A distributed multi-axle tracking control method for SRT based on softened terminal constraint MPC and PID

The four-module and six-axle Super Rail-guided Train (SRT) features an ultra-long body, a multi-articulated structure, and all-wheel active steering. However, in complex urban environments, it suffers from tail error amplification, poor tracking performance on small-radius curves, and strong inter-axle coupling effects. To address these challenges, this paper proposes a multi-axle coordinated tracking control method that integrates model predictive control (MPC) with softened terminal constraints and distributed preview PID control. First, a five-degree-of-freedom lateral dynamic model of the four-module and six-axle SRT is established based on the “placeholder method” and the Newton–Euler principle. On this basis, the Dynamic Relative Gain Array (DRGA) method is introduced to perform a quantitative analysis of the key coupling characteristics in the multi-input multi-output steering system, based on which a feedforward cooperative steering controller is designed to reduce inter-axle coupling effects. Second, an MPC controller with softened terminal constraints is developed for the leading unit, which enables tractor-level global optimization of the vehicle’s longitudinal and lateral positions as well as yaw motion, while improving the feasibility of the optimization problem under extreme curvature conditions. Furthermore, a distributed preview PID controller is constructed based on a time preview model, which enables independent path tracking of each rear axle and ensures fast convergence of tracking error. Finally, three typical simulation scenarios are established in the Matlab/Simulink environment, and the tracking performance and dynamic response characteristics of the proposed method are systematically evaluated under different vehicle speeds. The results demonstrate that, compared with the full-axle PID control strategy and the conventional hierarchical MPC strategy, the proposed method achieves superior tracking accuracy and control smoothness under various operating conditions, while maintaining the maximum lateral deviation within 0.16 m.