Optimal Control as a method for Diesel engine efficiency assessment including pressure and NOx constraints

The present paper studies the optimal heat release law in a Diesel engine to maximise the indicated efficiency subject to different constraints, namely: maximum cylinder pressure, maximum cylinder pressure derivative, and NOx emission restrictions. With this objective, a simple but also representative model of the combustion process has been implemented. The model consists of a 0D energy balance model aimed to provide the pressure and temperature evolutions in the high pressure loop of the engine thermodynamic cycle from the gas conditions at the intake valve closing and the heat release law. The gas pressure and temperature evolutions allow to compute the engine efficiency and NOx emissions. The comparison between model and experimental results shows that despite the model simplicity, it is able to reproduce the engine efficiency and NOx emissions. After the model identification and validation, the optimal control problem is posed and solved by means of Dynamic Programming (DP). Also, if only pressure constraints are considered, the paper proposes a solution that reduces the computation cost of the DP strategy in two orders of magnitude for the case being analysed. The solution provides a target heat release law to define injection strategies but also a more realistic maximum efficiency boundary than the ideal thermodynamic cycles usually employed to estimate the maximum engine efficiency.