## 5 Simulation Analysis
### Scenario 2  
To further verify the robustness of the controller, the anti-interference capability of different control methods under strong interference conditions was compared. The most representative tracking trajectory during the ROV's motion was selected (Formula (51)). A dual closed-loop sliding mode control scheme based on a nonlinear extended state observer (NESO-DSMC) was added for the comparison of control methods [26], to validate the superiority of the DDPG-LADRC controller's performance.  
The parameters for the Active Disturbance Rejection Control are set as follows: \(b_{0}=10\), \(w_{0}=5\), Because \(\beta_{1}=3\omega_{o},\ \beta_{2}=3\omega_{o}^{2},\ \beta_{3}=\omega_{o}^{3}\) which means \(\beta_{1}=15\), \(\beta_{2}=75\), \(\beta_{3}=125\). The relevant DDPG setting parameters are shown in Table 2 above. In addition, the controller parameters proposed in the NESO-DSMC are chosen as follows: \(\delta=0.01,\epsilon_{11}=\epsilon_{21}=\epsilon_{31}=0.5,\ \beta=0.1,\ \rho_{11}=100,\ \rho_{21}=300,\ \rho_{31}=1000,\ \gamma_{1}= \gamma_{2}=\gamma_{3}=\gamma_{4}=0.01,\)\(m=5,\ q=2,\ K_{y}=diag\{0.3,\ 0.3,\ 0.3,\ 0.3\},K_{v}=\text{diag}\{10,\ 10,\ 10,\ 10\}\)[26].  
The external interference added is shown in Equation (50). The added disturbance signal is related to the state of the ROV, and this signal is constantly changing.  
\[\begin{cases}f_{x}=40-1.65X-0.3Y^{2}-1.22Z^{2}-8Z\\ \qquad\qquad f_{y}=2.2X^{2}-2.5Y+0.3Z\\ \qquad f_{z}=18-2.1X^{2}-0.88Y^{2}-0.5Z^{2}\end{cases} \tag{50}\]  
The tracked trajectory is shown in Formula (51). This trajectory indicates that the ROV first descends vertically, then performs linear back-and-forth and spiral movements on a horizontal plane, accompanied by changes in depth and adjustments in heading, ultimately returning to a horizontal straight path. The initial position and attitude of the ROV are set as: \(X(0)=0\ \text{m},\ Y(0)=1\ \text{m},\ Z(0)=0\ \text{m},\ Phi(0)=0\ \text{rad}\).  
\[x_{d}(t)=\begin{cases}0\ \text{m},0\leq t\leq 20\ \text{s}\\  
observation error value for the observer in the \(X\)-direction is 0.00141, the maximum observation error in the \(Y\)-direction is 0.0016, and the maximum observation error in the \(Z\)-direction is 0.0021. DDPG-optimized LESO has achieved the estimation accuracy for disturbances that meet our requirements.  
Figure 11: _Cont._  
From Figure 12, it can be seen that LADRC, due to the issue of fixed parameters in the controller, is unable to eliminate steady-state errors in a short time. Under continuously changing external disturbances, LADRC cannot achieve optimal control performance. In the presence of significant uncertain disturbances, NESO-DSMC cannot reach the same level of error convergence accuracy as DDPG-LADRC. Tables 8 and 9 show the RMSE and MAE under different control methods, indicating that DDPG-LADRC has better robustness compared to LADRC and NESO-DSMC. DDPG-LADRC can eliminate steady-state errors within 5 s because it incorporates DDPG for online adjustment of LADRC parameters in response to uncertain disturbances caused by environmental changes, significantly improving the control accuracy of the system. This ensures that the ROV can maintain satisfactory control performance even in the presence of inaccurate model parameters and significant uncertain disturbances.  
Figure 12: ROV 3D trajectory and error.