One of the most overlooked and oversimplified components of an engine model used for model based air-to-fuel ratio (AFR) control and/or diagnostics is the exhaust gas dynamics model. Without a proper model of the exhaust system, the mixing of exhaust gases and the dynamic transport delays are challenging to capture accurately, even with a meticulous experimental calibration. By representing the exhaust system with a finite impulse response (FIR) model whose coefficients are based on physical properties, these effects can be predicted accurately and smoothly across the complete range of operating conditions. Through on-line and off-line techniques, this model can markedly improve the performance of both open loop and closed loop AFR control. Because a FIR model has a linear relationship between the input and the output, the input error trajectory can be identified from a single precatalyst oxygen sensor measurement. This technique can be used to supplement the calibration of either the feed-forward or feedback portion of the AFR controller. Additionally, the FIR model can be used for on-line estimation of cylinder imbalance errors. This model based approach to cylinder imbalance estimation has several advantages over the current empirically based methods including robustness and ease of calibration.

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