Extended State Filtering With Saturation-constrainted Observations and Active Disturbance Rejection Control of Position and Attitude for Drag-free Satellites
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摘要: 无拖曳卫星的本体姿态、卫星本体与测试质量间的相对位移及相对姿态的联合控制受到外部扰动、输入噪声、测量噪声及饱和约束、输入耦合以及状态耦合等因素的影响, 控制器的设计面临挑战. 本文采用基于扩张状态的卡尔曼滤波对系统状态和系统扰动进行实时估计, 引入自抗扰控制策略进行了控制器设计. 针对无拖曳控制子系统设计了测量饱和受限下的扩张状态估计算法, 并进行了信息融合. 在设计控制律时不仅考虑了对外部扰动的补偿, 还将系统状态间的耦合关系看成内部扰动进行补偿, 使得被控系统等价为“积分串联型系统”, 在此基础上实现了无拖曳卫星的联合控制. 数值仿真验证了方法的有效性和合理性.Abstract: The joint control of the drag-free satellite's attitude, the relative displacement and the relative attitude between the satellite body and the test mass is full of challenges because of the external disturbance, the input noise, the observation noise and the saturation constraint, the input coupling and the state coupling, etc. This paper introduces the extended state Kalman filter to estimate the system state and the system disturbance, and employs the active disturbance rejection control (ADRC) strategy to design the controller. For the drag-free control subsystem, the extended state estimation algorithm with saturation-constrainted observations is proposed, and then the multi-sensor information fusion algorithm is presented. Via compensating the external disturbance and regarding the coupling relationship among the system states as the internal disturbance to be also compensated, the control system is transformed to the “integral series system” and the joint control of the drag-free satellite is achieved. Numerical simulation is included to verify the effectiveness of the method.
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图 6 位移/速度的估计效果: 算法1 vs. 算法2
Fig. 6 Estimation of displacement/speed: Algorithm 1 vs. Algorithm 2
图 8 扰动估计效果: 融合算法3 vs. 算法1
Fig. 8 Estimation of disturbance: Algorithm 3 (fusion algorithm) vs. Algorithm 1
图 12 测试质量残余加速度功率谱密度
Fig. 12 Power spectral density of the test mass's residual acceleration
表 1
${ {\Upsilon}}$ 矩阵Table 1 The matrix of
${ {\Upsilon}}$ X 方向 Y 方向 Z 方向 $\left[ \; 1\;\;0\;\;0 \; \right]$ $\left[\; 0\;\;1\;\;0 \;\right]$ $\left[ \; 0\;\;0\;\;1 \;\right]$ 
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表 2 系统仿真参数
Table 2 System parameters in the simulation
变量 数值 ${m_{{\rm{tm}}}}$ 1 kg ${m_{{\rm{sc}}}}$ 1 050 kg ${I_{{\rm{tm}}}}$ $0.2667 \times {10^{ - 3} }{{I}_3}({\rm{kg} } \cdot { {\rm{m} }^{\rm{2} } })$ ${I_{{\rm{sc}}}}$ $\left[ {\begin{aligned}\;&{200}\;\;\;\;\;\;\;\;1\;\;\;\;\;\;\;\;\;2\\\;&\;\;1\;\;\;\;\;\;{2\;700}\;\;\;\;\;\;1\\ \;&\;\;2\;\;\;\;\;\;\;\;\; 1\;\;\; \;\;\;\;{2\;650} \end{aligned} } \right]({\rm{kg} } \cdot { {\rm{m} }^{\rm{2} } })$ ${K_{{\rm{trans}}}}$ $\left[ {\begin{aligned}\; & \;\;\;1\;\;\;\;\;\;\; {0.039}\;\;\;\;\;\; {0.039}\\\; &{0.039}\;\;\;\;\;\; \;1\;\;\;\;\;\;\;\;\; {0.039}\\\;&{0.039}\;\;\;\; {0.039}\;\;\;\; \;\;\;\;\;1 \end{aligned} } \right] \times {10^{ - 6} }{{\;({\rm{N}}/{\rm{m}})} }$ ${D_{{\rm{trans}}}}$ $1.4 \times {10^{ - 11} }{ {I}_3}\;({\rm{N} } \cdot {\rm{m} } \cdot {\rm{s/rad} })$ ${K_{{\rm{rot}}}}$ $\left[ {\begin{aligned} \;&\;1\;\;\;\;{10}\;\;{10}\\ \;&{10}\;\;\;\;1\;\;\;{10}\\\;&{10}\;\;\;{10}\;\;\;1 \end{aligned} } \right] \times {10^{ - 9} }\;({\rm{N} } \cdot {\rm{m/rad} })$ ${D_{{\rm{rot}}}}$ $1.4 \times {10^{ - 11} }{I_3}\;({\rm{N} } \cdot {\rm{m} } \cdot {\rm{s/rad} })$ ${{{T}}_{Dsc}}$ $\left[ {\begin{aligned} { - {\rm{12} }.{\rm{8 + 7} }.{\rm{7sin} }({\omega _d}{\rm{t} })}\\ { - {\rm{12} }.{\rm{8 + 7} }.{\rm{7sin} }({\omega _d}{\rm{ + } }\dfrac{ {2{\text{π} } } }{3})}\\ { - {\rm{12} }.{\rm{8 + 7} }.{\rm{7sin} }({\omega _d}{\rm{ + } }\dfrac{ {4{\text{π} } } }{3})} \end{aligned} } \right]({\rm{mN} } \cdot {\rm{m} })$ ${{{F}}_{Dsc}}$ $\left[ {\begin{aligned} { - {\rm{12} }.{\rm{8 + 7} }.{\rm{7sin} }({\omega _d}{\rm{t} })}\\ { - {\rm{12} }.{\rm{8 + 7} }.{\rm{7sin} }({\omega _d}{\rm{ + } }\dfrac{ {2{\text{π} } } }{3})}\\ { - {\rm{12} }.{\rm{8 + 7} }.{\rm{7sin} }({\omega _d}{\rm{ + } }\dfrac{ {4{\text{π} } } }{3})} \end{aligned} } \right]({\rm{mN} })$ ${{{T}}_{Dtm}}$ 0 $\omega_d$ $1.2 \times {10^{ - 3}}\;{\rm{Hz}}$
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