Stability of vehicle platoon control system with three types of delays
Article Text (Baidu Translation)
-
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.
-
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
-
[1] LI S E, ZHENG Y, LI K Q, et al. Dynamical modeling and distributed control of connected and automated vehicles: challenges and opportunities[J]. IEEE Intelligent Transportation Systems Magazine, 2017, 9(3): 46-58. doi: 10.1109/MITS.2017.2709781 [2] 张毅, 姚丹亚, 李力, 等. 智能车路协同系统关键技术与应用[J]. 交通运输系统工程与信息, 2021, 21(5): 40-51. https://www.cnki.com.cn/Article/CJFDTOTAL-YSXT202105006.htmZHANG Yi, YAO Dan-ya, LI Li, et al. Technologies and applications for intelligent vehicle-infrastructure cooperation systems[J]. Journal of Transportation Systems Engineering and Information Technology, 2021, 21(5): 40-51. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSXT202105006.htm [3] LI Da-peng, LIU Yan-jun, TONG Shao-cheng, et al. Neural networks-based adaptive control for nonlinear state constrained systems with input delay[J]. IEEE Transactions on Cybernetics, 2019, 49(4): 1249-1258. doi: 10.1109/TCYB.2018.2799683 [4] DENG Chao, CHE Wei-wei, WU Zheng-guang. A dynamic periodic event-triggered approach to consensus of heterogeneous linear multiagent systems with time-varying communication delays[J]. IEEE Transactions on Cybernetics, 2021, 51(4): 1812-1821. doi: 10.1109/TCYB.2020.3015746 [5] HUANG Da-rong, LI Shao-qian, ZHANG Zhen-yuan, et al. Design and analysis of longitudinal controller for the platoon with time-varying delay[J]. IEEE Transactions on Intelligent Transportation Systems, 2022, 23(12): 23628-23639. doi: 10.1109/TITS.2022.3200026 [6] LIU An-quan, LI Tao, GU Yu, et al. Cooperative extended state observer based control of vehicle platoons with arbitrarily small time headway[J]. Automatica, 2021, 129: 109678. doi: 10.1016/j.automatica.2021.109678 [7] WANG Bing-ying, ZHENG Jun, REN Qi-lei, et al. Analysis of the intra-platoon message delivery delay in a platoon of vehicles[J]. IEEE Transactions on Vehicular Technology, 2021, 70(7): 7012-7026. doi: 10.1109/TVT.2021.3076157 [8] PLOEG J, SHUKLA D P, VAN DE WOUW N, et al. Controller synthesis for string stability of vehicle platoons[J]. IEEE Transactions on Intelligent Transportation Systems, 2014, 15(2): 854-865. doi: 10.1109/TITS.2013.2291493 [9] ZHENG Y, LI S E, WANG J Q, et al. Stability and scalability of homogeneous vehicular platoon: study on the influence of information flow topologies[J]. IEEE Transactions on Intelligent Transportation Systems, 2016, 17(1): 14-26. doi: 10.1109/TITS.2015.2402153 [10] 李旭光, 张颖伟, 冯琳. 时滞系统的完全稳定性研究综述[J]. 控制与决策, 2018, 33(7): 1153-1170. https://www.cnki.com.cn/Article/CJFDTOTAL-KZYC201807001.htmLI Xu-guang, ZHANG Ying-wei, FENG Lin. Survey on complete stability study for time-delay systems[J]. Control and Decision, 2018, 33(7): 1153-1170. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-KZYC201807001.htm [11] AKKAYA S, AKBATI O, ERGENC A F. Stability analysis of connected vehicles with V2V communication and time delays: CTCR method via Bézout's resultant[J]. Transactions of the Institute of Measurement and Control, 2021, 43(8): 1802-1829. doi: 10.1177/0142331220981426 [12] ABOLFAZLI E, BESSELINK B, CHARALAMBOUS T. On time headway selection in platoons under the MPF topology in the presence of communication delays[J]. IEEE Transactions on Intelligent Transportation Systems, 2022, 23(7): 8881-8894. doi: 10.1109/TITS.2021.3087484 [13] GAO Q B, OLGAC N. Stability analysis for LTI systems with multiple time delays using the bounds of its imaginary spectra[J]. Systems and Control Letters, 2017, 102: 112-118. doi: 10.1016/j.sysconle.2017.02.003 [14] GUO Ge, KANG Jian, LEI Hong-bo, et al. Finite-time stabilization of a collection of connected vehicles subject to communication interruptions[J]. IEEE Transactions on Intelligent Transportation Systems, 2022, 23(8): 10627-10635. doi: 10.1109/TITS.2021.3095147 [15] GAO Q B, OLGAC N. Bounds of imaginary spectra of LTI systems in the domain of two of the multiple time delays[J]. Automatica, 2016, 72: 235-241. doi: 10.1016/j.automatica.2016.05.011 [16] CHEN Jian-zhong, LIANG Huan, LI Jing, et al. Connected automated vehicle platoon control with input saturation and variable time headway strategy[J]. IEEE Transactions on Intelligent Transportation Systems, 2021, 22(8): 4929-4940. doi: 10.1109/TITS.2020.2983468 [17] 李永福, 何昌鹏, 朱浩, 等. 