用于同步辐射的压电变形镜控制策略数值模拟  

Numerical simulation of piezoelectric bimorph mirror control strategy applied to synchrotron radiation

作　　者：王梓齐 樊凯 张军剑 冯志华[1,2] WANG Ziqi;FAN Kai;ZHANG Junjian;FENG Zhihua(Department of Precision Machinery and Precision Instrumentation,University of Science and Technology of China,Hefei 230026,China;Key Laboratory of Precision Scientific Instrumentation of Anhui Higher Education Institutes,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]中国科学技术大学精密机械与精密仪器系,安徽合肥230026 [2]中国科学技术大学精密科学仪器安徽普通高校重点实验室,安徽合肥230026

出　　处：《应用光学》2022年第1期23-29,共7页Journal of Applied Optics

基　　金：国家自然基金委海外青年学者基金(81728008);中国科学技术大学同步辐射联合基金。

摘　　要：为了提高同步辐射中压电变形镜的控制自由度和面形精度,解决压电致动单元数量过多引起的解算电压受噪声影响异常波动(过拟合)问题,建立了变形镜模型并进行仿真控制。通过有限元仿真获得36组压电响应方程,构建面形与电压的数学模型;为补偿重力造成的镜面畸变,以获得的椭圆面形分析并比较了使用最小二乘法和Tikhonov正则化两种电压解算方案的控制效果。结果表明:采用Tikhonov正则化算法反演后,面形控制误差相比最小二乘法降低了21.7%,相邻极板间电压波动极大值从1.019 kV下降为0.174 kV,反演结果符合工程实际要求;系统对测试噪声具有鲁棒性,相比最小二乘法有更加优越的应用价值。In order to improve the control degree of freedom and surface shape accuracy of the piezoelectric bimorph mirror(PBM)in synchrotron radiation,and to solve the problem of abnormal fluctuations of the calculated voltages(overfitting)affected by noise caused by the excessive number of piezoelectric actuation units,the PBM model was established and simulation control was carried out.The 36 sets of piezoelectric response equations were obtained through the finite element simulation,and the mathematical model of surface shape and voltage was constructed.To compensate the mirror surface distortion caused by gravity,the control effects of two voltage solutions using least square method(LSM)and Tikhonov regularization were analyzed and compared by obtained ellipse shape.The results show that after using Tikhonov regularization inversion,the surface shape control error is reduced by 21.7%compared with LSM,and the maximum voltage fluctuation between adjacent electrodes is reduced from 1.019 kV to 0.174 kV,which meet the actual requirements of engineering.The system is robust to tested noise,and has more superior application value than LSM.

关 键 词：同步辐射光学仪器 压电变形镜 正则化算法 TIKHONOV正则化 反问题求解 

分 类 号：TH744[机械工程—光学工程] O434.19[机械工程—仪器科学与技术]