A fast and accurate physics-based model for the NOx emissions of Diesel engines

To date, models for the nitrogen-oxide emissions of Diesel engines are either of empirical or phenomenological nature. The former are fast and quantitatively accurate in the identified region, but lack the generality and extrapolation capability of the latter. The model presented in this work combines the advantages of both model types and thus complies with typical requirements of computationally intensive fields such as dynamic optimisation and model-based control. This unique aggregation of features is achieved by extracting the most relevant physical phenomena and extending them by physically motivated empirical elements. Exploiting the assumptions made and using a setpoint-relative formulation leads to a simple model structure, comprising one map and 10 scalar parameters only. Execution speed is roughly 500 times faster than real-time and throughout the entire engine operating-range, also during transient operation, relative errors are below 10% even for the largest allowable, simultaneous variation of all inputs. Apart from engine speed and injected fuel-mass, the model requires the cylinder-charge, its composition, and the start of combustion with the corresponding pressure and temperature as inputs. The latter can either be obtained from measured in-cylinder pressure signals, or may be calculated from quantities provided by a model for the air path of the engine.