Sensitivity Equations Based Experiment Design and Adaptive Compensation of Transient Fuel Dynamics in Port-Fuel Injection Engines

In this paper we consider and address two topics relevant to calibration of parameters in transient fuel compensation algorithms. The first topic concerns the optimal selection of transient trajectories over which data are collected and identification of parameters in transient fuel model, the inverse of which constitutes a transient fuel compensation algorithm, is performed. We show that this problem can be formulated as an optimal control problem, and that this optimal control problem can berobust solved numerically. Even with the optimal transient trajectories, our results highlight a difficulty in identifying parameters in a transient fuel model if parameters in the model of exhaust gas mixing and in the model of the universal exhaust gas oxygen (UEGO) sensor are uncertain. The second topic addresses this difficulty through the use of adaptation to adjust parameters in a transient fuel compensation algorithm, until the deviation of measured fuel-to-air ratio from the commanded fuel-to-air ratio is sufficiently reduced. Our adaptation approach is shown to be robust to uncertainties in UEGO sensor and exhaust mixing dynamics. The theme common to both developments is the use of differential sensitivity equations.