基于多时滞PR控制器的异构车辆队列系统设计  

System design of heterogeneous vehicle platoon based on multi-delay proportional-retarded controller

作　　者：朱旭[1] 张琳虎 闫茂德[1] ZHU Xu;ZHANG Lin-hu;YAN Mao-de(School of Electronics and Control Engineering,Chang'an University,Xi'an 710064,Shaanxi,China)

机构地区：[1]长安大学电子与控制工程学院,陕西西安710064

出　　处：《交通运输工程学报》2024年第6期230-242,共13页Journal of Traffic and Transportation Engineering

基　　金：国家重点研发计划(2021YFA1000303);国家自然科学基金项目(62003054,52372406);陕西省重点研发计划(2023-YBGY-398)。

摘　　要：针对异构车辆队列,为有效利用时滞提升系统响应速度等控制性能,引入多时滞设计了一种比例-时滞(PR)控制器;使用隐函数定理及柯西-黎曼方程对车辆队列各子系统的特征方程进行了分析,提出了子系统的最右侧极点配置方法;确定了最右侧极点的可配置范围,并给出了关于控制器增益和时滞的设计指导规则;为了逐次增强各跟随车所对应子系统的稳定性,合理分离了各子系统的极点,提出了整个车辆队列的最右侧极点配置方法,并给出了弦稳定的充分条件。仿真结果表明:设计的多时滞PR控制器及所提出的最右侧极点配置方法,可精确地将异构车辆队列的极点配置在期望位置,并能同时保证车辆队列的内部稳定性与弦稳定性,且最右侧极点越小,系统响应速度越快;相较于单时滞PR控制器,该方法灵活地分离了各子系统的最右侧极点,并将系统调节时间减少了2.45%;与传统的比例-微分控制器(PD)相比,PR控制器在车辆乘坐舒适度和燃油效率方面有显著提升,改进幅度达到2~4个数量级;相同频率扰动下,PR与PD控制器作用下的加速度和控制输入的振幅比均始终小于1/3,当扰动频率为9Hz时,振幅比降至0.031。可见,所设计的多时滞PR控制器在响应速度、极点分离与抑制干扰等方面均有显著优势。To effectively utilize delays to enhance system response speed and other control performances,a proportional-retarded(PR)controller was designed for the heterogeneous vehicle platoon by introducing multi-delays.The characteristic equations of each subsystem of the vehicle platoon were analyzed by applying the implicit function theorem and Cauchy-Riemann equation,and the right-most pole assignment method was proposed for these subsystems.The available assignment ranges of the right-most poles were determined,and the guidelines for designing the controller gains and delays were given.To gradually increase the stability of the subsystems that corresponded to the follower vehicles,the poles of subsystems were separated reasonably,and a right-most pole assignment method was proposed for the entire vehicle platoon.Moreover,sufficient conditions for string stability were derived.Simulation results indicate that the designed multi-delay PR controller and the proposed right-most pole assignment method can accurately assign the pole of the heterogeneous vehicle platoon at the desired location,and both the internal stability and string stability of the vehicles are ensured.Moreover,a smaller right-most pole indicates a faster system response speed.Compared to a single-delay PR controller,the right-most poles of subsystems are flexibly separated via this method,the system setting time reduces by 2.45%.Compared with traditional proportional-derivative(PD)controllers,the PR controller shows significant improvements in ride comfort and fuel economy,with enhancement ranging from 2-4 orders of magnitude.Under the disturbances of the same frequency,the amplitude ratios of the acceleration and control input for both the PR and PD controllers remain consistently below 1/3,dropping to 0.031 when the frequency of the disturbances is 9 Hz.It can be seen that the designed multi-delay PR controller has significant advantages in response speed,pole separation,and disturbance suppression.

关 键 词：智能交通 异构车辆队列 最右侧极点配置方法 多时滞 比例-时滞控制器 响应速度 弦稳定性 

分 类 号：U491.255[交通运输工程—交通运输规划与管理]