Energy-Efficient Train Control (Advances in Industrial by Philip G. Howlett, Peter J. Pudney

By Philip G. Howlett, Peter J. Pudney

Rail is in all likelihood a really effective type of delivery, yet needs to be handy, trustworthy and cost effective to compete with highway and air shipping. optimum regulate can be utilized to discover energy-efficient riding recommendations for trains. This e-book describes the teach keep an eye on challenge and exhibits how an answer was once chanced on on the collage of South Australia. This learn was once used to increase the Metromiser procedure, which supplies energy-efficient riding suggestion on suburban trains. when you consider that then, this paintings has been converted to discover useful using concepts for long-haul trains. The authors describe the background of the matter, reviewing the fundamental mathematical research and correct options of limited optimisation. They define the modelling and answer of the matter and eventually clarify how the gas intake will be minimised for a trip, displaying the influence of velocity limits and song gradients at the optimum riding approach.

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Example text

The resistive acceleration -r(v) is defined by the formula r(v) = a + bv + cv2 where a, b, c > ° are real constants. To define this system precisely we let L ~( [0, T] ) denote the set of measurable and essentially bounded functions on the interval [0, T] with norm IluL = ess. sup lu(t)1 tE 0, T and let Co, l( [0, T]) denote the set of essentially Lipschitz functions on the interval [0, T] with norm Ilvll = Ilvll~ + IIDvll~. 1) defines a corresponding control u E V. = L ~ ([ 0, T] ). We consider the set ~ of all such feasible pairs (u, v) E 'llx 'V where Ilull~:::; 1 and v(O) = v(1) = 0.

However, efficient strategies still require only maximum power, speed-hold, coast and brake. If the performance characteristics of the train are known, efficient speed profiles can be calculated. For long-haul journeys, the performance characteristics of a train are generally not known before a journey commences-in fact, they will change during a journey as wagons are loaded or unloaded, or with changes in wind direction. Thus the future performance of the train must be estimated during the journey from observations of current and past performance.

The energy flows are illustrated in Figure 1-1. The equations of motion can be formulated with time as the independent variable and with position and speed as the dependent state variables. Although this formulation may seem more natural, it is often convenient to use an equivalent formulation with position as the independent variable and with time and speed as the dependent state variables. In the latter formulation it is necessary to control the evolution of time and speed as functions of position.

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