Hysteresis Compensation in State-of-Charge Estimation with a Nonlinear Double-Capacitor Li-Ion Battery Model

This paper focuses on hysteresis compensation to improve the accuracy of state-of-charge (SoC) estimation in a lithium-ion battery modeled using a recently developed nonlinear double-capacitor representation. 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 in this paper using a physically intuitive modified Preisach representation consisting of a series of hysterons which get switched on or off to produce the hysteresis phenomenon. The proposed model for the hysteresis term is not differentiable but is Lipschitz bounded. A nonlinear observer suitable for Lipschitz nonlinear systems is utilized to guarantee asymptotic stability. The observer design procedure consists of satisfying an LMI-transformable inequality on a set of vertices of a convex function. Experimental data from charging and discharging tests are used to determine the weights of the hysterons in the modified Preisach model. The developed observer is then evaluated using experimental battery data and shown to perform well.