In this work, the problem of reduction of energy consumption based on calculated speed, called eco-driving trajectory for tramway system is investigated, where some constraints on the states, control input and travel time are considered. Thanks to the operating speed range of the tramway, the non-linear model of the system can be approximated by linear one and is given in a state space distance based formulation. The problem studied in this work is to determine the speed profile that minimizes the cost function defined as the energy consumption. Firstly, the constrained optimization problem is formulated as Kuhn-Tucker conditions, which is the general form of the Pontryagin maximum principle, that yield to a local minimum. Then, the control strategy that ensure the efficient consumption for the tramway system is deduced based on the optimal control approach. This leads to the well known driving trajectory for the railway system, which is divided into four phases: acceleration, speed holding, coasting, and braking. On the other hand, the energy consumption analysis allows us to write the cost function as a sum of the kinetic energy to move the train and the resistance forces, by taking into account the gradient and limitations. Based on this analysis, the necessary condition for a is obtained. That ensure method is used to find energy-efficient driving trains. In this paper, we show how to calculate the critical switching points for an optimal strategy non-linear programming algorithm is used to solve the optimal control problem.
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