Disturbance Observer-Based Terminal Sliding Mode Control Approach for Virtual Coupling Train Set

To enhance line capacity in high-speed railways without new infrastructure, virtual coupling train sets (VCTSs) enable reduced inter-train distances via real-time communication and cooperative control. However, unknown disturbances and model uncertainties challenge VCTS performance, often causing chattering, slow convergence, and poor disturbance rejection. This paper proposes a novel finite-time extended state observer-based nonsingular terminal sliding mode (FTESO-NTSM) control strategy. The method integrates a nonsingular terminal sliding mode surface with a hyperbolic tangent-based reaching law to ensure fast convergence and chattering suppression, while a finite-time extended state observer estimates and compensates for lumped disturbances in real time. Lyapunov analysis rigorously proves finite-time stability. Numerical simulations under different initial statuses are conducted to validate the effectiveness of the proposed method. The results show that the maximum observation error achieves 0.0087 kN. The speed chattering magnitudes reach 0.00087 km/h, 0.0017 km/h, 0.0026 km/h, and 0.0034 km/h for the leading train and three followers, respectively. Furthermore, the convergence time of the followers is 56 s, 130 s, and 76 s, respectively. The results highlight that the proposed method can significantly improve line capacity and transportation efficiency.