• ISSN 0258-2724
  • CN 51-1277/U
  • EI Compendex
  • Scopus 收录
  • 全国中文核心期刊
  • 中国科技论文统计源期刊
  • 中国科学引文数据库来源期刊

二自由度磁浮列车悬浮系统时滞控制研究

王美琪 曾思恒 李源 刘鹏飞

王美琪, 曾思恒, 李源, 刘鹏飞. 二自由度磁浮列车悬浮系统时滞控制研究[J]. 西南交通大学学报. doi: 10.3969/j.issn.0258-2724.20230282
引用本文: 王美琪, 曾思恒, 李源, 刘鹏飞. 二自由度磁浮列车悬浮系统时滞控制研究[J]. 西南交通大学学报. doi: 10.3969/j.issn.0258-2724.20230282
WANG Meiqi, ZENG Siheng, LI Yuan, LIU Pengfei. Research on Time Lag Control of Levitation System of Two-Degree-of-Freedom Magnetic Levitation Train[J]. Journal of Southwest Jiaotong University. doi: 10.3969/j.issn.0258-2724.20230282
Citation: WANG Meiqi, ZENG Siheng, LI Yuan, LIU Pengfei. Research on Time Lag Control of Levitation System of Two-Degree-of-Freedom Magnetic Levitation Train[J]. Journal of Southwest Jiaotong University. doi: 10.3969/j.issn.0258-2724.20230282

二自由度磁浮列车悬浮系统时滞控制研究

doi: 10.3969/j.issn.0258-2724.20230282
基金项目: 国家自然科学基金(12102273)
详细信息
    作者简介:

    王美琪(1987—),男,副教授,博士,研究方向为非线性动力学、磁悬浮列车动力学与控制,E-mail:wangmeiqi@stdu.edu.cn

    通讯作者:

    刘鹏飞(1985—),男,副教授,博士,研究方向为列车-轨道耦合动力学、磁悬浮列车动力学与控制,E-mail:lpfswjtu@163.com

  • 中图分类号: O324

Research on Time Lag Control of Levitation System of Two-Degree-of-Freedom Magnetic Levitation Train

  • 摘要:

    为研究控制器时滞对磁浮列车悬浮系统稳定性的影响,首先,以位移-速度为反馈控制参数,建立考虑控制器时滞的二自由度磁浮列车悬浮系统模型;其次,通过Routh-Hurwitz稳定性判据得到无时滞系统的稳定性区域,同时,依据特征根穿越虚轴边界条件,获得系统发生Hopf分岔的控制器时滞临界值;最后,分析反馈控制参数及系统参数与控制器时滞临界值的关系. 研究结果表明:当系统参数一定时,控制器时滞临界值随位移控制增益的增大而减小,随速度控制增益的增大先增大后减小;当反馈控制参数一定时,控制器时滞临界值随二系刚度的增大而减小,随二系阻尼的增大而增大;当系统时滞以10−6数量级在时滞临界值附近渐渐增大时,系统会从稳定—周期运动—不稳定逐渐变化,期间发生超临界Hopf分岔.

     

  • 图 1  磁浮时滞模型

    Figure 1.  Time lag model of magnetic levitation

    图 2  Routh-Hurwitz稳定性范围

    Figure 2.  Routh-Hurwitz stability region

    图 3  无时滞稳定性验证

    Figure 3.  Stability verification without time lag

    图 4  控制器时滞临界值与反馈控制参数的关系

    Figure 4.  Relationship between critical value of controller time lag and feedback control parameters

    图 5  固有频率与反馈控制参数的关系

    Figure 5.  Relationship between natural frequency and feedback control parameters

    图 6  控制器时滞临界值与系统参数的关系

    Figure 6.  Relationship between critical value of controller time lag and system parameters

