Model-based state-of-charge estimation for a valve-regulated lead-acid battery using linear matrix inequalities

State-of-charge (SOC) estimation for valve-regulated lead-acid (VRLA) batteries is complicated by the switched linear nature of the underlying dynamics. A first principles nonlinear model is simplified to provide two switched linear models and linearized to produce charge, discharge, and averaged models. Luenberger and switched SOC estimators are developed based on these models and propagated using experimental data. A design methodology based on linear matrix inequalities (LMIs) is used in the switched SOC estimator design to obtain a switched Luenberger observer with guaranteed exponential stability. The results show that estimation errors are halved by including switching in the observer design.