Efficient generation of train speed profiles (Balmelli)

Abstract

The objective of the present thesis is the efficient generation of a single, optimal (energy- efficient) train speed profile for a given track route. The generated speed profile has to satisfy the equations of motion, physical limits (maximum velocity, acceleration limits) and schedule constraints (i.e. passing times and velocities at both the start and the end point of the track and intermediate control points as well). The problem has been formulated as an optimal control problem, and it has been solved both with the dynamic programming algorithm (DP) and with the Pontryagin maximum principle (PMP); and implemented in MATLAB. The resulting programs have been tested on the track between Zug and Luzern using the train parameters of the FLIRT (Swiss regional train). The program based on PMP showed to be much faster and also more accurate (in energy efficiency) than the one based on DP. With the same discretization of the displacement of 10 meters, the computation time for PMP is ~2 seconds and for DP is ~14 seconds.

Background and Task

Today's railway operating companies are pressured to increase the efficiency of heavily used railway networks. Increasing this efficiency by means of improving operational processes is the goal of a research project conducted by the SBB Infrastructure division, the Insitute of Transport Planning and Systems (IVT) and the Insitute of Operations Research (IFOR). The quality of online dispatching of running trains is a critical factor for the efficient operation of trains. IFOR is currently investigating an automated decision support system for the online control of train traffic.

This decision support system should use the available degrees of freedom for coordinating trains, the routing and the speed profile. The choice of the route is very important inside dense network areas (condensation zones) such as main stations, whereas the different speeds are exploited in sparse areas (compensation zones) connecting the condensation zones.

IFOR's current research approach uses theses zones to divide the network into trackable control regions, where each region has its own control system and feed-forward control actions between these systems allow the coordination of (zone) crossing trains. An important coordination concept is the effort to keep each zone self-contained as good as possible. To this end, boundary conditions at the zone borders (portals) are defined, which as long as they are fulfilled guarantee the self-contained control of trains inside the zones.

A boundary condition is a coordination point consisting of the tuple (location,time,speed). Each train running through a zone is therefore required to enter the zone at a specific location, time and with a required speed and has to leave the zone according to the exit boundary condition.

The model underlying the control system has the task to assign each train a train path containing the route and the speed profile, where no train paths can allocate an infrastructure element at the same time (conflict-free train paths). This model basically solves a combinatorial assignment problem, but requires first that for each train a suitable set of train paths respecting the boundary conditions and train dynamics (valid train paths) is available.