Nonlinear Circle-Criterion Observer Design for an Electrochemical Battery Model

Smart battery management systems require reliable information on the internal state of the battery, which are unavailable through direct measurements. Electrochemical models are relevant in this context as these describe the internal phenomena governing the battery dynamics. These models can thus be used to design observers, which provide estimates of the state variables online. In this paper, we consider a single particle electrochemical model of a lithium-ion battery given by a set of ordinary differential equations built from the spatial discretization of partial differential equations (PDEs) that locally describe the mass and charge transport of lithium. We then design a nonlinear observer, whose global exponential stability and robustness are guaranteed provided that a linear matrix inequality holds. The latter is shown to be verified for standard model parameters values. Simulation results based on plug-in hybrid electric vehicle tests on the original PDE model are presented, which illustrate the good performances of the observer in terms of speed of convergence and robustness.