Periodic adaptive learning operation control method for maglev trains using multi-harmonic estimation
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摘要:
为提高磁浮列车的运行控制位置及速度跟踪精度，针对磁浮列车在固定线路上周期性运行的特点，提出了一种基于多谐波阻力估计的模型参考周期自适应学习控制（MH-MRAC-PALC）方法。所设计的复合控制器由反馈控制、前馈控制和多谐波阻力估计补偿器3部分组成，并基于Lyapunov稳定性理论设计了估计补偿器参数更新率；MH-MRAC-PALC控制器通过融合当前周期实时数据与历史周期运行信息，实现对运行阻力的在线估计与动态补偿；基于磁悬浮试验线进行数值仿真，并将所设计控制器与常规比例-积分-微分（PID）控制器和MH-MRAC控制器进行对比分析。仿真结果表明：经过20个周期的学习，MH-MRAC-PALC控制器的位置跟踪性能显著提升，其均方根误差从首周期的0.076 4 m降至0.006 9 m，最大误差从0.254 8 m降至0.027 4 m；速度跟踪均方根误差从0.035 6 m·s-1降至0.002 9 m·s-1，最大误差从0.104 7 m·s-1降至0.012 2 m·s-1；相比之下，PID控制器的位置和速度均方根误差分别为0.633 6 m和0.076 3 m·s-1，MH-MRAC控制器分别为0.085 3 m和0.040 1 m·s-1；且经过20个运行周期学习后，MH-MRAC-PALC控制器已能准确估计多谐波阻力；存在未知阻力和坡道扰动的复杂工况下，该控制器表现出更强的抗干扰能力和更高的跟踪精度。相比于传统PID控制和MRAC控制，MH-MRAC-PALC控制方法通过周期学习机制实现了阻力准确估计，降低了位置及速度跟踪误差，显著提升了磁浮列车的运行控制性能。
Abstract:A model reference periodic adaptive learning control method based on multi-harmonic resistance estimation (MH-MRAC-PALC) was proposed according to the periodic operation characteristics of maglev trains on fixed routes to improve the operation control position and speed tracking accuracy of maglev trains. The designed composite controller consists of three parts: feedback control, feedforward control, and the multi-harmonic resistance estimation compensator. Meanwhile, based on Lyapunov stability theory, the parameter update rate of the estimation compensator was designed. By integrating real-time data of the current cycle and historical cycle operation information, online estimation and dynamic compensation of the operating resistance were achieved with the MH-MRAC-PALC controller. Based on the maglev test line, numerical simulation was conducted, and comparative analysis between the designed controller, conventional PID controller and MH-MRAC controller was carried out. The simulation results show that after 20 cycles of learning, the position tracking performance of the MH-MRAC-PALC controller is significantly improved, its root mean square error (RMSE) is reduced from 0.076 4 m in the first cycle to 0.006 9 m, and the maximum error is reduced from 0.254 8 to 0.027 4 m. Additionally, the speed tracking RMSE is reduced from 0.035 6 m·s-1 to 0.002 9 m·s-1, and the maximum error is reduced from 0.104 7 to 0.012 2 m·s-1. In comparison, the position and speed RMSEs of the PID controller are 0.633 6 m and 0.076 3 m·s-1, respectively, and those of the MH-MRAC controller are 0.085 3 m and 0.040 1 m·s-1, respectively. After 20 operation cycles of learning, the MH-MRAC-PALC controller can accurately estimate the multi-harmonic resistance. In complex working conditions with unknown resistance and slope disturbance, the controller exhibits stronger anti-interference ability and higher tracking accuracy. Compared with traditional PID control and MRAC control, the MH-MRAC-PALC control method achieves accurate resistance estimation, reduces the position and speed tracking errors, and significantly improves the operation control performance of maglev trains through the periodic learning mechanism.
