Control-oriented turbine power model for a variable-geometry turbocharger

A control-oriented model for the variable-geometry turbocharger is critical for model-based variable-geometry turbocharger control design. Typically, the variable-geometry turbocharger turbine power is modeled with a fixed mechanical efficiency of the turbocharger on the assumption of an isentropic process. The fixed-efficiency approach is an oversimplification and may lead to modeling errors because of an overpredicted or underpredicted compressor power. This leads to the use of lookup-table-based approaches for defining the mechanical efficiency of the turbocharger. Unfortunately, since the vane position of a variable-geometry turbocharger introduces a third dimension into these maps, real-time implementation requires three-dimensional interpolations with increased complexity. Map-based approaches offer greater fidelity in comparison with the fixed-efficiency approach but may introduce additional errors due to interpolation between the maps and extrapolation to extend the operational range outside the map. Interpolation errors can be managed by using dense maps with extensive flow bench testing; smooth extrapolation is necessary when the turbine is operated outside the mapped region, e.g. in low-flow and low-speed conditions. Extending the map to this region requires very precise flow control and measurement using a motor-driven compressor, which currently is not a standard test procedure. In this paper, a physics-based control-oriented model of the turbine power and the associated power loss is proposed and developed, where the turbine efficiency is modeled as a function of both the vane position of the variable-geometry turbocharger and the speed of the turbine shaft. As a result, the proposed model eliminates the interpolation errors with smooth extension to operational conditions outside typically mapped regions.