## 4 Experiment and Discussion  
RWA is one of the most important disturbance sources on the satellite. We used the RWA disturbance as the excitation source to acquire the FRF from the disturbance source to the sensitive payload. The test platform of microvibration was built, as shown in Figure 7, and mainly composed of the satellite, low-frequency suspension system, RWA controller, and signal acquisition system. Five acceleration sensors (numbered a1-a5) and three acceleration sensors (numbered a6-a8) were connected to the PM and the SM, respectively.  
We collected the acceleration information of the 8 sensors, when the RWA increased from 0 to 2000 rpm, at every 100 rpm. The accelerations of a1 sensor in 3 directions at 2000 rpm are shown in Figure 8. The figure shows that the test's signal-to-noise ratio was high and satisfied the test requirements.  
Figure 8: The accelerations of a1 sensor at 2000 rpm. (**a**) a\({}_{\mathrm{J}}\); (**b**) a\({}_{\mathrm{J}}\); (**c**) a\({}_{\mathrm{J}}\).  
Figure 7: Test platform for the microvibration.  
The gathered acceleration signals were transformed into displacement signals by quadratic integration, in order to fit the rigid-body displacement of each optical element, using Equation (17). Then, the image motion at each speed can be calculated by Equation (20). Through Equation (19), it is possible to determine the image motion at each speed, including the image motion at 0 rpm, 500 rpm, 1000 rpm, and 2000 rpm, as shown in Figure 9. The waterfall of the image motion is shown in Figure 10. The picture shows that when the RWA is at 600 rpm, there is a significant amplitude at 159.8 Hz.  
The FRF and coherence function at 600 rpm are shown in Figure 11. For simplicity, only H\({}_{16}\) and H\({}_{26}\) are shown. The figure shows that the coherence at 159.5 Hz is roughly equivalent to 0.8, demonstrating the dependability of the FRF at this frequency.  
Figure 10: The waterfall of image motion. (**a**) x-direction; (**b**) y-direction.  
Figure 9: The image motion at each speed. (**a**) 0 rpm; (**b**) 500 rpm; (**c**) 1000 rpm; (**d**) 2000 rpm.  
We can obtain the average value of the FRF at different speeds using Equation (39). We performed the same test using three distinct RWAs numbered Z01, Z02, and Z03, to validate the methodology suggested in this paper. The outcomes are depicted in Figure 12.  
Figure 11: The FRF and coherence at 600 rpm. (**a**) H\({}_{16}\); (**b**) H\({}_{26}\).  
Figure 12: _Cont._  
Figure 12: The FRF was obtained by different RWAs. (**a**) H\({}_{11}\); (**b**) H\({}_{12}\); (**c**) H\({}_{13}\); (**d**) H\({}_{14}\); (**e**) H\({}_{15}\); (**f**) H\({}_{16}\); (**g**) H\({}_{21}\); (**h**) H\({}_{22}\); (**i**) H\({}_{23}\); (**j**) H\({}_{24}\); (**k**) H\({}_{25}\); (**l**) H\({}_{26}\).  
As can be seen from Figure 12, the amplitude of the FRF for the low frequency is larger, especially between 23 Hz-30 Hz, 155 Hz-163 Hz, and 215 Hz-237 Hz. Due to the influence of noise, the amplitude of the FRF obtained by different RWAs at 23 Hz-30 Hz differs greatly, while the differences at other frequencies are small. The figure also demonstrates that, at frequencies around 160 Hz, \(F_{\rm x}\) has the least impact on the image motion in the x direction compared to \(F_{\rm z}\) and \(F_{\rm y}\), while \(M_{\rm z}\) has the greatest influence compared with \(M_{\rm x}\) and \(M_{\rm y}\). Further, \(M_{\rm z}\), \(M_{\rm x}\), and \(M_{\rm y}\) have a decreasing impact on the image motion in the y direction, near 230 Hz, while \(F_{\rm x}\), \(F_{\rm y}\), and \(F_{\rm z}\) have the same effect.