Virtual coupling, which provides great advantages in operational flexibility and line capacity, is an advanced signaling concept for the railway industry. The dynamic disturbances caused by line conditions might change the coupled movements of the train convoy into abnormal states, which means the speed difference and separation distance of the adjacent trains exceed the given thresholds. This paper proposes a method to maintain the coupled states using terminal sliding mode control (SMC) based on second-order nonlinear train dynamics, with a nonlinear observer eliminating the estimation error due to time-varying measurement delay. The controller calculates the optimal unit effective tractive force for the following train in real-time, taking the leader velocity and desired separation as control targets. The simulation of a two-train convoy on a high-speed railway is conducted including different abnormal scenarios. The results demonstrate that the proposed method eliminates the observation errors and achieves synchronous convergence of the tracking errors while guaranteeing passenger comfort, and that it outperforms traditional SMC.

虚拟耦合在运营灵活性和线路容量方面具有很大优势，是铁路行业的先进信号概念。线路条件引起的动态扰动可能使列车车队的耦合运动进入异常状态，即相邻列车的速度差和间隔距离超过给定的阈值。本文提出了一种使用基于二阶非线性列车动力学的终端滑模控制（SMC）来保持耦合状态的方法，其中非线性观测器消除了由于时变测量延迟引起的估计误差。控制器以领头速度和期望间距为控制目标，实时计算后车最优单元有效牵引力。对高速铁路上的两列火车车队进行了模拟，包括不同的异常场景。结果表明，该方法在保证乘客舒适度的同时，消除了观测误差，实现了跟踪误差的同步收敛，优于传统的SMC。