基于BFGS方法的列车速度预测控制研究

Research on predictive control of train speed based on BFGS method

列车速度控制是轨道交通发展领域的重要基础问题。面向真实列车速度控制应用场景的列车动力学模型及其控制器设计更具挑战性。一方面,传统基于反馈的无模型控制策略存在收敛速度慢、参数要求高、环境变化敏感等问题,目前难以从优化角度设计控制器且应对复杂系统的约束。另一方面,传统的列车单质点动力学模型很难解决高速列车运行过程中的非线性特性。针对上述瓶颈,首先对列车各节车厢进行受力分析,且考虑车厢间的安全距离,将相对位置和相对速度作为可变状态构建列车多质点模型。然后采用模型预测控制策略,综合考虑列车速度控制的非线性成本函数,处理列车运行过程中的复杂约束,预测控制系统的未来动态行为。然后,针对列车预测控制中的复杂动态约束非线性优化问题,设计对数障碍函数处理不等式约束,进而从拟牛顿法角度设计一种具有稳定收敛性的基于BFGS方法的列车速度预测控制算法,完成列车速度的精准跟踪控制。最后,以国内某线站间列车运行数据为例,与其他先进控制方法进行对比实验,以验证所提出的BFGS列车速度预测控制算法的优越性能。实验结果表明,本文所设计的基于BFGS方法的列车速度预测控制算法能够有效地减小列车速度跟踪误差和位移误差,提升列车速度跟踪精度,有利于保障列车的安全、准点、高效、平稳运行,为轨道交通列车速度控制技术发展提供新思路。

Train speed control is a crucial and fundamental problem in the development of rail transportation.Designing dynamic models and controllers for real-world train speed control applications is highly challenging.Traditional feedback-based model-free control strategies suffer from slow convergence,high parameter requirements,sensitivity to environmental changes,and difficulty in designing controllers from the optimization perspective,thus making it challenging to handle constraints in complex systems.On the other hand,traditional single-mass-point dynamic models of trains are inadequate in dealing with the nonlinear characteristics that arise from high-speed train operations.To address these challenges,a multi-mass-point model of the train was first constructed,which took into account the mechanical analysis of each carriage and the safe distance between them.In the proposed model,the relative position and relative velocity were considered as the variable states.Second,a model predictive control strategy was exploited to consider the nonlinear cost function of train speed control,handle complex constraints in train operations,and predict the future dynamic behavior of the control system.Third,for the nonlinear optimization problem in predictive train control with complex dynamic constraints,logarithmic barrier functions were used to handle inequality constraints.A BFGS-based predictive train speed algorithm with guaranteed stable convergence was developed from the perspective of quasi-Newton methods to achieve precise tracking control of train speed.Finally,a comparison experiment with other advanced control methods was conducted to verify the superior performance of the proposed BFGS-based predictive train speed algorithm by taking the train operation data between stations in China as an example.The experimental results show that the proposed BFGS-based predictive train speed algorithm designed in this paper can effectively reduce the train speed tracking error and displacement error,improve the tracking accuracy of train speed,and is conducive to ensuring the safety,punctuality,high efficiency,and stability of trains.The findings could provide a new idea for the development of rail transit train speed control technology.