Low-dimensional Models for Real-time Simulation of Internal Combustion Engines and Catalytic After-treatment Systems



Journal Title

Journal ISSN

Volume Title



The current trend towards simultaneously increasing fuel-to-wheels efficiency while reducing emissions from transportation system powertrains requires system level optimization realized through real-time multivariable control. Such an optimization can be accomplished using low-order fundamentals (first-principles) based models for each of the engine sub-systems, i.e. in-cylinder combustion processes, exhaust after-treatment systems, mechanical and electrical systems (for hybrid vehicles) and sensor and control systems.

In this work, we develop a four-mode low-dimensional model for the in-cylinder combustion process in an internal combustion engine. The lumped parameter ordinary differential equation model is based on two mixing times that capture the reactant diffusional limitations inside the cylinder and mixing limitations caused by the input and exit stream distribution. For given fuel inlet conditions, the model predicts the exhaust composition of regulated gases (total unburned HC's, CO, and NOx as well as the in-cylinder pressure and temperature. The results show good qualitative and fair quantitative agreement with the experimental results published in the literature and demonstrate the possibility of such low-dimensional model for real-time control.

In the second part of this work, we propose a low-dimensional model of the three-way catalytic converter (TWC) for control and diagnostics. Traditionally, the TWC is controlled via an inner-loop and outer-loop strategy using a downstream and upstream oxygen sensor. With this control structure, we rely on the oxygen sensor voltage to indicate whether the catalyst has saturated. However, if the oxidation state of the catalyst could be estimated, than a more pro-active TWC control strategy would be feasible. A reduced order model is achieved by approximating the transverse gradients using multiple concentration modes and the concepts of internal and external mass transfer coefficients, spatial averaging over the axial length and simplified chemistry by lumping the oxidants and the reductants. The model performance is tested and validated using data on actual vehicle emissions resulting in good agreement. The computational efficiency and the ability of the model to predict fractional oxidation state (FOS) and total oxygen storage capacity (TOSC) make it a novel tool for real-time fueling control to minimize emissions and diagnostics of catalyst aging.



Combustion, Three-way catalysts, Low-dimensional models, Monoliths, Catalysis, Kinetics, Ceria, Fundamental based modeling, Controls, Mathematical modeling