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分数阶PID扭矩控制在边驱耦合轻轨车辆的应用研究

戚壮 张文莲 王美琪 刘鹏飞 刘永强

戚壮, 张文莲, 王美琪, 刘鹏飞, 刘永强. 分数阶PID扭矩控制在边驱耦合轻轨车辆的应用研究. 自动化学报, 2020, 46(3): 482−494 doi: 10.16383/j.aas.c190084
引用本文: 戚壮, 张文莲, 王美琪, 刘鹏飞, 刘永强. 分数阶PID扭矩控制在边驱耦合轻轨车辆的应用研究. 自动化学报, 2020, 46(3): 482−494 doi: 10.16383/j.aas.c190084
Qi Zhuang, Zhang Wen-Lian, Wang Mei-Qi, Liu Peng-Fei, Liu Yong-Qiang. Study for the application of fractional order PID torque control in side-drive coupled tram. Acta Automatica Sinica, 2020, 46(3): 482−494 doi: 10.16383/j.aas.c190084
Citation: Qi Zhuang, Zhang Wen-Lian, Wang Mei-Qi, Liu Peng-Fei, Liu Yong-Qiang. Study for the application of fractional order PID torque control in side-drive coupled tram. Acta Automatica Sinica, 2020, 46(3): 482−494 doi: 10.16383/j.aas.c190084

分数阶PID扭矩控制在边驱耦合轻轨车辆的应用研究

doi: 10.16383/j.aas.c190084
基金项目: 国家自然科学基金(11790282, 11702179), 河北省自然科学基金(A2018210064), 河北省高等学校青年拔尖人才计划项目(BJ2017001)资助
详细信息
    作者简介:

    戚壮:博士, 讲师, 本科和博士期间就读于西南交通大学, 并于法国里昂中央理工大学获硕士学位, 现任石家庄铁道大学车辆工程系主任. 长期从事高速列车动力学、城轨车辆动力学及刚柔耦合动力学研究, 目前主持及参与国家级、省部级及横向课题共计10余项. 本文通信作者. E-mail: qizhuang@stdu.edu.cn

    张文莲:石家庄铁道大学电气与电子工程学院助教. 获西安交通大学硕士学位. 主要研究方向为电子科学与技术, 超大规模集成电路设计. E-mail: wl_zhang@stdu.deu.cn

    王美琪:石家庄铁道大学机械工程学院讲师, 现任机械电子工程系主任. 获燕山大学学士学位与博士学位. 主要研究方向为非线性动力学, 重载列车纵向动力学及神经网络算法. E-mail: wangmeiqi@stdu.edu.cn

    刘鹏飞:石家庄铁道大学车辆工程系副教授. 主要研究方向为列车纵向动力学及车辆 − 轨道耦合动力学. E-mail: pfliu@stdu.edu.cn

    刘永强:石家庄铁道大学教授. 主要研究方向为车辆动力学与控制, 旋转机械故障诊断. E-mail: liuyq@stdu.edu.cn

Study for the Application of Fractional Order PID Torque Control in Side-drive Coupled Tram

Funds: Supported by National Natural Science Foundation of China (11790282, 11702179), Natural Science Foundation of Hebei Province, China (A2018210064), and Program for the Top Young Innovative Talents of Higher Learning Institutions of Hebei province (BJ2017001)
  • 摘要: 边驱耦合独立轮对(Independently rotating wheelset, IRW)技术是 100 %低地板轻轨车(Low floor tram, LFT)的关键技术之一, 边驱电机的扭矩控制策略直接影响轻轨车的动力学性能. 本文基于5自由度独立轮对的轨行机理, 搭建了考虑边驱传动系统的单节轻轨车动力学模型. 应用了一种分数阶PID (Fractional order PID, FOPID)扭矩控制策略, 优化了车辆的曲线通过性能. 采用Riemann-Liouville (RL) 分数阶微积分理论及Oustaloup滤波器数值逼近法构成FOPID控制器, 通过寻优运算对FOPID参数进行整定, 在Simulink平台下建立了整车的集成控制系统.通过扭矩控制器与整车动力学模型s函数联合仿真的方式,开展了100 % 低地板轻轨车辆的直线与曲线运行特性研究, 并将计算结果与无控制的独立轮对模型、传统轮对模型进行了对比分析. 研究结果表明, 在直线运行下, FOPID控制下的轻轨车能够提高车辆的稳定性, 受控轮对的抗轨道不平顺激扰能力较强. 在大半径曲线下, 无控制的独立轮对曲线通过性较差, 而受分数阶PID控制的独立轮对能够表现出与传统轮对一样优异的曲线通过性能; 在小半径曲线下, 分数阶PID扭矩控制策略能够使轻轨车获得足够的导向力, 曲线通过性能明显优于其他模型.
    1)   收稿日期 2019-02-12    录用日期 2019-10-28 Manuscript received February 12, 2019; accepted October 28, 2019 国家自然科学基金 (11790282, 11702179), 河北省自然科学基金 (A2018210064), 河北省高等学校青年拔尖人才计划项目 (BJ2017001) 资助 Supported by National Natural Science Foundation of China (11790282, 11702179), Natural Science Foundation of Hebei Province of China (A2018210064), and Program for the Top Young
    2)  Innovative Talents of Higher Learning Institutions of Hebei Province (BJ2017001) 本文责任编委 阳春华 Recommended by Associate Editor YANG Chun-Hua 1. 石家庄铁道大学机械工程学院 石家庄 050043    2. 石家庄铁道大学电气工程学院 石家庄 050043 1. School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043    2. School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043
  • 图  1  独立轮对受力

