空间引力波探测无拖曳卫星有限频域抗扰控制器设计
doi: 10.11728/cjss2024.05.2024-0022 cstr: 32142.14.cjss2024.05.2024-0022
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徐乾蛟 男, 1994年11月出生于山东省德州市, 现为北京理工大学自动化学院在读博士研究生, 主要研究方向为频域控制、连续系统控制、引力波探测三星无拖曳控制等. E-mail: 3220215148@bit.edu.cn -
崔冰 男, 1990年1月出生于山东省冠县, 现为北京理工大学自动化学院副教授、博士生导师, 主要研究方向为多智能体协同控制、航天器姿态控制与姿态协同、引力波探测三星无拖曳控制等. E-mail: bing.cui@bit.edu.cn
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Design of Finite Frequency Domain Disturbance Rejection Controller for the Drag-free Spacecraft in Space-borne Gravitational Wave Detection
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摘要: 在空间引力波探测任务中, 有限测量频域约束以及高精度控制指标使双参考质量无拖曳卫星控制器设计面临诸多技术难题. 基于此, 本文提出了一种基于广义Kalman-Yakubovich-Popov(GKYP)引理的有限频域抗扰控制器设计方法. 针对探测任务中指定频段内的性能约束, 结合灵敏度和补灵敏度控制指标, 在指定频段下构建了具有频率响应函数形式的有限频域控制性能指标. 提出了具有固定阶数特性的输出反馈控制结构, 并基于GKYP引理建立了控制器参数选取方法, 构建了有限频域抗扰控制器设计方法. 不同于现有的无拖曳控制器设计方法, 该设计方法可以有效降低控制指标的保守性, 同时在指定频段下实现了控制器的精确设计, 从而降低控制器阶数. 数值仿真表明, 本文所提方法在复杂扰动和噪声影响下可以满足无拖曳系统各回路控制性能指标.Abstract: In space-borne gravitational wave detection, there are technical challenges in designing the controller for the drag-free spacecraft with dual test masses. These difficulties arise from constraints within the limited measurement frequency domain and the necessity for a high-precision control index. In this paper, a design method of disturbance rejection controller in the finite frequency domain based on the generalized Kalman-Yakubovich-Popov (GKYP) lemma is proposed. Firstly, to address the performance constraints within the designated frequency band of the detection mission, a finite frequency domain control performance index in the form of a frequency response function is constructed. This index is meticulously developed by amalgamating the sensitivity and complementary sensitivity control indexes. Then, a control structure with fixed-order characteristics for output feedback is proposed, and a method for selecting controller parameters based on the GKYP lemma is established. By this, a finite frequency domain disturbance-resistant controller design method is constructed. In contrast to current drag-free controller design methods, the proposed approach significantly diminishes the conservatism in the control index. This realizes the precise design of the controller in the specified frequency band, ultimately resulting in a reduction in the order of the controller. Finally, numerical simulations demonstrate that the proposed method successfully meets the control performance index for each loop of the drag-free system even in the presence of complex disturbances and noises.
