Optimal Step Responses in Diesel-Electric Systems

Abstract— A non-linear four state-three input mean value engine model, incorporating the important turbocharger dynamics, is used to study optimal control of a diesel-electric powertrain during transients. The optimization is conducted for two different criteria, both time and fuel optimal control, and both engine speed and output power are considered free variables in the optimization. The transients considered are steps from idle to a target power and the results of the optimization show that the solutions can be divided into two categories, depending on requested power. The resulting control strategies are also seen to be valid for other initial conditions than idle. For steps to high power the controls for both criteria follow a similar structure, a structure given by the maximum torque line and the smoke-limiter. The main difference between fuel and time optimal control is the end operating point, and how this is approached. The fuel optimal control builds more kinetic energy in the turbocharger, reducing the necessary amount of kinetic energy in the system to produce the requested power. It is found that the fact that it does not approach the fuel optimal operating point relates to the amount of produced energy required to get there. For steps to low output powers the optimal controls deal with the turbocharger dynamics in a fundamentally different way.