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Vehicle emissions and fuel economy in real-world driving conditions are currently under considerable scrutiny. Key to achieving optimum performance for a given hardware set and control scheme is a calibration that optimizes controller gains such that inputs are scheduled over the operating space to minimize emissions and maximize fuel economy. Generating a suitable calibration requires data that is both precise and accurate, this data is used to generate models that are deployed as part of the calibration optimization process. This paper evaluates the repeatability of typical steady-state measurements used for calibration of engine controllers that will ultimately determine vehicle level emissions for homologation include Real Driving Emissions (RDE). Stabilization requirements as indicated by three different measurements are evaluated and shown to be different within the same experiment, depending on the metric used.

Models of hybrid powertrains are used to establish the best combination of conventional engine power and electric motor power for the current driving situation. The model is characteristic for having two control inputs and one output constraint: the total torque should be equal to the torque requested by the driver. To eliminate the constraint, several alternative formulations are used, considering engine power or motor power or even the ratio between them as a single control input. From this input and the constraint, both power levels can be deduced. There are different popular choices for this one control input. This paper presents a novel model based on an input linearizing transformation. It is demonstrably superior to alternative model forms, in that the core dynamics of the model (battery state of energy) are linear, and the non-linearities of the model are pushed into the inputs and outputs in a Wiener/Hammerstein form.

The process of engine mapping in the automotive industry identifies steady-state engine responses by running an engine at a given operating point (speed and load) until its output has settled. While the time simulating this process with a computational model for one set of parameters is relatively short, the cumulative time to map all possible combinations becomes computationally inefficient. This work presents an alternative method for mapping out the steady-state response of an engine in simulation by applying bifurcation theory. The bifurcation approach used in this work allows the engine’s steady-state response to be traced through the model’s state-parameter space under the simultaneous variation of one or more model parameters. To demonstrate this approach, a bifurcation analysis of a simplified nonlinear engine model is presented.