Control-Oriented Input-Delay Model of the Distributed Temperature of a SI Engine Exhaust Catalyst

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 account for the conversion efficiency. Relevance of this real-time compliant model is qualitatively supported by experimental data.KeywordsDriving CyclePartial Differential EquationDistribute Parameter ModelExhaust Mass FlowPartial Differential Equation ModelThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.