## 7 Parameter Optimization of Terminal Sliding Film Controller Based on JLSCOA  
### Fitness Function  
In this paper, we take the terminal sliding film controller of the power positioning system based on the \"New Hongzhu\" ship of Dalian Maritime University as the research object, and search for the optimal values of two parameters that have a big influence on the control results: the parameter \(\delta\) used to eliminate the jitter vibration, and the control gain \(\lambda\) on the surface of the sliding mode, and design the adaptivity function as follows:  
\[\mathrm{J}=\int_{0}^{\infty}\mathrm{c}|\mathrm{e}_{2}|+\mathrm{b}|\tau_{2}| \,\mathrm{dt} \tag{31}\]  
where the coefficients \(\mathrm{c}\) and \(\mathrm{b}\) are the weights of the system error and the control quantity, respectively, representing the importance of the energy consumption requirement and the error tracking requirement [14]. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Performance Metrics** & **Algorithm** & \(f_{7}\)**(c)** & \(f_{8}\)**(c3)** & \(f_{9}\)**(c)** & \(f_{10}\)**(c)** & \(f_{11}\)**(c)** & \(f_{12}\)**(c3)** \\ \hline \multirow{4}{*}{Optimum} & COA & \(5.3372\times 10^{-68}\) & 0 & \(8.88178\times 10^{-16}\) & 0 & 0.017523 & 1.3716 \\  & WOA & \(0.000141843\) & 0 & \(8.88178\times 10^{-16}\) & 0 & 0.006018538 & 0.13838868 \\  & SSA & \(0.000148498\) & 0 & \(8.88178\times 10^{-16}\) & 0 & \(3.52005\times 10^{-13}\) & \(8.91756\times 10^{-10}\) \\  & JLSCOA & \(1.0804\times 10^{-68}\) & 0 & \(8.88178\times 10^{-16}\) & 0 & 0.00029373 & 0.30306 \\ \hline \multirow{4}{*}{Worst} & COA & \(0.00026533\) & 0 & \(8.88178\times 10^{-16}\) & 0 & 0.070164 & 2.7724 \\  & WOA & \(0.014814868\) & \(1.13687\times 10^{-13}\) & \(7.99361\times 10^{-5}\) & 0.10806285 & 5.024915688 & 1.059936774 \\  & SSA & \(0.001858923\) & \(3.97904\times 10^{-13}\) & \(2.22045\times 10^{-14}\) & 0 & 628590\(\times 10^{-8}\) & \(4.30752\times 10^{-68}\) \\  & JLSCOA & \(0.00031593\) & 0 & \(8.88178\times 10^{-16}\) & 0 & 0.041731 & 2.9686 \\ \hline \multirow{4}{*}{average value} & COA & \(7.1152\times 10^{-65}\) & 0 & \(8.88178\times 10^{-16}\) & 0 & 0.03922 & 2.2403 \\  & WOA & \(0.00264973\) & \(5.68434\times 10^{-15}\) & \(3.90799\times 10^{-15}\) & 0.005403142 & 0.271157034 & 0.550541975 \\  & SSA & \(0.000673495\) & \(1.98952\times 10^{-14}\) & \(2.13163\times 10^{-15}\) & 0 & \(1.13735\times 10^{-68}\) & \(4.26727\times 10^{-67}\) \\  & JLSCOA & \(7.188\times 10^{-65}\) & 0 & \(8.88178\times 10^{-16}\) & 0 & 0.013921 & 1.2916 \\ \hline \multirow{4}{*}{standard deviation} & COA & \(5.9868\times 10^{-68}\) & 0 & 0 & 0 & 0.016068 & 0.31585 \\  & WOA & \(0.003484452\) & \(2.54211\times 10^{-14}\) & \(2.08959\times 10^{-15}\) & 0.024163588 & 1.1189687 & 0.289743143 \\ \cline{1-1}  & SSA & \(0.000547679\) & \(8.8974\times 10^{-14}\) & \(4.70079\times 10^{-15}\) & 0 & 1.7765 \(\times 10^{-68}\) & \(9.75527\times 10^{-67}\) \\ \cline{1-1}  & JLSCOA & \(7.3469\times 10^{-65}\) & 0 & 0 & 0 & 0.010383 & 0.8121 \\ \hline \end{tabular}
\end{table} 
Table 5: Comparison of the performance of four algorithms, such as COA, JLSCOA, WOA, and SSA, for solving multi-peak benchmark tests. Using the \"Xin Hongzhuan\" ship from Dalian Maritime University as the simulation object, performance verification of the terminal sliding mode controller optimized by JLSCOA is conducted in an ideal environment. The initial position of the ship is set to [0 m, 0 m, 0\({}^{\circ}\)], and the desired position is set to [5 m, 5 m, 10\({}^{\circ}\)]. Other controller parameters are set as \(k_{2}=1,\xi_{2}=1.1,a=0.5,k=10\). The simulation time is 600 s. Figures 4-6 show the results. Figures 4-6 are the curves of the change of position, speed, and control force of the ship's three freedoms. Figure 4: Ship position and pitch angle variation curve. Figure 3: Fitness function iteration variation curve.