Application of BP neural network tracking differentiator in maglev train suspension control
Article Text (Baidu Translation)
-
摘要: 为提升磁浮列车悬浮运行的安全性和稳定性，以列车悬浮控制系统为研究对象，研究了基于BP神经网络(BP-NN)实时自适应调节跟踪微分器(TD)参数的问题；为避免TD算法中非线性复杂运算，以二阶最速时间系统和状态反步法构造具备线性特征的最速控制综合函数，提出了一种离散形式的最速跟踪微分器(FST-TD)，并对其进行严格的频域及收敛性分析；针对FST-TD应对不规则输入信号时参数调节不及时的问题，引入BP-NN自学习能力与自适应不确定系统的动态特性，提出基于BP-NN参数自适应调节的最速跟踪微分器(BP-FST-TD)算法，其中BP-NN通过反向传播算法在线更新权值实现参数自适应调节，FST-TD根据自适应参数对复杂、多工况下的输入信号实时的跟踪滤波；为验证算法的有效性和实用性，以磁浮列车悬浮控制系统中的含随机噪声间隙信号为研究对象，对BP-FST-TD的实时跟踪滤波能力进行了研究。研究结果表明：FST-TD具有较好的滤波与微分提取能力，收敛性分析表明其具有无颤振、无超调的特点，且算法表达式中不含复杂的非线性运算，形式相对简单；FST-TD在多种输入信号的跟踪过程中均能够保持良好的光滑度与相位品质；与传统的TD算法相比，BP-FST-TD在工况1、2的间隙信号平均绝对误差分别降低了32.6%、61.8%，时间乘绝对误差积分分别降低了51.8%、70.2%，证明了BP-FST-TD良好的跟踪滤波性能，能够有效抑制磁浮列车间隙传感器在不同运行工况下的随机噪声。可见，基于BP-FST-TD的悬浮控制系统能够有效控制列车稳定悬浮运行，研究结果为其他工程领域的跟踪微分器控制参数优化提供了新的思路和方法。Abstract: To improve the safety and stability of maglev train suspension operation, the train suspension control system was selected as the research object, the real-time adaptive adjustment of tracking differentiator (TD) parameters based on the BP neural network (BP-NN) was analyzed. To avoid nonlinear complex operations in the TD algorithm, a fastest control synthesis function with linear characteristics was constructed using the second-order fastest time system and the state backstepping method, and a discrete form of fastest TD (FST-TD) was proposed. Frequency domain and convergence analysis was rigorously conducted on the proposed algorithm. For the issue of delayed parameter adjustment when FST-TD encountered irregular input signals, the self-learning capability of BP-NN and the dynamic characteristics of the adaptive uncertain system were integrated to propose a FST-TD based on BP-NN (BP-FST-TD) algorithm. In this algorithm, BP-NN parameter adaptive adjustment was achieved through online updated weights by the backpropagation algorithm. FST-TD performed real-time tracking and filtering of complex, multi-condition input signals based on the adaptive parameters. To validate the algorithm's effectiveness and practicality, the real-time tracking and filtering performance of BP-FST-TD was examined using gap signals with random noise in the maglev train suspension control system. Research results show that FST-TD has decent filtering and differentiation capabilities. The convergence analysis reveals that it exhibits no oscillation or overshoot. Furthermore, this FST-TD structure, without complex nonlinear operation, is relatively straightforward in design. The FST-TD maintains ideal smoothness and phase integrity during the tracking of various input signals. Under working conditions 1 and 2, the BP-FST-TD reduces the mean absolute error (MAE) of the gap signals by 32.6% and 61.8% respectively compared to traditional TD algorithms. Besides, the integrals of time-weighted absolute error reduce by 51.8% and 70.2%, respectively. These findings substantiate the effective tracking and filtering performance of BP-FST-TD, and the algorithm effectively suppresses random noise from the gap sensors under various operational conditions of the maglev train. Thus, it can be concluded that the suspension control system based on BP-FST-TD effectively ensures the stable suspension operation of the train. The research results offer novel approaches and methods for TD control parameter optimization in other engineering domains.
