# Control-oriented input-delay model of the distributed temperature of a SI engine exhaust catalyst

May 2014 Category: Delay systems | All

**Authors**: D. Bresch-Pietri, T. Leroy, and N. Petit, in Low complexity controllers for time-delay systems, pp. 173-188, C. Bonnet, H. Mounier, H.Özbay and A. Seuret Ed., 2014, Springer

This chapter aims at showing how a particular class of input delay ordinary differential equations, in which the time- and input-dependent delay is defined through an implicit integral equation, can be used to model accurately the internal temperature of a Spark-Ignited engine catalyst. The modeling approach is grounded on a one-dimensional distributed parameter model, which is approximated by a time-varying first-order delay system whose dynamics parameters (time constant, delay, gains) are obtained through a simple analytic reduction procedure. Following recent works, the distributed heat generation resulting from pollutant conversion is shown here to be equivalent to an inlet temperature entering the system at a virtual front inside the catalyst. The gain of this new input introduces a coupling to ac- count for the conversion efficiency. Relevance of this real-time compliant model is qualitatively supported by experimental data.

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**BibTeX**:

@Incollection{,

author = {D. Bresch-Pietri, T. Leroy, and N. Petit},

title = {Control-oriented input-delay model of the distributed temperature of a SI engine exhaust catalyst},

booktitle = {Low complexity controllers for time-delay systems},

editor = {C. Bonnet, H. Mounier, H.Özbay and A. Seuret},

publisher = {Springer},

address = {},

pages = {173-188},

year = {2014},

abstract = {This chapter aims at showing how a particular class of input delay ordinary differential equations, in which the time- and input-dependent delay is defined through an implicit integral equation, can be used to model accurately the internal temperature of a Spark-Ignited engine catalyst. The modeling approach is grounded on a one-dimensional distributed parameter model, which is approximated by a time-varying first-order delay system whose dynamics parameters (time constant, delay, gains) are obtained through a simple analytic reduction procedure. Following recent works, the distributed heat generation resulting from pollutant conversion is shown here to be equivalent to an inlet temperature entering the system at a virtual front inside the catalyst. The gain of this new input introduces a coupling to ac- count for the conversion efficiency. Relevance of this real-time compliant model is qualitatively supported by experimental data.},

keywords = {}}