## 5 Simulation Analysis
\(\omega_{sea}\) is related to the frequency of wave excitation. On this basis, the effects of waves on the hull are as follows:  
\[\left\{ \begin{array}{l}R_{x}=6\sin((\pi/3)\mathrm{t})\\ R_{y}=3\sin((\pi/3)\mathrm{t})\\ R_{z}=0.5\sin((\pi/3)\mathrm{t})\end{array} \right\} \begin{cases}T_{x}=0.1\sin( (\pi/3)\mathrm{t})\\ T_{y}=0.1\sin((\pi/3)\mathrm{t})\\ T_{z}=0.3\sin((\pi/3)\mathrm{t})\end{cases}  \tag{59}\]  
If the CDPDR performs derusting at anchorage, external disturbances, such as wind, will also increase. At 4 s, the sea wind and other external disturbances imposed are as follows:  
\[\left\{ \begin{array}{l}f_{x}=60\cos(0.6(\mathrm{t}-4))\\ f_{y}=60\cos(0.6(\mathrm{t}-4))\\ f_{z}=60\cos(0.6(\mathrm{t}-4))\\ \end{array} \right\} \begin{cases}\omega_{x}=0.4\cos(0.6(\mathrm{t}-4))\\ \omega_{y}=0.6\cos(0.6(\mathrm{t}-4))\\ \omega_{z}=0.4\cos(0.6(\mathrm{t}-4))\end{cases}  \tag{60}\]  
The reaction force in the \(y\)-direction is given by the uniform random number module. Considering that the reaction force on the motion platform may be greater due to the influence of wave excitation, the reaction force range of working condition 1 is enlarged by 1.55 times. The maximum and minimum values are 80 N and 60 N, respectively, and the sampling time is 0.05 s.  
The CDPDR motion trajectory and initial values of various items are the same as before, the simulation time is 12 s. The simulation result under condition 2 is shown in Figure 10. Similar to working condition 1, the initial error is effectively reduced within 1 s, indicating that the controller has fast response speed and small overshoot. Because the external interference excitation is applied at 4 s, the angle tracking error is quite large, but the tracking effect soon comes back, indicating that the controller has good robustness. It can be obtained from Figure 10c-f that the maximum trajectory error is 3 cm and the maximum angle error is 1\({}^{\circ}\). The maximum velocity error is 0.2 m/s, and the maximum angular velocity error is 18 deg/s. The overall error is greater than condition 1 because of the severe sea condition, but the tracking accuracy can still meet the work requirements. Trend of controller parameters is shown in Figure 11. After the dead zone technique is used for tuning, the parameters of the adaptive law remain stable after a certain period of time. It is indicated that the parameters of the sliding mode surface fluctuate within a very small range and gradually approach zero, and then the trajectory tracking converges. Figure 11b also verifies this, the sliding surface parameters fluctuate within 0.5. Due to the external disturbance exerted to the motion platform at 4 s, the parameters of the adaptive law and the sliding surface are timely changed. The force and torque output results are shown in Figure 12. It can be clearly seen from Figure 12a that the cable tension value before optimization appears negative, which is completely inconsistent with the actual situation and needs to be optimized through the tension optimization algorithm. The optimized cable tension changes smoothly and continuously within the set upper and lower limits. It can be seen from Figure 12c that the trend of the motor torque is basically consistent with the optimized cable tension value. Figure 10: The simulation results with wave excitation: (**a**) position tracking; (**b**) angle tracking; (**c**) position deviation; (**d**) angular deviation; (**e**) velocity deviation; (**f**) angular velocity deviation. The 3D trajectory tracking effect is shown in Figure 13. As can be seen from the figure, cable tension pulls the motion platform from the starting position to the desired position to begin the derusting operation. When starting the derusting operation, the \(y\)-direction is subjected to the action of the reaction force, resulting in a large deviation. At 4 s, external disturbances, such as sea wind, are exerted to the motion platform, and the trajectory tracking error value becomes larger at this time. About 1 s later, the deviation gradually decreases.