    Fig.  1  Force diagram of IRW

    2  单节车动力学拓扑结构

    图例: 1. 车体 2. 转向架构架 3. 独立轮对 4. 电机 5. 联轴器 6. 传动轴 7. 一系悬挂 8. 二系悬挂

    2  Topological structure of a single vehicle

    Legend: 1. carbody 2. bogie frame 3. IRW 4. electromotor 5. coupler 6. drive shaft 7. primary suspension 8. secondary suspension

    图  3  单节车动力学模型

    Fig.  3  Dynamics model of a single vehicle

    图  4  对分数阶系统的分段折线逼近

    Fig.  4  Piecewise polyline approximation for a fractional order system

    图  5  PID控制器示意图

    Fig.  5  Schematic diagram of PID controller

    图  6  PID控制器示意图

    Fig.  6  Schematic diagram of PID controller

    图  7  控制器参数整定流程图

    Fig.  7  Flow chart of parameters setting of controller

    图  8  控制器参数在整定过程中的变化

    Fig.  8  Flow chart of parameters setting of controller

    图  9  分数阶与整数阶PID控制器作用下系统阶跃响应对比

    Fig.  9  System step response under fractional order PID controller and integral order PID controller

    图  10  临界速度计算结果

    Fig.  10  Results of critical velocity

    图  11  控制器的失稳现象

    Fig.  11  Instability phenomenon of controller

    图  12  无控制策略的独立轮对临界速度校核

    Fig.  12  Critical velocity for the IRW without controller

    图  13  传统轮对的临界速度校核

    Fig.  13  Critical velocity for the traditional wheelset

    图  14  轨道不平顺

    Fig.  14  Track irregularity

    图  15  轨道不平顺下的动态响应

    Fig.  15  Dynamic response under track irregularity

    图  16  理想曲线通过状态

    Fig.  16  Ideal condition of curve negotiation

    图  17  车辆通过曲线的时域响应

    Fig.  17  History response of vehicle curve negotiation

    图  18  通过不同半径曲线的稳态性能对比

    Fig.  18  Comparison of steady performance in different radius curves

    表  1  主要动力学参数

    Table  1  Main dynamics parameters

    项目 数值 单位
    车辆定距 10 m
    转向架轴距 1.8 m
    名义滚动圆半径 0.3 m
    等效踏面锥度 0.15
    一系悬挂垂向刚度 1.6 MN/mm
    一系悬挂水平刚度 5.0 MN/mm
    二系悬挂垂向刚度 0.24 MN/mm
    二系悬挂水平刚度 0.17 MN/mm
    横向减振器阻尼 58.8 kN·s/m
    车体质量 13 t
    车体转动惯量(侧滚/点头/摇头) 30/150/150 t·m2
    构架质量 1.4 t
    构架转动惯量(侧滚/点头/摇头) 0.7/1.4/2.0 t·m2
    锥齿轮传动比 2
    下载: 导出CSV

    表  2  控制器参数

    Table  2  Parameters of controllers

    参数 初始控制器 整定后控制器 整数阶控制器
    Kp 100 371.52 371.52
    Ki 100 60.61 60.61
    Kd 100 130.18 130.18
    λ 1 0.32 1
    μ 1 0.86 1
    ITAE 0.5678 0.1086 0.2183
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-02-12
  • 录用日期:  2019-10-28
  • 网络出版日期:  2020-03-30
  • 刊出日期:  2020-03-30

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