Semi-physical mean-value NOx model for diesel engine control

In this paper, a new physics-based model for the prediction of NOx emissions produced by diesel engines is presented. The aim of this work is to provide a Mean-Value Model (MVM) adapted for control design and online estimation. The proposed approach is based on the simplification of a zero-dimensional thermodynamic model. Only the main phenomena taking part in NOx formation are kept and they are described at a time scale of one engine cycle. A new model is proposed to estimate the burned gas temperature, known to have a strong impact on thermal NOx formation rate, from the first-order input variables on NOx emissions: burned gas ratio and start of combustion. This model is based on a discrete variable: the maximum burned gas temperature. The MVM for the maximum burned gas temperature, associated with a meanvalue NOx formation kinetic model, constitutes our mean-value NOx model. The adaptation of the burned gas temperature model enables to highly improve the accuracy of our crank-angle based model compared to purely physical models, and this accuracy is kept despite the simplification to a MVM. Thus, our MVM presents a sufficient accuracy for engine control purposes in both steady-state and transient operating conditions. This accuracy is achieved with only four parameters identified using a limited number of experimental data.