Model Order Reduction of 1D Diffusion Systems Via Residue Grouping

A model order reduction method is developed and applied to 1D diffusion systems with negative real eigenvalues. Spatially distributed residues are found either analytically (from a transcendental transfer function) or numerically (from a finite element or finite difference state space model), and residues with similar eigenvalues are grouped together to reduce the model order. Two examples are presented from a model of a lithium ion electrochemical cell. Reduced order grouped models are compared to full order models and models of the same order in which optimal eigenvalues and residues are found numerically. The grouped models give near-optimal performance with roughly $1∕20$ the computation time of the full order models and require 1000–5000 times less CPU time for numerical identification compared to the optimization procedure.