Nilsson, T., Froberg, A., and Aslund, J., "Optimal Operation of a Turbocharged Diesel Engine during Transients," SAE Int. J. Engines 5(2):571-578, 2012, doi:10.4271/2012-01-0711.
Recent development has renewed the interest in drivetrain concepts which give a higher degree of freedom by disconnecting the engine and vehicle speeds. This freedom raises the demand for active control, which especially during transients is not trivial but of which the quality is crucial for the success of the drivetrain concept. In this work the fuel optimal solution for a turbocharged diesel engine connected to a load which does not restrict the engine speed is derived, analysed and utilized for finding a suboptimal operating point trajectory. We use a Willan s efficiency model for the engine, expanded with a first order delay dependent torque reduction representing the turbocharger pressure, and study different output power transients. The analysis is made with dynamic programming, Pontryagin's maximum principle and a suboptimal strategy based on the static optimal operating points. We present a method for using Pontryagin's maximum principle for deriving the optimal operating point trajectory. The time needed for computation was reduced a factor >100 compared to dynamic programming, but this method is only applicable to load cases with steps between different high output powers. We also present a suboptimal method which shows a <1% increase in fuel consumption compared to the optimal, while reducing the time needed for computation a factor >1000 compared to dynamic programming.