长大下坡区间货运列车周期性制动研究
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摘要
针对货运列车在长大下坡道空气制动无法恒速且相邻两次空气制动之间需满足缓解再充风约束的特点,以司机实际操纵中普遍采用的50～70kPa减压调速为依据,建立货运列车的最优控制问题,研究其在长大下坡道上的最优操纵策略,基于极大值原理分析"全力制动-全电制动-全力制动"的周期性制动控制策略的最优性,以及列车入坡、出坡应满足的必要条件,提出长大下坡道及其相邻区间列车运行最优控制的数值求解算法。以SS6B型电力机车牵引50节重车进行仿真验证,结果表明:在准点的前提下,与模糊专家系统相比,采用的周期性制动策略能实现9.8%节能效果,证明本文算法正确、有效。
For the non-constant speed that the train keeps on the steep downhill section when air braking is applied and for the train air recharging time that must be guaranteed between two adjacent air brakes,the optimal control problem of the freight train operation was established in this paper based on the 50～70kPa pressure reducing speed regulation commonly applied during the train operation.The optimal manipulation strategies were investigated while a train was on the long steep downhill section.According to the analysis of the optimality of the periodic braking control strategy-"full braking-full electrical braking-full braking"based on the Pontryagin's maximum principle,as well as the analysis of the necessary conditions when a train entered and left the steep downhill section,a numerical algorithm about the optimal control of a train on the steep downhill section and its adjacent section was put forward.Simulation verification was performed with an SS6 Blocomotive and 50 fully loaded vehicles.The results show that,under the condition of train punctuality,the periodic braking strategy adopted in this paper can achieve up to 9.8%train operation energy saving compared with the fuzzy expert system,which proves the correctness and effectiveness of the algorithm.
For the non-constant speed that the train keeps on the steep downhill section when air braking is applied and for the train air recharging time that must be guaranteed between two adjacent air brakes,the optimal control problem of the freight train operation was established in this paper based on the 50～70kPa pressure reducing speed regulation commonly applied during the train operation.The optimal manipulation strategies were investigated while a train was on the long steep downhill section.According to the analysis of the optimality of the periodic braking control strategy-"full braking-full electrical braking-full braking"based on the Pontryagin's maximum principle,as well as the analysis of the necessary conditions when a train entered and left the steep downhill section,a numerical algorithm about the optimal control of a train on the steep downhill section and its adjacent section was put forward.Simulation verification was performed with an SS6 Blocomotive and 50 fully loaded vehicles.The results show that,under the condition of train punctuality,the periodic braking strategy adopted in this paper can achieve up to 9.8%train operation energy saving compared with the fuzzy expert system,which proves the correctness and effectiveness of the algorithm.
引文
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[2]马大炜.制动系统对大秦线重载列车的影响[J].铁道机车车辆,2000,20(6):9-13.MA Dawei.Influence of the Braking System on Daqin Line Heavy Haul Trains[J].Railway Locomotive&Car,2000,20(6):9-13.
[3]耿志修,李学峰,张波.大秦线重载列车运行仿真计算研究[J].中国铁道科学,2008,29(3):88-93.GENG Zhixiu,LI Xuefeng,ZHANG Bo.Simulation Study of Heavy Haul Train Operation on Daqin Railway[J].China Railway Science,2008,29(3):88-93.
[4]张波.重载组合列车牵引及制动系统的试验与仿真研究[D].北京:中国铁道科学研究院,2009.
[5]KHMELNITSKY E.On an Optimal Control Problem of Train Operation[J].IEEE Transactions on Automatic Control,2000,45(7):1257-1266.
[6]XUAN V.Analysis of Necessary Conditions for the Optimal Control of a Train[D].Australia:University of South Australia,2006.
[7]HOWLETT P G,PUDNEY P J,XUAN V.Local Energy Minimization in Optimal Train Control[J].Automatica,2009(45):2692-2698.
[8]AMIE R A,PHIL G H,PETER J P,et al.Energy-efficient Train Control:From Local Convexity to Global Optimization and Uniqueness[J].Automatica,2013,49(10):3072-3078.
[9]CHENG Jiaxin,HOWLETT P.Application of Critical Velocities to the Minimisation of Fuel Consumption in the Control of Trains[J].1991International Federation of Automatic Control,1992,29(1):165-169.
[10]HOWLETT P.Optimal Strategies for the Control of a Train[J].Automatica,1996,32(4):519-532.
[11]朱金陵,李会超,王青元,等.列车节能控制的优化分析[J].中国铁道科学,2008,29(2):104-108.ZHU Jinling,LI Huichao,WANG Qingyuan,et al.Operation Analysis on the Energy Saving Control for Trains[J].China Railway Science,2008,29(2):104-108.
[12]LIANG Z H,WANG Q Y,LIN X.Energy-efficient Handling of Electric Multiple Unit Based on Maximum Principle[C]//IEEE.Proceedings of the 33rd Chinese Control Conference.Nanjing:IEEE,2014:3415-3423.
[13]王青元,冯晓云,朱金陵,等.考虑再生制动能量利用的高速列车节能最优控制仿真研究[J].中国铁道科学,2015,36(1):96-103.WANG Qingyuan,FENG Xiaoyun,ZHU Jinling,et al.Simulation Study on Optimal Energy-efficient Control of High Speed Train Considering Regenerative Brake Energy[J].China Railway Science,2015,36(1):96-103.
[14]中华人民共和国铁道部.TB/T 1407—1998列车牵引计算规程[S].北京:中国铁道出版社,1998.
[15]Desineni Subbaram Naidu.Optimal Control Systems[M].New York:CRC PRESS,2003.
[16]济南铁路局机务处.电力机车优化操纵基本知识及操纵方法[M].北京:中国铁道出版社,2010.