A Physical Two-Zone NO_x Model Intended for Embedded Implementation

Abstract

This paper offers a two-zone N O x model suitable for vehicle on-board, on-line implementation. Similar N O x modeling attempts have previously been undertaken. The hereby suggested method does however offer clear and important benefits over the previously methods, utilizing a significantly different method to handle temperature calculations within the (two) different zones avoiding iterative computation. The new method significantly improves calculation speed and, most important of all, reduces implementation complexity while still maintaining reasonable accuracy and the physical interpretation of earlier suggested methods. The equations commonly used to compute N O x emissions is also rewritten in order to suit a two-zone N O x model. An algorithm which can be used to compute N O x emissions is presented and the intended contribution of the paper is a N O x model, implementation feasible for an embedded system, e.g. embedded processor or embedded electronic hardware (FPGA). For that purpose parts of the algorithm can be pre-computed and stored in tables allowing significant acceleration of the computation.

A Fast Physical NOx Model Implemented on an Embedded System

“…As a 'benchmark' comparison a 'golden model' was used. This golden model was exactly the same as presented in [10].…”

“…This work aims to fill the gap in the area of high resolution, on-line N O x modeling by developing a computationally efficient and fast algorithm implementing the model described in [10]. The performance goal of the algorithm is 'in-cycle' performance, meaning to be able to compute the N O formation during the same cycle it occurs with a high time resolution.…”

“…The model used here is described in deep detail in [10], proving the mathematical concept and evaluating its performance. In order to explain the process of developing an algorithm implementing the model a rudimentary description of the model is never the less included in the paper.…”

Real-time capable virtual NOx sensor for diesel engines based on a two-Zone thermodynamic model

“…Besides the inputs of gas properties this also influences the complexity of governing equations through the inclusion of the partial derivatives of internal energy and gas constant. Some of the RT two-zone models are using constant gas properties in the calculation of the thermodynamic parameters [18,19]. This modeling depth might not provide sufficiently profound basis for achieving high accuracy of the results as will be shown in the Results section of this paper.…”

“…As some of the RT two-zone NO x models are using constant gas properties in the calculation of the thermodynamic parameters [18,19], in this analysis importance to consider variable gas properties to establish a sound basis for modeling NO x emissions is demonstrated. To demonstrate this, two different cases were analyzed (Fig.…”