Modeling and inverse compensation control of hysteresis nonlinear characteristics of piezoelectric steering mirror

Overview: Piezoelectric tilt mirror in adaptive optics system is usually used to correct the wavefront distortion caused by atmospheric turbulence in real time. However, piezoelectric ceramic materials often have inherent hysteretic characteristics. In practical application, such hysteresis makes the control of piezoelectric tilt mirror difficult. The hysteretic characteristic of piezoelectric ceramics is that two displacement curves of piezoelectric ceramics do not coincide with each other in the process of pressure rise and pressure fall. The main characteristic is that the output displacement of the piezoelectric actuator at the next moment depends not only on the input voltage and output displacement at the current moment, but also on the input voltage at the previous moment. The results show that the nonlinear tracking error caused by the asymmetry of hysteresis curve is more than 15% in the case of uncontrolled open loop. Therefore, non-linear hysteresis compensation is essential to achieve high accuracy control of tip/tilt mirror (TTM), so the hysteresis phenomenon needs to be modeled and compensated by the established model. Many scholars have studied the hysteresis and non-linearity of piezoelectric tilt mirror. The traditional hysteresis and non-linearity models include Preisach model, KP model, PI model, etc. However, the parameters of these models are difficult to solve and the calculation is complex, which is not conducive to the application in engineering practice. In this paper, the hysteresis model of piezoelectric tilt mirror is constructed by introducing the hysteresis operator and using the Bayesian regularization training algorithm to train BP neural network. The final experimental results show that the hysteresis model of piezoelectric tilt mirror constructed by BP neural network has a relatively accurate identification capability, where the hysteresis size in the X direction is reduced from 6.5% to 1.3%, the identification error range of positive model is between -0.048 arcmin to +0.048 arcmin, the minimum root-mean-square error (RMSE) is 0.0106 arcmin, and the relative error is 0.0119. The model identification error range of the inverse hysteresis operator used in the experiment is -0.035 V to +0.03 V, the minimum RMSE is 0.0132 V, and the relative error is 0.0124. The hysteresis in the Y direction was reduced from 7.1% to 1.6%. The positive model identification error range of BP hysteresis operator adopted in the experiment was -0.048 arcmin to +0.05 arcmin, the minimum RMSE was 0.0112 arcmin, and the relative error was 0.0134. The model identification error range of the adopted inverse hysteresis operator is -0.04 V to +0.04 V, the minimum RMSE is 0.0148 V, and the relative error is 0.0142. For the piezoelectric tilt mirror developed by Institute of Optics and Electronics, Chinese Academy of Sciences, the model established has relatively accurate identification ability.