresis model of piezoelectric ceramic actuators constructed by BP neural network has more accurate identification capability. The relative error of the positive model is 0.0127 and the relative error of the inverse model is 0.014. The nonlinearity of the piezoelectric Displacement/μm actuators has been reduced from 14.6% to 1.43%.