Lithium-Sulfur Battery State Estimation Using an Inverse Dynamics Model

This paper examines the lithium-sulfur (Li-S) battery state estimation problem. Li-S batteries promise to deliver higher energy storage capacities per unit mass compared to today's lithium-ion batteries. This is particularly attractive for applications such as aviation electrification. Unfortunately, state estimation for Li-S batteries is quite challenging due to the high order and nonlinearity of the underlying physics. Previous research builds Li-S battery models, parameterizes them from experimental data, and utilizes them for state estimation. Model complexity is visible as a challenge throughout this literature, including the fact that many existing Li-S battery models take the form of differential algebraic equations (DAEs). We address this complexity challenge by making three contributions to the literature. First, we employ model causality inversion to translate an existing Li-S battery model in the literature from DAEs to explicit ordinary differential equations (ODEs). Second, we show that the resulting <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$7^{\text {th}}$</tex> order ODE model contains two redundant state variables, thereby reducing it to a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$5^{\text {th}}$</tex> order model. Finally, we exploit the structure of the model to construct a simple switching state estimation law. Simulation studies show that this enables accurate state estimation using a much simpler approach compared to the literature.