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Development of propulsion control systems frequently involves large-scale transient simulations, e.g. Monte Carlo simulations or drive-cycle optimizations, which require fast dynamic plant models. Models of the air-path—for internal combustion engines or fuel cells—can exhibit stiff behavior, though, causing slow numerical simulations due to either using an implicit solver or sampling much faster than the bandwidth of interest to maintain stability. This paper proposes a method to reduce air-path model stiffness by adding an impedance in series with potentially stiff components, e.g. throttles, valves, compressors, and turbines, thereby allowing the use of a fast-explicit solver. An impedance, by electrical analogy, is a frequency-dependent resistance to flow, which is shaped to suppress the high-frequency dynamics causing air-path stiffness, while maintaining model accuracy in the bandwidth of interest.

Many excellent papers have been written about the subject of estimating engine-out NOx on diesel engines based on real-time available data. The claimed accuracy of these models is typically around 6-10% on validation data sets with known inputs. This reported accuracy typically ignores input uncertainties, thus arriving at an optimistic estimate of the model accuracy in a real-time application. In our paper we analyze the effect of input uncertainty on the accuracy of engine-out NOx estimates via a numerical Monte Carlo simulation and show that this effect can be significant. Even though our model is based on an in-cylinder pressure sensor, this sensor is limited in its capability to reduce the effect of other measured inputs on the model.