Control Of Piezoelectric Deformable Mirror Based On Neural Network And Hysteresis Model

Adaptive optics technology is to measure and feedback the external optical wavefront aberration in real time,and to realize the real-time correction of the wavefront aberration by controlling the mirror shape of the deformable mirror,so as to improve the resolution of the system.At first,the adaptive optical system was used in astronomical observation to compensate for the influence of atmospheric turbulence on optical imaging.At present,adaptive optics technology has been widely used in many aspects,such as astronomical observation,laser processing,retinal imaging and so on.Piezoelectric deformable mirrors have been widely used in adaptive optical systems due to their remarkable performance advantages,but the inherent hysteresis nonlinear characteristic of piezoelectric ceramics affects the control performance of adaptive optical system seriously.The aim of this paper is to eliminate or compensate the hysteresis nonlinearity of the piezoelectric deformable mirror so as to improve the control accuracy and efficiency of the piezoelectric deformable mirror.It is mainly content as follows:(1)The hysteresis nonlinearity characteristics of piezoelectric deformable mirror is analyzed,the modeling process of Prandtl-Ishlinskii(PI)hysteresis model and BackPropagation(BP)neural network model based on PI hysteresis operator is described in detail,and its inverse model is obtained.At the same time,according to the conventional control scheme of piezoelectric deformable mirror,the control scheme of piezoelectric deformable mirror with hysteresis compensation is defined.(2)An adaptive optical system experimental test platform based on hartmann wavefront sensor was built.The hysteresis characteristic curves of the piezoelectric deformable mirror are acquired by using the experimental platform,and the hysteresis model and inverse model are established for multiple actuators of the piezoelectric deformable mirror.The PI hysteresis model established can well fit the measured hysteresis curve,and the fitting error range of the central actuator is-2.5 ~ 2.3 nm.The BP neural network based on PI hysteresis operator can also well fit the measured hysteresis curve,and the(Root-mean-Square,RMS)value of the fitting error of the central actuator is 1.6 nm.(3)In order to verify the effectiveness of the hysteresis model,the open-loop and closedloop control experiments were carried out for the typical aberration of the piezoelectric deformable mirror.In the open-loop control experiment,for the correction of astigmatism(Z3)aberration,the control result based on PI hysteresis inverse model compensation method can be used to reconstruct the target surface shape well.The reconstruction accuracy is improved by 55.5%.The closed-loop control scheme based on PI hysteresis model is used in closedloop control experiments,and closed-loop correction experiments of static aberrations and dynamic aberrations are carried out respectively.Experimental results show that in the closedloop correction of static aberrations,the hysteresis elimination algorithm has a faster correction rate than the uneliminated algorithm.For the wavefront aberrations with an average value of 168 nm root-mean square,the residual error after correction is reduced from 33 nm before hysteresis compensation to 25 nm after hysteresis compensation,and the overall correction performance is improved by 24.7%.It proves that the proposed method can be efficiently used in the adaptive optics system with piezoelectric deformable mirror.