A computationally efficient Kalman filter based estimator for updating look-up tables applied to NOx estimation in diesel engines

Abstract

No-x estimation in diesel engines is an up-to-date problem but still some issues need to be solved. Raw sensor signals are not fast enough for real-time use while control-oriented models suffer from drift and aging. A control-oriented gray box model based on engine maps and calibrated off-line is used as benchmark model for No-x estimation. Calibration effort is important and engine data-dependent. This motivates the use of adaptive look-up tables. In addition to, look-up tables are often used in automotive control systems and there is a need for systematic methods that can estimate or update them on-line. For that purpose, Kalman filter (KF) based methods are explored as having the interesting property of tracking estimation error in a covariance matrix. Nevertheless, when coping with large systems, the computational burden is high, in terms of time and memory, compromising its implementation in commercial electronic control units. However look-up table estimation has a structure, that is here exploited to develop a memory and computationally efficient approximation to the KF, named Simplified Kalman filter (SKF). Convergence and robustness is evaluated in simulation and compared to both a full KF and a minimal steady-state version, that neglects the variance information. SKF is used for the online calibration of an adaptive model for No-x estimation in dynamic engine cycles. Prediction results are compared with the ones of the benchmark model and of the other methods. Furthermore, actual online estimation of No-x is solved by means of the proposed adaptive structure. Results on dynamic tests with a diesel engine and the computational study demonstrate the feasibility and capabilities of the method for an implementation in engine control units. (C) 2013 Elsevier Ltd. All rights reserved.