铁道科学与工程学报2025，Vol.22Issue(10)：4307-4319,13.DOI:10.19713/j.cnki.43-1423/u.T20250021
基于PID控制时滞的高速磁浮车-桥系统动力稳定性分析
Dynamic stability analysis of high speed maglev vehicle-bridge system based on PID control time delay
摘要
Abstract
Time delay is unavoidable in each link of levitation control of maglev train,which causes the system to undergo complex dynamics behavior and endanger the safety of train operation in severe cases;therefore,it is necessary to study the time delay stability of high-speed maglev vehicle-bridge system.First,based on the single electromagnet model,the proportional-integral-derivative(PID)was taken as the control parameter of the system,and the electromagnetic force calculation formula and the transfer function of the closed-loop system considering the control time delay were derived.Meanwhile,through the Routh stability criterion,the value requirements of the control parameters as well as the explicit functional expressions of the relationship between the critical time delay and the control parameters were obtained.Second,a spatially coupled vibration model of high-speed maglev vehicle-bridge system consisting of 5 trains and 10 spans of simply supported girder bridge was constructed,and the correctness of the model was verified by comparing with the measured data.Finally,based on this coupled vibration model,the validity of the explicit function expression was examined,and the effects of the control parameters,air spring stiffness,lateral preload force and track stiffness on the critical time delay were analyzed.The results show that the critical time delay value of the suspension system in the vehicle-bridge model is 10.1 ms,which is close to the theoretical value of 9.98 ms.The critical time delay value of the guidance system is 11 ms,which is slightly larger than the theoretical value of 9.94 ms.The explicit function obtained from the theoretical derivation can be used to approximate the critical time delay of the system,and the critical time delay is proportional to the integral and differential gain coefficients and approximately inversely proportional to the proportional gain coefficient.The critical time delay of the suspension system shows an increase and then a gradual and smooth change with the increase of the air spring stiffness,and the critical time delay of the guidance system shows a decrease and then a gradual and smooth change with the increase of the lateral preload force.The time delay stability of the system is slightly better under the flexible track compared to the rigid track.Decreasing the proportional and integral gain coefficients,increasing the differential gain coefficient,increasing the air spring stiffness and reducing the lateral preload improve the time-delay stability of the vehicle-bridge system.关键词
高速磁浮车辆/车-桥耦合振动/时滞/稳定性分析/传递函数/PID控制Key words
high-speed maglev vehicle/vehicle-bridge coupled vibration/time delay/stability analysis/transfer function/PID control分类
交通运输引用本文复制引用
卜秀孟,王力东,邵壮,张东风,韩艳..基于PID控制时滞的高速磁浮车-桥系统动力稳定性分析[J].铁道科学与工程学报,2025,22(10):4307-4319,13.基金项目
国家自然科学基金资助项目(52208459,52478494) （52208459,52478494）
中铁工程设计咨询集团有限公司科技开发课题-高速磁悬浮道岔关键技术研究(研2022-33) （研2022-33）
长沙市杰出青年科技人才培养计划(kq2506015) （kq2506015）
湖南省研究生科研创新项目(CX20240766) （CX20240766）
