摘要
基于列车准点节能运行最优控制的必要条件,应用庞特里亚金极大值原理推导最大牵引、惰行、最大电制动和最大综合制动4种非奇异最优控制工况下的伴随方程;在定义最优切换点集合和切换方向的基础上,给出车速低于限速时非奇异最优控制工况间的最优切换规则,以及车速触及限速时3种奇异最优控制工况(部分牵引、部分电制动和部分综合制动)间、非奇异最优控制工况与奇异最优控制工况间、非奇异最优控制工况间的最优切换规则;根据最优切换规则,求解最优控制工况序列及其对应的最优速度,以及最优控制工况间最优切换发生的时机。
Based on the necessary conditions of the punctual and energy efficient operation of trains,Pontryagin maximum principle was used to deduce the adjoint equations for four types of non-singular optimal control conditions,namely,full power traction,coasting,full electric braking and full integrated braking.On the basis of defining the optimal switching point set and switching directions,the optimal switching rules were proposed for four non-singular optimal control conditions without touching the speed limit.Furthermore,the optimal switching rules were also presented for three groups of optimal control conditions with touching the speed limit.The first group consisted of three singular optimal control conditions which were partial power traction,partial electric braking and partial integrated braking.The second group was the optimal switching among singular optimal control conditions and non-singular ones.The third group was the optimal switching among non-singular optimal control conditions.In the end,the optimal control sequence,the corresponding optimal speed and the optimal switching time were solved according to optimal switching rules.
出处
《中国铁道科学》
EI
CAS
CSCD
北大核心
2016年第2期91-98,共8页
China Railway Science
基金
国家自然科学基金资助项目(U11344205)
关键词
节能驾驶
极大值原理
再生制动
最优控制
最优切换
Energy-efficient operation of train
Maximum principle
Regenerative brake
Optimal control
Optimal switching
