Energy-efficient train control

Howlett, Phil; Milroy, IP; Pudney, Peter

doi:10.1016/0967-0661(94)90198-8

Cited by 175 publications

(143 citation statements)

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“…Following the work of Cheng and Howlett [16,18] we assume that n is even and that if k is even if k is odd terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0334270000000746 [12] Optimal driving strategies for a train on a track with continuously varying gradient 399 for k < n. In this regard we note that it has been shown by Howlett [9,10] that any time interval of non-negative measurable control can be approximated as accurately as we please by a sequence of alternate coast and power controls. To find a strategy of optimal type we must solve the key equations.…”

Section: An Algorithm For Solving the Key Equationsmentioning

confidence: 95%

“…In practical terms the important points are the observations that only a finite number of discrete control settings are allowed, that each setting determines a constant rate of fuel supply and that the power developed by the locomotive is directly proportional to the rate of fuel supply. This model has been studied in detail by Cheng and Howlett [15,16,17,18], Howlett [9,10] and Howlett et al [11,12,13,14]. In general terms it is now known that an optimal strategy contains segments of maximum power, speedhold, coast and brake.…”

Section: Previous Researchmentioning

confidence: 99%

“…The Mechanical Energy model was introduced by Milroy [19] and has since been discussed by Howlett [5,6,7,8], Asnis et al [1] and Benjamin et al [2]. This model was also discussed in the recent review paper by Howlett et al [12]. In this model the applied acceleration is the control variable and the cost of the strategy is the mechanical energy required to drive the train.…”

Section: Previous Researchmentioning

confidence: 99%

“…Although Equations (6) and (7) are directly applicable to a point mass train it is important to remark that similar equations with a modified average gradient acceleration can be used to describe a train with distributed mass. This issue is discussed elsewhere by Howlett et al [11,12]. It is often convenient to rewrite the equations of motion in the form ax v and dv Hfi K ()…”

Section: Previous Researchmentioning

confidence: 99%

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Optimal driving strategies for a train on a track with continuously varying gradient

Howlett¹,

Jia-xing²

1997

J. Aust. Math. Soc. Series B, Appl. Math

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This paper derives key equations for the determination of optimal control strategies in an important engineering application. A train travels from one station to the next along a track with continuously varying gradient. 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. This assumption is based on the control mechanism for a typical diesel-electric locomotive. For each setting the power developed by the locomotive is directly proportional to the rate of fuel supply. We assume a single level of braking acceleration. For each fixed finite sequence of control settings we show that fuel consumption is minimised only if the settings are changed when certain key equations are satisfied. The strategy determined by these equations is called a strategy of optimal type. We show that the equations can be derived using an intuitive limit procedure applied to corresponding equations obtained by Howlett [9,10] in the case of a piecewise constant gradient. The equations will also be derived directly by extending the methods used by Howlett. We discuss a basic solution procedure for the key equations and apply the procedure to find a strategy of optimal type in appropriate specific examples.

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Section: An Algorithm For Solving the Key Equationsmentioning

confidence: 95%

Section: Previous Researchmentioning

confidence: 99%

Section: Previous Researchmentioning

confidence: 99%

Section: Previous Researchmentioning

confidence: 99%

See 2 more Smart Citations

Optimal driving strategies for a train on a track with continuously varying gradient

Howlett¹,

Jia-xing²

1997

J. Aust. Math. Soc. Series B, Appl. Math

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“…The operation strategy of eco-driving is to optimize the speed profile of each train, while the utilization of regenerative braking energy is for one train to re-use the energy generated by the braking of other trains. The first topic has been well studied by many researchers [3][4][5][6][7][8][9][10][11][12][13][14][15], while the latter is a rather new approach. It is based on the practice that the acceleration process consumes energy from the power supply network whereas the braking process returns energy to the supply network.…”

Section: Introductionmentioning

confidence: 99%

An Integrated Energy-Efficient Operation Methodology for Metro Systems Based on a Real Case of Shanghai Metro Line One

Gong

Zhang

et al. 2014

Energies

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Metro systems are one of the most important transportation systems in people's lives. Due to the huge amount of energy it consumes every day, highly-efficient operation of a metro system will lead to significant energy savings. In this paper, a new integrated Energy-efficient Operation Methodology (EOM) for metro systems is proposed and validated. Compared with other energy saving methods, EOM does not incur additional cost. In addition, it provides solutions to the frequent disturbance problems in the metro systems. EOM can be divided into two parts: Timetable Optimization (TO) and Compensational Driving Strategy Algorithm (CDSA). First, to get a basic energy-saving effect, a genetic algorithm is used to modify the dwell time of each stop to obtain the most optimal energy-efficient timetable. Then, in order to save additional energy when disturbances happen, a novel CDSA algorithm is formulated and proposed based on the foregoing method. To validate the correctness and effectiveness of the energy-savings possible with EOM, a real case of Shanghai Metro Line One (SMLO) is studied, where EOM was applied. The result shows that a significant amount of energy can be saved by using EOM. OPEN ACCESSEnergies 2014, 7 7306

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Immersion and Invariance Based Robust Adaptive Control of High‐Speed Train with Guaranteed Prescribed Performance Bounds

Luo¹,

Xu²,

Liu³

2015

Asian Journal of Control

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This paper proposes a novel robust adaptive algorithm for train tracking control with guaranteed prescribed transient and steady-state performance. As speed increases, the inherent time-varying uncertainties and unmodeled dynamics in the longitudinal dynamics of a high-speed train seriously impacts the tracking performance of automatic train operation. To improve train operation performance, an estimator based on immersion and invariance technology is developed to recover the unknown and time-varying plant parameters, and it renders the estimation error converging to a bounded residual set exponentially while providing more freedom for the controller. After certain error transformation, the prescribed tracking performance is introduced into the controller design. Then, an input-to-stable stable controller is developed through the backstepping technique, and it is proven that stabilization of the transformed system is sufficient to guarantee the prescribed performance. Rigorous theoretical analysis for the presented algorithm is provided, and a series of simulation studies also are given to verify the effectiveness of it.

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Energy-efficient train control

Cited by 175 publications

References 3 publications

Optimal driving strategies for a train on a track with continuously varying gradient

Optimal driving strategies for a train on a track with continuously varying gradient

An Integrated Energy-Efficient Operation Methodology for Metro Systems Based on a Real Case of Shanghai Metro Line One

Immersion and Invariance Based Robust Adaptive Control of High‐Speed Train with Guaranteed Prescribed Performance Bounds

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