Functional Observer Design for Li-Ion Battery State of Charge Estimation via Descriptor Systems Theory

This paper addresses the problem of Li-ion battery state of charge (SOC) estimation by proposing a novel functional observer for linear descriptor systems. The battery is modeled as a discrete-time linear descriptor system represented by simultaneous difference and algebraic equations (DAEs). The model is achieved by employing a linear approximation of the battery’s open-circuit voltage (OCV). A first-order equivalent circuit model (ECM) of battery is used because of its simplicity, reliability, and balance of accuracy. A new set of sufficient conditions for the existence of the functional observer is directly provided in terms of system coefficient matrices. Besides the purely algebraic approach, the observer design is also formulated in terms of a feasible linear matrix inequality (LMI) problem. A constant current charge and discharge are employed to evaluate the performance of the proposed observer. The results demonstrate the effectiveness of both the battery modeling and the observer design approach in estimating the SOC.