Effect of control time delay on high-speed maglev vehicle-bridge-wind system

Time delay is unavoidable in practical engineering, and it causes the system to undergo complex dynamic behavior. Therefore, clarifying its effect on the system will help to accurately assess the safety and stability of high-speed maglev vehicles operating on bridges under crosswind conditions. The proportional-integral-derivative (PID) is used as a feedback controller to derive the transfer function of the closed-loop system considering the gap feedback time delay. The calculation formula for the critical time delay of the system is obtained using the Routh criterion. A spatially coupled vibration model of the maglev train-bridge-wind system considering the control delay is established, and the accuracy of the model is verified by comparing it with the field measurement results. The responses of the train and bridge under different time delays, wind speeds, and control parameters are calculated. The results show that in the train-bridge-wind coupled vibration model, the critical time delay of the suspension system is basically the same as the theoretical value, while the critical time delay of the guidance system slightly exceeds the theoretical value. Vehicle dynamic response increases with wind speed and time delay. The greater the wind speed, the greater the effect of time delay on the dynamic response of the bridge and the train. The time delay will reduce the wind speed threshold for safe and smooth train operation, which is 30 m/s and 15 m/s for lateral acceleration of the car body for time delays of 0 ms and 10.5 ms, respectively. By appropriately reducing the proportional and integral gain coefficient and increasing the differential gain coefficient, the effect of the control time delay on the system can be mitigated.