In order to track the speed profile, a case study using a linear quadratic regulator (LQR) is addressed in this paper. A time-invariant nonlinear train motion model is constructed. To apply LQR, the quadratic term of the aerodynamic drag and the rolling mechanical resistance is linearized. Gradient resistance, curve resistance, and other environmental disturbance are not considered in this paper. An LQR algorithm with constraints is proposed to track a given reference speed profile. Maximum error and cumulative error are used in the evaluation of the tracking performance. The tracking results in plots, parameters tuning, and performance analysis are shown. The results show that the proposed LQR algorithm is able to track the given 1200 seconds speed profile, the cumulative error can be controlled within 4.7478m/s, and the maximum absolute error is 0.90839m/s. The output of the control variable u is also given.

This paper presents a train robust control method to optimize train operation based on the concept virtual coupling on train platoon. This approach is inspired by the recent development of platoon control for autonomous vehicles, and it is hoped that this platoon control can be applied to railway transportation. We use a decentralized model predictive control (MPC) to control leading train and followers together. To solve the complexity minimax objective function, we reformulated objective function as a minimization problem subject to linear matrix inequalities (LMIs). We defined four weight parameters to evaluate the model. Simulation result indicated that based on the premise of platoon stability, increase the performance parameters to obtain an optimal solution. We show that after the virtual coupling of less than two minutes, the gap distance between two consecutive trains is reduced and the capacity is increased while ensuring safey.