## 3 Control Strategy
For the disturbance observer in the inner loop, because \(G_{n}(s)\) is usually regular, \({G_{n}}^{-1}(s)\) is irregular and not realizable, so it is necessary to introduce a filter \(\mathrm{Q}(\mathrm{s})\) to make \(\mathrm{Q}(\mathrm{s}){G_{n}}^{-1}(s)\) realizable. Therefore, it is required that the relative order of \(\mathrm{Q}(\mathrm{s})\) be greater than or equal to that of \(G_{n}(s)\), that is, \(k_{\mathrm{Q}}\geq k_{\mathrm{G}}\). The closed-loop transfer function of the inner loop can be obtained when the effects of \(T_{e}\) and \(\Delta(\mathrm{s})\) on the system are collectively referred to as disturbances and defined as \(\mathrm{d}\). \[y=G_{u_{i}}^{y}(s)u_{i}+G_{d}^{y}(s)d+G_{\zeta}^{y}(s)\zeta \tag{35}\]  
where  
\[G_{u_{i}}^{y}(s)=\frac{y}{u_{i}}=G_{n}(s) \tag{36}\]  
\[G_{d_{1}}^{y}(s)=\frac{y}{d}=G_{n}(s)(1-Q(s)) \tag{37}\]  
\[G_{\zeta}^{y}(s)=\frac{y}{\zeta}=Q(s) \tag{38}\]  
It can be seen that the effect of disturbance and noise on the system results is determined by \(\mathrm{Q}(\mathrm{s})\) and \(1\)-\(\mathrm{Q}(\mathrm{s})\). Here, \(\mathrm{Q}(\mathrm{s})\) is the sensitivity function of the system and \(1\)-\(\mathrm{Q}(\mathrm{s})\) is the complementary sensitivity function of the system. For the systems, since disturbances usually occur in the low-frequency band and noise usually occurs in the high-frequency band, it is necessary to design a low-pass filter \(\mathrm{Q}(\mathrm{s})\) to suppress \(\xi\) in the high-frequency band and \(1\)-\(\mathrm{Q}(\mathrm{s})\) to suppress \(\mathrm{d}\) in the low-frequency band. Using the above control method, a set of load simulation equipment consisting of a direct current motor (DC) and mechanical transmission equipment is simulated in this paper. The transfer function of the DC motor is known as  
\[G(s)=\frac{T_{m}(s)}{u_{i}(s)}=\frac{4798}{0.000743s^{2}+0.00726s+1} \tag{39}\]  
The transfer function of the mechanical transmission equipment is  
\[J(s)=\frac{\omega(s)}{T_{m}(s)}=\frac{1}{507s+24} \tag{40}\]  
By simultaneously considering the two formulas, we can get  
\[G_{n}(s)=\frac{T_{m}(s)}{u_{i}(s)}\cdot\frac{\omega(s)}{T_{m}(s)}=\frac{4798} {(0.000743s^{2}+0.00726s+1)(507s+24)} \tag{41}\]  
Figure 11: Control loop with a disturbance observer. Based on the above conditions, the DOB for the system with the transfer function \(G_{n}(s)\) is designed by using the \(H_{\infty}\) mixed sensitivity method. The optimal filter transfer function is  
Figure 10:0  
The outer loop controller \(C(s)\) is designed as the PI controller, and the transfer function is  
Figure 10:1  
According to the above model, a tracked vehicle with an equivalent inertia of 3180 kg\(\cdot\)m\({}^{2}\) is simulated. The control model is established in Simulink and the speed response under a random torque signal is simulated, and the results are shown in Figure 10:2 Because of the large amplitude transformation of random signals, this type of signal also acts as the interference signal affecting the system, and the output speed deviates greatly from the theoretical speed under the control of the traditional 1 DOF loop. Furthermore, by applying the 2 DOF system with DOB described in this paper, it is found that the speed deviation of the system decreases significantly. Therefore, it can be seen that the control loop has an obvious effect on stabilizing the system and reducing the deviation.