# Research on Variable Universe Fuzzy Multi-Parameter Self-Tuning PID Control of Bridge Crane
## 4 Simulation Analysis
### Simulation and Analysis  
To compare the effectiveness of the three control methods for the bridge crane's load anti-sway and positioning under the same operating conditions, we evaluated two performance metrics for each method. For positioning control, we evaluated the maximum overshoot (\(M_{P}\)) and settling time of the trolley's position (\(T_{S}\)). For anti-sway control, we evaluated the maximum swing angle (\(\theta_{max}\)) and stabilization time of the load (\(T_{S}\)). Figures 6 and 7 display the control results of the three methods for the positioning of the trolley and the swing angle of the load, respectively. Table 4 summarizes the performance of each evaluation index for the three control methods.  
Based on Figures 6 and 7, it is observed that the VUFMS-PID controller for the bridge crane exhibits the lowest maximum swing angle among the three control methods. Specifically, the maximum swing angle of the load is 0.66 deg for the VUFMS-PID controller, while the FUZZY-PID and PID controllers have maximum swing angles of 0.88 deg and 1.08 deg, respectively. This indicates that the VUFMS-PID controller reduces the maximum swing angle by 0.22 deg and 0.42 deg compared to the FUZZY-PID and PID controllers, respectively, under the same operating conditions. Furthermore, the maximum swing angle of 1.005 deg reported in the literature [10] for a PSO-optimized LQR controller is 0.345 deg (29.1%) higher than that of the VUFMS-PID controller proposed in this study.  
Figure 5: Fuzzy turner surface of \(\Delta K_{D}\).  
Regarding the stabilization time of the swing angle, the VUFMS-PID controller has the shortest stabilization time of 8.81 s compared to the FUZZY-PID and PID controllers, which have stabilization times of 9.11 s and 11.85 s, respectively. It is worth noting that literature [10] reported a stabilization time of 9.3 s for swing angle control which is larger than the VUFMS-PID controller's swing angle.  
For trolley positioning, the VUFMS-PID controller exhibits the shortest stabilization time of 7.9 s, followed by the FUZZY-PID and PID controllers with stabilization times of 11.15 s and 11.01 s, respectively. In addition, the VUFMS-PID controller has zero overshoot for trolley positioning, while the FUZZY-PID and PID controllers exhibit varying degrees of overshoot.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Output**} & \multirow{2}{*}{**Performances**} & \multicolumn{5}{c}{**Methods**} \\ \cline{3-6}  & & **VUFMS-PID** & **FUZZY-PID** & **PID** & **Reference [10]** \\ \hline \multirow{2}{*}{\(x\)} & \(T_{S}\) (s) & 7.9 & 11.15 & 11.01 & 9.3 \\ \cline{2-6}  & \(M_{P}\) (\%) & 0 & 2.8 & 6.8 & 0 \\ \hline \multirow{2}{*}{\(\theta\)} & \(T_{S}\) (s) & 8.81 & 9.12 & 11.85 & / \\ \cline{2-6}  & \(\theta_{\text{max}}\) (deg) & 0.66 & 0.88 & 1.08 & 1.005 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Performances obtained using VUFMS-PID, FUZZY-PID and PID controller for the bridge crane.  
Figure 6: Trolley’s position (x) using VUFMS-PID, FUZZY-PID and PID controller.  
Figure 7: Overhead crane’s swing angle (\(\theta\)) VUFMS-PID, FUZZY-PID and PID controller.  
Based on the above analysis, it can be concluded that the bridge crane system controlled by the VUFMS-PID controller has the smallest overshoot, the smallest swing angle, and the shortest stabilization time for trolley positioning compared to the FUZZY-PID controller, PID controller, and LQR controller proposed in the literature [10], under the same operating conditions. As a result of the evaluation, it can be concluded that the VUFMS-PID controller exhibits the best control performance for the bridge crane system.