Distributed model predictive tracking control for virtual track trains based on the generalized dynamic model

The dynamics model of multi-unit virtual track trains (VTT) is inherently complex, and existing control methods face challenges in simultaneously ensuring both high-precision trajectory tracking and vehicle stability. This paper proposes a generalized modeling method for the VTT of four-unit and six-axis, along with a distributed model predictive control (MPC) strategy approach. Initially, separate models for the wheel, center of mass, and hinge plate are developed. The “placeholder method” of wheels is applied to establish the dynamics model of single unit, and the six-degree-of-freedom dynamics model of VTT is derived using the hinge plate’s “placeholder method.” Next, an MPC tracking controller is designed by analyzing the error between the desired and real-time positions of the train, which enables the train to follow the target trajectory. Under the consideration of multiple constraints, the controller calculates the optimal wheel angle for the first axle of the first unit. Finally, the optimal wheel angle for the first axle is used as input to design the MPC stability controller, and the control objective of the optimization algorithm is to minimize the error between the expected centroid sideslip angles and angular velocity of hinge plate. Simulation results under both single-line and circular curve tracking conditions demonstrate that distributed MPC strategy is able to simultaneously maintain high-precision trajectory tracking and stability of VTT. Furthermore, the proposed modeling approach exhibits excellent scalability, effectively reducing the modeling complexity and significantly improving modeling efficiency.