Study for the Application of Fractional Order PID Torque Control in Side-drive Coupled Tram
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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.Abstract: Side-drive coupled independently rotating wheelset (IRW) is one of the key technologies for the 100 % low floor tram (LFT). The torque control strategy of side-drive electrical motor directly affects the dynamics behaviors of the LFT. Based on the track running mechanism of the IRW with 5 degrees of freedom, the dynamics model of a single LFT was constructed taking the side-drive transmission system into consideration. A fractional order PID (FOPID) torque control strategy was applied to optimize the vehicle′ s curve negotiation performance. The FOPID controller, which was achieved by Riemann-Liouville (RL) fractional integration and the Oustaloup filter approximation and whose parameters were set by the evolutionary operation, was built in the Simulink platform. The 100 % LFT′ s dynamics performance on tangent track and curve was studied by the co-simulation method between the torque controller and the s-function. The results were compared with the IRW model without controller and the traditional wheelset. The research indicates that, in the tangent track case, FOPID controller can improve the vehicle′ s stability and the controlled wheelset′ s robustness to track irregularity is stronger; in the large radius curve case, the curve negotiation performance of the IRW without controller is poor, while the IRW with FOPID controller can perform well like the traditional wheelset; in the small radius curve case, FOPID torque control strategy can provide enough leading force for the LFT on the small radius curve, which makes the curve negotiation performance of IRW with FOPID controller better than the other 2 models.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 Young2) 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
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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 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 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 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 − 
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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
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