The dynamic model of lithium-ion batteries has typical nonlinearities and uncertainties

the estimation accuracy of the state of charge(SOC) of the lithium-ion batteries directly affects the effect of the monitoring and controlling in battery management system(BMS). To enhance the estimation accuracy of the SOC of the lithium-ion batteries

an adaptive sliding mode observer

which based on a variable gain for lithium-ion battery SOC estimating model is proposed. By using the robustness of the sliding mode observer and based on the second-order RC equivalent circuit model

an integral term is introduced in conventional sliding mode surface to improve the robustness on sliding mode surface

and a gradient descent rule is adopted to achieve gain adaptation to reduce the chattering of observer and improve prediction accuracy and robustness. Simultaneously

the stability of the proposed method is proved using Lyapunov theory. Finally

the proposed method is validated and compared with the sliding mode observe(SMO) method under dynamic stress test(DST) and Federal urban driving schedule(FUDS) conditions. The proposed method has less chattering in estimation with higher estimation accuracy and good robustness.