Hostname: page-component-7bb8b95d7b-fmk2r Total loading time: 0 Render date: 2024-09-26T02:05:40.497Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal driving strategies for a train journey with speed limits

Published online by Cambridge University Press:  17 February 2009

Peter Pudney  and
Phil Howlett
Peter Pudney
Affiliation:
Scheduling and Control Group, University of South Australia, Adelaide, Australia
Phil Howlett
Affiliation:
Scheduling and Control Group, University of South Australia, Adelaide, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

How should a vehicle he driven to minimise fuel consumption? In this paper we consider the case where a train is to be driven along a straight, level track, but where speed limits may apply over parts of the track. The journey is to be completed within a specified time using as little fuel as possible.

For a journey without speed limits, the optimal driving strategy typically requires full power, speed holding, coasting and full braking, in that order. The holding speed and braking speed can be determined from the vehicle characteristics and the time available to complete the journey. If the vehicle has discrete control settings, the holding phase should be approximated by alternate coast and power phases between two critical speeds.

For a journey with speed limits, a similar strategy applies. For each given journey time there is a unique holding speed. On intervals of track where the speed limit is below the desired holding speed, the speed must be held at the limit. If braking is necessary on an interval, the speed at which braking commences is determined in part by the holding speed for the interval. For vehicles with discrete control, speed-holding is approximated by alternate coast and power phases between two critical speeds, or between a lower critical speed and the speed limit.

Type
Research Article
Information
The ANZIAM Journal , Volume 36 , Issue 1 , July 1994 , pp. 38 - 49
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Asnis, I. A., Dmitruk, A. V. and Osmolovskii, N. P., “Solution of the problem of the energetically optimal control of the motion of a train by the maximum principle”, USSR Computational Mathematics and Mathematical Physics 25 (1985) 37–44.CrossRefGoogle Scholar
[2]Benjamin, B. R., Long, A. M., Milroy, I. P., Payne, R. L. and Pudney, P. J., “Control of railway vehicles for energy conservation and improved timekeeping”, Proc. of the Conference on Railway Engineering, 1987.Google Scholar
[3]Howlett, P. G., Pudney, P. J. and Benjamin, B. R., “Determination of optimal driving strategies for the control of a train”, (to appear), Proc. CTAC 91.Google Scholar
[4]Howlett, Phil, “An optimal strategy for the control of a train”, J. Austral. Math. Soc., Ser. B 31 (1990) 454–471.CrossRefGoogle Scholar
[5]Howlett, Phil, “Optimal strategies for the control of a train on a track with non-constant gradient”, (submitted), 1992.Google Scholar
[6]Jaixin, Cheng and Howlett, Phil, “A note on the calculation of optimal strategies for the minimisation of fuel consumption in the control of trains”, (to appear), IEEE Transactions on Automatic Control.Google Scholar
[7]Jiaxin, Cheng and Howlett, Phil, “Application of critical velocities to the minimisation of fuel consumption in the control of trains”, Automatica 28 (1) (1992) 165–169.CrossRefGoogle Scholar
[8]Kraft, K. H. and Schnieder, E., “Optimale trajektorien im spurgebundenen schnellverkehr (optimal trajectories for rapid transit systems)”, in Regelungstechnik 29, Jahrgang, 1981).Google Scholar
[9]Milroy, I. P., “Aspects of automatic train control”, Ph. D. Thesis, Loughborough University, 1980.Google Scholar