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图 8 5阶控制器频域控制性能
Figure 8. Frequency domain control performance of the 5th order controllers
图 9 无拖曳控制回路($ {x_1},{\text{ }}{z_1},{\text{ }}{x_2} $)位移误差PSD
Figure 9. PSD of displacement error in the drag-free control loop ($ {x_1},{\text{ }}{z_1},{\text{ }}{x_2} $)
图 10 卫星姿态($ {\phi }_{\text{b}} $, $ {\psi }_{\text{b}}$, ${\theta _{\text{b}}}$)误差PSD
Figure 10. PSD of the satellite attitude (${\phi _{\text{b}}},{\text{ }}{\psi _{\text{b}}},{\text{ }}{\theta _{\text{b}}}$) error
图 13 静电悬浮控制回路位移控制PSD
Figure 13. PSD of displacement control in the suspension control loop
图 14 静电悬浮控制回路姿态控制PSD
Figure 14. PSD of attitude control in the suspension control loop
图 11 静电悬浮控制回路位移误差PSD
Figure 11. PSD of displacement error in the suspension control loop
图 15 KG4控制器作用下无拖曳控制回路位移误差PSD
Figure 15. PSD of displacement error in the drag-free control loop under the action of KG4 controller
图 16 KH5控制器作用下无拖曳控制回路位移误差PSD
Figure 16. PSD of displacement error in the drag-free control loop under the action of KH5 controller
图 17 在5阶控制器作用下y1方向上位移误差PSD
Figure 17. PSD of displacement error in y1 direction under the action of the 5th order controllers
图 18 x1方向上的5阶控制器控制输出PSD
Figure 18. PSD of control output of the 5th order controllers in the x1 direction
图 19 z1方向上的5阶控制器控制输出PSD
Figure 19. PSD of control output of the 5th order controllers in the z1 direction
图 20 y1方向上的5阶控制器控制输出PSD
Figure 20. PSD of control output of the 5th order controllers in the y1 direction
图 21 y1方向上的5阶控制器控制输出曲线
Figure 21. Control output curve of the 5th order controllers in the y1 direction
表 1 各自由度控制要求
Table 1. Control requirement for each degree of freedom
控制回路 控制自由度 位姿误差要求/
(m·rad·Hz–0.5)控制输入要求/
(m·rad·s–2Hz–0.5)无拖曳控制回路 x1, x2, z1 $4 \times {10^{ - 9}}$ － 静电悬浮
控制回路y1, y2, z2 $2 \times {10^{ - 8}}$ $ 3 \times {10^{ - 13}} $ $ {\phi _1}, $$ {\psi _1}, $$ {\theta _1} $
$ {\phi _2}, $$ {\psi _2}, $$ {\theta _2} $$6 \times {10^{ - 7}}$ $2.5 \times {10^{ - 11}}$ 姿态控制回路 $ {\phi _{\text{b}}} $, $ {\psi _{\text{b}}} $, $ {\theta _{\text{b}}} $ $3 \times {10^{ - 9}}$ － 
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表 2 ${\boldsymbol{\varPsi}} $在不同频域条件下的取值
Table 2. Values of ${\boldsymbol{\varPsi}} $ under the different frequency domain conditions
低频 中频 高频 $w$ $ 0 \leqslant \left| w \right| \leqslant {w_{\text{l}}} $ ${w_1} \leqslant w \leqslant {w_2}$ $\left| w \right| \geqslant {w_{\text{h}}} \geqslant 0$ ${\boldsymbol{\varPsi}} $ $\left[ {\begin{array}{*{20}{c}} { - 1}&0 \\ 0&{w_{\text{l}}^{\text{2}}} \end{array}} \right]$ $\left[ {\begin{array}{*{20}{c}} { - 1}&{j{w_{\text{c}}}} \\ { - j{w_{\text{c}}}}&{ - {w_1}{w_2}} \end{array}} \right]$ $\left[ {\begin{array}{*{20}{c}} 1&0 \\ 0&{ - w_{\text{h}}^2} \end{array}} \right]$
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表 3 仿真参数
Table 3. Simulation parameters
参数 取值 卫星平台 质量/kg 350 转动惯量/${\text{(kg}} \cdot {{\text{m}}^{\text{2}}})$ $\left[ {\begin{array}{*{20}{c}} {158.1}&{ - 8.626}&{0.8819} \\ { - 8.626}&{163.1}&{0.1913} \\ {0.8819}&{0.1913}&{297.1} \end{array}} \right]{\text{ }}$ 检测质量 质量/kg 1.96 转动惯量/${\text{(kg}} \cdot {{\text{m}}^{\text{2}}})$ $\left[ {\begin{array}{*{20}{c}} {6.913}&0&0 \\ 0&{6.913}&0 \\ 0&0&{6.913} \end{array}} \right] \times {10^{ - 4}}$ – 仿真时间/s ${10^5}$ – 控制周期/s 0.1
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