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图 6 随机干扰下的位置与速度跟踪误差曲线
Figure 6. Position and velocity tracking error curves under random noise
表 1 磁悬浮列车试验线路数据
Table 1. Experimental track data of maglev trains
里程区间/m 坡度/‰ 0~15 450 0.0 15 450~20 450 -33.0 20 450~30 450 120.0 30 450~34 450 -1.2 34 450~50 000 0.0 
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表 2 仿真参数
Table 2. Simulation parameters
动力学参数 $ m\mathrm{、}{k}_{\mathrm{N}}\mathrm{、}{K}_{\mathrm{f}} $ 307 000、6、1 C1控制器 $ {k}_{\mathrm{p}}\mathrm{、}{k}_{\mathrm{i}}\mathrm{、}{k}_{\mathrm{d}} $ 7、0.01、0.01 C2/C3控制器 $ {k}_{1}\mathrm{、}{k}_{2} $ 7、0.01 MRAC学习系数 $ {\gamma }_{0}\mathrm{、}{\gamma }_{1}\mathrm{、}{\gamma }_{2} $ 90、0.1、0.1 PALC学习系数 $ {\eta }_{0}\mathrm{、}{\eta }_{1}\mathrm{、}{\eta }_{2} $ 0.005、78 534、78 534
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表 3 控制系统性能指标定量对比
Table 3. Quantitative comparison of control system performance indicators
控制器 运行阶段 $ {e}_{\mathrm{x}} $（t）的RMSE/m $ {e}_{\mathrm{x}} $（t）的MAE/m $ {e}_{\mathrm{v}} $（t）的RMSE/（m·s-1） $ {e}_{\mathrm{v}} $（t）的MAE/（m·s-1） C1 1~20周期 0.633 6 1.149 2 0.076 3 0.456 7 C1（噪声工况） 1~20周期 0.647 5 1.301 3 0.356 0 1.206 2 C2 1~20周期 0.085 3 0.253 0 0.040 1 0.249 1 C3 第1周期 0.076 4 0.254 8 0.035 6 0.104 7 第20周期 0.006 9 0.027 4 0.002 9 0.012 2 C3（噪声工况） 第1周期 0.211 1 0.602 6 0.102 5 0.272 3 第20周期 0.052 5 0.176 8 0.026 9 0.096 4
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[1] KIM J, HA C W, KING G B, et al. Experimental development of levitation control for a high-accuracy magnetic levitation transport system[J]. ISA Transactions, 2020, 101: 358-365. doi: 10.1016/j.isatra.2020.01.026 [2] 熊嘉阳, 沈志云, 池茂儒, 等. 高速磁悬浮列车技术综述[J]. 交通运输工程学报, 2025, 25(2): 1-23. doi: 10.19818/j.cnki.1671-1637.2025.02.001 XIONG Jia-yang, SHEN Zhi-yun, CHI Mao-ru, et al. Review on high-speed maglev train technology[J]. Journal of Traffic and Transportation Engineering, 2025, 25(2): 1-23. doi: 10.19818/j.cnki.1671-1637.2025.02.001 [3] FANG X C, LIN S, WANG X F, et al. Model predictive current control of traction permanent magnet synchronous motors in six-step operation for railway application[J]. IEEE Transactions on Industrial Electronics, 2022, 69(9): 8751-8759. doi: 10.1109/TIE.2021.3114695 [4] ZHONG Z Y, WU W, MA G T, et al. Study of the demagnetization behavior of no-insulation persistent-current mode HTS coils under external AC fields by 3D FEM simulation[J]. Superconductor Science and Technology, 2024, 37(4): 045011. doi: 10.1088/1361-6668/ad2300 [5] OPPENEIGER B, LANZA L, SCHELL M, et al. Model predictive control of a magnetic levitation system with prescribed output tracking performance[J]. Control Engineering Practice, 2024, 151: 106018. doi: 10.1016/j.conengprac.2024.106018 [6] ZHANG J B, XING L, ZHANG D, et al. Modeling and simulation for electromagnetic emission of maglev train[C]//IEEE. 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC). New York: IEEE, 2019: 1. [7] LI Y G, HU Y S. Comparative study on harmonic current suppression of dual three-phase PMSM based on LMS adaptive linear neuron and resonant controller[C]//IEEE. 2023 26th International Conference on Electrical Machines and Systems (ICEMS). New York: IEEE, 2023: 2755-2760. [8] ZHANG L, GAO Y, LIN T T, et al. Comparative analysis of crosswind influence on aerodynamic characteristics of superconducting and normal-conducting high-speed maglev trains[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2025, 265: 106182. doi: 10.1016/j.jweia.2025.106182 [9] 马卫华, 罗世辉, 张敏, 等. 中低速磁浮车辆研究综述[J]. 交通运输工程学报, 2021, 21(1): 199-216. doi: 10.19818/j.cnki.1671-1637.2021.01.009 MA Wei-hua, LUO Shi-hui, ZHANG Min, et al. Research review on medium and low speed maglev vehicle[J]. Journal of Traffic and Transportation Engineering, 2021, 21(1): 199-216. doi: 10.19818/j.cnki.1671-1637.2021.01.009 [10] 姚拴宝, 柳宁, 杜俊涛, 等. 