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摘要: 针对含输入时延、跟随车之间的通信时延、领航车广播时延的车辆队列控制系统，研究了其内部稳定性和队列稳定性；在内部稳定性方面，提出了一种融合克罗内克和与特征根聚类(CTCR)法的方法，获得了系统内部稳定的充分必要条件；在队列稳定性方面，为了保证干扰沿车辆队列向后传播不扩散，给出了队列稳定的充分条件，揭示了队列稳定性独立于跟随车之间的通信时延；在此基础上，给出了可保证队列稳定的时延上界与车辆控制器增益设计范围。仿真结果表明：当满足所提稳定性条件时，车辆队列控制系统可同时保持内部稳定和队列稳定；所提内部稳定性方法求解的时延边界是完整、精确的，理论推导结果与仿真试验结果的误差小于0.1 s，且仿真时间比Bézout结式消元快2个数量级，比Sylvester结式消元快3个数量级，表明该方法大幅度降低了传统特征根聚类法的运算量；车间状态误差可在15 s内快速减小并趋近于0；在所有车辆恒速行驶时，车间保持50 m期望安全距离；在领航车以0.4 m·s-2加速和0.6 m·s-2减速过程中，跟随车的速度和加速度随领航车变化，车辆位置误差小于0.5 m，且沿车辆队列向后传播不扩散。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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图 2 子系统在时延谱域的核心超曲面
Figure 2. Kernal hypersurfaces of subsystems in delay-spectral domain
图 3 τ3=0.1 s时车辆队列各子系统的时延边界
Figure 3. Delay margins of subsystems of vehicle platoon at τ3=0.1 s
图 5 点a处车辆队列的位置误差和速度
Figure 5. Spacing errors and velocities of vehicle platoon at point a
图 6 点b处车辆队列的位置误差和速度
Figure 6. Spacing errors and velocities of vehicle platoon at point b
图 7 点c处车辆队列的位置误差和速度
Figure 7. Spacing errors and velocities of vehicle platoon at point c
图 8 试验1中车辆队列的状态与位置误差
Figure 8. States and spacing errors of vehicle platoon in experiment 1
图 10 试验2中车辆队列的状态与位置误差
Figure 10. States and spacing errors of vehicle platoon in experiment 2
图 11 试验3中车辆队列的状态与位置误差
Figure 11. States and spacing errors of vehicle platoon in experiment 3
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