A Low Order Model of SCR-in-DPF Systems with Proper Orthogonal Decomposition

Abstract

This paper presents a method to achieve a low order system model of the urea-based SCR catalyst coated filter (SCR-in-DPF or SCRF or SDPF), while preserving a high degree of fidelity. Proper orthogonal decomposition (POD), also known as principal component analysis (PCA), or Karhunen-Loéve decomposition (KLD), is a statistical method which achieves model order reduction by extracting the dominant characteristic modes of the system and devises a low-dimensional approximation on that basis. The motivation for using the POD approach is that the low-order model directly derives from the high-fidelity model (or experimental data) thereby retains the physics of the system. POD, with Galerkin projection, is applied to the 1D + 1D SCR-in-DPF model using ammonia surface coverage and wall temperature as the dominant system states to achieve model order reduction. The performance of the low-order POD model (with only a few basis modes) shows good agreement with the high fidelity model in steady and transient states analyses. This shows the promise of the application of POD in exhaust after-treatment system (EATS) modelling to achieve high fidelity low order models. In addition system control design is easier for the reduced order model using a modern approach. We demonstrate the performance of a model-based controller applied to the low-order POD model to minimize ammonia slip for a transient test cycle.