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

• New control-oriented model to predict NOx emissions in diesel engines.
• Semi-physical mean-value burned gas temperature and average NOx kinetic models.
• Experimental validation of the virtual NOx sensor in steady-state and transient operations.
• Computation time compliant for online NOx estimation on series ECU.

A semi-physical model has been developed to predict nitrogen oxide (NOx) emissions produced by diesel engines. This model is suitable for online NOx estimation and for model-based engine control. It is derived from a zero-dimensional thermodynamic model which was simplified by only retaining main phenomena contributing to NOx formation. The crank angle evolution of the burned gas temperature, which has a strong impact on NOx formation rate, is described by a semi-empirical model whose key variable is the maximum burned gas temperature. This variable presents a good correlation with the molar fraction of NOx at the end of combustion and can be expressed as a function of the intake burned gas ratio and the start of combustion. The maximum burned gas temperature sub-model is then coupled to an averaged NOx formation kinetic model (based on the Zeldovich mechanism) to form a mean-value model for NOx computation. This latter model was validated using data sets recorded in two diesel engines for steady-state operating conditions as well as for several driving cycles including parametric variations of the engine calibration.