Control Of Piezoelectric Deformable Mirror Based On PI Hysteresis Model

Adaptive optics(AO)technology has been widely used in many areas by controlling the deformation mirror(DM),such as astronomical telescopes,biotechnology,laser industry,retinal imaging and laser communication,and so on.Piezoelectric DM is attractive for its high resolution,fast response speed,big driving.But the hysteresis nonlinearity of piezoelectric DM directly educes the open-loop control precision and the closed-loop operation bandwidth,limiting its applications in AO system.The purpose of this paper is to eliminate the hysteresis nonlinearity of piezoelectric DM,The main research work are introduced as follows.(1)Firstly,the hysteresis nonlinearity of piezoelectric DM was analyzed.The control plan of piezoelectric DM was put forward,which based on hysteretic model.And the PI hysteresis model was described in detail.Then the selection and identification of the hysteresis model parameters were given.And PI inverse model were calculated.(2)Then the AO system has been built with a hartmann wavefront sensor.PI hysteresis model was used to establish the hysteresis behavior of the annular actuator.The least square method was used to identify the weight value of PI hysteresis model.When the number of operators was 9,the comprehensive performance was better.The open-loop control experimental results show that: the hysteresis could reduce from 9.3% to 1.2%.When reconstructing the focal plane of the triangle wave amplitude value(the amplitude is 0.43 ?m),the RMS value of its reconstruction error was decreased from 14.6 nm to 4 nm.Reconstruction precision was increased by 72.6%.When reconstructing the defocus surface with random amplitude,the RMS value of its reconstruction error was decreased from 13.7 nm to 3.5 nm.Reconstruction precision was increased by 74.5%.(3)In the end,the control voltage of the 19 element piezoelectric DM was calculated by using the PI hysteresis inverse model,which could eliminate the hysteresis.Experimental results show that: the hysteresis could reduce from 10% to 1%.When reconstructing the classic astigmatism aberration,about Z3,the RMS value of its reconstruction error was decreased from 14.4 nm to 2.4 nm.Reconstruction precision was increased by 83.3%.When refactoring random complex surface shape(coefficient of Z3,Z4,Z5 and Z6 were 0.25,0.2,0.25,0.25 ?m).Error coefficient decreased from-12.2,-12.4,-7.0,-12.2 nm to-6.4,-6.4,-2.4,-6.5 nm.Precision was increased by 50%.