Modeling And Correction Of Nonlinear Hysteresis For The Effect Of Piezoelectric Actuator Based On Neural Network

Adaptive optics technology is a fast-growing new optical technology that enables highprecision control of beam direction and intensity distribution by performing fast measurements and high-precision control of optical wavefront while actively controlling the phase.The core of adaptive optics technology is the wavefront corrector,which mainly includes a deformable mirror(abbreviated as Deformable Mirror)and a tilted mirror(abbreviated as Tip/Tilt Mirror,TTM).The piezoelectric ceramic material itself has inherent hysteresis characteristics,means that the two displacement curves of the piezoelectric ceramic material do not coincide during the step of boosting and depressurizing,the displacement amounts are inconsistent,and existing a displacement difference.Its main feature is that the output at the next moment depends not only on the input and output at the current moment,but also on the input at the previous moment.Studies have shown that in the case of uncontrolled open loop,the nonlinear tracking error caused by the asymmetry of the hysteresis curve reaches more than 15%.Therefore,the hysteresis nonlinear compensation is very important for the realization of TTM high-precision control.The hysteresis phenomenon needs to be modeled and compensated by the established model.The research goal of this paper is to analyze and model the hysteresis nonlinear phenomenon exhibited by the piezoelectric tilt mirror in the adaptive optics system and the piezoelectric ceramic actuator,then achieve the hysteresis compensation for hysteretic nonlinear systems.In this project,the hysteresis nonlinearity is taken as the core,and the piezoelectric ceramic actuator and piezoelectric tilt mirror are taken as the research object.The research and analysis of the hysteresis system are carried out.The main work and research results are as follows:(1)Aiming at the hysteresis nonlinear characteristics exhibited by piezoelectric ceramic actuators and piezoelectric tilt mirrors,the modeling methods of various types of hysteretic nonlinear systems are investigated.Based on the strong data processing capability and high recognition ability of neural networks,BP neural network is used to train and build models.Since the neural network can't directly deal with the multimapping relationship,this paper uses the spatial expansion-based approach to extend the input of the neural network model.The hysteresis operator is introduced as a onedimensional input of the neural network,and the hysteresis operator formula suitable for the object studied in this paper is determined.(2)The training algorithm used in the neural network for hysteresis modeling is studied.Various BP neural network training algorithms are discussed,such as the steepest gradient descent algorithm,Powell-Beale variable gradient algorithm,Levinberg algorithm,etc.Comparing the error of each training algorithm to the model established by neural network,the Bayesian regularization method is used to train the neural network hysteresis model and verify the validity of the model.(3)Taking piezoelectric ceramic actuator,piezoelectric tilt mirror and bimorph actuator as the research object,the hysteresis inverse model is analyzed and established to compensate the hysteresis system.(4)The experimental schemes for piezoelectric ceramic actuators,piezoelectric tilt mirrors and bimorph actuators are designed.Each research object is explained.Combining the established hysteresis nonlinear model with the research object.Then analyze the accuracy of the system on tracking the input desired signal and the linearity between the input desired signal and the output signal.Experiments show that the neural network-based hysteresis nonlinear inverse model used in this paper is better for the hysteresis compensation effect of the studied object than the traditional modeling algorithm(MPI algorithm).It can make the linearity better than 2% which meet the needs of the actual application process.