具有迟滞补偿的单压电变形镜的闭环校正性能
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摘要
对具有迟滞补偿的单压电变形镜的闭环校正性能进行了研究。提出了基于Prandtl-Ishlinskii(PI)迟滞模型的变形镜闭环控制算法,搭建了基于哈特曼波前传感器的自适应光学测试平台,分别进行了静态像差和动态像差的闭环校正实验。实验结果表明:在静态像差的闭环校正中,迟滞消除算法比未消除算法具有更快的校正速度;对于波前像差均方根的平均值为168nm的动态像差,校正后的残差从消除前的33nm降低到校正后的25nm,证明了所提算法可有效应用于压电变形镜自适应光学系统。
This study investigated the correction performance of closed-loop control with hysteresis compensation for apiezoelectric unimorph deformable mirror.A closed-loop control algorithm based on the Prandtl-Ishlinskii hysteresis model was established herein.In addition,an adaptive optics test platform based on the Hartmann wavefront sensor was built.The closed-loop correction experiments of static and dynamic aberrations were performed.The experimental results show that for the closed-loop correction of static aberrations,the correction speed of the algorithm with hysteresis compensation is faster than that without compensation.Further,for the dynamic aberrations with an average root-mean-square value of 168 nm,the residual error after correction is reduced from 33 nm before hysteresis compensation to 25 nm after hysteresis compensation.These results prove that the proposed method can be efficiently used in an adaptive optics system with a piezoelectric deformable mirror.
This study investigated the correction performance of closed-loop control with hysteresis compensation for apiezoelectric unimorph deformable mirror.A closed-loop control algorithm based on the Prandtl-Ishlinskii hysteresis model was established herein.In addition,an adaptive optics test platform based on the Hartmann wavefront sensor was built.The closed-loop correction experiments of static and dynamic aberrations were performed.The experimental results show that for the closed-loop correction of static aberrations,the correction speed of the algorithm with hysteresis compensation is faster than that without compensation.Further,for the dynamic aberrations with an average root-mean-square value of 168 nm,the residual error after correction is reduced from 33 nm before hysteresis compensation to 25 nm after hysteresis compensation.These results prove that the proposed method can be efficiently used in an adaptive optics system with a piezoelectric deformable mirror.
引文
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[13]Tian L,Chen J J,Cui Y G,et al.Open-loop control of unimorph piezoelectric deformable mirror based on PI hysteresis model[J].Chinese Journal of Scientific Instrument,2017,38(1):136-142.田雷,陈俊杰,崔玉国,等.基于PI迟滞模型的单压电变形镜开环控制[J].仪器仪表学报,2017,38(1):136-142.
[14]Chen B,Yang J,Li X Y,et al.Comparison of two close-loop control methods in adaptive optics with wavefront curvature sensing[J].Acta Optica Sinica,2016,36(3):0301003.陈波,杨靖,李新阳,等.波前曲率传感自适应光学两种闭环控制方法的对比[J].光学学报,2016,36(3):0301003.
[15]Kalman D.A singularly valuable decomposition:the SVD of a matrix[J].The College Mathematics Journal,1996,27(1):2-23.
[16]Yi J G,Chang S,Shen Y T.Disturbance-observerbased hysteresis compensation for piezoelectric actuators[J].ASME Transactions on Mechatronics,2009,14(4):456-464.
[17]Kuhnen K.Modeling,identification and compensation of complex hysteretic nonlinearities:a modified Prandtl-Ishlinskii approach[J].European Journal of Control,2003,9(4):407-418.
[18]Rakotondrabe M,Clévy C,Lutz P.Complete open loop control of hysteretic,creeped,and oscillating piezoelectric cantilevers[J].IEEE Transactions on Automation Science and Engineering,2010,7(3):440-450.
[19]Ma J Q,Liu Y,He T,et al.Double drive modes unimorph deformable mirror for low-cost adaptive optics[J].Applied Optics,2011,50(29):5647-5654.
[20]Wu C H,Zhang X F,Chen W L,et al.Fundus imaging system based on tomographic adaptive optics[J].Acta Optica Sinica,2017,37(4):0411002.武楚晗,张晓芳,陈蔚林,等.基于层析传感的自适应光学眼底成像系统[J].光学学报,2017,37(4):0411002.
