## 5 Simulation Analysis
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Values** & **Parameters** & **Values** \\ \hline \(m\) & 5 kg & \(I_{PP}\) & diag(0.03,0.03, 0.06)kg \(\cdot\) \\ \(\mathbf{h}\) & 0.3 m & \(D\) & 0.25 m \\ \(\mathbf{H}\) & 1.9 m & \(D\) & 1.4 m \\ \(\mathbf{x_{CS}^{S}}\) & \((-1\,,0\,,\,2.555)^{T}\text{m}\) & \(G\) & \(-9.8\) kg/m\({}^{2}\) \\ \(T_{lim}\) & 20 N & \(T_{lim}\) & 500 N \\ \(\mathbf{J_{m}}\) & 0.01 kg \(\cdot\) m\({}^{2}\) & \(\mathbf{V_{m}}\) & 0.01 Nms \\ \(\mathbf{r}\) & 0.1 m & \(r_{pully}\) & 12 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 2: System simulation parameters. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Parameters** & \(p\) & \(q\) & \(\mu\) & \(\mathbf{k_{1}}\) & \(\mathbf{k_{2}}\) & \(\mathbf{\beta}\) & \(\mathbf{\lambda_{0}}(0)\) & \(\mathbf{\lambda_{1}}(0)\) & \(\mathbf{\lambda_{2}}(0)\) & \(\mathbf{\ell_{0}}\) & \(\mathbf{\ell_{1}}\) & \(\mathbf{\ell_{2}}\) & \(\mathbf{\epsilon}\) \\ \hline Values & 5 & 3 & 0.1 & diag (3,..., 3) & (3,..., 3) & (50,..., 50) & 0 & 0 & 1 & 1 & 1 & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Controller parameters. In addition, the \(y\)-direction of the CDPDR motion platform is perpendicular to the working surface, so the disturbance force in the \(y\)-direction should also include the reaction force. The reaction force \(\mathbf{F}_{gun}\) of a water gun can be expressed as  
\[\mathbf{F}_{gun}=1.745\mathbf{Q}\sqrt{\mathbf{P}_{press}} \tag{56}\]  
where \(\mathbf{P}_{press}\) is the water pressure. The pressure range of medium pressure water gun is generally 1.6-2.5 Mpa, and the water gun pressure here is selected as 1.8 Mpa. \(\mathbf{Q}\) is the water flow, specifically expressed as  
\[\mathbf{Q}=\frac{3\pi\mathbf{r}_{outlet}^{2}}{4}\mathbf{V} \tag{57}\]  
where \(\mathbf{V}=\sqrt{2g\mathbf{h}_{press}}\) is the water velocity. \(\mathbf{h}_{press}\) is a value calculated as the height of the water column, 1 Mpa = 100 m water column height. \(\mathbf{r}_{outlet}=1.5\) mm is the outlet radius. It is calculated that \(\mathbf{F}_{gun}=41.68\) N. With the safety margin remaining, the maximum value is 50 N. The uniform random number module of MATLAB/Simulink is used to simulate the reaction force. Its maximum and minimum values are 40 N and 50 N, respectively, and the sampling time is 0.05 s.  
The simulation results are shown in Figure 9. It can be seen that for the operation scene without wave excitation, the initial deviation is significantly reduced within 1 s.  
Figure 8: The kinematic simulation result: (**a**) cable length variation diagram; (**b**) cable velocity variation diagram; (**c**) cable acceleration variation diagram. Because of the disturbance torque, the angle error around the \(y\)-axis is relatively larger. The external disturbances at 4 s, trajectory and angle tracking error values become larger, but the tracking effect recovers after about 1s. It can be obtained from Figure 9d,e that the maximum trajectory error is 4 mm, and the maximum angle error is 0.6\({}^{\circ}\). The maximum velocity error is 0.06 m/s, and the maximum angular velocity error is 10 deg/s. For working condition 1, position errors in the millimeters range, and the angle error is within 1\({}^{\circ}\), which can meet the needs of the operation. Condition 2: in view of the situation that the ship is derusting at anchorage, it is considered that the CDPDR will be stimulated by the moving base at this time. Under the influence of wave excitation, the ship moves with 6-DOF. The ship's base motions are time varying and nonlinear; to simplify the problems studied, the ship moving base excitation can be expressed as  
\[T_{sea}=A_{sea}\sin(\omega_{sea}t) \tag{58}\]  
Figure 9: The simulation results without wave excitation: (**a**) \(x\)-direction trajectory tracking; (**b**) \(z\)-direction trajectory tracking; (**c**) \(y\)-direction angle tracking; (**d**) trajectory tracking error; (**e**) velocity tracking error. where \(A_{sea}\) is the angle or displacement amplitude of the ship's motions.