    图 7  固有频率与系统控制参数的关系

    Figure 7.  Relationship between natural frequency and system parameters

    图 8  τ=0.000 900 s,τ<τ0时的系统响应

    Figure 8.  System response with time lag τ=0.000 900 s, τ<τ0

    图 9  τ=0.001 000 s,τ>τ0时的系统响应

    Figure 9.  System response with time lag τ=0.001 000 s, τ>τ0

    图 10  τ=0.000 986 s,τ>τ0时的系统响应

    Figure 10.  System response with time lag τ=0.000 986 s, τ>τ0

    图 11  UM模型建立示意

    Figure 11.  UM model establishment

    图 12  内部控制模块示意

    Figure 12.  Internal control module

    图 13  τ=0.000 900 s,τ <τ0时的系统响应

    Figure 13.  System response with time lag τ=0.000 900 s, τ<τ0

    图 14  τ=0.001 000 s,τ>τ0时的系统响应

    Figure 14.  System response with time lag τ=0.001 000 s, τ>τ0

  • [1] 张舒,徐鉴. 时滞耦合系统非线性动力学的研究进展[J]. 力学学报,2017,49(3): 565-587.

    ZHANG Shu, XU Jian. Review on nonlinear dynamics in systems with coulpling delays[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 565-587.
    [2] 李帅,周继磊,任传波,等. 时变参数时滞减振控制研究[J]. 力学学报,2018,50(1): 99-108.

    LI Shuai, ZHOU Jilei, REN Chuanbo, et al. The research of time delay vibration control with time-varying parameters[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(1): 99-108.
    [3] 王在华,胡海岩. 时滞动力系统的稳定性与分岔:从理论走向应用[J]. 力学进展,2013,43(1): 3-20.

    WANG Zaihua, HU Haiyan. Stability and bifurcation of delayed dynamic systems: from theory to application[J]. Advances in Mechanics, 2013, 43(1): 3-20.
    [4] 公徐路,许鹏飞. 含时滞反馈与涨落质量的记忆阻尼系统的随机共振[J]. 力学学报,2018,50(4): 880-889.

    GONG Xulu, XU Pengfei. Stochastic resonance of a memorial-damped system with time delay feedback and fluctuating mass[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(4): 880-889.
    [5] TAFFO G I K, SIEWE M S, TCHAWOUA C. Stability switches and bifurcation in a two-degrees-of-freedom nonlinear quarter-car with small time-delayed feedback control[J]. Chaos, Solitons & Fractals, 2016, 87(1): 226-239.
    [6] 马卫华,胡俊雄,李铁,等. EMS型中低速磁浮列车悬浮架技术研究综述[J]. 西南交通大学学报,2023,58(4): 20-733.

    MA Weihua, HU Junxiong, LI Tie, et al. Technologies research review of electro-magnetic suspension medium-low-speed maglev train levitation frame[J]. Journal of Southwest Jiaotong University, 2023, 58(4): 20-733.
    [7] LEE H W, KIM K C, LEE J. Review of maglev train technologies[J]. IEEE Transactions on Magnetics, 2006, 42(7): 1917-1925. doi: 10.1109/TMAG.2006.875842
    [8] 刘士苋,王磊,王路忠,等. 电动悬浮列车及车载超导磁体研究综述[J]. 西南交通大学学报,2023,58(4): 734-753.

    LIU Shixian, WANG Lei, WANG Luzhong, et al. Review on electrodynamic suspension trains and on-board superconducting magnets[J]. Journal of Southwest Jiaotong University, 2023, 58(4): 734-753.
    [9] ZHANG L L, HUANG L H, ZHANG Z Z. Stability and Hopf bifurcation of the maglev system with delayed position and speed feedback control[J]. Nonlinear Dynamics, 2009, 57(1): 197-207.
    [10] YAU J D. Response of a maglev vehicle moving on a two-span flexible guideway[J]. Journal of Mechanics, 2010, 26(1): 95-103. doi: 10.1017/S1727719100003762
    [11] ZHANG Z Z, ZHANG L L. Hopf bifurcation of time-delayed feedback control for maglev system with flexible guideway[J]. Applied Mathematics and Computation, 2013, 219(11): 6106-6112. doi: 10.1016/j.amc.2012.12.045
    [12] 王洪坡. EMS型低速磁浮列车/轨道系统的动力相互作用问题研究[D]. 长沙:国防科学技术大学,2007.
    [13] 翟婉明,赵春发. 磁浮车辆/轨道系统动力学(Ⅰ)——磁/轨相互作用及稳定性[J]. 机械工程学报,2005,41(7): 1-10. doi: 10.3901/JME.2005.07.001

