Research on control parameters of high-speed maglev train under stochastic track irregularities随机轨道不平顺下高速磁浮列车的控制参数研究
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Wang WX, Wang B, Deng G, Ma LF, 2024. Research on control parameters of high-speed maglev train under stochastic track irregularities. Probabilistic Engineering Mechanics, 77: 103664.DOI: 10.1016/j.probengmech.2024.103664
磁悬浮列车在运行阶段会遇到轨道不平顺，由于其固有的随机特性，对控制系统的完整性提出了严峻的挑战，尤其在高速磁浮列车的背景下更为显著。本研究旨在全面考察轨道不平顺随机激励下的控制参数。通过利用虚拟激励方法建立严格的随机响应分析模型，本研究深入探讨了电磁悬浮型高速磁悬浮列车-刚性轨道系统的动力特性。基于磁悬浮列车响应的功率谱密度，提出了量化控制稳定性和运行稳定性的评价指标。随后，根据这些指标，提出了一组推荐的比例-微分控制参数范围，以满足评价指标的要求。研究表明，比例-微分控制参数的变化会对系统稳定性具有显著影响，主要是通过改变固有频率和阻尼比来体现。具体来说，控制稳定性与比例-微分控制参数的增加呈正相关，而运行稳定性则表现出复杂的关系—随比例系数增加，运行稳定性最初有所提升，但随微分系数增加，尽管逐渐趋缓，但仍表现出下降趋势。比例-微分控制参数的建议取值范围根据电磁系统的相关物理参数 (如质量、静态悬浮电流和静态悬浮间隙) 及 Sperling 指标和悬浮间隙变化等因素确定。关键词: 高速磁悬浮列车, 比例-微分控制参数, 随机作用, 虚拟激励法During operational phases, maglev trains encounter track irregularities, presenting a formidable challenge to the integrity of their control systems owing to the inherently stochastic nature, a challenge accentuated in the context of high-speed maglev trains. This study aims to comprehensively examine control parameters within the context of stochastic excitation resulting from track irregularities. Through the development of a rigorous stochastic response analysis model utilizing the pseudo excitation method, the investigation delves into the dynamics of an EMS-type high-speed maglev train-rigid track system. Evaluation indices, derived from the power spectral density of the maglev train's response, are established to quantify both control stability and operational stability. Subsequently, based on these indices, a recommended range of PD control parameters is proposed, accounting for the requirements stipulated by the evaluation metrics. The study elucidates that variation in PD control parameters exert discernible effects on the system's stability, primarily altering the nature frequency and damping ratio. Specifically, control stability demonstrates a positive correlation with increasing PD control parameters, while operational stability exhibits a nuanced relationship—initially bolstered by escalating proportional coefficients but subsequently tempered, albeit gradually, with heightened derivative coefficients. The delineated range of values for PD control parameters is meticulously determined, considering pertinent physical parameters of the electromagnetic system, such as mass, static suspension current, and static suspension gap, alongside factors like the Sperling indicator and suspension gap variation.
Keywords: High-speed maglev train; PD control parameters; Stochastic action; Pseudo excitation method.![]()
Fig. 1. Simplified model of a maglev train
Fig. 2. PD control principle
Fig. 3. Fundamental concept of PEM
Fig. 4. Magnitude of the suspension gap variation
图 5: 悬浮间隙变化功率谱密度与磁浮轨道不平顺功率谱密度的对比Fig. 5. Comparison of the suspension gap variation PSD and the maglev track irregularities PSD
图 6: 磁浮车体加速度功率谱密度与磁浮轨道不平顺二阶导数功率谱密度的对比Fig. 6. Comparison of the maglev vehicle body acceleration PSD and the maglev track irregularities second-order derivative PSD
Fig. 7. Stationarity index components at each frequency
Fig. 8. Effect of proportional coefficients on control stability
图 9: 比例系数对磁浮车体加速度功率谱密度的影响Fig. 9. Effect of proportional coefficients on the maglev vehicle body acceleration PSD
Fig. 10. Effect of proportional coefficients on operational stability
Fig. 11. Effect of derivative coefficients on control stability
图 12: 微分系数对磁浮车体加速度功率谱密度的影响Fig. 12. Effect of derivative coefficients on the maglev vehicle body acceleration PSD
Fig. 13. Effect of derivative coefficients on operational stability
图 14: 比例-微分控制参数对悬浮间隙变化标准差的影响Fig. 14. Effect of PD control parameters on the standard deviation of suspension gap variation
图 15: 比例-微分控制参数对 Sperling 指标的影响Fig. 15. Effect of PD control parameters on the sperling indicator
图 16: 比例-微分控制参数对磁浮车体加速度标准差的影响Fig. 16. Effect of PD control parameters on the standard deviation of maglev vehicle body acceleration
Fig. 17. Recommended range of values for PD control parameters
作者信息 | Authors
西南交通大学 (Southwest Jiaotong University) 桥梁工程系
汪斌 Bin Wang, 通讯作者 (Corresp.)西南交通大学 (Southwest Jiaotong University) 桥梁工程系Email: wangbinwvb@swjtu.edu.cn
西南交通大学 (Southwest Jiaotong University) 桥梁工程系
西南交通大学 (Southwest Jiaotong University) 桥梁工程系
律梦泽 M.Z. Lyu | 编辑 (Ed)
P.D. Spanos | 审校 (Rev)
陈建兵 J.B. Chen | 审校 (Rev)
彭勇波 Y.B. Peng | 审校 (Rev)
