H Ko, T Koseki, M Miyatake
COMPUTERS IN RAILWAY SIX 15 103-112 2004年 最終著者
An algorithm optimizing the train running profile with Bellman's Dynamic programming (DP) is investigated in this paper. An optimal train running trajectory which minimizes amount of total consumed energy has been produced under fixed origin and destination, stipulated running time, limited electric motive force and electric brake by VVVF controlled induction motor/generator blended with mechanical brake, several local speed constraints and local inclines. Many previous works on this area adopt the numerical techniques of calculus of variations, Pontryagin's maximum principle, incremental method, and so on. But these methods often meet some difficulties accounting for complicated actual train running preconditions, e.g. complicated functions which describe electrical motive/brake torque, local constraints of state variables as speed limits, nonlinear running resistance and variable grade profile. DP can cope with such complicated conditions. It can directly deal with such difficult constraints of an optimal control problem, except for terminal boundary condition. In a DP process of a former research, the position and velocity of train and total running time were divided into nonuniform lattice and the numerical algorithm solved state equations partially and calculated interpolated local valuation. The authors have made the improvements for reducing the calculation time of the optimization process and improving the accuracy of the solution. An optimal run-curve can be obtained in a practically acceptable computational time even when it is applied to actual complicated running conditions. The required error of distance and speed at destination is less than 0.6m and 0.1m/sec respectively. The authors have concluded that the small error guarantees the reliability of the results.