Stability of PID control system for vehicle platoon with input delay and communication delay
-
摘要: 针对含输入时延与通信时延的车辆队列PID控制系统，分析了其内部稳定性和队列稳定性，研究了内部稳定的充要条件，求解了完整、精确的时延边界；在内部稳定性分析中，考虑输入时延与通信时延影响下车辆队列PID控制系统为中立型双时延系统的特点，结合Rekasius代换和劳斯表，提出了关于中立算子的系统强稳定充要条件；在此基础上，为了便于PID参数的快速选取，推导了一种形式更为简练的系统强稳定充分条件；在强稳定条件下，基于特征根聚类法求解了系统完整、精确的时延边界；针对具有奇数辆跟随车的车辆队列，推导了无关车辆队列规模的输入时延上界；在队列稳定性分析中，为了保证干扰和误差沿车辆队列向后传播不发散，分析了车间误差传递函数，给出了双时延影响下队列稳定的充分条件。仿真结果表明：在含输入时延与通信时延的分布式PID控制器作用下，车辆队列控制系统可同时保证内部稳定和队列稳定；车间状态误差可在15 s内快速减小并趋近于零；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0.5 m·s-2加速和0.8 m·s-2减速时，跟随车的速度和加速度随领航车变化，并在领航车速度稳定时一致；车辆队列在不同行驶工况下，由领航车加、减速引起的车间位置误差小于0.2 m，且沿车辆队列向后传播不发散。Abstract: The internal stability and string stability of the PID control system were analyzed for vehicle platoon with input delay and communication delay, the sufficient and necessary conditions of the internal stability were emphatically studied, and the exhaustive and exact time delay margins were derived. In the internal stability analysis, considering that the PID control system for vehicle platoon is a neutral time delay system with input delay and communication delay, the sufficient and necessary strong stability conditions were proposed by analyzing the stability of the neutral operator via Rekasius substitution and Routh table. In order to facilitate selecting the PID parameters, a sufficient condition with a more concise form was derived. Then, the clustering method of characteristic roots was applied to obtain the exhaustive and exact time delay margins. Considering the vehicle platoon with an odd number of following vehicles, the upper bound of the input delay, which was independent of the scale of the vehicle platoon, was derived. In order to ensure that the interference and error propagated backward along the vehicle platoon without divergence, the error transfer function among the vehicles was analyzed, and the sufficient condition of string stability under the influence of two delays was given. Simulation results show that the internal stability and string stability of vehicle platoon can be guaranteed simultaneously by the distributed PID controllers under communication delay and input delay. The state errors quickly converge to zero within 15 s. When the velocities of the vehicles are constant, an desired safe distance maintains 50 m between the successive vehicles. When the leader vehicle accelerates at 0.5 m·s-2 and decelerates at 0.8 m·s-2, the velocities and accelerations of the following vehicles asymptotically change with those of the leader and are consistent with the leader when the leader's velocity is constant. Under the different driving conditions, the spacing errors caused by the acceleration and deceleration of the leader are less than 0.2 m, and propagate backward along vehicle platoon without divergence. 1 tab, 11 figs, 36 refs.
-
图 4 试验2中车辆队列各个子系统的时延边界
Figure 4. Time delay margins of subsystems of vehicle platoon in Example 2
图 5 试验2中车辆队列的时延边界与时延谱域
Figure 5. Time delay margins and spectral domains of vehicle platoon in Example 2
图 6 试验2中点a处车辆队列的位置误差和速度
Figure 6. Spacing errors and velocities of vehicle platoon at point a in Example 2
图 7 试验2中点b处车辆队列的位置误差和速度
Figure 7. Spacing errors and velocities of vehicle platoon at point b in Example 2
图 8 试验2中点c处车辆队列的位置误差和速度
Figure 8. Spacing errors and velocities of vehicle platoon at point c in Example 2
图 9 试验3中车辆队列的状态与位置误差
Figure 9. States and spacing errors of vehicle platoon in Example 3
图 10 试验4中车辆队列的状态与位置误差
Figure 10. States and spacing errors of vehicle platoon in Example 4
图 11 试验5中车辆队列的状态与位置误差
Figure 11. States and spacing errors of vehicle platoon in Example 5
表 1 车辆队列参数和分布式PID控制器参数
Table 1. Parameters of vehicle platoon and distributed PID controller
η/s d0/m kb kf kl kPr kPv kPa kIr kIv kIa kDr kDv kDa 0.79 50 0.794 0.026 1.000 1.300 3.800 1.293 0.907 0.221 0.197 0.213 0.047 0.051 
下载: 导出CSV
-
[1] MENOUAR H, GUVENC I, AKKAYA K, et al. UAV-enabled intelligent transportation systems for the smart city: applications and challenges[J]. IEEE Communications Magazine, 2017, 55(3): 22-28. doi: 10.1109/MCOM.2017.1600238CM [2] LI Sheng-bo Eben, ZHENG Yang, LI Ke-qiang, 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 [3] JIA Dong-yao, LU Ke-jie, WANG Jian-ping, et al. A survey on platoon-based vehicular cyber-physical systems[J]. IEEE Communications Surveys and Tutorials, 2016, 18(1): 263-284. doi: 10.1109/COMST.2015.2410831 [4] DEY K C, YAN Li, WANG Xu-jie, et al. A review of communication, driver characteristics, and controls aspects of cooperative adaptive cruise control (CACC)[J]. IEEE Transactions on Intelligent Transportation Systems, 2016, 17(2): 491-509. doi: 10.1109/TITS.2015.2483063 [5] LIU Yong-gui, PAN Chuang, GAO Huan-li, et al. Cooperative spacing control for interconnected vehicle systems with input delays[J]. IEEE Transactions on Vehicular Technology, 2017, 66(12): 10692-10704. doi: 10.1109/TVT.2017.2712146 [6] ZHENG