## 5 Simulation Analysis  
In this part, in order to verify the accuracy and validity of the CDPDR dynamic model and control strategy, the dynamic simulation verification is carried out. The kinematic and dynamic models are constructed in MATLAB/Simulink with the software version R2019a. The pose parameters of the motion platform are provided to the controller, and then CDPDR and its control strategy are applied to different operation scenarios. The controller time step is set to 1 ms, the motor delay time is 2 ms, and other parameters required for the simulation are shown in Table 2.  
It is worth noting that \(\mathbf{m}\), \(\mathbf{I_{PP}}\), \(\mathbf{d}\) and \(\mathbf{D}\) are the parameters of the size of the motion platform prototype, which can be selected according to the mass and shape of the motion platform in practical applications; \(\mathbf{x_{CS}^{S}}\), \(\mathbf{h}\), \(\mathbf{H}\), \(\mathbf{r}\), \(r_{pully}\), \(\mathbf{J_{m}}\) and \(\mathbf{V_{m}}\) is the relative position parameter of the CDPDR and the parameter of the motor. The parameter values selected in this article are representative, and these parameters can be re-selected in practical applications. Initially, the pose of the ship relative to the inertial frame is set as \(\mathbf{x_{SO}^{O}}(0)=(0\,,\,0\,,\,0)^{T}\text{m}\), \(\mathbf{\theta_{SO}^{O}}(0)=(0\,,\,0\,,\,0)^{T}\text{deg}\). The initial position of the motion platform relative to the inertial frame is \(\mathbf{x_{PO}^{O}}(0)=(0.2\,,\,0\,,\,2.9)^{T}\text{m}\), and the initial angle is \(\mathbf{\theta_{PO}^{O}}(0)=(0\,,\,5\,,\,0)^{T}\text{deg}\). The initial velocity is \(\mathbf{x_{PO}^{O}}(0)=(0\,,\,0\,,\,0)^{T}\text{m}/\text{s}\), and the initial angular velocity is \(\mathbf{\omega_{PO}^{O}}(0)=(0\,,\,0\,,\,0)^{T}\text{deg}/\text{s}\). The controller parameters are set as shown in Table 3.  
The target trajectory of the motion platform relative to the pulley frame \(C\) of the CDPDR is  
\[ \begin{cases}\mathbf{x_{PC}^{C}}=0.35\cos(\omega\text{t})+0.6\\ \mathbf{x_{PC}^{C}}=0.35\sin(\omega\text{t})+0.7\\ \mathbf{\theta_{PC}^{C}}=(\pi/48)\text{t}\end{cases}  \tag{53}\]  
where \(\omega=2\pi/T\) is the angular velocity of the motion platform. \(T=12\) s is the moving period of the motion platform. The kinematic simulation result is shown in Figure 8. When the trajectory is circular, the cable length, velocity and acceleration change uniformly and continuously. Condition 1: or the scenario that CDPDR performs derusting operations when the ship is docked at the port, considering that the waves have little interference to the ship. Firstly, the simulation analysis without wave excitation is carried out. In general, the disturbance can be expressed as  
\[T_{dist}=A_{dist}\cos(\omega_{dist}(\text{t}-\text{t}_{0})) \tag{54}\]  
where \(A_{dist}\) is the amplitude of interference force. \(\omega_{dist}\) is related to the frequency of the interference force, and \(\text{t}_{0}\) is the time at which the interference force appears. In actual operation, external disturbances, such as sea breezes, generally do not occur continuously, but suddenly appear at a certain moment. Additionally, the sudden disturbance generally has a greater impact on the effect of the controller. In order to verify the robustness of the controller, external disturbances, such as sea wind, are given at 4 s. The disturbances are given as  
\[ \begin{cases}f_{x}=30\cos(0.6(\text{t}-4))\\ f_{y}=30\cos(0.6(\text{t}-4))\\ f_{z}=30\cos(0.6(\text{t}-4))\end{cases}\begin{cases}\omega_{x}=0.2\cos(0.6( \text{t}-4))\\ \omega_{y}=0.3\cos(0.6(\text{t}-4))\\ \omega_{z}=0.2\cos(0.6(\text{t}-4))\end{cases}  \tag{55}\]