    ZHAI Wanming, ZHAO Chunfa. Dynamics of maglev vehicle/ guideway systems(I)—Magnet/rail interaction and system stability[J]. Journal of Mechanical Engineering, 2005, 41(7): 1-10. doi: 10.3901/JME.2005.07.001
    [14] DONG H, ZENG J, XIE J H, et al. Bifurcation\instability forms of high speed railway vehicles[J]. Science China Technological Sciences, 2013, 56(7): 1685-1696. doi: 10.1007/s11431-013-5254-x
    [15] 苏红建. 基于车路耦合磁悬浮列车非线性振动控制研究[D]. 淄博:山东理工大学,2022.
    [16] XU J Q, CHEN C, GAO D G, et al. Nonlinear dynamic analysis on maglev train system with flexible guideway and double time-delay feedback control[J]. Journal of Vibroengineering, 2017, 19(8): 6346-6362. doi: 10.21595/jve.2017.18970
    [17] 陈晓昊,马卫华. 控制器时滞对磁浮系统稳定性影响分析[J]. 机车电传动,2019(2): 139-143,147.

    CHEN Xiaohao, MA Weihua. Analysis on the effect of controller time delay on the stability of maglev system[J]. Electric Drive for Locomotives, 2019(2): 139-143,147.
    [18] LI J H, LI J, ZHOU D F, et al. Self-excited vibration problems of maglev vehicle-bridge interaction system[J]. Journal of Central South University, 2014, 21(11): 4184-4192. doi: 10.1007/s11771-014-2414-5
    [19] 王洪坡,李杰. 一类非自治位置时滞反馈控制系统的亚谐共振响应[J]. 物理学报,2007,56(5): 2504-2516. doi: 10.7498/aps.56.2504

    WANG Hongpo, LI Jie. Sub-harmonic resonances of the non-autonomous system with delayed position feedback control[J]. Acta Physica Sinica, 2007, 56(5): 2504-2516. doi: 10.7498/aps.56.2504
    [20] WANG H P, LI J, ZHANG K. Stability and Hopf bifurcation of the maglev system with delayed speed feedback control[J]. Acta Automatica Sinica, 2007, 33(8): 829-834. doi: 10.1360/aas-007-0829
    [21] WANG H P, LI J, ZHANG K. Non-resonant response, bifurcation and oscillation suppression of a non-autonomous system with delayed position feedback control[J]. Nonlinear Dynamics, 2008, 51(3): 447-464.
    [22] WANG H P, LI J, ZHANG K. Sup-resonant response of a nonautonomous maglev system with delayed acceleration feedback control[J]. IEEE Transactions on Magnetics, 2008, 44(10): 2338-2350.
    [23] 吴晗,曾晓辉,史禾慕. 考虑间隙反馈控制时滞的磁浮车辆稳定性研究[J]. 力学学报,2019,51(2): 550-557.

    WU Han, ZENG Xiaohui, SHI Hemu. Stability analysis of maglev vehicle with delayed position feedback control[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(2): 550-557.
    [24] 沈飞,武建军. 时滞反馈磁浮控制系统的周期运动稳定性分析[J]. 兰州大学学报(自然科学版),2008,44(5): 131-136.

