基于混合灵敏度的空间望远镜次镜调整机构鲁棒控制
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摘要
次镜调整机构作为空间望远镜主动光学调整的核心组件,为实现在轨实时快速调整,其调整精度和动态性能均有比较严格的要求。机构常采用Stewart平台结构形式,基于逆运动学模型和关节空间PID控制相结合的方法,由于受到模型的非线性和不确定性、扰动及耦合的影响,难以取得较为满意的效果。为解决该问题,从机电动力学模型出发,将平台各支杆间耦合因素表征为外部干扰,建立了互相解耦的关节机电模型。依据模型辨识结果采用乘性不确定性描述模型摄动,依据模型误差界和性能指标要求设计混合灵敏度加权函数。针对虚轴极点问题,采用扩展H∞方法,将复杂动力学系统的控制器设计问题转化为堆叠S/T/KS混合灵敏度问题。在Matlab中求解得到鲁棒控制器,并在DSP中完成数字算法实现。仿真分析及试验结果表明,鲁棒控制器具有更好的鲁棒性、扰动抑制性能和动态特性,能够满足空间应用的可靠性需求。
Secondary mirror adjustment mechanisms are core elements of active optics used for the adjustment of space telescopes.For real-time rapid adjustments in orbit,great demands are put on their adjusting accuracy and dynamic characteristics. Because of nonlinearity, uncertainty,disturbances,and coupling of the system,sufficient control cannot be easily achieved by traditional methods based on intermixing PID systems and inverse kinematics.Focusing on this problem,an uncoupled electromechanical model was proposed by transforming the joint couple dynamics into external disturbances.The model uncertainty was represented by the multiplicative uncertainty resulting from the system identification,and the mixed sensitivity function was designed according to the model error bound and performance index.By using the extended method to deal with theimaginary axis pole,the complex dynamic system was transformed into a stacked S/T/KS problem.A robust controller was designed by MATLAB and a digital algorithm was realized using DSP.The improved robustness,disturbance rejection,and dynamic characteristics were verified by both simulations and experimental results,proving that space-reliable application can be achieved.
Secondary mirror adjustment mechanisms are core elements of active optics used for the adjustment of space telescopes.For real-time rapid adjustments in orbit,great demands are put on their adjusting accuracy and dynamic characteristics. Because of nonlinearity, uncertainty,disturbances,and coupling of the system,sufficient control cannot be easily achieved by traditional methods based on intermixing PID systems and inverse kinematics.Focusing on this problem,an uncoupled electromechanical model was proposed by transforming the joint couple dynamics into external disturbances.The model uncertainty was represented by the multiplicative uncertainty resulting from the system identification,and the mixed sensitivity function was designed according to the model error bound and performance index.By using the extended method to deal with theimaginary axis pole,the complex dynamic system was transformed into a stacked S/T/KS problem.A robust controller was designed by MATLAB and a digital algorithm was realized using DSP.The improved robustness,disturbance rejection,and dynamic characteristics were verified by both simulations and experimental results,proving that space-reliable application can be achieved.
引文
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[2]LASLANDES M,HUGOT E,FERRARI M,et al..Space active optics:toward optimized correcting mirrors for future large spaceborne observatories[J].Proceedings of SPIE,2011,8167:816713.
[3]岳丹.基于相位差算法的拼接镜共相误差探测与图像复原的研究[D].长春:中国科学院研究生院(长春光学精密机械与物理研究所),2016.YUE D.Co-phasing of the Segmented Telescope and Image Retrieval Based on Phase Diversity Algorithm[D].Changchun:Graduate University of Chinese Academy of Sciences(Changchun Institute of Optics,Fine Mechanics and Physics),2016.(in Chinese)
[4]吴亚平,张天序,桑农,等.大视场主动光学成像系统的成像研究[J].光学精密工程,2000,8(2):106-109.WU Y P,ZHANG T X,SANG N,et al..Imaging of active optical imaging system with a wide field of view[J].Opt.Precision Eng.,2000,8(2):106-109.(in Chinese)
[5]BELYP Y.The Design and Construction of Large Optical Telescopes[M].New York:Springer,2003.
