Energy-efficient Control of Freight Trains on Steep Gradients

Many researches about energy-efficient control of freight trains are mainly based on the assumption that the track is non-steep. However, steep downhill/uphill gradients are very common in China's freight lines, where trains cannot maintain a constant speed on steep gradients. In this paper, the motion of a freight train is formulated with a continuous control model, and the optimal control when Partial Traction is interrupted by steep gradients are discussed. To avoid the complex calculation of differential equations on steep gradients, this paper introduces a new method which minimizes the fluctuation of speed on steep gradients and its necessary conditions are developed to solve optimal switching points. Finally, the simulation examples demonstrate that the proposed method with less calculation time performs better than the method of adjoint variable.