2. Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China;
3. University of Chinese Academy of Sciences, Beijing 100049, China
Overview: Adaptive optics is used to correct the wavefront distortion caused by atmospheric turbulence in real time. The tilt mirrors and deformable mirrors in adaptive optics system usually use 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. Due to the limitation of computation quantity and dimension of traditional hysteresis model, it is difficult to find the analytic inverse model, which is not conducive to the application of engineering practice. Neural network can approximate any nonlinear curve and owns the adaptive learning ability, strong fault tolerance and the very high ability of system identification, data processing ability and the ability of fast parallel computing, which makes the neural network widely used in nonlinear system modeling. It can be inferred from incomplete or noisy data in the training process and can be easily combined with the controller design. In the application of neural network, the input and output relationship of mapping is one-to-one or many-to-one mapping relationship, but the relationship between voltage and displacement of piezoelectric ceramic actuator is one-to-many mapping relations, neural network cannot deal directly with this nonlinear mapping. In this paper, by introducing a hysteresis operators to expand the input voltage of piezoelectric ceramic actuator in neural network input space, the multimapping of hysteresis is transformed into one-to-one mapping in 3D space. In the transformed space, the neural network is used to approximate the one-to-one mapping and a hysteresis non-linearity based on the neural network is established, the one-dimensional feature is introduced for the input of neural network by constructing the hysteresis operator. In this paper, the Powell-Beale algorithm, Levenberg-Marquardt algorithm and Bayesian regularization algorithm are compared, and the Bayesian regularization training algorithm was used to train BP neural network to construct the positive hysteresis model and inverse model of piezoelectric ceramic actuators, and an experimental study was conducted on a piezoelectric actuator developed by Institute of Optics and Electronics, Chinese Academy of Sciences. According to the established model, the hysteresis positive model, inverse model and hysteresis compensation experiment of piezoelectric ceramic actuator are carried out. 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 actuators has been reduced from 14.6% to 1.43%.