On-Line Adaptation of Grid-Based Look-up Tables Using a Fast Linear Regression Technique

Abstract

Advanced control systems require accurate process models, while processes are often both nonlinear and time variant. After introducing the identification of nonlinear processes with grid-based look-up tables, a new learning algorithm for on-line adaptation of look-up tables is proposed. Using a linear regression approach, this new adaptation algorithm considerably reduces the convergence time in relation to conventional gradient-based adaptation algorithms. An application example and experimental results are shown for the learning feedforward control of the ignition angle of a spark ignition engine.

Modelling and observation of exhaust gas concentrations for diesel engine control

“…A well-known method consists of using a step transition in the measured quantity [10]. However, usual means for providing step-like transition in gas concentration are complex set-ups with fast valves and synthetic gas mixes [11], which can hardly being implemented on-board.…”

“…Two algorithms are designed based on the KF for a computationally efficient table updating: a simplified KF (SKF) which manipulates the covariance matrix P and the associated updates efficiently, and a steady-state approach for the KF (SSKF) which directly neglects covariance information. Both methods are inspired by the works presented in [10][11][12].…”

“…A RT NO x model is proposed using EGRλ ¡1 for representing the intake oxygen jointly with maps and corrections fitting the operating point dependency [11]. The model scheme is outlined in Figure 4.8.…”

“…Selection of the model structure. In order to find a suitable model equation for a RT NO x model, different structures may be used [11,12]. Both correlations have advantages and drawbacks: single point fitting is more flexible than two point for mathematical adjustment but with a smaller accuracy in points far from the nominal, however the single point one is easier to calibrate as only one map or reference must be tuned.…”

“…The modern diesel engine comprises of variable geometry turbocharging [10] for increasing the intake air mass flow, common-rail systems for allowing multiple and controlled injections [11], an exhaust gas recirculation (EGR) [12] for reducing NO x and different after-treatment (AT) systems [13] such as the diesel particulate filter (DPF) for trapping soot, the diesel oxidation catalyst (DOC) for eliminating HC and the selective catalyst reduction (SCR) or the lean NO x trap (LNT) for removing NO x . These advances make the diesel engine a sophisticated system that requires an engine control unit (ECU) for an appropriate management and a growing complexity on calibration and implementation.…”