Active Vibration Control of Truss Structures for Large Space Telescopes Based on Cable Actuators
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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出方法的有效性，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。
Abstract:The membrane diffraction is a new imaging method for space telescopes. It makes a hot research topic in space telescope technology with lots of advantages, such as light weight, easy foldability and high optical imaging accuracy. The active vibration control of the truss structure of a kind of membrane diffraction space telescope was investigated, and an active vibration control strategy was proposed based on cable actuators. Firstly, the dynamic model for the telescope truss structure was established. Then the particle swarm optimization algorithm was used to study the arrangement optimization of cable actuators. The active control law for the structure vibration was designed with the classical linear quadratic regulator method. Finally, the numerical simulation results verify the effectiveness of the proposed method. In the numerical simulations, the relationship between the number of cable actuators and the required time for the structure to regain stability was studied in detail.
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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) the structure of the membrane diffraction space telescope; (b) the structure of a truss element; (c) the triangular frame structure of the truss bottom and top
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 4 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. The 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 component size elastic modulus
E/GPadensity
ρ/(kg/m³)Poisson’s
ratio μRayleigh damping coefficient length
l/mcross-sectional area
A/m2α β triangular frame 0.68 2.5×10−3 70 2700 0.3 0.05 0.03 longitudinal beam 1.245 7.07×10−4 70 2700 connecting beam 0.3926 2.5×10−3 7000 2700 simplified beam of the rigid plate 0.3926 2.5×10−3 7000 2700 simplified beam of the
primary mirror7.9556 2.5×10−3 7000 2700 
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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 1st 4 natural frequencies of the membrane diffraction space telescope (unit: Hz)
natural frequency 1st order 2nd order 3rd order 4th order theoretical model 0.15337 0.15337 0.22946 0.63599 ANSYS 0.15314 0.15314 0.23549 0.63464 error ε/% 0.15019 0.15019 2.56062 0.21272
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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 N cable actuator position time t/s number N cable actuator position time 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
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