压电式倾斜镜迟滞特性及其实验研究
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摘要
空间激光通信精瞄系统中压电式倾斜镜存在的迟滞非线性特性,不仅降低了精瞄系统定位精度,而且对信标光的捕获以及链路的稳定性造成影响。针对该问题,提出一种基于PLAY迟滞算子改进Prandtl-Ishlinskii(P-I)数学模型及参数辨识方法,利用该模型对迟滞特性进行前馈线性化逆补偿。为进一步提高系统跟踪精度,在线性化的基础上,设计了静态输出反馈控制器,形成复合控制方法,并设计了激光通信终端精瞄系统实验,验证了该复合方法的有效性。通过对系统输入不同频率等幅和减幅正弦控制信号进行测试,结果表明,改进P-I模型最大拟合误差在1%之内,前馈模型逆补偿使压电陶瓷执行器(PEA)的线性度误差由5%减小到1%以内,复合控制方法系统跟踪误差降低了80%。
In a precision pointing system for space laser communication,the hysteresis nonlinearity of the steering mirror driven by the piezoelectric actuator(PEA)can not only reduce its pointing accuracy greatly,but also affect the acquisition of beacon light and link stability.To address this issue,an improved Prandtl-Ishlinskii(P-I)model based on the PLAY hysteresis operator and a parameter identification method are presented,and on this basis,a feedforward linearized inverse compensation method for the steering mirror is proposed.In order to further improve the tracking accuracy of the system,on the basis of linearization,a static output feedback controller is designed to form a composite control method,and a laser communication terminal precision sighting system experiment is designed to verify the effectiveness of the composite method,in which sine signals with different frequencies and amplitudes are input.Experiment results show that the maximum fitting error of the improved P-I model is less than 1%.Inverse compensation of the feedforward model can reduce the linearity error of the PEA from 5%to less than 1%.Tracking errors of the system based on the compound method are reduced by 80%.
In a precision pointing system for space laser communication,the hysteresis nonlinearity of the steering mirror driven by the piezoelectric actuator(PEA)can not only reduce its pointing accuracy greatly,but also affect the acquisition of beacon light and link stability.To address this issue,an improved Prandtl-Ishlinskii(P-I)model based on the PLAY hysteresis operator and a parameter identification method are presented,and on this basis,a feedforward linearized inverse compensation method for the steering mirror is proposed.In order to further improve the tracking accuracy of the system,on the basis of linearization,a static output feedback controller is designed to form a composite control method,and a laser communication terminal precision sighting system experiment is designed to verify the effectiveness of the composite method,in which sine signals with different frequencies and amplitudes are input.Experiment results show that the maximum fitting error of the improved P-I model is less than 1%.Inverse compensation of the feedforward model can reduce the linearity error of the PEA from 5%to less than 1%.Tracking errors of the system based on the compound method are reduced by 80%.
引文
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[3]Lu N,Ke X Z,Zhang H.Research on APT coarse tracking in free-space laser communication[J].Infrared and Laser Engineering,2010,39(5):943-949.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.
[4]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.
[5]Massad J E,Smith R C.Adomain wall model for hysteresis in ferroelastic materials[J].Journal of Intelligent Material Systems&Structures,2003,14(7):455-471.
[6]Smith R C,Hatch A G,Mukherjee B,et al.A homogenized energy model for hysteresis in ferroelectric materials:general density formulation[J].Journal of Intelligent Material Systems&Structures,2005,16(9):713-732.
[7]Hegewald T,Kaltenbacher B,Kaltenbacher M,et al.Efficient modeling of ferroelectric behavior for the analysis of piezoceramic actuators[J].Journal of Intelligent Material Systems&Structures,2008,19(10):1117-1129.
[8]Preisach F.ber die magnetische Nachwirkung[J].Zeitschrift für Physik,1935,94(5/6):277-302.
[9]Krasnosel′skiǐM A,PokrovskiǐA V.Systems with hysteresis[M].Berlin:Springer Science&Business Media,1989,11(3):393-406.
[10]Wen Y K.Equivalent linearization for hysteretic systems under random excitation[J].Journal of Applied Mechanics,1980,47(1):150-154.
[11]Goldfarb M,Celanovic N.Modeling piezoelectric stack actuators for control of micro-manipulation[J].IEEE Control Systems,1997,17(3):69-79.
[12]Duhem P.Die dauerndennderungen und die Thermodynamik:IX[J].Zeitschrift für Physikalische Chemie,1903,43U(1):695-700.
[13]Newcomb C V,Flinn I.Improving the linearity of piezoelectric ceramic actuators[J].Electronics Letters,1982,18(11):442-444.
[14]Tan X B,Baras J S.Adaptive identification and control of hysteresis in smart materials[J].IEEE Transactions on Automatic Control,2005,50(6):827-839.
[15]Dang X J,Tan Y H.An inner product-based dynamic neural network hysteresis model for piezoceramic actuators[J].Sensors and Actuators A:Physical,2005,121(2):535-542.
[16]Janaideh M A,Rakotondrabe M,Aljanaideh O.Further results on hysteresis compensation of smart micropositioning systems with the inverse PrandtlIshlinskii compensator[J].IEEE Transactions on Control Systems Technology,2016,24(2):428-439.
[17]Macki J W,Nistri P,Zecca P.Mathematical models for hysteresis[J].SIAM Review,1993,35(1):94-123.
[18]Zheng F,Wang Q G,Lee T H.On the design of multivariable PID controllers via LMI approach[J].Automatica,2002,38(3):517-526.
[19]Cao Y Y,Lam J,Sun Y X.Static output feedback stabilization:an ILMI approach[J].Automatica,1998,34(12):1641-1645.