Observer-based Longitudinal Control for Connected and Automated Vehicles Platoon Subject to Communication Delay
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摘要: 考虑通信延时影响的车辆队列控制问题, 提出了一种基于观测器的分布式车辆队列纵向控制器. 首先, 基于分层控制策略分别设计上下层控制器, 通过上层控制器优化期望加速度, 下层控制器克服车辆模型非线性实现期望加速度和实际加速度的一致, 上层控制器设计过程中, 基于三阶线性化车辆模型, 考虑观测器、车辆动态耦合特性和通信延时, 提出一种通信延时环境下基于观测器的车辆队列控制器, 利用观测器估计领导车辆加速度信息从而减轻通信负担. 然后利用Lyapunov-Krasovskii方法分析了车辆队列的稳定性, 并得出了通信延时上界, 同时利用传递函数方法分析了串稳定性. 最后通过数值仿真验证上层控制器的有效性和稳定性, 在此基础上, 利用PreScan软件中高保真车辆动态模型, 验证了所提分层控制策略的有效性.Abstract: This paper proposes a distributed longitudinal controller subject to communication delay based on the observer. Firstly, the high-level and low-level controllers are designed respectively based on the hierarchical control strategy, where the desired acceleration is optimized by the high-level controller and the low-level controller is proposed to follow it. In the design process of the high-level controller, a new distributed controller is proposed based on the third-order dynamics model jointly the communication delays, observer, and dynamic coupling characteristics of vehicles. In particular, the acceleration of the leader vehicle is estimated by the observer for reducing the communication costs. Then, the stability of the proposed controller is analyzed using the Lyapunov-Krasovskii method, and an estimate of the delay bound is provided. The string stability of the platoon is analyzed using the transfer function method. Finally, the effectiveness and stability of the high-level controller are verified by numerical simulation. Furthermore, the effectiveness of the proposed controller is verified by simulations using a high-fidelity vehicle dynamic model in PreScan.
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图 6 位置图: (a) 文献[12]-无延时, (b) 文献[12]-
$\tau (t) \in [0.1,\;0.2]{\rm{s}}$ , (c) 控制器 (14) -无延时,(d) 控制器(14)-$\tau (t) \in [0.1,\;0.2]{\rm{s}}$ Fig. 6 Position profile: (a) controller in [12]- no time delay, (b) controller in [12]-
$\tau (t) \in [0.1,\;0.2]{\rm{s}}$ , (c) controller (14)- no time delay, (d) controller (14)-$\tau (t) \in [0.1,\;0.2]{\rm{s}}$ .
图 7 速度图: (a) 文献[12]-无延时, (b) 文献[12]-
$\tau (t) \in [0.1,\;0.2]{\rm{s}}$ , (c) 控制器 (14) -无延时,(d) 控制器(14)-$\tau (t) \in [0.1,\;0.2]{\rm{s}}$ .Fig. 7 Velocity profile: (a) controller in [12]- no time delay, (b) controller in [12]-
$\tau (t) \in [0.1,\;0.2]{\rm{s}}$ , (c) controller (14)- no time delay, (d) controller (14)-$\tau (t) \in [0.1,\;0.2]{\rm{s}}$ .
图 8 加速度图: (a) 文献[12]-无延时, (b) 文献[12]-
$\tau (t) \in [0.1,\;0.2]{\rm{s}}$ , (c) 控制器 (14) -无延时,(d) 控制器(14)-$\tau (t) \in [0.1,\;0.2]{\rm{s}}$ Fig. 8 Acceleration profile: (a) controller in [12]- no time delay, (b) controller in [12]-
$\tau (t) \in [0.1,\;0.2]{\rm{s}}$ , (c) controller (14)- no time delay, (d) controller (14)-$\tau (t) \in [0.1,\;0.2]{\rm{s}}$ 
图 9 间距误差图: (a) 文献[12]-无延时, (b) 文献[12]-
$\tau (t) \in [0.1,\;0.2]{\rm{s}}$ , (c) 控制器 (14) -无延时,(d) 控制器(14)-$\tau (t) \in [0.1,\;0.2]{\rm{s}}$ Fig. 9 Spacing error profile: (a) controller in [12]- no time delay, (b) controller in [12]-
$\tau (t) \in [0.1,\;0.2]{\rm{s}}$ , (c) controller (14)- no time delay, (d) controller (14)-$\tau (t) \in [0.1,\;0.2]{\rm{s}}$ 
图 10
${z_{2,i}}(t)$ 和${\hat z_{2,i}}(t)$ : (a) 控制器 (14) -无延时, (b) 控制器 (14)-$\tau (t) \in [0.1,\;0.2]{\rm{s}}$ .Fig. 10
${z_{2,i}}(t)$ and${\hat z_{2,i}}(t)$ : (a) controller (14)- no time delay, (b) controller (14)-$\tau (t) \in [0.1,\;0.2]{\rm{s}}$ 
图 11 基于PreScan/Simulink联合仿真平台框架示意图
Fig. 11 Framework of the PreScan/Simulink-based Co-Simulation platform
表 1 控制器参数
Table 1 Controller parameters
参数 数值 单位 $\alpha $ $0.67$ ${{\rm{s}}^{ - 1}}$ ${g_{o,1}}$ $0.12$ ${{\rm{s}}^{ - 2}}$ ${g_{o,2}}$ $0.52$ ${{\rm{s}}^{ - 1}}$ ${g_{o,3}}$ $0.3$ — ${V_1}$ $6.75$ ${\rm{m/s}}$ ${V_2}$ $7.91$ ${\rm{m/s}}$ ${C_1}$ $0.13$ ${{\rm{m}}^{ - 1}}$ ${C_2}$ $1.59$ — ${h_1}$ $30$ — ${h_2}$ $12$ — ${k_P}$ $10$ — ${k_I}$ $0.3$ — ${k_D}$ $0.1$ — $\vartheta $ $0.1$ ${\rm{m/}}{{\rm{s}}^2}$ 
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表 2 PreScan中车辆模型参数
Table 2 The parameters of vehicle model in PreScan
参数 数值 单位 $m$ $1532$ ${\rm{kg}}$ $g$ $9.8$ ${\rm{m/}}{{\rm{s}}^2}$ ${l_c}$ $4.63$ ${\rm{m}}$ ${C_A}$ $0.31$ ${\rm{kg/m}}$ ${i_0}$ $2.7$ — ${\eta _{\rm{T}}}$ $1$ — $f$ $0.01$ —
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