Reduced order model design for three way catalytic converter temperature dynamics

This paper presents a reduced order model for three way catalyst (TWC) temperature dynamics developed using Proper Orthogonal Decomposition (POD) and Galerkin projection method. The TWC thermal dynamics are described using a set of coupled, non-linear partial differential equations (PDEs). The Galerkin projection method is applied to the PDE-model to construct a set of ordinary differential equations (ODEs) to describe the dynamics of the system. POD extracts a low dimensional basis functions from a high dimensional data set obtained by numerical simulation of the system. This is achieved by performing singular value decomposition (SVD) on the data set and selecting the basis functions corresponding to the most dominant eigenvalues of the system. Using the POD basis functions along with Galerkin projection leads to a low order ODE system that captures the system dynamics described by the physics based model. The results obtained indicate that the a three state reduced-order model obtained using POD-Galerkin is able to capture the thermal dynamics with satisfactory accuracy. The development of the newly proposed control oriented model for TWC thermal dynamics is carried out using experimental data collected from a TWC running on the Federal Test Protocol (FTP) driving cycle.