Peter Pudney

Brief paper: Local energy minimization in optimal train control

The calculation of optimal driving strategies for on-board control of freight trains is a challenging task. In this paper we calculate the critical switching points for a globally optimal strategy on a track with steep gradients using a new local energy minimization principle. The method has been used successfully in Australia to calculate optimal switching points and hence provide in-cab advice to train drivers on long-haul freight trains.

Energy-Efficient Train Control

Abstract Over the past decade, the Scheduling and Control Group has conducted an extensive program of research into the theory and practice of energy-efficient train control. Two distinct systems have been developed for providing train drivers with advice on energy-efficient driving strategies. In normal operation, the Metromiser system for suburban railways is achieving fuel savings in excess of 13% and dramatic improvements in timekeeping. The Long-Haul Fuel Conservation System provides driving advice and dynamic rescheduling on long-haul rail networks. The paper outlines the theoretical basis for our work, and illustrates results with selected examples.

Energy-efficient train control

Abstract Over the past decade, the Scheduling and Control Group has conducted an extensive program of research into the theory and practice of energy-efficient train control. Two distinct systems have been developed for providing train drivers with advice on energy-efficient driving strategies. In normal operation, the Metromiser system for suburban railways is achieving fuel savings in excess of 13% and dramatic improvements in timekeeping. The Long-Haul Fuel Conservation System provides driving advice and dynamic rescheduling on long-haul rail networks. The paper outlines the theoretical basis for the work, and illustrates results with selected examples.

Optimal driving strategies for a train journey with speed limits

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.

Energy-efficient train control: The two-train separation problem on level track

Abstract When two trains travel in the same direction along the same track it is a common safety requirement that they must be separated by at least one signal. If the signals are located at fixed positions, they divide the track into separate sections and the safety requirement means that two trains cannot occupy the same section at the same time. Safe separation can be ensured by specifying supplementary section clearance times which define the latest allowed exit time for the leading train and the earliest possible entry time for the following train. The clearance times could initially be based on an existing timetable but we will show that adjusting these times can substantially decrease the total energy required by the trains. In this paper we find driving strategies that minimize total energy consumption and allow both trains to finish on time while adhering to the separation constraints imposed by the supplementary clearance times. We establish a new necessary condition to check whether a set of specified clearance times is optimal and discuss a heuristic procedure to find the optimal clearance times and the corresponding speed profiles. We illustrate our methods with a simplified but realistic case study.

Optimal train control: Analysis of a new local optimization principle

It is known that the optimal driving strategy for a train takes the form of a power-speedhold-coast-brake strategy unless the track contains steep grades. In such cases the predominant speedhold mode must be interrupted by phases of power on steep uphill sections and phases of coast on steep downhill sections. The Freightmiser device is used by Pacific National to provide on-board advice to train drivers about energy efficient driving strategies. Freightmiser uses a fast and efficient numerical algorithm to solve a key local energy minimization problem and hence find the optimal switching points. Although the numerical algorithm converges to a feasible solution there is no direct proof that the solution is unique. We explain the basic ideas behind the local energy minimization principle and use an extended perturbation analysis to derive various equivalent forms of the necessary conditions.

Critical Speed Control of a Solar Car

The World Solar Challenge is a 3000 km race for solar powered cars across the Australian continent from Darwin to Adelaide. Each car is powered by a panel of photovoltaic cells which convert sunlight into electrical power. The power can be used directly to drive the car or stored in a battery for later use. Previous papers (P. Howlett, P. Pudney, T. Tarnopolskaya, and D. Gates, IMA Journal of Mathematics Applied in Business and Industry vol. 8, pp. 59–81, 1997; P.G. Howlett and P.J. Pudney, Dynamics of Continuous, Discrete and Impulsive Systems vol. 4, pp. 553–567, 1998) using a simplified model of the battery, have shown that the optimal strategy is essentially a speedholding strategy. In this paper, with a more realistic model of the battery, we show that the optimal driving strategy is a critical speed strategy. For an optimal journey with no beginning and no ending the solar car must always travel at the critical speed. For an optimal journey of finite length the speed must be close to the critical speed for most of the journey. The critical speed depends on the solar power and will normally vary slowly with time.

Generating Train Plans with Problem Space Search

Planning train movements is difficult and time-consuming, particularly on long-haul rail networks, where many track segments are used by trains moving in opposite directions. A detailed train plan must specify the sequence of track segments to be used by each train, and when each track segment will be occupied. A good train plan will move trains through the network in a way that minimises the total cost associated with late arrivals at key intermediate and final destinations.

The Train Control Problem

In 1977–78 Milroy [1] considered the problem of driving a train from one station to the next along a level track within a given allowable time in such a way that energy consumption is minimised. He used the energy flows in the traction and braking systems of the train to derive state variable equations with time as the independent variable and position and speed as the dependent state variables. He used an heuristic application of the Pontryagin Principle to conclude that the optimal driving strategy consisted of a maximum acceleration-coast-brake control sequence. Subsequent studies confirmed the optimality of this control sequence for short journeys, and showed that a speed-hold phase should be included on longer journeys.

Efficient Admission Control based on Predicted Traffic Characteristics

As the use of bandwidth hungry applications such as video conferencing increases, ensuring quality of service (QoS) becomes increasingly important. In wireless access networks such as WiFi and WiMax, admission control is necessary to control QoS. Many admission control methods use the mean bitrate of a flow to determine if it can be allowed, however there is a lack of methods that accurately assess variable bit rate flows. We propose a simple alternative method that uses the bitrate statistics of each flow to approximate the probability of exceeding the medium bandwidth. A new flow is permitted only if the probability of exceeding the channel bandwidth is sufficiently low.