Model Predictive Control for Real-time Position Tracking of a Catenary-free Tram

Abstract Automatic Train (or Tram) Operation (ATO) systems have been widely studied in the last decade to guarantee energy-efficient operation. Speed profiles and timetables are derived by applying optimization methods geared towards finding the optimal trade-off between journey time, emissions and energy efficiency. An on-board controller is required to track such optimal trajectories, despite model uncertainties. Due to the non-linear dynamics and non-holonomic constraints on both inputs and outputs, the tracking of such trajectories represents a difficult task. This paper deals with the design of the tracking algorithm, for a catenary-free tram, with regenerative braking. A Model Predictive Control (MPC) approach is used to track the optimal position profile. Thanks to the ability to easily deal with multivariable systems, make use of the references and disturbances preview, and enforce time-varying input/output constraints, MPC is the perfect candidate to fulfill this task. The proposed MPC formulation is simple enough to be implemented in real-time, with a quadratic programming solver. Results show that the algorithm tracks the position reference, and guarantees punctuality and comfort, while enforcing time-varying constraints on vehicle velocity, electrical machine and friction forces. The results are also confirmed in the case of operation with model mismatch.