## 4 Experimental Verification  
The experimental devices of the TCS are shown in Figure 7. To verify the analyses above, we used two TCS platforms both driven by voice coil motors. One of them is called a stabilization platform, which is used to stabilize the laser light. The other one is called a disturbance platform and is utilized to simulate external disturbances. The stabilization platform is mounted above the disturbance platform. Since both of the platforms are two-axis systems, we only focused on one axis due to their symmetry. The laser light that comes from the light source is reflected using a rotating mirror and then detected using the CCD (TMC-6740 CL, NI Corporation, Austin, TX, USA). The CCD calculates position errors between the laser light and the center position of the CCD. The MEMS accelerometers (Model 1221, SILICON DESIGNS, Seattle, WA, USA) and the MEMS gyroscopes (XW-FG70, Starneto, Beijing, China) are mounted on the stabilization platform to acquire the angular acceleration and velocity, respectively. The CCD works at a 100 Hz sampling rate with a time delay of two frames, and the other sensors all update at 5000 Hz. The simulated disturbance is set as a sinusoidal signal of varying frequencies produced by a dynamic signal analyzer (DSA). To detect the disturbance suppression performance of the TCS, the stabilization platform works on the closed-loop mode and the disturbance platform works on the open-loop mode. As shown in Figure 8, the open-loop acceleration response of the TCS is measured using a DSA which scans for 1-1000 Hz. The frequency characteristic at low and intermediate frequency can be measured in high precision because of the high bandwidth of the MEMS accelerometer [11; 12]. Figure 7: The experimental devices. The nominal plant of acceleration open-loop object, which is acquired by identifying the result of the DSA, is depicted in Equation (19). The controller of the acceleration feedback control loop is designed as Equation (20). Its integration element is used to partly offset the differential elements and resonance in \(\widetilde{G}_{a}(s)\). Adding quadratic integration elements in \(C_{a}(s)\) can easily cause integral saturation. As the acceleration feedback control loop has largely improved the characters of the controlled object, the controllers \(C_{v}(s)C_{p}(s)\) of the velocity feedback control loop and position feedback control loop could be simply designed as proportion-integration (PI) controllers, as presented in Equation (21). \[\widetilde{G}_{a}(s)=\frac{0.0019s^{2}}{(0.00059s^{2}+0.00175s+1)(0.00037s+1)} \tag{19}\]  
\[C_{a}(s)=\frac{106.89(0.12s+1)}{s(9.8e-05s+1)(0.075s+1)} \tag{20}\]  
\[C_{v}(s)=\frac{0.97415(0.2s+1)}{s},\;C_{p}(s)=\frac{5(3.8s+1)}{s} \tag{21}\]  
According to the analyses in Section 3, drift rejection ability can be improved by introducing a MDOB. However, the enhancement of disturbance suppression and the improvement of drift rejection are contradictory according to Equations (11) and (12). Different types of MEMS accelerometers have different characters which affect the suitable values of constant \(K\). After adjustments, one of the suitable values of \(K\) is constant 70, and the MDOB controller is designed as follows:  
\[C_{f}=\frac{K}{s}\widetilde{G}_{a}{}^{-1}=\frac{70}{s}.\frac{(0.00059s^{2}+0.0 0175s+1)(0.00037s+1)}{0.0019s^{2}} \tag{22}\]  
In order to show the influence of the drift of the MEMS accelerometer, the DOB method is also used in the electro-optical system. Quadratic integration is not utilized in the DOB controller to avoid integral saturation and the DOB controller is designed as Equation (23) according to Reference [30]. \[C_{f\_DOB}=\frac{20161(0.00037s+1)}{s^{2}+655.4s+63165} \tag{23}\]  
In order to verify the impact of the MDOB under actual environments where disturbances are mostly at low frequencies, some experiments, the results of which are shown in Figure 9, were carried out.