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基于绳索作动器的大型太空望远镜桁架结构的振动主动控制

唐颖卓 卢光宇 蔡国平

唐颖卓,卢光宇,蔡国平. 基于绳索作动器的大型太空望远镜桁架结构的振动主动控制 [J]. 应用数学和力学,2021,43(X):1-9 doi: 10.21656/1000-0887.420217
引用本文: 唐颖卓,卢光宇,蔡国平. 基于绳索作动器的大型太空望远镜桁架结构的振动主动控制 [J]. 应用数学和力学,2021,43(X):1-9 doi: 10.21656/1000-0887.420217
TANG Yingzhuo, LU Guangyu, CAI Guoping. Active Vibration Control for Truss Structure of a Large Space Telescope Based on Cable Actuators[J]. Applied Mathematics and Mechanics. doi: 10.21656/1000-0887.420217
Citation: TANG Yingzhuo, LU Guangyu, CAI Guoping. Active Vibration Control for Truss Structure of a Large Space Telescope Based on Cable Actuators[J]. Applied Mathematics and Mechanics. doi: 10.21656/1000-0887.420217

基于绳索作动器的大型太空望远镜桁架结构的振动主动控制

doi: 10.21656/1000-0887.420217
基金项目: 国家自然科学基金(1217020835;12102252);中国博士后科学基金(2021M692070)
详细信息
    作者简介:

    唐颖卓(1997—),女,硕士(Email:tangzhaozhao@sjtu.edu.cn)

    蔡国平(1965—),男,教授,博士,博士生导师(通讯作者。 E-mail:caigp@sjtu.edu.cn)

  • 中图分类号: O322;V476

Active Vibration Control for Truss Structure of a Large Space Telescope Based on Cable Actuators

  • 摘要: 薄膜衍射是一种新型的太空望远镜的成像方式,它具有轻质、易折叠与展开、光学成像精度高等许多优点,是当今太空望远镜技术的研究热点。该文针对一类薄膜衍射太空望远镜桁架结构的振动主动控制进行了研究,提出了一种基于绳索作动器的振动主动控制策略。首先建立了望远镜桁架结构的动力学模型,然后采用粒子群优化算法研究了绳索作动器的优化布置,进而采用最优控制方法设计了结构振动的主动控制律,最后通过数值仿真验证了所给方法的有效性,并详细研究了绳索作动器数量与结构振动稳定时间之间的对应关系。
  • 图  1  薄膜衍射太空望远镜结构示意图: (a) 薄膜衍射太空望远镜结构图;(b) 桁架单元结构图;(c) 桁架底部、顶部的三角框架结构图

    Figure  1.  Schematic diagram of the membrane diffraction space telescope: (a) structure of the membrane diffraction space telescope; (b) structure of a truss element; (c) the triangular frame structure of the bottom and top of the truss

    图  2  薄膜衍射太空望远镜前四阶模态振型:(a) 一阶振型;(b) 二阶振型;(c) 三阶振型;(d) 四阶振型

    Figure  2.  The 1st four modal shapes of the membrane diffraction space telescope:(a) the 1st order mode; (b) the 2nd order mode; (c) the 3rd order mode; (d) the 4th order mode

    图  3  绳索作动器数量与系统稳定所需时间关系曲线

    Figure  3.  The correlation curve between the number of cable actuators and the time required for system stabilization

    图  4  桁架结构上 P 点竖直方向的位移响应曲线

    Figure  4.  Displacement response curve of point P in the vertical direction of the truss structure

    表  1  薄膜衍射太空望远镜结构的物理参数

    Table  1.   Physical parameters of the structure of the membrane diffraction space telescope

    structural componentssizeelastic modulus
    E/GPa
    density
    ρ/(kg/m³)
    Poisson's
    ratio
    Rayleigh damping coefficient
    length
    l/m
    cross-sectional area
    A/m2
    αβ
    triangular frame0.682.5×10−37027000.30.050.03
    longitudinal beam1.2457.07×10−4702700
    connecting beam0.39262.5×10−370002700
    simplified beam of the rigid plate0.39262.5×10−370002700
    simplified beam of the
    primary mirror
    7.95562.5×10−370002700
    下载: 导出CSV

    表  2  薄膜衍射太空望远镜的前四阶固有频率(单位: Hz)

    Table  2.   The first four natural frequencies of the membrane diffraction space telescope (unit: Hz)

    natural frequenciesthe 1st orderthe 2nd orderthe 3rd orderthe 4th order
    theoretical model0.153370.153370.229460.63599
    ANSYS0.153140.153140.235490.63464
    error ε/%0.150190.150192.560620.21272
    下载: 导出CSV

