A Hierarchical MPC Approach for Arriving-Phase Operation of Virtually Coupled Train Set

Arriving phase is an essential part of the virtually coupled train set (VCTS) operation in metros and significantly influences efficiency. This paper proposes a synchronous and precise control problem in VCTS arriving-phase operation and designs a hierarchical control approach to solve this problem. First, the control problem of VCTS arriving-phase operation is mathematically modeled, capturing the uncertain disturbances and measurement errors in train dynamics and considering input and safety constraints. Then, a two-layer control framework is designed, with the upper layer for coordinated trajectory planning and the lower layer for offset-free tracking of each train (unit) in VCTS. Specifically, in the upper layer, all units in VCTS are coordinated in an optimization problem to generate the reference trajectories that increase the synchronicity of arrival; in the lower layer, to track the reference trajectory, we propose an offset-free model predictive control (MPC) approach, which is based on an observer to handle uncertain disturbances and measurement errors. The stability of the offset-free MPC approach is proved, such that all units in VCTS can arrive at the station synchronously and precisely. Finally, experimental results demonstrate the performance of the proposed hierarchical approach.