$H_{\infty }$-Based Nonlinear Observer Design for State of Charge Estimation of Lithium-Ion Battery With Polynomial Parameters

This paper focuses on the state-of-charge (SOC) estimation of the Lithium-ion battery in electric vehicles based on an H_∞-based nonlinear observer. First, the second-order RC equivalent circuit model is introduced by utilizing the physical behavior of the battery. Then, the parameters in the second-order RC model are identified as polynomial functions with respect to SOC. Meanwhile, the battery model with constant parameters is also introduced for comparison. Due to that the battery model is undetectable, an one-sided Lipschitz condition is proposed to ensure that the nonlinear function in output equation can play a positive role in the observer design. After that, a nonlinear observer design criterion is presented based on the H_∞ method, which is formulated as linear matrix inequalities. Compared with existing nonlinear observer-based SOC estimation methods, the proposed observer design criterion does not depend on any estimates of the unknown variables. Consequently, the convergence of the proposed nonlinear observer is guaranteed for various operating conditions. Finally, one static and three dynamic operation conditions are given to show the efficiency of the proposed nonlinear observer by comparing with the classic extended Kalman filter and the nonlinear observer for constant parameters.