A bias correction method for fast fuel-to-air ratio estimation in diesel engines

λ probes in turbocharged diesel engines are usually located downstream of the turbine, exhibiting a good dynamic response but a significant delay because of the exhaust line transport and the hardware itself. With the introduction of after-treatment systems, new sensors that can measure the exhaust concentrations are required for optimal control and diagnosis. Zirconia-based potentiometric sensors permit the measurement of nitrogen oxides and oxygen with the same hardware. However, their dynamic response is slower and more filtered than that of traditional λ probes and, in addition, the sensor location downstream of the after-treatment systems increases this problem. The paper uses a Kalman filter for online dynamic estimation of the relative fuel-to-air ratio λ⁻¹ in a turbocharged diesel engine. The combination of a fast drifted fuel-to-air ratio model with a slow but accurate zirconia sensor permits the model bias to be corrected. This bias is modelled with a look-up table depending on the engine operating point and is integrated online on the basis of the Kalman filter output. The calculation burden is alleviated by using the converged gain of the steady-state Kalman filter, precalculated offline. Finally, robustness conditions for stopping the bias updating are included in order to account for the sensor and model uncertainties. The proposed algorithm and sensor layout are successfully proved in a turbocharged diesel engine. Experimental and simulation results are included to support validation of the algorithm.