Volume 24 Issue 2
Apr.  2024
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ZHU Xu, SUN Zhuo, ZHANG Ze-hua, YAN Mao-de. Stability of vehicle platoon control system with three types of delays[J]. Journal of Traffic and Transportation Engineering, 2024, 24(2): 254-266. doi: 10.19818/j.cnki.1671-1637.2024.02.018
Citation: ZHU Xu, SUN Zhuo, ZHANG Ze-hua, YAN Mao-de. Stability of vehicle platoon control system with three types of delays[J]. Journal of Traffic and Transportation Engineering, 2024, 24(2): 254-266. doi: 10.19818/j.cnki.1671-1637.2024.02.018
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Stability of vehicle platoon control system with three types of delays

doi: 10.19818/j.cnki.1671-1637.2024.02.018

  • School of Electronics and Control Engineering, Chang'an University, Xi'an 710064, Shaanxi, China

Funds:

National Key Research and Development Program of China 2021YFA1000303

National Natural Science Foundation of China 62003054

Key Research and Development Program of Shaanxi Province 2023-YBGY-398

More Information
  • Author Bio:

    ZHU Xu(1987-), male, associate professor, PhD, zx@gfscw.cn

  • Received Date: 2023-10-23
  • Publish Date: 2024-04-30
    Abstract
  • The internal stability and string stability of the vehicle platoon control system incorporating input delay, vehicle to vehicle communication delay, and broadcast delay of the lead vehicle were studied. In terms of internal stability, a method combining the Kronecker sum and cluster treatment of characteristic root (CTCR) method was proposed, in which the necessary and sufficient conditions for the internal stability of the system were obtained. In terms of string stability, the sufficient conditions were proposed to ensure that the disturbances propagated backward along the vehicle platoon without divergence. It was revealed that the string stability was independent of the vehicle to vehicle communication delay. On this basis, the upper bound of the delays and design range of the vehicle controller gains were provided to guarantee string stability. Simulation results show that the vehicle platoon control system can maintain both the internal stability and string stability simultaneously when the proposed stability conditions are satisfied. The delay margins obtained by the proposed internal stability method are both complete and exact, with the error between theoretically derived results and simulation experiment results being less than 0.1 s. In addition, the simulation time is two orders of magnitude shorter than the Bézout resultant elimination and three orders of magnitude shorter than the Sylvester resultant elimination. This indicates that the proposed method significantly reduces the computational burden of the traditional CTCR method. The state errors between vehicles quickly converge to 0 within 15 s. When the velocities of all vehicles are constant, a desired safe distance of 50 m between the successive vehicles is maintained. When the leader vehicle accelerates at 0.4 m·s-2 and decelerates at 0.6 m·s-2, the velocities and accelerations of the following vehicles change accordingly, while the spacing errors between vehicles remain less than 0.5 m, and these errors propagate backward along the vehicle platoon without divergence.

     

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