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

This chapter aims at showing how a particular class of input delay ordinary differential equations, in which the timeand 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 account for the conversion efficiency. Relevance of this real-time compliant model is qualitatively supported by experimental data.