[2]Sun L,Huang L,Yan M,et al.Simulational and experimental investigation on the dynamic high frequency aberration of the deformable mirror[J].Optics Express,2017,25(26):32853-32866.
[3]Chen K,Chen J J,Mao Y X,et al.Simulation and experiment of 214-element unimorph deformable mirror with edge-driven[J].Acta Photonica Sinica,2016,45(8):44-49.陈凯,陈俊杰,毛宇昕,等.带边缘驱动的214单元单压电变形镜仿真与实验[J].光子学报,2016,45(8):44-49.
[4]Lin X D,Liu X Y,Wang J L,et al.Development and performance test of the 961-element deformable mirror[J].Acta Optica Sinica,2013,33(6):0601001.林旭东,刘欣悦,王建立,等.961单元变形镜研制及性能测试[J].光学学报,2013,33(6):0601001.
[5]Song H,Vdovin G,Fraanje R,et al.Extracting hysteresis from nonlinear measurement of wavefrontsensorless adaptive optics system[J].Optics Letters,2009,34(1):61-63.
[6]Gu G Y,Zhu L M,Su C Y,et al.Modeling and control of piezo-actuated nanopositioning stages:a survey[J].IEEE Transactions on Automation Science&Engineering,2016,13(1):313-332.
[7]Cao Y,Chen X B.A survey of modeling and control issues for piezo-electric actuators[J].Journal of Dynamic Systems,Measurement&Control,2015,137(1):014001.
[8]Sutor A,Rupitsch S J,Lerch R.A Preisach-based hysteresis model for magnetic and ferroelectric hysteresis[J].Applied Physics A,2010,100(2):425-430.
[9]Zhang J,Merced E,Sepúlveda N,et al.Optimal compression of generalized Prandtl-Ishlinskii hysteresis models[J].Automatica,2015,57:170-179.
[10]Zhang J,Merced E,Sepúlveda N,et al.Optimal compression of generalized Prandtl-Ishlinskii hysteresis models[J].Automatica,2015,57:170-179.
[11]Oh J,Bernstein D S.Semilinear Duhem model for rate-independent and rate-dependent hysteresis[J].IEEE Transactions on Automatic Control,2005,50(5):631-645.
[12]Dubra A,Massa J S,Paterson C.Preisach classical and nonlinear modeling of hysteresis in piezoceramic deformable mirrors[J].Optics Express,2005,13(22):9062.
[13]Tian L,Chen J J,Cui Y G,et al.Open-loop control of unimorph piezoelectric deformable mirror based on PI hysteresis model[J].Chinese Journal of Scientific Instrument,2017,38(1):136-142.田雷,陈俊杰,崔玉国,等.基于PI迟滞模型的单压电变形镜开环控制[J].仪器仪表学报,2017,38(1):136-142.
[14]Chen B,Yang J,Li X Y,et al.Comparison of two close-loop control methods in adaptive optics with wavefront curvature sensing[J].Acta Optica Sinica,2016,36(3):0301003.陈波,杨靖,李新阳,等.波前曲率传感自适应光学两种闭环控制方法的对比[J].光学学报,2016,36(3):0301003.
[15]Kalman D.A singularly valuable decomposition:the SVD of a matrix[J].The College Mathematics Journal,1996,27(1):2-23.
[16]Yi J G,Chang S,Shen Y T.Disturbance-observerbased hysteresis compensation for piezoelectric actuators[J].ASME Transactions on Mechatronics,2009,14(4):456-464.
[17]Kuhnen K.Modeling,identification and compensation of complex hysteretic nonlinearities:a modified Prandtl-Ishlinskii approach[J].European Journal of Control,2003,9(4):407-418.
[18]Rakotondrabe M,Clévy C,Lutz P.Complete open loop control of hysteretic,creeped,and oscillating piezoelectric cantilevers[J].IEEE Transactions on Automation Science and Engineering,2010,7(3):440-450.
[19]Ma J Q,Liu Y,He T,et al.Double drive modes unimorph deformable mirror for low-cost adaptive optics[J].Applied Optics,2011,50(29):5647-5654.
[20]Wu C H,Zhang X F,Chen W L,et al.Fundus imaging system based on tomographic adaptive optics[J].Acta Optica Sinica,2017,37(4):0411002.武楚晗,张晓芳,陈蔚林,等.基于层析传感的自适应光学眼底成像系统[J].光学学报,2017,37(4):0411002.