# Phase Plane Trajectory Planning for Double Pendulum Crane Anti-Sway Control
## 5 Experimental Verification  
The proposed control method has good control performance in simulation. The proposed method is verified on the mobile lifting gantry crane anti-sway control experimental platform. The platform size is 3 m \(\times\) 4 m, and it consists of an industrial computer, a PLC (Siemens S-71200), a frequency converter (Invt Goodrivr350-19) and a trolley drive mechanism. The industrial computer uses the Windows 10 operating system and uses the Modbus TCP protocol to communicate with the PLC through the host computer program. The position of the trolley is measured using laser ranging. The laser ranging (OD Series) has a measurement range of 0-4 m and an accuracy of \(\pm\)1 mm. The swing angle detection system uses two cameras (Lumenera's Lt225) to measure the swing angle, with a frame rate of 50 frames per second and an accuracy of \(\pm\)0.05\({}^{\circ}\). The crane experimental system is shown in Figure 9. Under the premise of keeping the crane system parameters unchanged, the actual control effect of the proposed control method is verified experimentally and compared with the simulation results.  
The target displacement of the trolley is 1.5 m, and rope length \(l_{1}\) is 1 m, \(l_{2}\) is 0.5 m. The hook mass \(m_{1}\) is 10 kg and the load mass \(m_{2}\) is 20 kg.  
Figure 8: (**a**) Hook swing angle; (**b**) load swing angle.  
Figure 9: Crane experimental system.  
The comparison results between the experiment and the simulation are shown in Figures 10 and 11. The experimental results show that the actual time for the trolley to reach the target position is consistent with the simulation, and the actual maximum hook swing angle and load swing angle are both within the constraint range. Due to the inevitable external interference and hardware conditions in the experiment, the experimental curve will have slight fluctuations but the overall trend of the experimental curve is consistent with the simulation curve. Therefore, the proposed control method still achieves good control performance in the physical experiment.  
In order to show the robustness of this method to the influence of mass factors, the figure shows the swing of the hook and the load with a load mass of 20 kg and 40 kg, respectively. As can be seen from the figure below, the controller scheme is not greatly affected by mass changes and has strong robustness.  
Figure 12 shows the comparison between the anti-sway control simulation and the experiment for loads of different masses. The results showed that the change in load mass has little effect on the dynamic response trend of the swing angle, and the swing angle attenuation law under different masses is consistent. Specifically, despite the significant difference in load mass (from 20 kg to 40 kg), the proposed control method can still effectively suppress the load swing, and the swing angle peak value and steady-state time do not show obvious fluctuations, showing that the control strategy has strong robustness to changes in mass parameters. This result indirectly verifies the control model's adaptability to the load and provides a theoretical basis for anti-sway control in quality uncertain scenarios in actual engineering.  
Figure 11: (**a**) Comparison of experimental and simulation results of hook swing angle; (**b**) comparison of experimental and simulation results of load swing angle.  
Figure 10: Comparison of experimental and simulation results of trolley displacement.