Robust adaptive anti-saturation control of virtually coupled train sets under communication delay

In virtually coupled multi-train systems, maintaining a stable and safe distance between adjacent trains is essential. However, input saturation and communication delays may adversely impact the operation of the coupled train system, making it challenging to ensure safe distances. To address these issues, an anti-saturation control algorithm is proposed to ensure the safe operation of the multi-train system under these adverse conditions. First, based on the dynamic model of multiple high-speed trains, a dynamic smoothing hyperbolic tangent saturation function was developed, with saturation limits varying according to train speed. Subsequently, a dynamic smoothing anti-saturation compensator was designed. Second, to account for communication delays between trains, a delay state prediction algorithm was established. Third, an adaptive sliding mode controller was formulated to address uncertainties in the system’s internal parameters. The anti-saturation compensator was then incorporated into the controller, resulting in the design of a delay-timeliness-eliminating anti-saturation robust controller. Using Lyapunov stability theory, this algorithm was proven to effectively mitigate the impact of input saturation and communication delays, ensuring the stable operation of the train system and maintaining safe distances between adjacent trains. Finally, the superiority of the proposed algorithm was validated through comparative simulations and experiments.