Yang, LI Sheng-bo Eben, WANG Jian-qiang, 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 [7] 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 [8] XU Li-wei, ZHUANG Wei-chao, YIN Guo-dong, et al. Energy-oriented cruising strategy design of vehicle platoon considering communication delay and disturbance[J]. Transportation Research Part C: Emerging Technologies, 2019, 107: 34-53. doi: 10.1016/j.trc.2019.07.019 [9] 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 [10] 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 [11] 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 [12] 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 [13] OLGAC N, VYHLÍDAL T, SIPAHI R. A new perspective in the stability assessment of neutral systems with multiple and cross-talking delays[J]. SIAM Journal on Control and Optimization, 2008, 47(1): 327-344. doi: 10.1137/070679302 [14] GAO Qing-bin, 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 [15] GAO Qing-bin, 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 [16] 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 [17] 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 [18] 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 [19] 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 [20] DEVIKA K B, ROHITH G, SHREYA YELLAPANTULA V R, et al. A dynamics-based adaptive string stable controller for connected heavy road vehicle platoon safety[J]. IEEE Access, 2020, 8: 209886-209903. doi: 10.1109/ACCESS.2020.3039797 [21] 蔡迢阳. 基于τ分解方法的几类时滞系统稳定性分析[D]. 沈阳: 东北大学, 2014.CAI Tiao-yang. Stability analysis of several classes of time delay systems based on the τ decomposition method[D]. Shenyang: Northeastern University, 2014. (in Chinese) [22] 王洪海. 时滞系统的特征根分布及控制器设计研究[D]. 沈阳: 东北大学, 2017.WANG Hong-hai. Study on eigenvalue distribution and controller design for time delay systems[D]. Shenyang: Northeastern University, 2017. (in Chinese) [23] YU Xin-yi, YANG Fan, ZOU Chao, et al. Stabilization parametric region of distributed PID controllers for general first-order multi-agent systems with time delay[J]. IEEE/CAA Journal of Automatica Sinica, 2020, 7(6): 1555-1564. doi: 10.1109/JAS.2019.1911627 [24] FIENGO G, LUI D G, PETRILLO A, et al. Distributed robust PID control for leader tracking in uncertain connected ground vehicles with V2V communication delay[J]. IEEE/ASME Transactions on Mechatronics, 2019, 24(3): 1153-1165. doi: 10.1109/TMECH.2019.2907053 [25] SOUZA F O. An exact LMI condition for the strong delay-independent stability analysis of neutral delay systems[J]. International Journal of Robust and Nonlinear Control, 2018, 28(17): 5375-5385. doi: 10.1002/rnc.4324 [26] LI Zhao-yan, LAM J, WANG Yong. Stability analysis of linear stochastic neutral-type time-delay systems with two delays[J]. Automatica, 2018, 91: 179-189. doi: 10.1016/j.automatica.2018.01.014 [27] FU Pei-lin, NICULESCU S I, CHEN Jie. Stability of linear neutral time-delay systems: Exact conditions via matrix pencil solutions[J]. IEEE Transactions on Automatic Control, 2006, 51(6): 1063-1069. doi: 10.1109/TAC.2006.876804 [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] SONG Yun-xia, MICHIELS W, ZHOU Bin, et al. Strong stability analysis of linear delay-difference equations with multiple time delays[J]. IEEE Transactions on Automatic Control, 2021, 66(8): 3741-3748. doi: 10.1109/TAC.2020.3027660 [30] MELCHOR-AGUILAR D. On Lyapunov functionals for linear functional difference equations[J]. Systems and Control Letters, 2019, 127: 1-5. doi: 10.1016/j.sysconle.2019.03.008 [31] SIPAHI R, OLGAC N, BREDA D. A stability study on first-order neutral systems with three rationally independent time delays[J]. International Journal of Systems Science, 2010, 41(12): 1445-1455. doi: 10.1080/00207720903353625 [32] CAREY G F, SEPEHRNOORI K. Gershgorin theory for stiffness and stability of evolution systems and convection-diffusion[J]. Computer Methods in Applied Mechanics and Engineering, 1980, 22(1): 23-48. doi: 10.1016/0045-7825(80)90049-3 [33] GAO Qing-bin, ZALLUHOGLU U, OLGAC N. Investigation of local stability transitions in the spectral delay space and delay space[J]. Journal of Dynamic Systems, Measurement, and Control, 2014, 136(5): 051011. doi: 10.1115/1.4027171 [34] FAZELINIA H, SIPAHI R, OLGAC N. Stability robustness analysis of multiple time-delayed systems using "building block" concept[J]. IEEE Transactions on Automatic Control, 2007, 52(5): 799-810. doi: 10.1109/TAC.2007.898076 [35] GAO Qing-bin, OLGAC N. Optimal sign inverting control for time-delayed systems, a concept study with experiments[J]. International Journal of Control, 2015, 88(1): 113-122. doi: 10.1080/00207179.2014.941409 [36] PILBAUER D, VYHLÍDAL T, MICHIELS W. Optimized design of robust resonator with distributed time-delay[J]. Journal of Sound and Vibration, 2019, 443: 576-590. doi: 10.1016/j.jsv.2018.12.002 -
点击查看大图
图(11) / 表(1)
计量
- 文章访问数: 599
- HTML全文浏览量: 274
- PDF下载量: 89
- 被引次数: 0
