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Differentiated coordinated control for heavy-haul combined trains under cyclic braking
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DOI：10.1080/00423114.2026.2679630.png)
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Abstract
En 中文
The operation of heavy-haul combined trains on long and steep downgrades poses significant safety challenges. Cyclic braking under such conditions may induce uneven distribution of longitudinal forces and generate large longitudinal impulses. For trains in a distributed-power configuration, differentiated coordination between the leader and follower locomotives can help mitigate these negative effects. This paper proposes a model predictive control (MPC) strategy to improve the longitudinal dynamic performance of heavy-haul combined trains during cyclic braking. In the controller design, the exceedance area of coupler forces above a prescribed threshold is adopted as the primary objective, with the peak and mean coupler-force indices incorporated into a comprehensive evaluation framework. Using an integrated train dynamics model that combines an explicit time-integration scheme with a multi-segment linear (MSL) draft-gear model, the MPC framework predicts future responses over a two-step horizon and performs receding-horizon optimisation to generate differentiated dynamic-braking commands for the leader and follower locomotives, with the objective of optimising longitudinal train dynamics. The proposed strategy is validated in Universal Mechanism (UM) and compared with a reference synchronous-control strategy, and the results show that the proposed method can improve the longitudinal dynamic performance during cyclic braking. Over the full cyclic-braking sequence, the optimised strategy achieves an 11.95% reduction in peak tensile coupler force, a 3.24% reduction in peak compressive coupler force, and a 25.97% reduction in the exceedance area of coupler forces above 600 KN. These results demonstrate the effectiveness of the proposed strategy in enhancing operational safety on long and steep downgrades.
Keywords:
Heavy-haul train
cyclic braking
differentiated coordinated control
model predictive control
receding-horizon optimisation
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