Distributed Cooperative Control of Virtually Coupled High-Speed Trains With Consideration of Ride Comfort

The high-speed trains (HSTs) play a pivotal role in transportation, and its level of comfort distinctly impacts the travel experience of passengers. In this work, a distributed tube-based model predictive control (TMPC) method is proposed to address the cooperative control of virtually coupled HSTs, which improves the ride comfort of passengers while enhancing the railway capacity. Firstly, a nonlinear MPC scheme based on the nominal dynamics model of the train is developed to address the cooperative operation among multiple HSTs with different initial states. Especially, the constraints related to the ride comfort, including the acceleration and acceleration change rate, are transformed into the input and input increment constraints of the MPC respectively. Besides, the constraints of velocity and tracking interval related to the train operation safety are also considered in the design of the MPC. The recursive feasibility and stability of the MPC are proved theoretically. Secondly, an auxiliary feedback control system (AFCS) is devised based on the actual dynamics model of the train to deal with the external disturbances while enhancing the train operation stability and ride comfort. Specifically, the AFCS consists of a discrete-time sliding mode control and a discrete-time disturbance observer, utilizing the optimal state sequences generated by the MPC as a reference for the feedback control. Additionally, the stability of the AFCS is strictly proved. Finally, the effectiveness of the proposed distributed TMPC is verified by simulation.