-
图 2 FST-TD幅频与相频响应曲线
Figure 2. Amplitude-frequency and phase-frequency response curves of FST-TD
图 5 输入信号为cos(3k)+sin(2k)时的3种TD输出曲线
Figure 5. Output curves of three TDs when input signal is cos(3k)+sin(2k)
图 6 输入信号为awgn{sgn[cos(k)], 50}时的3种TD输出曲线
Figure 6. Output curves of three TDs when input signal is awgn{sgn[cos(k)], 50}
图 9 工况1下磁浮车悬浮间隙输出曲线
Figure 9. Suspension gap output curves of maglev train under working condition 1
图 10 工况2下磁浮车悬浮间隙输出曲线
Figure 10. Suspension gap output curves of maglev train under working condition 2
表 1 输入信号为cos(3k)+sin(2k)时的IAE与ISE对比
Table 1. Comparison of IAE and ISE when input signal is cos(3k)+sin(2k)
算法 FHAN-TD FST-TD BP-FST-TD IAE 0.056 0 0.050 2 0.021 9 ISE 0.031 9 0.027 2 0.010 4 
下载: 导出CSV
表 2 输入信号为awgn{sgn[cos(k)], 50}时的MAE对比
Table 2. Comparison of MAEs when input signal is awgn{sgn[cos(k)], 50}
算法 FHAN-TD FST-TD BP-FST-TD 跟踪滤波 0.012 5 0.009 1 0.006 5 微分估计 0.765 5 0.527 8 0.286 3
下载: 导出CSV
表 3 工况1下悬浮间隙的MAE和ITAE对比
Table 3. Comparison of MAE and ITAE for suspension gap under working condition 1
算法 FHAN-TD FST-TD BP-FST-TD MAE 0.004 6 0.004 0 0.003 1 ITAE 0.001 1 0.000 8 0.000 5
下载: 导出CSV
表 4 工况2下悬浮间隙的MAE和ITAE对比
Table 4. Comparison of MAE and ITAE for suspension gap under working condition 2
算法 FHAN-TD FST-TD BP-FST-TD MAE 0.011 0 0.006 9 0.004 2 ITAE 0.002 1 0.001 0 0.000 6
下载: 导出CSV
-
[1] BEAULOYE L, DEHEZ B, LIN Guo-bin. Permanent magnet electrodynamic suspensions applied to maglev transportation systems: a review[J]. IEEE Transactions on Transportation Electrification, 2023, 9(1): 748-758. [2] 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.1671-1637.2021.01.009MA Wei-hua, LUO Shi-hui, ZHANG Min, et al. Overview of research on medium and low speed maglev vehicles[J]. Journal of Transportation Engineering, 2021, 21(1): 199-216. doi: 10.19818/j.cnki.1671-1637.2021.01.009 [3] SUN You-gang, XU Jun-qi, LIN Guo-bin, et al. RBF neural network-based supervisor control for maglev vehicles on an elastic track with network time delay[J]. IEEE Transactions on Industrial Informatics, 2022, 18(1): 509-519. [4] CHEN Chen, XU Jun-qi, LIN Guo-bin, et al. Sliding mode bifurcation control based on acceleration feedback correction adaptive compensation for maglev train suspension system with time-varying disturbance[J]. IEEE Transactions on Transportation Electrification, 2022, 8(2): 2273-2287. [5] 张文进, 林志坚, 张睿杨, 等. 基于新型跟踪微分器的磁浮车悬浮控制算法研究[J]. 铁道科学与工程学报, 2023, 20(10): 3954-3964.ZHANG Wen-jin, LIN Zhi-jian, ZHANG Rui-yang, et al. Design and applications of the maglev train suspension control algorithm via the improved tracking differentiator[J]. Journal of Railway Science and Engineering, 2023, 20(10): 3954-3964. [6] 靖永志, 冯伟, 王森, 等. 磁浮车间隙传感器无线供电与信号同步传输方法[J]. 西南大学学报, 2023, 58(4): 965-974.JING Yong-zhi, FENG Wei, WANG Sen, et al. Simultaneous wireless power and data transmission method for maglev vehicle gap sensor[J]. Journal of Southwest Jiaotong University, 2023, 58(4): 965-974. [7] LBRIR S. Linear time-derivative trackers[J]. Automatica, 2004, 40(3): 397-405. doi: 10.1016/j.automatica.2003.09.020 [8] LIU Jian-xing, SHEN Xiao-ning, ABRAHAM M A, et al. Sliding mode control of grid-connected neutral-point-clamped converters via high-gain observer[J]. IEEE Transactions on Industrial Electronics, 2022, 69(4): 4010-4021. [9] WETZLINGER R M, REICHHARTINGER M, HORN M. Robust-exact-differentiator-inspired discrete-time differentiation[J]. IEEE Transactions on Automatic Control, 2022, 67(6): 3059-3066. [10] WANG Juan, ZHANG He-hong, XIAO Gao-xi, et al. A comparison study of tracking differentiator and robust exact differentiator[C]//IEEE. 2020 Chinese Automation Congress (CAC). New York: IEEE, 2020: 1359-1364. [11] GU Nan, WANG Dan, PENG Zhou-hua, et al. Observer-based finite-time control for distributed path maneuvering of underactuated unmanned surface vehicles with collision avoidance and connectivity preservation[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(8): 5105-5115. [12] 韩京清, 袁露林. 