Development of a Kalman filter estimator for simulation and control of particulate matter distribution of a diesel catalyzed particulate filter

Abstract

The knowledge of the temperature and particulate matter mass distribution is essential for monitoring the performance and durability of a catalyzed particulate filter. A catalyzed particulate filter model was developed, and it showed capability to accurately predict temperature and particulate matter mass distribution and pressure drop across the catalyzed particulate filter. However, the high-fidelity model is computationally demanding. Therefore, a reduced order multi-zone particulate filter model was developed to reduce computational complexity with an acceptable level of accuracy. In order to develop a reduced order model, a parametric study was carried out to determine the number of zones necessary for aftertreatment control applications. The catalyzed particulate filter model was further reduced by carrying out a sensitivity study of the selected model assumptions. The reduced order multi-zone particulate filter model with 5 × 5 zones was selected to develop a catalyzed particulate filter state estimator considering its computational time and accuracy. Next, a Kalman filter–based catalyzed particulate filter estimator was developed to estimate unknown states of the catalyzed particulate filter such as temperature and particulate matter mass distribution and pressure drop (ΔP) using the sensor inputs to the engine electronic control unit and the reduced order multi-zone particulate filter model. A diesel oxidation catalyst estimator was also integrated with the catalyzed particulate filter estimator in order to provide estimates of diesel oxidation catalyst outlet concentrations of NO₂ and hydrocarbons and inlet temperature for the catalyzed particulate filter estimator. The combined diesel oxidation catalyst–catalyzed particulate filter estimator was validated for an active regeneration experiment. The validation results for catalyzed particulate filter temperature distribution showed that the root mean square temperature error by using the diesel oxidation catalyst–catalyzed particulate filter estimator is within 3.2 °C compared to the experimental data. Similarly, the ΔP estimator closely simulated the measured total ΔP and the estimated cake pressure drop error is within 0.2 kPa compared to the high-fidelity catalyzed particulate filter model.