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Urea-selective catalytic reduction (SCR) after-treatment systems are used for reducing oxides of nitrogen (NOx) emissions in medium and heavy duty diesel vehicles. This paper addresses control-oriented modeling, starting from first-principles, of SCR after-treatment systems. Appropriate simplifications are made to yield governing equations of the Urea-SCR. The resulting nonlinear partial differential equations (PDEs) are discretized and linearized to yield a family of linear finite-dimensional state-space models of the SCR at different operating points. It is further shown that this family of models can be reduced to three operating regions. Within each region, parametric dependencies of the system on physical mechanisms are derived. Further model reduction is shown to be possible in each of the three regions resulting in a second-order linear model with sufficient accuracy.

The optimized design of an exhaust emission system in terms of performance, cost, packaging, and engine control strategy will be a key part of competitively meeting future more stringent emission standards. Extensive use of vehicle experiments to evaluate design system tradeoffs is far too time consuming and expensive. Imperative to successfully meeting the challenges of future emission regulations and cost constraints is the development of an exhaust system simulation model which offers the ability to sort through major design alternatives quickly while assisting in the interpretation of experimental data. Previously, detailed catalyst models have been developed which require the specification of intricate kinetic mechanisms to determine overall catalyst performance. While yielding extremely valuable results, these models use complex numerical algorithms to solve multiple partial differential equations which are time consuming and occasionally numerically unstable.