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

NOx 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 NOx 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 Nox 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 Nox 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.

Carlos Guardiola, Benjamin Pla, David Blanco-Rodriguez and Lars Eriksson

Control Engineering Practice, 2013

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