Controlling electric traction drives for minimum energy wastage

The inclusion of a gradient load, as a fixed but arbitrary function of distance travelled, is investigated within the design of an optimal controller for electric traction drives. A successful approach is shown to involve (a) the sub-division of a journey into N piecewise constant-gradient stages, (b) the interative solution of the state and costate system equations at each stage transition and (c) the use of general dynamic programming to optimise the overall journey with respect to the initial velocities and subsequent stage times at each transition. Step (b) is achieved utilising a sensitivity model for initial costate iteration based on analytic zero-gradient solutions. The iterative scheme is shown to be stable for all conditions other than large downhill gradients, reverse-time integration being necessary under such circumstances. The minimisation of the combined mechanical and electrical energy losses is advocated and savings from 15 to 25% are demonstrated.