Control of braking for automatic train operation

An important function of an Automatic Train Operation (ATO) system is to control braking to bring a train to a standstill at a specific location in a smooth and safe manner. To minimise journey times and to improve throughput on a rail network, the time required for braking needs to be minimised. This paper considers braking as an optimal, minimum time control problem and applies the solution as a feedforward braking traction. A feedback controller is then used to ensure that the train speed follows the optimal solution. The feedback is based on a PID controller to align with the existing structure of the ATO system. By considering the controller as a Lur'e system, the Popov criterion provides a limit on the allowable slope of the braking curve and the optimal profile is modified to ensure that this constraint is satisfied. The performance of the controller is evaluated on an industry supplied simulation of the train dynamics.