## 3 Results and Discussion
### Active Control Analysis
#### 3.2.3 Control Effect Verification  
* Two harmonic excitations with excitation frequency of 20 rad/s and amplitude of 1 \(\upmu\)m and 5 \(\upmu\)m act on the Optomechanical coupling active control system. It can be seen from Figure 16 that in the resonant band, the peak value of the output light angle response reaches the pointing threshold index in the whole frequency domain after the velocity feedback gain \(g_{P}\) control is applied. After the displacement feedback gain \(g_{I}\) control is applied, the peak value of the output light angle response reaches the pointing threshold index only in the 20 rad/s resonant band, but it does not reach the pointing threshold index in the low and high frequency bands. The displacement feedback gain requires the range of the excitation frequency band. The joint control of velocity feedback gain \(g_{P}\) and displacement feedback gain \(g_{I}\) achieves the pointing threshold in the whole frequency domain, but the control effect of ultralow frequency is not as good as that of velocity feedback gain \(g_{P}\). Figure 15: The corresponding relationship between the parameters of the pointing threshold and the amplitude of the output light angle response when the phase difference \(\Delta\varphi=\pi\) is less than 0.2 \(\upmu\)rad: (**a**) The corresponding relationship between the ratio of the excitation amplitude and the peak value of the output light angle response when the excitation frequency changes from low frequency to high frequency; (**b**) the corresponding relationship between the active feedback gain and the peak value of the output light angle response of the Optomechanical system with 10 rad/s excitation frequency; (**c**) the corresponding relationship between the active feedback gain and the peak value of the output light angle response of the Optomechanical system with 20 rad/s excitation frequency; (**d**) the corresponding relationship between the active feedback gain and the peak value of the output light angle response of the Optomechanical system under the 30 rad/s excitation frequency. * Two broadband white noise excitations with power spectral density \(10^{-10}\) g\({}^{2}\)/Hz and \(5\times 10^{-10}\) g\({}^{2}\)/Hz act on the Optomechanical coupling active control system. It can be seen from Figure 17a that there is displacement deviation in the 5 times amplitude ratio broadband white noise excitation signal, which causes the optical axis deviation to a certain extent. Figure 17b shows the peak value of output light angle response of the velocity feedback gain \(g_{P}\) control has reached more than 94% attenuation near the 20 rad/s frequency band, and there is not too much control effect in the ultralow frequency part. It can be seen from Figure 17c that \(g_{I}\) can reduce the peak value of angle response near 20 rad/s frequency band, and the control of low frequency below 10 rad/s is obvious, but it will lead to high frequency and low peak value. As can be seen from Figure 17d, through the joint control of \(g_{I}\) and \(g_{P}\), the peak value brought by a under separate control can be reduced. Among all the control methods, the peak attenuation of angular response can reach 98.13%, which is close to two orders of magnitude. When the excitation frequency band is concentrated near the natural frequency, \(g_{P}\) control is better. When the excitation frequency band is concentrated in the middle and low frequency region, the control \(g_{I}\) is better. When the excitation frequency band is full frequency domain, the joint control of \(g_{I}\) and \(g_{P}\) is better. Figure 16: 20 rad/s harmonic excitation with and without the control of the spatial filter output light angle response peak comparison: (**a**) Harmonic excitation signal; (**b**) velocity feedback gain \(g_{P}\) control; (**c**) displacement feedback gain \(g_{I}\) control; (**d**) velocity feedback gain \(g_{P}\) and displacement feedback gain \(g_{I}\) joint control.