## 5 Experimental Verification
### The Improvement of the ADA with the Combination of EOB and DOB  
According to Equation (22), the DOB controller \(Q_{2}\) is not the ideal value and a concession should be made. Parameter b can determine the starting point of disturbance compensation. Considering that the used FOG in this experiment had a poor performance below about 1 Hz, the actually used \(Q_{2}\) was set as Equation (25) and all the parameters of controllers were listed in Table 1.  
\[Q_{2}=\frac{0.00072s^{2}+0.0202s+1}{2.3(s+5)}\cdot\frac{1}{0.0065s+1} \tag{25}\]  
The disturbance suppression bode response is presented in Figure 15, which involved four situations in all, showing the pure VPDC structure and the various combinations of EOB and DOB based on VPDC; the VPDC without any feedforward had a relatively poor ADA, especially in the middle frequency domain of about 5 Hz, which approached 0 dB. The EOB has apparently promoted the ADA of the low frequency below 1 Hz, sometimes (for example, on a ship) there would be a shake of carrier with a strong amplitude. The reason why the promotion was restricted at the frequency of 0.1 Hz was that the performance of the system almost reached the limitation under this noise condition. The DOB mainly worked at the medium frequency, where there was a maximum increase of \(-20\) dB, because the measured signals and the reference model were relatively more accurate in this band. With the simultaneous help of EOB and DOB, the ADA had an improvement (at least \(-10\) dB) in both the low and medium frequencies, which means that the system's precision would nearly be  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Controllers** & \(\mathbf{C_{p}}\) & \(\mathbf{C_{v}}\) & \(\mathbf{Q_{1}}\) & \(\mathbf{Q_{2}}\) \\ \hline \multirow{4}{*}{Parameters} & \(\frac{\pi}{4\tau}=39.25\) & \(k_{v}=16.8\) & & \(K=2.3\) \\  & & \(T_{c}=0.0005\) & & \(b=5\) \\ \cline{1-1}  & \(\frac{\pi}{4\tau}=39.25\) & \(T_{v}=0.0003\) & \(T=0.12\) & \(T_{1}=0.0065\) \\ \cline{1-1}  & & \(\omega_{n}=5.9\)Hz & & \(\omega_{n}=5.9\)Hz \\ \cline{1-1}  & & \(\xi=0.3764\) & & \(\xi=0.3764\) \\ \hline \end{tabular}
\end{table}
Table 1: The parameters of controllers. When EOB is added, \(C_{p}\) should be changed to \(\mathbf{C^{\prime}}_{p}=0.8\mathbf{C_{p}}\) for sufficient PM and GM according to the previous analysis.  
Figure 14: The residual tracking errors in different frequencies.  
increased by an order of magnitude. The proposed method could not enhance the very high-frequency ADA, which mainly depended on the mechanical design. Figure 16 shows the time-domain residual error with a given disturbance signal of different frequencies. Obviously, with the proposed way, the residual error was reduced below 30 Hz.  
In order to verify the level of accuracy under the actual engineering conditions, we should detect the residual errors when simultaneously giving the target signal and disturbances to the system. In Figure 17, the results were presented and there was huge promotion. The target signal was 0.28\({}^{\circ}\) 0.2 Hz and the disturbances consisted of 0.28\({}^{\circ}\) 0.5 Hz, 0.0028\({}^{\circ}\) 5 Hz and 0.028\({}^{\circ}\) 50 Hz. The RMS error of  
Figure 16: The residual stabilization errors in different frequencies.  
Figure 15: The disturbance suppression response of the MOTS.  
the pure VPDC was 8.6504\" and the RMS error with additional EOB and DOB was 1.8111\", signifying that the proposed way of observation was valid.