Suboptimal control strategies for multilocomotive powered trains

This paper introduces two different controllers for the handling of very long multipowered trains, including braking operations. The purpose of the controller is to minimize coupler forces and velocity deviations from reference values due to grade changes and other disturbances. The controller is superimposed on a throttling and braking schedule which is assumed to be known beforehand. Due to the constraints on the inputs (especially the braking inputs) and the coupler forces that cannot be neglected, a linear control cannot be applied straightforward. Therefore, a switching policy is chosen such that a piecewise linear system results. The linear suboptimal controllers acting between the switching moments are derived from two different small scale train models using standard optimal control design. One model represents a reduced order model of the long train, the other one uses a short train configuration consisting of fewer cars than the given train, where the cars however preserve the original characteristics. From the obtained weighting patterns, a control law for the large scale system is derived. Since not all the states are assumed to be measurable, a simple observer-like structure is used for the estimation of the important missing states needed for the control. Simulation results are presented for a train consisting of three locomotives and sixty cars operating over various grade profiles.