The gas exchange process in a modern diesel engine is generally modeled using manufacturer-provided performance maps that describe mass flows through, and efficiencies of, the turbine and compressor. These maps are typically implemented as look-up tables requiring multiple interpolations based on pressure ratios across the turbine and compressor, as well as the turbocharger shaft speed. In the case of variable-geometry turbochargers, the nozzle position is also an input to these maps. This method of interpolating or extrapolating data is undesirable when modeling for estimation and control, and though there have been several previous efforts to reduce dependence on turbomachinery maps, many of these approaches are complex and not easily implemented in engine control systems. As such, the aim of this paper is to reduce turbocharger maps to analytical functions for models amenable to estimation and control.
Some properties of analytical functions related to Borel distribution series
