The event-triggered intermittent control of the time-delay high-speed train in cruise movement

Purpose The purpose of this paper is to study the cruise performance and control cost of a delayed high-speed train (HST) under the restricted event-triggered intermittent control (REIC) with and without input delay, so as to put forward a rationale for reducing the control cost of HST cruise operation while ensuring speed tracking performance during the cruise phase of the HST system with parameter uncertainty and input state delay. Design/methodology/approach Considering the impact of various time delays on the operation of HST, and based on systems with state delays both with and without input delays, a REIC scheme is proposed for HST systems operating under state delays, with and without input delays. This strategy is controlled by state-related events, including the initiation and termination of control. It is worth noting that this method achieves a reduction in control costs while meeting lower control rates. In addition, it improves the conditions for starting and terminating control, breaking away from the previous methods of relying only on time or state-based starting control but based on time termination control. Then, the Lyapunov stability theorem is utilized to analyze that the proposed method can effectively ensure the stable cruising operation of HST. Meanwhile, the stable cruising operation curve and coupler displacement curve of HST are provided through numerical simulation. In addition, comparisons are made with intermittent cruise control based on time and event-triggered aperiodic intermittent control. Findings The simulation results of delayed HST cruising operation under the REIC scheme show that the proposed method can reduce the control rate while effectively ensuring stable cruising of HST. Specifically, in the case of only state delay, as the delay ratio increases, both the control rate and the number of control cycles decrease, that is, the number of control actions decreases from 44 without delay state to 37 under full state delay, and the control rate decreases from 28.84% to 16.22%. Furthermore, when the system has both state delay and control input delay, the performance under the proposed control method is consistent with the case where only state delay exists. The number of controls was reduced from 39 when the proportion of delayed state items was zero to 24 under full state delay, and the control rate decreased from 0.4469 to 0.2826, a nearly 20% reduction. In addition, compared with time-triggered periodic and apreiodic intermittent control (TIC) methods and the event-triggered aperiodic intermittent control (E-AIC) method, the REIC method reduces the control rate by 15% and the control cost by 5%. Originality/value The numerical simulation data obtained in this study can provide a theoretical evidence for designing control methods that reduce the control costs and energy consumption of HST cruise operations while ensuring stable train operation.