This paper presents state estimation for a system of diffusion equations coupled in the boundary appearing in reduced electrochemical models of lithium-ion batteries with multiple active materials in single electrodes. The observer is synthesized from a single particle model and is based on the backstepping method for partial differential equations. The observer is suitable for state of charge estimation in battery management systems and is an extension of existing backstepping observers which were derived only for cells with electrodes of single active materials. Observer gains still can be computed analytically in terms of Bessel and modified Bessel functions. This extension is motivated by the trend in cell manufacturing to use multiple active materials to combine power and energy characteristics or reduce degradation.
Electrode-Level State Estimation in Lithium-ion Batteries via Kalman Decomposition