## 5 Simulation Experiments
### Anti-Disturbance Simulation Experiments  
Additionally, during practical operations, bridge cranes often encounter various sources of disturbances. These disturbances may stem from operator commands or external environmental uncertainties such as wind forces, fluctuations in payloads, and environmental noise, among others. These disturbances can potentially affect the crane's performance and lead to deterioration or failure of the control system. To validate the robustness of the algorithm, disturbance tests were conducted on the system to simulate its responses under different disturbances and influences. The algorithm's resistance to disturbances was evaluated accordingly. To simulate the effects of wind forces and environmental noise on bridge cranes operating outdoors, white noise was added to the feedback signal during the simulation period of 15-20 s. Figures 19-22 illustrate the trolley position and effective payload swing angle curves of the bridge crane under two types of white noise disturbances. Table 10 presents the performance indicators of the system after being subjected to disturbances. In Figures 19 and 21, the ISSA algorithm demonstrates the minimum peak time and steady-state time, measuring 15.825 and 24.058, and 24.248 and 23.016, respectively. In Figures 20 and 22, the maximum swing angle achieved by the ISSA algorithm is 0.052 and 0.014, respectively, both lower than the corresponding values for the other four algorithms. The steady-state times are 24.403 and 25.299, respectively, both lower than the PSO algorithm's 10.149 and 9.104. It can be observed that under external disturbances, the ISSA algorithm exhibits the optimal response and recovery speeds among the five algorithms, demonstrating the favorable stability of the bridge crane system controlled by the ISSA algorithm-optimized PID controller in the presence of disturbances. Figure 19: Trolley position control effects for five algorithms under white noise 1. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\
\begin{tabular}{c} **Working** \\ **Condition** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Improved PID** \\ **Controller** \\ \end{tabular} } & \multicolumn{4}{c}{**Trolley Position**} & \multicolumn{2}{c}{**Payload Swing Angle**} \\ \cline{3-8}  & & **Peak Time** & **Overshoot** & **Steady-State** & **Steady-State** & **Max Angle** & **Steady State** \\  & & **(s)** & **(\%)** & **Time (s)** & **Value (m)** & **(rad)** & **Time (s)** \\ \hline \multirow{8}{*}{3} & PSO & 8.083 & 0.7\% & 19.707 & 4.945 & 0.330 & 46.358 \\  & SA & 12.094 & 0 & 19.338 & 4.958 & 0.261 & 39.254 \\  & WOA & 8.370 & 0.26\% & 10.907 & 4.994 & 0.258 & 26.358 \\  & SSA & 8.411 & 0.44\% & 7.551 & 4.994 & 0.253 & 17.985 \\  & ISSA & 8.247 & 0.42\% & 7.469 & 4.995 & 0.236 & 16.194 \\ \hline \multirow{8}{*}{4} & PSO & 12.311 & 0 & 12.675 & 4.950 & 0.285 & 11.060 \\  & SA & 12.635 & 0 & 14.090 & 4.953 & 0.247 & 11.896 \\  & WOA & 11.867 & 0 & 11.988 & 4.994 & 0.186 & 8.791 \\  & SSA & 6.853 & 0 & 7.379 & 4.997 & 0.149 & 7.925 \\  & ISSA & 6.070 & 0 & 6.585 & 4.998 & 0.145 & 7.716 \\ \hline \multirow{8}{*}{5} & PSO & 8.228 & 0.72\% & 19.953 & 4.951 & 0.294 & 29.776 \\  & SA & 12.473 & 0 & 15.263 & 4.953 & 0.233 & 28.343 \\ \cline{1-1}  & WOA & 8.389 & 0 & 10.532 & 4.994 & 0.216 & 16.463 \\ \cline{1-1}  & SSA & 8.592 & 0 & 7.460 & 4.998 & 0.200 & 11.896 \\ \cline{1-1}  & ISSA & 8.147 & 0 & 7.136 & 4.998 & 0.189 & 11.687 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: _Cont._Figure 21: Trolley position control effects for five algorithms under white noise 2. Figure 22: Payload swing angle suppression effects for five algorithms under white noise 2. At \(t=10\) s during simulation, a step signal with a magnitude of 2 is introduced into the expected position signal of the trolley to simulate the requirement of operator command change. Figures 23 and 24 depict the trolley position curve and payload swing angle curve, respectively, after the input command change.