# An Anti-Swing Closed-Loop Control Strategy for Overhead Cranes
## 4 Simulation and Experiment  
Simulations in the environment of MATLAB/Simulink and experiments based on a laboratory-scale overhead crane were implemented to validate the performance of the proposed control strategy as shown in Figure 4. As for the simulation, a Luenberger full-dimensional state observer was used to estimate the real-time swing angle. (1) Simulation  
The simulation parameters of the overhead crane were as follows: \(m=50\) kg, \(l=3\) m and \(M=70\) kg, \(g=9.8\) m/s\({}^{2}\). The control strategy was validated under the different conditions of expected horizontal move distance \(x_{d}\) and expected arriving time \(t_{f}\). **Simulation 1**. : _Expected horizontal move distance and expected time was \(x_{d}=5\) m, \(t_{f}=30\) s._  
**Simulation 2**. : _Expected horizontal move distance and expected time was \(x_{d}=10\) m, \(t_{f}=30\) s._  
**Simulation 3**. : _Expected horizontal move distance and expected time was \(x_{d}=10\) m, \(t_{f}=30\) s._  
_During the transportation process, a duration of \(1\) s of white noise disturbance was added at \(t_{1}=5\) s, \(t_{2}=15\) s, and \(t_{3}=25\) s._  
**Simulation 4**. : _Expected horizontal move distance and expected time was \(x_{d}=10\) m, \(t_{f}=30\) s.Since Proportion Integration Differentiation (PID) and its improved algorithm currently are the main approach to solve the swing problem, the method proposed in this article (abbreviated as MPC-EID) was also compared with the classical double-closed-loop PID (abbreviated as DPID) and fuzzy-PID (abbreviated as FPID). We also compared our  
Figure 4: The simulation structure of the proposed anti-swing closed-loop control system. method with the method that adopts an internal model with the equivalent input disturbance (abbreviated as IEID) control algorithm, which is the same idea in the model establishment of the underactuated system._  
It can be seen from Figures 5 and 6 that when the crane is moving horizontally, the swing angle is always within 1 degree, and the swing angle has almost decreased to 0 degrees when the crane reaches the target location within the expected time \(t_{f}\). The entire control process is more natural and smooth. From Figure 7, the swing angle has some fluctuations when 1 s of white noise disturbance is added to the control system, but it can quickly return to the normal swing within a certain period of time. Figure 5: Result of simulation 1. Figure 6: Result of simulation 2. From the simulation results of the four kinds of methods in Figure 8, we can see that the FPID and DPID methods have quite similar results. As for the time taken to arrive at the target location, the least time is taken by the FPID and DPID methods and the most time by the IEID method. As for the time for the swing angle value to reach zero degrees, the FPID and DPID methods both take about 30 s (the DPID method actually goes a little bit faster than the FPID method), the IEID method takes 35 s, and the MPC-EID method takes 31 s. However, the maximum swing angle by the DPID method can reach more than 0.6 degrees, and the minimum swing angle by the IEID method can reach 0.5 degrees. The MPC-EID method has moderate performance, which is the relatively best solution for safety and efficiency in real applications. Figure 8: Result of simulation 4. Figure 7: Result of simulation 3. (2) Experiments  
A lab was specially built to validate the proposed method, as shown in Figure 9. The experimental platform used three Alternating Current (AC) asynchronous motors to drive the trolley to move on the track. The maximum speed was 1 m/s. Due to the limitation of the experimental site, the track length of the crane was 5.5 m, the actual usable length was 5 m, and the maximum rope length was 3 m. The maximum payload mass was 1 t. The moving distance sensor used in this experiment could achieve an accuracy of 1 mm. Using the aircraft attitude angle sensor, the dynamic swing angle and the static swing angle accuracy could reach 0.01\({}^{\circ}\). The friction coefficient was 0.2.