## 4 Experiment  
In view of the problem that the coupling effect between two-axes four-gimbal seriously affects the stability precision, it is necessary to combine the coupling relationship of rotational inertia of each gimbal axis for disturbance suppression analysis. Because of the effectiveness of the interference observer (DOB) in suppressing external interference [19; 20], in this paper, an interference observer suitable for the ultralight two-axis four-gimbal electro-optical pod is studied.  
As shown in Figure 13, the control object is set as the ultralight two-axis four-gimbal system, and the minimum phase system under ideal state is adopted. The nominal inverse model of the controlled object is \(Js+B\). Based on the kinematic coupling analysis and modeling, a DOB disturbance observer is used to study self-correcting disturbance suppression. The traditional DOB controller is improved to a time-varying DOB controller with rotational inertia. At the same time, the results of the moment of inertia analysis after the modeling mentioned in this paper are substituted into the nominal inverse model \(J_{n}\) of each gimbal control loop. Realize the real-time change of \(J_{n}\) following the change of gimbal angle \(\theta\). The control loop of the outer roll gimbal A was given sinusoidal interference as an example, and a Matlab Simulink simulation comparison experiment was carried out.  
The rotational inertia of the rotating axis changes in real time. First, the parameters of the traditional PID controller are set as follows: \(K_{p}=20,K_{i}=6\). As can be seen from Table 4, the initial parameters of rotational inertia are set as \(J=J_{XA}=0.176\times 10^{-1}\mathrm{kg}\cdot\mathrm{m}^{2}\). The parameters of the disturbance observer and its low-pass filter are set as follows: \(B=0.002\),\(g=200,B_{n}=0.002\). From the  
Figure 12: The ultralight two-axis four-gimbal electro-optical pod torque comparison validation. (**a**) Inner roll gimbal; (**b**) inner pitch gimbal; (**c**) outer roll gimbal; (**d**) outer pitch gimbal.  
Figure 13: Disturbance suppression output diagram of outer roll gimbal A.  
motion coupling and modeling analysis, it can be known that the coupling rotational inertia on the outer roll gimbal A is  
\[\begin{array}{l}J=(\cos\theta_{E}\cos^{2}\theta_{e}-\sin\theta_{E}\cos\theta_{a }\sin\theta_{e}\cos\theta_{e})J_{Xe}+\\ (\cos\theta_{E}\sin^{2}\theta_{e}-\sin\theta_{E}\sin\theta_{a}\cos\theta_{a} \cos^{2}\theta_{e})J_{Ze}+\cos\theta_{E}J_{XE}+J_{XA}\end{array}, \tag{25}\]  
Figures 14 and 15 verify the optimality of the velocity loop's traditional PID control, the traditional DOB disturbance suppression control, the improved DOB self-correcting disturbance suppression control, and the low-pass filter parameter selection. Set the system input amplitude to 0. The input amplitude of sine wave disturbance is 10 rad/s, and the frequency is 8 Hz. As shown in Figure 14, in order to facilitate the observation of the experimental results, the output value of the improved DOB was taken as negative gain output Scope which was distinguished from the other three waveforms. Further observation of the experimental results shows that  
\[\Delta X<\Delta Y, \tag{26}\]  
Figure 14: Disturbance suppression output diagram of outer roll gimbal A.  
Figure 15: Comparison diagram of disturbance suppression output of outer roll gimbal A.  
The results show that the disturbance suppression impact of DOB method with dynamics model is increased by up to 90% better than PID. As shown in Figure 13, this is defined as  
\[e=d-d^{\prime}, \tag{27}\]  
As shown in Figure 16, by comparing the two figures, it can be known that the estimated deviation of traditional DOB disturbance suppression is \(e=0.51\) and the estimated deviation of the improved DOB disturbance suppression is \(e=0.43\). The results show that the disturbance suppression impact of DOB method with dynamics model is increased by up to 25% compared to the traditional DOB.