  Accurate estimation of the internal states of lithium-ion batteries is key
towards improving their management for safety, efficiency and longevity
purposes. Various approaches exist in the literature in this context, among
which designing an observer based on an electrochemical model of the battery
dynamics. With this approach, the performance of the observer depends on the
accuracy of the considered model. It appears that electrochemical models, and
thus their associated observer, typically require to be of high dimension to
generate accurate internal variables. In this work, we present a method to
mitigate this limitation by correcting the lithium concentrations generated by
a general class of finite-dimensional electrochemical models such that they
asymptotically match those generated by the original partial differential
equations (PDE) they are based on, for constant input currents. These
corrections apply irrespectively of the order of the considered
finite-dimensional model. The proposed correction leads to a new state space
model for which we design observers, whose global, robust convergences are
supported by a Lyapunov analysis. Both numerical and experimental validations
are presented, which show the improvement of the accuracy of the state
estimates as a result of the proposed corrections.