[6]林旭东,陈涛,王建立,等.拼接镜的主动光学面形控制[J].光学精密工程,2009,17(1):98-103.LIN X D,CHEN T,WANG J L,et al..Active optics figure control of segmented mirror[J].Opt.Precision Eng.,2009,17(1):98-103.(in Chinese)
[7]MERLET J P.Parallel Robots[M].2nd ed..Dordrecht,The Netherlands:Springer,2006.
[8]曹小涛,孙天宇,赵运隆,等.空间大口径望远镜稳像系统发展现状及趋势[J].中国光学,2014,7(5):739-748.CAO X T,SUN T Y,ZHAO Y L,et al..Current status and development tendency of image stabilization system of large aperture space telescope[J].Chinese Optics,2014,7(5):739-748.(in Chinese)
[9]顾营迎,霍琦,李昂,等.用于光学遥感器耐受卫星平台微振动环境地面测试的六自由度平台[J].光学精密工程,2016,24(9):2200-2207.GU Y Y,HUO Q,LI A,et al..Six DOF platform applied in ground test of optical remote sensor alleviation margin in satellite micro-vibration environment[J].Opt.Precision Eng.,2016,24(9):2200-2207.(in Chinese)
[10]邓赛,景奉水,梁自泽,等.FAST馈源支撑系统位姿分配方法研究[J].光学精密工程,2017,25(2):375-384.DENG S,JING F SH,LIANG Z Z,et al..Research on pose distribution algorithm of FAST feed support system[J].Opt.Precision Eng.,2017,25(2):375-384.(in Chinese)
[11]张景旭,安其昌,李剑锋,等.基于机构条件数的30m望远镜三镜Stewart平台[J].光学精密工程,2014,22(4):890-896.ZHANG J X,AN Q CH,LI J F,et al..Third mirror Stewart platform of TMT based on mechanism condition number[J].Opt.Precision Eng.,2014,22(4):890-896.(in Chinese)
[12]MCINROYJ E,HAMANN J C.Design and control of flexure jointed hexapods[J].IEEE Transactions on Robotics and Automation,2000,16(4):372-381.
[13]KELLY R,SANTIBEZ V,LORA A.Control of Robot Manipulators in Joint Space[M].London:Springer,2005.
[14]宫全一.基于6自由度Stewart平台的控制系统研究及参数整定[D].天津:天津大学,2008.GONG Q Y.Research on Control System and Its Parameters Tuning of Stewart Platform[D].Tianjin:Tianjin University,2008.(in Chinese)
[15]LU Y J,ZHU W B,REN G X.Feedback control of a cable-driven Gough-Stewart platform[J].IEEE Transactions on Robotics,2006,22(1):198-202.
[16]史剑.大射电望远镜精调Stewart平台控制及实验研究[D].西安:西安电子科技大学,2009.SHI J.Control and Experiment of the Fine Tuning Stewart Platform for the Large Radio Telescope[D].Xi'an:Xidian University,2009.(in Chinese)
[17]王卫东.大射电望远镜精调Stewart平台非线性PID控制[D].西安:西安电子科技大学,2007.WANG W D.Nonlinear PID Control of the Stewart Platform for the Square Kilometers Array[D].Xi'an:Xidian University,2007.(in Chinese)
[18]RYUJ H.Parallel Manipulators:New Developments[M].Vienna,Austria:I-Tech Education and Publishing,2008.
[19]GAWRONSKI W K.Advanced Structural Dynamics and Active Control of Structures[M].New York:Springer,2004.
[20]杨维帆,徐抒岩,曹小涛,等.空间光学遥感器扫描控制系统设计[J].光学精密工程,2014,22(2):397-405.YANG W F,XU SH Y,CAO X T,et al..Design of scanning control system for space optical remote sensor[J].Opt.Precision Eng.,2014,22(2):397-405.(in Chinese)
[21]SKOGESTAD S,POSTLETHWAITE I.Multivariable Feedback Control:Analysis and Design[M].2nd ed..New York:John Wiley&Sons,2001.
[22]ZHOUK M,DOYLE J C.Essentials of Robust Control[M].Upper Saddle River,NJ:Prentice Hall,1999.
[23]王天玉.载足式机器人单关节驱动系统H!控制器的设计[D].哈尔滨:哈尔滨工业大学,2016.WANG T Y.Design of H!Controller for Hydraulic Actuator of Heavy-load Legged Robot Joint[D].Harbin:Harbin Institute of Technology,2016.(in Chinese)