通信延时环境下异质网联车辆队列非线性纵向控制[J]. 自动化学报, 2021, 47(12): 2841-2856. https://www.cnki.com.cn/Article/CJFDTOTAL-MOTO202112011.htmLI Yong-fu, HE Chang-peng, ZHU Hao, et al. Nonlinear longitudinal control for heterogeneous connected vehicle platoon in the presence of communication delays[J]. Acta Automatica Sinica, 2021, 47(12): 2841-2856. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-MOTO202112011.htm [18] SHI Min, YU Ya-juan, XU Qi. Delay-dependent consensus condition for a class of fractional-order linear multi-agent systems with input time-delay[J]. International Journal of Systems Science, 2019, 50(4): 669-678. doi: 10.1080/00207721.2019.1567865 [19] SADEK B A, HOUSSAINE T E, NOREDDINE C. Small- gain theorem and finite-frequency analysis of TCP/AQM system with time varying delay[J]. IET Control Theory and Applications, 2019, 13(13): 1971-1982. doi: 10.1049/iet-cta.2018.6466 [20] CEPEDA-GOMEZ R, OLGAC N. Consensus analysis with large and multiple communication delays using spectral delay space concept[J]. International Journal of Control, 2011, 84(12): 1996-2007. doi: 10.1080/00207179.2011.631151 [21] 朱旭, 张泽华, 闫茂德. 含输入时延与通信时延的车辆队列PID控制系统稳定性[J]. 交通运输工程学报, 2022, 22(3): 184-198. doi: 10.19818/j.cnki.1671-1637.2022.03.015ZHU Xu, ZHANG Ze-hua, YAN Mao-de. Stability of PID control system for vehicle platoon with input delay and communication delay[J]. Journal of Traffic and Transportation Engineering, 2022, 22(3): 184-198. (in Chinese) doi: 10.19818/j.cnki.1671-1637.2022.03.015 [22] GONG Jian, CAO Jin-de, ZHAO Yuan, et al. Sampling- based cooperative adaptive cruise control subject to communication delays and actuator lags[J]. Mathematics and Computers in Simulation, 2020, 171: 13-25. doi: 10.1016/j.matcom.2019.10.012 [23] HU San-gen, WEN Hui-ying, XU Lun-hui, et al. Stability of platoon of adaptive cruise control vehicles with time delay[J]. Transportation Letters, 2019, 11(9): 506-515. doi: 10.1080/19427867.2017.1407488 [24] XING H T, PLOEG J, NIJMEIJER H. Padé approximation of delays in cooperative ACC based on string stability requirements[J]. IEEE Transactions on Intelligent Vehicles, 2016, 1(3): 277-286. doi: 10.1109/TIV.2017.2662482 [25] LIU Yong-gui, GAO Huan-li. Stability, scalability, speedability, and string stability of connected vehicle systems[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2022, 52(5): 2819-2832. doi: 10.1109/TSMC.2021.3054794 [26] CHEHARDOLI H, HOMAEINEZHAD M R, GHASEMI A. Control design and stability analysis of homogeneous traffic flow under time delay: a new spacing policy[J]. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 2019, 233(3): 622-635. doi: 10.1177/0954407017751789 [27] ALIKOC B, ERGENC A F. A polynomial method for stability analysis of LTI systems independent of delays[J]. SIAM Journal on Control and Optimization, 2017, 55(4): 2661-2683. doi: 10.1137/16M1077726 [28] ZHOU Bin, LIU Qing-song. Input delay compensation for neutral type time-delay systems[J]. Automatica, 2017, 78: 309-319. doi: 10.1016/j.automatica.2016.12.015 [29] GAIDHANE V H, HOTE Y V. An improved approach for stability analysis of discrete system[J]. Journal of Control, Automation and Electrical Systems, 2018, 29(5): 535-540. doi: 10.1007/s40313-018-0396-5 [30] CEPEDA-GOMEZ R, OLGAC N. Stability of formation control using a consensus protocol under directed communications with two time delays and delay scheduling[J]. International Journal of Systems Science, 2016, 47(2): 433-449. doi: 10.1080/00207721.2014.886745 [31] BIAN You-gang, ZHENG Yang, REN Wei, et al. Reducing time headway for platooning of connected vehicles via V2V communication[J]. Transportation Research Part C: Emerging Technologies, 2019, 102: 87-105. doi: 10.1016/j.trc.2019.03.002 -
下载:
点击查看大图
图(11) / 表(1)
计量
- 文章访问数: 589
- HTML全文浏览量: 87
- PDF下载量: 64
- 被引次数: 0
