Application of BP neural network tracking differentiator in maglev train suspension control
Article Text (Baidu Translation)
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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.
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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 
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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
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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
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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
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