Determination of the transfer function between the injected flow-rate and high-pressure time histories for improved control of common rail diesel engines

Theoretical and experimental methodologies have been proposed and illustrated to determine the transfer function between the injected flow-rate and the rail pressure for common rail injection systems. An analytical transfer function has been calculated in the frequency domain, utilizing a previously developed lumped parameter model of the overall hydraulic layout of a common rail system. The predicted transfer function has been compared, in a Bode diagram, with an experimental estimation of the transfer function, based on the measured rail pressure and injected flow-rate time histories that were acquired at the hydraulic rig for different working conditions. The experimental estimation of the transfer function has been worked out by applying a selective spectral technique in order to reduce the effects of measurement noise on the rail pressure and injected flow-rate time histories. The accuracy of the model-derived transfer function has been improved significantly by integrating a pressure control system sub-model, which includes the action of the electronic control unit on the rail pressure time history through the pressure regulator, in the hydraulic model of the common rail circuit. Finally, the time histories of the rail pressure, predicted by means of the complete injection apparatus model, have been compared with the corresponding experimental traces at different working conditions and a very satisfactory agreement has in general been found. The methodologies proposed for the accurate evaluation of the transfer function between the injected flow-rate and the rail pressure time histories can be applied to diesel engines in order to implement innovative closed-loop strategies for the injected mass control.