On Rigorous Model-Order Reduction of the Thermal and Oxygen Storage Dynamics of Three Way Catalytic Converters

Abstract

We present a reduced-order model (ROM) for the temperature and oxygen storage dynamics of three way catalysts (TWCs). The thermal and oxygen storage dynamics are described using a set of coupled, nonlinear partial differential equations (PDEs) developed and experimentally validated in previous research. Advancements in on-board diagnostic (OBD) design are moving in the direction of using physics-based models that would retain as much physical insights as possible. Retaining the one-dimensional (1D) evolution of the internal storage dynamics along the device length is key for the development of accurate emission control strategies. In this work, we adopt the numerical projection orthogonal approach combined with the analytical features of Galerkin reduction method to define a set of ordinary differential equations (ODEs) to describe the oxygen storage and temperature dynamics throughout the device life. Using experimental data collected over three TWC devices, each of different age, and under the excitation of different real drive cycles, we validate the model and quantify the relation between the number of reduced-order states versus model accuracy for devices both new and at different stages of life. The input dependent characteristics of the developed reduced-model model is also investigated using a power spectral density (PSD) analysis. Finally, we show that an initial tuning of the reduced model parameters for a fresh catalyst guarantees satisfactory modeling performance throughout the device life, regardless of the driving scenario.