基于改进PI模型的压电陶瓷迟滞特性补偿控制
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摘要
压电陶瓷执行器的迟滞特性会降低星间激光通信精瞄系统的定位精度,对信标光的捕获以及链路的稳定性造成影响。针对这一问题,通过分析压电陶瓷执行器迟滞特性产生机理,提出一种基于PLAY迟滞算子的改进(Prandtl-Ishlinskii,PI)数学模型及其辨识方法,并利用该模型对压电陶瓷执行器迟滞特性进行前馈线性化逆补偿。并通过实验来验证数学模型和线性化的有效性,实验结果表明,通过对系统输入不同频率下等幅和减幅正弦控制信号来验证前馈逆补偿性能时,改进的模型最大拟合误差均在1%之内,通过前馈模型逆补偿的控制方法可使压电陶瓷驱动的线性度误差由5%减小到1%以内,并且改进PI模型在计算复杂度上由O(n)简化为O(1)。
The hysteretic nonlinearity of the piezoelectric actuator( PEA) will greatly reduce the pointing accuracy of a precision pointing system for inter-satellite laser communication,and affect the acquisition of beacon and link stability. To address this issue,an improved Prandtl-Ishlinskii( PI) model based on the PLAY hysteresis operator and parameter identification method is presented to characterize the hysteresis of the PEA. Based on this basis,a feedback forward linearization method for the piezoelectric is proposed and its effectiveness of mathematical model and linearization is verified. The experimental results show that the inverse of this model with maximum error less than 1% is employed for feedforward compensation of the PEA hysteresis to obtain an approximately linear system. The improved PI model entails less computation than the original PI model. The performance the feedforward compensation is verified by experiments using control signals with different frequencies, and with constant and decreasing amplitudes respectively. The results show that the feedforward inverse model compensation can reduce the linearity error of the PEA from 5% to less than 1%,which Prandtl-Ishlinskii model in computational complexity simplified from O( n) to O( 1).
The hysteretic nonlinearity of the piezoelectric actuator( PEA) will greatly reduce the pointing accuracy of a precision pointing system for inter-satellite laser communication,and affect the acquisition of beacon and link stability. To address this issue,an improved Prandtl-Ishlinskii( PI) model based on the PLAY hysteresis operator and parameter identification method is presented to characterize the hysteresis of the PEA. Based on this basis,a feedback forward linearization method for the piezoelectric is proposed and its effectiveness of mathematical model and linearization is verified. The experimental results show that the inverse of this model with maximum error less than 1% is employed for feedforward compensation of the PEA hysteresis to obtain an approximately linear system. The improved PI model entails less computation than the original PI model. The performance the feedforward compensation is verified by experiments using control signals with different frequencies, and with constant and decreasing amplitudes respectively. The results show that the feedforward inverse model compensation can reduce the linearity error of the PEA from 5% to less than 1%,which Prandtl-Ishlinskii model in computational complexity simplified from O( n) to O( 1).
引文
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[3]DEVASIA S,ELEFTHERIOU E,MOHEIMMANI S O R.A survey of control issues in nanopositioning[J].IEEE Transactions on Control Systems Technology,2007,15(5):802-823.
[4]GREGORY M,HEINE F F,H KEMPNER H,et al.Commercial optical inter-satellite communication at high data rates[J].Optical Engineering,2012,53(3):031202.
[5]HEMMATI H.深空光通信[M].北京:清华大学出版社,2009:283-296.HEMMATI H.Deep space optical communications[M].Beijing:Tsinghua University Press,2009:283-296.
[6]ARVIZU A,SANTOS J,DOMINGUEZ E,et al.ATP subsystem for optical communications on a cubesat[C].IEEE International Conferences on Space Optical Systems and Applications,2015:1-5.
[7]李锐,李洪祚,唐雁峰,等.空间光通信复合轴APT系统[J].红外与激光工程,2011,40(7):13 33-1336.LI R,LI H Z,TANG Y F,et al.Compound-axis APT system in space optical communication[J].Infrared and Laser Engineering,2011,40(7):1333-1336.
[8]卢宁,柯熙政,张华.自由空间激光通信中APT粗跟踪研究[J].红外与激光工程,2010,39(5):943-949.LU N,KE X ZH,ZHANG H.Research on APT coarse tracking in free-space laser communication[J].Infrared and Laser Engineering,Infrared and Laser Engineering,2010,39(5):943-949.
[9]TANG T,HUANG Y M,FU CH Y,et al.Acceleration feedback of a CCD-based track-ing loop for fast steering mirror[J].Optical Engineering,2009:48(1):1-6.
[10]MOHEIMANI S O R.Accurate and fast nanopositioning with piezoelectric tube scanners:Emerging trends and future challenges[J].Review of Scientific Instruments,2008,79(5):1-11.
[11]LIU W J,LIAO W J,JIA K M,et al.Hysteresis property of tip-tilt-piston micromirror based on tilt-andlateral shift-free piezoelectric unimorph actuator[J].Integrated Ferroelectrics,2014,150(1):14-22.
[12]IYER R V,TAN X B,KRISHNAPRASAD P S.Approximate inversion of the Preisach hysteresis operator with application to control of smart actuators[J].IEEE Transactions on Automatic Control,2005,50(6):798-810.
[13]XIAO SH L,LI Y M.Modeling and high dynamic compensating the tate-dependent hysteresis of piezoelectirc actuators via a novel modified inverse Preisach model[J].IEEE Transactions on Control Systems Technology,2012,21(5):1549-1557.
[14]PREISACH F.über die magnetische Nachwirkung[J].Zeits Chrift für Physik,1935,94(5):277-302.
[15]GE P,JOUANEH M.Generalized preisach model for hysteresis nonlinearity of piezoceramic actuators[J].Pre-cision Engineering,1997,20(2):99-111.
[16]李黎,刘向东,王伟,等.压电陶瓷执行器迟滞特性的广义非线性Preisach模型及其数值实现[J].光学精密工程,2007,15(5):706-712.LI L,LIU X D,WANG W,et al.Generalized nonlinear Preisach model for hysteresis nonlinearity of piezoceramic actuator and its numerical implementation[J].Optical and Preisach Engineering,2007,15(5):706-712.
[17]HABINEZA D,RAKOTONDRABE M,GORREC Y.Bouc-Wen modeling and feedforward control of multivariable hysteresis in piezoelectric systems:Application to a 3-Do F piezo tube scanner[J].IEEE Transactions on Control Systems Technology,2015,23(5):1797-18 06.
[18]王钰锋,郭咏新,毛剑琴.压电作动器的率相关迟滞建模与跟踪控制[J].光学精密工程,2014,22(3):616-625.WANG Y F,GUO Y X,MAO J Q.Rate-de pendent modeling and tracking control of piezoelectric actuators[J].Optics and Precision Engineering,2014,22(3):616-625.
[19]LIU Y F,SHAN J J,QI N M.Creep modeling and identification for piezoelectric actuators based on fractional-order system[J].Mechatronics,2013,23(7):840-847.
[20]BIGGIO M,OLIVERI A,STELLINO F,et al.A circuit model of hysteresis and creep[J].IEEE Transactions on Circuits and systems,2015,62(5):501-505.
[21]MOHAMMAD A J,MICKY R,OMAR A.Further results on hysteresis compensation of smart micropositioning systems with the inverse prandtl–ishlinskii compensator[J].IEEE Transactions on Control System Technology,2016,24(2):428-439.
[22]张学福,王丽坤.现代压电学[M].北京:科学出版社,2002:93-97.ZHANG F X,WANG L K.Modern piezoelectricity[M].Beijing:Science Press,2002:93-97.