Hysteresis Compensation and Nonlinear Observer Design for State-of-Charge Estimation Using a Nonlinear Double-Capacitor Li-Ion Battery Model

Abstract

This article focuses on state-of-charge (SoC) estimation for a lithium-ion battery modeled using a recently developed nonlinear double-capacitor representation that has been shown to be highly accurate. The measurement equation of the model has two nonlinear functions, one of them being significant hysteresis in voltage as a function of the SoC. The hysteresis term is modeled using a physically intuitive modified Preisach representation consisting of a series of hysterons which get switched <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</small> or <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">off</small> to produce the hysteresis phenomenon. The proposed model for the hysteresis term is not differentiable but is Lipschitz bounded. A custom nonlinear observer is designed for this class of nonlinear systems using Lyapunov analysis to guarantee asymptotic stability. The observer design procedure consists of satisfying a linear matrix inequality on a set of vertices of a convex function. The developed observer is evaluated using experimental battery data. Experimental data is also used to determine the weights of the hysterons in the data-based modified Preisach model. The nonlinear observer performs well, yielding accurate SoC estimates in the presence of hysteresis. The nonlinear observer is also compared with the extended Kalman filter and the unscented Kalman filter, and is seen to provide superior performance for the same application due to its guaranteed global convergence properties. A broad technical contribution of this article is the development of an observer design method to handle the presence of hysteresis in nonlinear systems.