    SHEN Fei, WU Jianjun. Stability analysis of periodic motion of the maglev system with delayed velocity feedback control[J]. Journal of Lanzhou University (Natural Sciences), 2008, 44(5): 131-136.
    [25] SUN Y G, XU J Q, CHEN C, et al. Reinforcement learning-based optimal tracking control for levitation system of maglev vehicle with input time delay[J]. IEEE Transactions on Instrumentation Measurement, 2022, 71(8): 3142059.1-3142059.13.
    [26] ZHANG L L, HUANG L H, ZHANG Z Z. Hopf bifurcation of the maglev time-delay feedback system via pseudo-oscillator analysis[J]. Mathematical and Computer Modelling, 2010, 52(5/6): 667-673.
    [27] CUI X K, LI H L, ZHANG L, et al. Complete synchronization for discrete-time fractional-order coupled neural networks with time delays[J]. Chaos, Solitons & Fractals, 2023, 174:113772.1-113772.8.
    [28] FENG Y H, HU L J. On the quasi-controllability of continuous-time dynamic fuzzy control systems[J]. Chaos, Solitons & Fractals, 2006, 30(1): 177-188.
    [29] DE OLIVEIRA EVALD P J D, HOLLWEG G V, TAMBARA R V, et al. Lyapunov stability analysis of a robust model reference adaptive PI controller for systems with matched and unmatched dynamics[J]. Journal of the Franklin Institute, 2022, 359(13): 6659-6689. doi: 10.1016/j.jfranklin.2022.07.014
    [30] SOLGI Y, FATEHI A, NIKOOFARD A, et al. Design of optimal PID controller for multivariable time-varying delay discrete-time systems using non-monotonic Lyapunov-Krasovskii approach[J]. Journal of the Franklin Institute, 2021, 358(13): 6634-6665. doi: 10.1016/j.jfranklin.2021.06.026
    [31] BORASE R P, MAGHADE D K, SONDKAR S Y, et al. A review of PID control, tuning methods and applications[J]. International Journal of Dynamics and Control, 2021, 9(2): 818-827. doi: 10.1007/s40435-020-00665-4
    [32] 陈志贤,李忠继,杨吉忠,等. 常导高速电磁悬浮车辆二系悬挂结构对比优化[J]. 机械工程学报,2022,58(10): 160-168,179. doi: 10.3901/JME.2022.10.160

    CHEN Zhixian, LI Zhongji, YANG Jizhong, et al. Comparison and optimization of secondary suspension structure of high speed EMS vehicle[J]. Journal of Mechanical Engineering, 2022, 58(10): 160-168,179. doi: 10.3901/JME.2022.10.160
    [33] WU H, ZENG X H, GAO D G, et al. Dynamic stability of an electromagnetic suspension maglev vehicle under steady aerodynamic load[J]. Applied Mathematical Modelling, 2021, 97: 483-500. doi: 10.1016/j.apm.2021.04.008
    [34] 黎松奇,张昆仑,陈殷,等. 弹性轨道上磁浮车辆动力稳定性判断方法[J]. 交通运输工程学报,2015,15(1): 43-49.

    LI Songqi, ZHANG Kunlun, CHEN Yin, et al. Judgment method of maglev vehicle dynamic stability on flexible track[J]. Journal of Traffic and Transportation Engineering, 2015, 15(1): 43-49.
    [35] 吴晗,曾晓辉. 气动升力下磁浮车辆非线性响应研究[J]. 机械工程学报,2021,57(14): 223-231. doi: 10.3901/JME.2021.14.223

    WU Han, ZENG Xiaohui. Nonlinear dynamics of maglev vehicle under aerodynamic lift[J]. Journal of Mechanical Engineering, 2021, 57(14): 223-231. doi: 10.3901/JME.2021.14.223
    [36] 张继业,杨翊仁,曾京. Hopf分岔的代数判据及其在车辆动力学中的应用[J]. 力学学报,2000,32(5): 596-605.

    ZHANG Jiye, YANG Yiren, ZENG Jing. An algorithm crterion for Hopf bifurcation and its applications in vehicle dynamics[J]. Acta Mechanica Sinica, 2000, 32(5): 596-605.
    [37] CHEN X H, MA W H, LUO S H. Study on stability and bifurcation of electromagnet-track beam coupling system for EMS maglev vehicle[J]. Nonlinear Dynamics, 2020, 101(4): 2181-2193. doi: 10.1007/s11071-020-05917-8
    [38] 张玲玲. 磁浮列车悬浮系统的Hopf分岔及滑模控制研究[D]. 长沙:湖南大学,2010.
    [39] 梁鑫. 磁浮列车车轨耦合振动分析及试验研究[D]. 成都:西南交通大学,2015.
  • 加载中
图(14)
计量
  • 文章访问数:  40
  • HTML全文浏览量:  18
  • PDF下载量:  9
  • 被引次数: 0
出版历程
  • 收稿日期:  2023-06-11
  • 录用日期:  2024-04-15
  • 修回日期:  2023-09-12
  • 网络出版日期:  2024-04-29

目录

    /

    返回文章
    返回