Time-varying frequency identification of space solar power station based on variable forgetting factor
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摘要:
考虑空间太阳能电站(SSPS)在轨运行时帆板旋转所导致的系统变构型特征，提出一种变遗忘因子广义子空间跟踪器(VFF-GYAST)递推辨识方法，在轨辨识该时变动力学系统的模态频率参数，以提高GYAST方法对于这类时变系统的跟踪能力。基于模态综合技术和子结构方法，建立多旋转关节构型SSPS(MJ-SSPS)的时变姿态-振动耦合动力学方程；根据投影子空间理论，通过计算系统均方差来确定递推过程中的时变遗忘因子，以提高GYAST方法的跟踪性能并辨识得到系统的时变伪模态频率参数。数值仿真结果表明：所提方法能够有效地识别该大型柔性系统的时变频率参数。与传统的递推子空间方法相比，所提方法具有较高的抗噪声干扰能力，在低量测信噪比时所提方法对于频率辨识结果的相对误差的平均值小于5%，且对时变系统的跟踪性能优于基于固定遗忘因子的原始方法。
Abstract:By considering changes in the structural configuration caused by the rotation of the solar panel in the space solar power station (SSPS) during in-orbit operation, a variable forgetting factor generalized yet another subspace tracker (VFF-GYAST) method was proposed to identify the modal frequency parameters of the time-varying dynamic system in orbit. As a result, the tracking ability of the original GYAST method for the time-varying system was improved. First, the time-varying attitude-vibration coupling dynamic equation of the multirotary-joint SSPS (MJ-SSPS) was established based on modal synthesis technology and the substructure method. Based on the projection subspace theory, the time-varying forgetting factor in the recursive procedure was determined by computing the system’s mean square error, and thus the tracking performance of the original GYAST method was increased, and the time-varying pseudo modal frequency parameters of the system were identified. The computation results of numerical simulation show that the proposed method can effectively identify the time-varying frequency parameters of the large flexible system. Compared with the conventional recursive subspace method, the proposed method has higher noise-immunity ability. When the measured signal-to-noise-ratio is low, the average value of the relative error of the frequency identification results for the proposed method is still smaller than 5%. In addition, the tracking performance of the proposed method for the time-varying system is better than that of the original method with a fixed forgetting factor.
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图 3 推力器的布设位置和相应的推力方向（t=0 s）
Figure 3. Location of thrusters and corresponding direction of thrust forces (t = 0 s)
图 5 帆板末端节点513在x和z方向的振动位移响应
Figure 5. Displacement responses for node 513 at the end of solar panel in x and z directions
图 8 ${\omega _{\text{r}}}$=0.01 rad/s时，前10阶模态频率的理论值
Figure 8. Theory values of the first 10 order modal frequencies in ${\omega _{\text{r}}}$= 0.01 rad/s
图 9 ${\omega _{\text{r}}}$=0.01 rad/s时，第3阶和第10阶模态频率辨识结果
Figure 9. Identification results of the 3rd and 10th order modal frequencies in ${\omega _{\text{r}}}$= 0.01 rad/s
图 10 不同转速情况下可变遗忘因子随时间的变化
Figure 10. Change of variable forgetting factor with time at different rotation speeds
表 1 模型的几何和质量属性
Table 1. Geometric and mass properties of model
帆板p1和p2的面积/m2 微波天线a的半径/m 微波天线的质量${m_{\text{a}}}$/kg 帆板p1和p2的质量${m_{{\text{p}}1}}$与${m_{{\text{p2}}}}$/kg 帆板转动速度${\omega _{\text{r}}}$/(rad·s−1) 3000 ×1000 500 4×106 3×106 0.001 
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表 2 MJ-SSPS中每个部件的前10阶模态频率
Table 2. The first 10 order modal frequencies of each component in MJ-SSPS
频率阶次 模态频率/Hz 微波天线a 太阳能帆板p1和p2 1 0.0510 0.0223 2 0.0942 0.0789 3 0.1643 0.1320 4 0.1930 0.1463 5 0.2614 0.4135 6 0.3611 0.4142 7 0.3612 0.7385 8 0.3676 0.7973 9 0.4069 0.9237 10 0.4631 0.9967
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表 3 ${{\boldsymbol{v}}_{{\bf{SNR}}}}$为40 dB时，前10阶模态频率的相对误差
Table 3. Relative errors of the first 10 order modal frequencies in ${{\boldsymbol{v}}_{{\bf{SNR}}}}$= 40 dB
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表 4 ${{\boldsymbol{v}}_{{\bf{SNR}}}}$为20 dB时，前10阶模态频率的相对误差
Table 4. Relative errors of the first 10 order modal frequencies in ${{\boldsymbol{v}}_{{\bf{SNR}}}}$= 20 dB
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表 5 ωr=0.01 rad/s时，前10阶模态频率的相对误差
Table 5. Relative errors of the first 10 order modal frequencies in ωr= 0.01 rad/s
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