# Research on Variable Universe Fuzzy Multi-Parameter Self-Tuning PID Control of Bridge Crane
## 5 Robustness Analysis
### Experimental Simulation Analysis under Disturbance Conditions  
To verify the robustness of the controller in controlling the crane under interference, a simulation is conducted. The crane may encounter sudden interferences such as strong winds or environmental noise when working outdoors, hence it is crucial to test the robustness of the proposed controller. The parameters of the crane under four working conditions are selected as the control objects, and the parameters of each working condition are shown in Table 9 below. The proposed VUFMS-PID controller, FUZZY-PID controller, and traditional PID controller are used to control the crane under the interference of side winds and environmental disturbances. The overshoot, positioning time, maximum swing angle, and swinging time of the load during crane positioning are used as evaluation indicators, and the simulation results are shown in the following Figures. In order to better demonstrate the real-time adjustment effect of the proposed control strategy on PID controller gains, Figure 14 shows the real-time output results of PID gains for the fuzzy controller of the trolley positioning system under environmental noise interference and working condition 1. From Figure 14, it can be seen that in order to reduce the impact of environmental noise on the control system, the output of PID gains also exhibits a pulsating change, similar to the environmental noise. From Figures 15-22, it is observed that under the influence of strong wind and environmental noise disturbances, the crane controlled by the proposed VUFMS-PID controller exhibits the smallest maximum swing angle of the load under crosswind disturbance compared to the other two controllers, and it stabilized the quickest in each working condition. Additionally, the VUFMS-PID controller produced the smallest overshoot when positioning the trolley. Through the above analysis, it is evident that the proposed VUFMS-PID controller exhibits excellent control performance in multiple working conditions and outperforms the other two controllers in handling crosswind and environmental noise disturbances. The fuzzy control system's domain adjustment makes the controller highly adaptable and robust, leading to better control precision and stability. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Output**} & \multirow{2}{*}{**Performances**} & \multicolumn{3}{c}{**Methods**} \\ \cline{3-5}  & & **VUFMS-PID** & **FUZZY-PID** & **PID** \\ \hline \multirow{3}{*}{\(x\)} & \(T_{\text{S}}\) (s) & 10.13 & 11.88 & 11.05 \\ \cline{2-5}  & \(M_{\text{P}}\) (\%) & 0.6 & 3.8 & 7.0 \\ \hline \multirow{3}{*}{\(\theta\)} & \(T_{\text{S}}\) (s) & 9.38 & 10.56 & 12.05 \\ \cline{2-5}  & \(\theta_{\text{max}}\) (\({}^{\circ}\)) & 0.57 & 0.84 & 1.03 \\ \hline \end{tabular}
\end{table} 
Table 8: Performances obtained using VUFMS-PID, FUZZY-PID, and PID controller under working condition 3. \begin{table}
\begin{tabular}{c c c c} \hline \multicolumn{1}{c}{**Working Condition**} & **Rope Length (m)** & **Payload Weight (kg)** & **Trolley Weight (kg)** \\ \hline
1 & 1 & 5 & 10 \\ \hline
2 & 1.5 & 5 & 10 \\ \hline
3 & 1.5 & 8 & 10 \\ \hline
4 & 1 & 8 & 10 \\ \hline \end{tabular}
\end{table} 
Table 9: Parameters of the crane under four working conditions. Figure 16: Payload’s swing angle using VUFMS-PID, FUZZY-PID and PID controller under working condition 1 with a crosswind and white noise. Figure 14: The output results of the PID gain of the fuzzy controller for trolley positioning under working condition 1. Figure 15: Trolley’s position using VUFMS-PID, FUZZY-PID and PID controller under working condition 1 with a crosswind and white noise. Figure 19: Trolley’s position using VUFMS-PID, FUZZY-PID and PID controller under working condition 3 with a crosswind and white noise. Figure 17: Trolley’s position using VUFMS-PID, FUZZY-PID and PID controller under working condition 2 with a crosswind and white noise.