高速磁悬浮列车底部结构对气动升力的影响规律研究[J]. 铁道学报, 2025, 47(7): 9-17.YAO Shuan-bao, LIU Ning, DU Jun-tao, et al. Research on influence of bottom structure of high-speed maglev trains on aerodynamic lift force[J]. Journal of the China Railway Society, 2025, 47(7): 9-17. [11] 熊嘉阳, 邓自刚. 高速磁悬浮轨道交通研究进展[J]. 交通运输工程学报, 2021, 21(1): 177-198. doi: 10.19818/j.cnki.1671-1637.2021.01.008XIONG Jia-yang, DENG Zi-gang. Research progress of high-speed maglev rail transit[J]. Journal of Traffic and Transportation Engineering, 2021, 21(1): 177-198. doi: 10.19818/j.cnki.1671-1637.2021.01.008 [12] CHEN C, XU J Q, JI W, et al. Sliding mode robust adaptive control of maglev vehicle's nonlinear suspension system based on flexible track: Design and experiment[J]. IEEE Access, 2019, 7: 41874-41884. doi: 10.1109/ACCESS.2019.2906245 [13] KANG J S, HUANG X Y, XIA C, et al. Ultralocal model-free adaptive supertwisting nonsingular terminal sliding mode control for magnetic levitation system[J]. IEEE Transactions on Industrial Electronics, 2024, 71(5): 5187-5194. doi: 10.1109/TIE.2023.3285925 [14] ROY S B, BHASIN S, KAR I N. Combined MRAC for unknown MIMO LTI systems with parameter convergence [J]. IEEE Transactions on Automatic Control, 2018, 63(1): 283-290. doi: 10.1109/TAC.2017.2725955 [15] WANG H R, SCURLOCK B, POWELL N, et al. MRAC with adaptive uncertainty bounds via operator-valued reproducing kernels[J]. IEEE Control Systems Letters, 2023, 7: 3771-3776. doi: 10.1109/LCSYS.2023.3340241 [16] HAN L, WEN X H, CHEN G L. New general MRAS adaptive scheme to estimate stator and rotor resistance of induction motors[C]//IEEE. Conference Record of the 2006 IEEE Industry Applications Conference. New York: IEEE, 2006: 1775-1780. [17] LI Z, JIN S T, WEI Y Z, et al. A data-driven control algorithm with time delay compensation based on optimized recursive adaptive identification for magnetic levitation systems[J]. IEEE Transactions on Automation Science and Engineering, 2025, 22: 12922-12936. doi: 10.1109/TASE.2025.3543411 [18] XU J Q, SUN Y G, GAO D G, et al. Dynamic modeling and adaptive sliding mode control for a maglev train system based on a magnetic flux observer[J]. IEEE Access, 2018, 6: 31571-31579. doi: 10.1109/ACCESS.2018.2836348 [19] 刘诗雨. 基于引力粒子群算法的高速列车优化控制研究[D]. 南昌: 华东交通大学, 2023: 3.LIU Shi-yu. Research on optimal control of high-speed train based on gravity particle swarm optimization algorithm[D]. Nanchang: East China Jiaotong University, 2023: 3. [20] ZHAO X Y, WANG L M. Bounded control of PMLSM servo system based on fractional order barrier function adaptive super-twisting approach[J]. Control Engineering Practice, 2025, 154: 106131. doi: 10.1016/j.conengprac.2024.106131 [21] 汪斌, 王伟旭, 孙体佳, 等. 磁悬浮列车磁浮力的计算与分析[J]. 铁道学报, 2023, 45(11): 61-69.WANG Bin, WANG Wei-xu, SUN Ti-jia, et al. Calculation and analysis of magnetic suspension force of maglev trains [J]. Journal of the China Railway Society, 2023, 45(11): 61-69. [22] 边旭, 边宏远, 梁艳萍. 基于磁网络法的外转子永磁同步电机的磁场分析[J]. 电机与控制学报, 2025, 29(2): 96-104, 115.BIAN Xu, BIAN Hong-yuan, LIANG Yan-ping. Magnetic field analysis of external rotor permanent magnet synchronous motor based on magnetic circuit network[J]. Electric Machines and Control, 2025, 29(2): 96-104, 115. [23] 于青松. 中低速磁浮列车牵引性能研究[J]. 城市轨道交通研究, 2022, 25(2): 74-76, 81.YU Qing-song. Study on traction performance of medium-low speed maglev vehicles[J]. Urban Mass Transit, 2022, 25(2): 74-76, 81. [24] GUO X, YIN Z G, ZHANG Y Q, et al. Position sensorless control of PMLSM based on adaptive complex coefficient sliding mode observer[J]. Energy Reports, 2022, 8: 687-695. [25] RAGHUNATHAN R S, KIM H D, SETOGUCHI T. Aerodynamics of high-speed railway train[J]. Progress in Aerospace Sciences, 2002, 38(6/7): 469-514. -
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