Development of ECU Capable Grey-Box Models from Detailed Models—Application to a SCR Reactor

Selective catalytic reduction (SCR) of NOx with NH₃ is a widely used after-treatment technology for reducing the NOx emissions from diesel engines. Mathematical models play an important role in analyzing and optimizing SCR reactors and also in controller design. Detailed mathematical models of SCR reactors consist of a number of coupled differential and algebraic equations, which can only be solved numerically. Due to the limited computational capability of engine control unit (ECU) and hardware-in-loop (HIL) systems, it is not practical to solve detailed model equations on these systems in real time, and hence, there is a need for reduced-order models. In this work, we provide a systematic procedure for deriving reduced-order models from detailed models of a SCR reactor. This systematic procedure consists of making reasonable assumptions, good input signal design, and system identification procedure. The reduced-order model consists of non-stiff system of equations which can be solved with an explicit solver, is two to three orders of magnitude faster than the detailed model, and has same level of accuracy as detailed model. The proposed model remains fundamental-based, with model parameters directly related to physical and chemical properties of the catalyst, and can be used on ECU and HIL systems to predict ammonia storage, NOx conversion efficiency, and ammonia slip during transient operating conditions. Moreover, it is shown that the model equations can be easily linearized around various operating points, thus allowing the development of advanced control strategies based on linear control theory. Although mainly demonstrated in the context of SCR reactors, the procedures can be applied to other monolith reactors as well.