Current turbocharger models are based on characteristic maps derived from experimental measurements taken under steady conditions on dedicated gas stand facility. Under these conditions heat transfer is ignored and consequently the predictive performances of the models are compromised, particularly under the part load and dynamic operating conditions that are representative of real powertrain operations.
This paper proposes to apply a dynamic mathematical model that uses a polynomial structure, the Volterra Series, for the modelling of the turbocharger system. The model is calculated directly from measured performance data using an extended least squares regression. In this way, both compressor and turbine are modelled together based on data from dynamic experiments rather than steady flow data from a gas stand. The modelling approach has been applied to dynamic data taken from a physics based model, acting as a virtual test cell. Varying frequency sinusoidal signals were applied to the compressor and turbine pressure ratios and turbine inlet temperature to drive the physic model.
The results show that, for both turbine and compressor the coefficient of determination (R2) values of outlet temperature, mass flow and apparent efficiency models are close to 1. Furthermore, by comprising the RMSE for predicting a transient event, the Volterra series showed a much better accuracy than a conventional map based model with the improvements in outlet gas temperatures from 18°C to 4°C and 34°C to 9°C for compressor and turbine respectively. The Volterra series shows the potential to get a much more accurate dynamic engine model, which demonstrates the potential of this approach to replace current modelling approaches for simulation and controller applications.