Including Drag Phases in Numerical Optimal Control of Diesel Engines

This paper shows how drag phases in driving cycles can be included in a framework for the numerical optimal control of Diesel engines. We first consider a straightforward implementation derived from the procedure to operate an engine on a homologation cycle. Due to the non-causal nature of the optimal-control problem, the resulting controls, however, produce an arbitrarily high drag torque. In order to obtain results which are more suitable to derive or assess causal control strategies, we suggest an adaptation of the problem formulation. This adaptation allows the tradeoff between the reduction of the fuel consumption on the driving cycle and the driveability of the vehicle to be adjusted. As side benefits, the optimal-control problem becomes simpler to formulate, and its numerical solution converges faster due to a reduction of the search space.