    表  3  绳索作动器的数量、最优位置与结构稳定所需时间

    Table  3.   Number of cable actuators, optimal positions and reqiured time for structural stabilization

    number Npositions of cable actuatorstime t/snumber Npositions of cable actuatorstime t/s
    1 (3, 2, 5) 133.93 11 (1, 2, 6), (1, 5, 5), (1, 25, 4), (2, 2, 4), (2, 3, 1), (2, 8, 4), (2, 19, 4), (3, 1, 5), (3, 2, 3), (3, 4, 1), (3, 9, 1) 33.01
    2 (3, 2, 1), (3,27,6) 104.48 12 (1, 1, 5), (1, 4, 6), (1, 22, 4), (1, 27, 1), (2, 4, 4), (2, 6, 4), (2, 29, 6), (3, 2, 1), (3, 10, 2), (3, 10, 5), (3, 12, 2), (3, 21, 3) 32.95
    3 (1, 2, 5), (1, 29, 1), (3 ,2 ,2) 81.47 13 (1, 1, 6), (1, 5, 3), (1, 10, 5), (1, 29, 3), (2, 2, 3), (2, 6, 1), (2, 7, 3), (2, 8, 4), (2, 23, 5), (3, 3, 1), (3, 5, 1), (3, 15, 1), (3, 28, 5) 29.80
    4 (1, 3, 8), (2, 4, 4), (3, 1, 1), (3, 27, 5) 65.45 14 (1, 2, 6), (1, 14, 6), (1, 26, 1), (2, 1, 2), (2, 2, 3), (2, 6, 4), (2, 25, 2), (3, 2, 2), (3, 2, 6), (3, 6, 2), (3, 8, 1),
    (3, 17, 3), (3, 25, 4), (3, 26, 5)
    29.64
    5 (1, 3, 6), (1, 28, 2), (2, 2, 4), (3, 2, 2), (3, 3, 5) 55.78 15 (1, 4, 2), (1, 4, 5), (1, 8, 5), (2, 2, 4), (2, 2, 5), (2, 3, 4), (2, 22, 3), (2, 29, 6), (3, 1, 1), (3, 1, 4), (3, 2, 1), (3, 4, 2), (3, 5, 5), (3, 6, 4), (3,29,3) 26.49
    6 (1, 1, 5), (1, 28, 4), (2, 1 ,4), (2, 3, 1), (3, 4, 1), (3, 28, 6) 52.56 16 (1, 2, 6), (1, 6, 5), (1, 7, 6), (1, 18, 4), (1, 26, 3), (1, 27, 2), (2, 2, 4), (2, 20, 3), (2, 22, 3), (2, 27, 5), (3, 2, 1), (3, 2, 2), (3, 2, 4),
    (3, 4, 2), (3, 7, 1), (3 ,24, 6)
    26.38
    7 (1, 3, 5), (1, 29, 3), (2, 2, 2), (2, 5, 4), (3, 2, 2), (3, 4, 5), (3, 29, 6) 45.97 17 (1, 2, 1), (1, 4, 4), (1, 6, 6), (2, 2, 3), (2, 2, 6), (2, 3, 3), (2, 5, 3), (2, 8, 2), (2, 13, 3), (2, 26, 1), (2, 30, 5), (3, 3, 2), (3, 4, 2), (3, 10, 2), (3, 11, 2), (3, 23, 2), (3, 29, 4) 23.24
    8 (1, 2, 6), (1, 25, 2), (2, 3, 3), (2, 24, 6), (3, 1, 2), (3, 3, 2), (3, 4, 5), (3, 27, 4) 42.83 18 (1, 3, 6), (1, 4, 6), (1, 9, 5), (1, 13, 5), (1, 28, 2), (2, 1, 2), (2, 1, 3), (2, 2, 4), (2, 6, 1), (2, 11, 1), (2, 26, 6), (2, 30, 5), (3, 1, 4),
    (3, 2, 1), (3, 7, 1), (3, 20, 1), (3, 27, 2), (3, 28, 5)
    23.42
    9 (1, 2, 6), (1, 30, 1), (2, 1, 2), (2, 1, 3), (2, 2, 3), (2, 24, 6), (3, 3, 2), (3, 4, 1), (3, 30, 4) 39.42 19 (1, 2, 6), (1, 6, 3), (1, 6, 6), (1, 10, 5), (1, 30, 1), (2, 2, 3), (2, 5, 4), (2, 6, 4), (2, 8, 3), (2, 12, 3), (2, 23, 6), (2, 26, 3), (2, 29, 3), (2, 30, 1), (3, 2, 1), (3, 3, 1), (3, 6, 2), (3, 20, 6), (3, 25, 3) 23.20
    10 (1, 5, 5), (1, 6, 5), (1, 25, 4), (2, 2, 4), (2, 3, 2), (3, 1, 2), (3, 3, 2), (3, 12, 2), (3, 23, 6), (3 ,28 ,3) 39.22 20 (1, 2, 6), (1, 4, 5), (1, 6, 5), (1, 9, 1), (1, 26, 4), (1, 28, 1), (2, 1, 6), (2, 3, 4), (2, 5, 3), (2, 7, 4), (2, 8, 2), (2, 16, 3), (2, 26, 2), (3, 2, 6), (3, 3, 1), (3, 5, 4), (3, 6, 2), (3, 12, 1), (3, 12, 6), (3, 15, 6) 23.02
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-07-28
  • 录用日期:  2021-07-28
  • 修回日期:  2021-10-11
  • 网络出版日期:  2021-12-30

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