跟踪微分器的离散形式[J]. 系统科学与数学, 1999, 19(3): 268-273. doi: 10.3969/j.issn.1000-0577.1999.03.003HAN Jing-qing, YUAN Lu-lin. Discrete-time form of tracking differentiator[J]. Systems Science and Complexity, 1999, 19(3): 268-273. doi: 10.3969/j.issn.1000-0577.1999.03.003 [13] HAN Jing-qing. From PID to active disturbance rejection control[J]. IEEE Transactions on Industrial Electronics, 2009, 56(3): 900-906. doi: 10.1109/TIE.2008.2011621 [14] ZHANG He-hong, XIAO Gao-xi, YU Xing-huo, et al. On convergence performance of discrete-time optimal control based tracking differentiator[J]. IEEE Transactions on Industrial Electronics, 2021, 68(4): 3359-3369. [15] 张文跃, 佟来生, 王滢, 等. 跟踪微分器在磁浮列车悬浮间隙处理中的应用[J]. 城市轨道交通研究, 2021, 24(3): 26-29.ZHANG Wen-yue, TONG Lai-sheng, WANG Ying, et al. Application of tracking differentiator in maglev train suspension gap disposal[J]. Urban Mass Transit, 2021, 24(3): 26-29. [16] 谢云德, 李云钢, 龙志强, 等. 一种基于边界特征线且特征点可变的二阶非线性离散跟踪微分器及在测速定位系统中的应用[J]. 自动化学报, 2014, 40(5): 952-964.XIE Yun-de, LI Yun-gang, LONG Zhi-qiang, et al. Discrete second-order nonlinear tracking-differentiator based on boundary characteristic curves and variable characteristic points and its application to velocity and position detection system[J]. Acta Automatica Sinica, 2014, 40(5): 952-964. [17] ZHANG He-hong, XIE Yun-de, XIAO Gao-xi, et al. A simple discrete-time tracking differentiator and its application to speed and position detection system for a maglev train[J]. IEEE Transactions on Control Systems Technology, 2019, 27(4): 1728-1734. [18] 王辉, 钟晓波, 沈钢. 基于Kalman滤波的弹性轨道上的磁悬浮车辆控制方法[J]. 中南大学学报(自然科学版), 2014, 45(3): 965-972.WANG Hui, ZHONG Xiao-bo, SHEN Gang. Levitation control strategy for maglev on elastic track based on Kalman filter[J]. Journal of Central South University (Science and Technology), 2014, 45(3): 965-972. [19] HAO Jun, ZHANG Guo-shan, LIU Wan-quan, et al. Data-driven tracking control based on LM and PID neural network with relay feedback for discrete nonlinear systems[J]. IEEE Transactions on Industrial Electronics, 2021, 68(11): 11587-11597. [20] REN Qiao, ZHANG Jin-min, ZHOU He-chao, et al. Robust adaptive levitation control for medium and low-speed maglev with magnetic saturation and eddy current effect[J]. Journal of Vibration Engineering and Technologies, 2024, 12: 2835-2849. [21] SUN You-gang, XU Jun-qi, LIN Guo-bin, et al. RBF neural network-based supervisor control for maglev vehicles on an elastic track with network time delay[J]. IEEE Transactions on Industrial Informatics, 2022, 18(1): 509-519. [22] ZHANG Tie-lin, JIA Shun-cheng, CHENG Xiang, et al. Tuning convolutional spiking neural network with biologically plausible reward propagation[J]. IEEE Transactions on Neural Networks and Learning Systems, 2022, 33(12): 1621-7631. [23] 杨广慧, 杜立夫, 李辉, 等. 基于BP神经网络的飞行器参数辨识与自适应控制[J]. 航天控制, 2021, 39(5): 3-7.YANG Guang-hui, DU Li-fu, LI Hui, et al. Parameter identification and adaptive control of aircraft based on BP neural network[J]. Aerospace Control, 2021, 39(5): 3-7. [24] LIU Xiao-ning, KE Zhi-hao, CHEN Yin-ning, et al. The feasibility of designing a back propagation neural network to predict the levitation force of high-temperature superconducting magnetic levitation[J]. Superconductor Science and Technology, 2022, 35(4): 1-11. [25] WANG Shao-shuai, ZHU Huang-qiu, WU Meng-yao, et al. Active disturbance rejection decoupling control for three-degree-of-freedom six-pole active magnetic bearing based on BP neural network[J]. IEEE Transactions on Applied Superconductivity, 2020, 4(30): 1-5. -
点击查看大图
图(10) / 表(4)
计量
- 文章访问数: 30
- HTML全文浏览量: 34
- PDF下载量: 5
- 被引次数: 0
