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

Abstract

Selective catalytic reduction (SCR) of NOx with NH 3 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 fundamentalbased, 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.

An Overview of Lean Exhaust deNOx Aftertreatment Technologies and NOx Emission Regulations in the European Union

“…This has allowed the utilisation of 1D heterogeneous PFR models with a detailed kinetic scheme also for real-time applications. Another example of progressive simplification of an SCR advanced model useful for model-based control can be found in the work of Gundlapally et al [119].…”

Data-driven control of automotive diesel engines and after-treatment systems: State of the art and future challenges

“…Therefore, gray-box models consisting of simple chemical-physical models and data-driven models were studied to describe the SCR system dynamics. A gray-box model based on the reduced-order model and physics equations was presented in Gundlapally et al 150 As the reduced-order model consists of several non-stiff equations, it’s efficient to reduce the computational burden. Furthermore, the authors in Zanardo et al 151 depicted a gray approach including a simple first principle model and output error model.…”

“…Applied algorithms Irfan et al, 139 Faghihi and Shamekhi, 141 Zhang et al, 142 Meierjurgen et al, 143 Sui and Hall 144 NN Liu et al, 147 Zhao and Zhang 148 SVM Stadlbauer et al, 137 Zanardo et al 151 OLS Jiang et al 52 FCM, PLS Tayamon et al 149 RPEM Gundlapally et al 150 others practical control of diesel engines and aftertreatment systems.…”

Development of a Nonequilibrium Multisite Kinetic Model for NH3-SCR of NOx on CHA Cu-SAPO-34: Impact of Active Site Configurations and Locations

“…Several global , and detailed ,, non-equilibrium kinetic models for NH 3 -SCR have been proposed for Cu-based zeolite catalysts, as shown in Table . A robust and accurate predictive physico-chemical model is not only valuable for reducing the time and cost of new catalyst development but also, for instance, to control NO x emissions for an embedded SCR sensor system. , Most models are based on fundamental studies and are established following steady state (isothermal and isobar experiments with constant inlet concentrations) or transient sets of experiments (with steep variations from one equilibrium to another or in continuous nonequilibrium conditions); in these studies, the complexity of the devised reaction mechanisms depends heavily on the experimental objective and the phenomena under consideration, including hydrothermal aging, poisoning effects, hydrodynamic impacts, or gas–solid transfer measurements. ,, Thus, by focussing on a limited area, the number of estimated parameters related to the mechanism and the cost in data set and CPU requirements can be maintained at a low level. On the other hand, the model complexity will increase with a detailed modeling approach, multiplying the number of equations, kinetic parameters for estimation, and the interdependency between reactions.…”