APPLICATION OF CRITICAL VELOCITIES TO THE MINIMIZATION OF FUEL CONSUMPTION IN THE CONTROL OF TRAINS

This paper introduces a method for the determination of optimal control strategies in an important engineering application. A train travels from one station to the next along a level track. The journey must be completed within a given time and it is desirable to minimise fuel consumption. We assume that only certain discrete throttle settings are possible and that each setting determines a constant rate of fuel supply. In each case the power developed by the locomotive is directly proportional to the rate of fuel supply. For a given sequence of throttle settings we show that fuel consumption is minimised if the settings are changed only when the velocity reaches one of the critical values. We call this strategy a strategy of optimal type. It is now possible to determine the strategy which minimises fuel consumption by considering only strategies of optimal type. Several realistic examples are given and we discuss systematic numerical calculations procedures.