# Development of Active Microvibration Isolation System for Precision Space Payload
## 4 Experimental Validation
### Analysis of Experimental Results  
The experimental system was installed on an optical platform, and its environmental vibration was regarded as the input disturbance. The disturbance is transmitted to the load platform through springs, etc. Through the feedback control of eight vibration isolation modules, the vibration in three directions of the load platform is suppressed. Owing to the limitation of the channel numbers, only four vibration isolation modules can be used in the experiment of hybrid control to suppress the vibration in Z direction.  
The time-domain signals of the base platform and load platform in the x-, y-, and z-axes are shown in Figure 9a,b. The disturbance in each axis of the base platform is less than 1 mg, which is closer to the vibration response of the roof of the FY-4 satellite. With the  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Unit** \\ \hline Mass M & 25 & Kg \\ Stiffness K & 88,000 & N/m \\ Damping C & 17.6 & Ns/m \\ Resonant frequency \(\omega_{2}\) & 10.12 & Hz \\ Resonant frequency \(\omega_{x}\) & 6.38 & Hz \\ Resonant frequency \(\omega_{y}\) & 6.71 & Hz \\ Sensor sensitivity \(K_{S}\) & 1000 & V/g \\ Gain of VCM \(K_{V}\) & 1.2 & N/A \\ Gain of Driver \(K_{A}\) & 0.2 & A/V \\ \hline \hline \end{tabular}
\end{table}
Table 2: Physical parameters of experimental system.  
Figure 8: Schematic diagram of experimental system.  
feedback control, for the x and y axes, the acceleration amplitude of the time domain was suppressed from 0.2-0.5 mg to 20 \(\upmu\)g at most, and for the z axis, the acceleration amplitude was suppressed from 1 mg to 40 \(\upmu\)g. Figure 9c,d present the PSD and root cumulative PSD plots within 200 Hz, which shows that the addition of feedback leads to improvements in performance in the frequency domain. For the x and y axes, the root cumulative PSD was reduced from 9.78 \(\times\) 10\({}^{-5}\) g and 9.22 \(\times\) 10\({}^{-5}\) g to 6.52 \(\times\) 10\({}^{-6}\) g and 6.17 \(\times\) 10\({}^{-6}\) g, respectively, with an attenuation rate of 93.3%. For the low-frequency band within 10 Hz, the attenuation rate of the vibration reached 94.2%. For z-axis, the root cumulative PSD was reduced from 2.89 \(\times\) 10\({}^{-4}\) g to 8.96 \(\times\) 10\({}^{-6}\) g, and the attenuation rates within 200 Hz and 10 Hz were 96.9% and 93.4%, respectively. The root integration of the PSD within 200 Hz of each axis reached the \(\upmu\)g level.  
Figure 9: The performance of active vibration isolation with feedback control in three-axis. (**a**) Time domain acceleration of base platform; (**b**) Time domain acceleration of load platform; (**c**) Measured PSD; (**d**) Measured root cumulative PSD.  
To verify the effect of hybrid control, a comparative experiment of feedback control and hybrid control was carried out along the z axis. An extra acceleration sensor was installed on the base platform of the vibration isolation system to collect the acceleration signal as the input source of the feedforward loop. As shown in Figure 10, the low-frequency suppression effect of hybrid control within 10 Hz is more evident than that of feedback control, and further attenuation can be realized near 24 Hz, which is the resonant frequency of the optical platform. With hybrid control, the acceleration amplitude of the time domain was suppressed to 20 \(\upmu\)g, the root cumulative PSD within 200 Hz was reduced to 7.2 \(\times\) 10\({}^{-6}\) g, which improved by 18.8% compared with the feedback control. The attenuation rates within 200 Hz and 10 Hz were 97.4% and 95.9%, respectively.  
Figure 10: The performance of active vibration isolation with feedback and hybrid control in \(Z\)-axis. (**a**) Time domain; (**b**) Measured PSD; (**c**) Measured root cumulative PSD.