Cooperative control of virtually coupled trains: a fixed-time anti-windup sliding mode control method

Abstract This paper proposes a fixed-time sliding mode control method based on a sliding-mode disturbance observer to address disturbance uncertainties, speed limits, and actuator saturation in virtually coupled train sets (VCTSs). First, a dynamic model of the VCTS is established, lumping basic, additional, and external time-varying resistances into a total disturbance. A sliding-mode disturbance observer with fixed-time convergence is then designed for real-time estimation and compensation of this total disturbance. Speed and actuator constraints are converted into unit-mass control input saturation limits, while an anti-windup compensator dynamically eliminates saturation errors. Furthermore, a fixed-time anti-windup non-singular fast terminal sliding-mode controller is developed, integrating a non-singular fast terminal sliding surface with a double-power reaching law. Lyapunov stability theory rigorously proves the system’s fixed-time convergence. Simulations using Type-A train parameters and Beijing Subway Line 19 data show that, compared with the best baseline method, the proposed method reduces the mean absolute errors in displacement and velocity by 97.90% and 88.70%, respectively, while reducing the root-mean-square variation rate of the control input by 3.8% and the average steady-state chattering index by 89.98%. Ultimately, this approach successfully balances tracking accuracy, disturbance rejection, control-input smoothness, and chattering suppression under multiple constraints.