Fast Adaptive Observers for Battery Management Systems

The underlying models of lithium-ion batteries are spatiotemporal and, therefore, consist of partial differential equations (PDEs), as they have to capture spatiotemporal electrochemical mechanisms. As parametric uncertainty increases, often PDE models become inadequate as modeling errors due to parameter uncertainty are much larger than those due to model reduction to ordinary differential equations (ODEs). In this paper, we focus on a linear ODE model derived from the PDE combined with algebraic nonlinearities to carry out parameter identification. The ODE model captures the diffusion dynamics while the nonlinearities capture the overpotential and open-circuit potential aspects. The parameter identification method consists of a matrix-regressor adaptive observer, whose regressors are composed using both the states of the linear dynamic model and suitably constructed basis functions of the algebraic nonlinearities. Under conditions of persistent excitation, the parameter and state estimation errors are shown to converge to zero if the overpotential is known, and to a compact set if the overpotential is unknown. A PDE-based single-particle model is used as the truth model to evaluate the accuracy of the proposed adaptive observer. It is shown that the adaptive observer is able to carry out fast estimation of internal states for a battery management system, such as the state of charge and state of health, under a range of operating conditions.