Interval Observer Design for an Uncertain Time-Varying Quasi-Linear System Model of Lithium-Ion Batteries

Lithium-ion batteries are currently used in numerous applications, for example in electric vehicles and energy storage systems. Accurately estimating the dynamic behavior is crucial to safely and efficiently charge and discharge the battery cells. This can be done with the help of stochastic or interval based identification routines which require an accurate state estimation. In previous works, we used an interval observer based on a Luenberger observer structure to estimate the lower and upper bounds of the state variables. However, with this approach it was necessary to use specified input current profiles to charge or discharge the battery cells, otherwise, the estimation uncertainty increased over time. In this paper, we aim to estimate the state variables during system operation without using specified input current profiles. A promising approach is a TNL observer, which was introduced for uncertain time-invariant systems in the literature, that provides multiple design degrees of freedom. The TNL observer is extended to an uncertain time-varying system model of lithium-ion batteries in this work. The time-varying part is herein considered with two different approaches. At first, a nominal system model is considered where the time-varying part is treated as a measurement uncertainty and secondly it is considered using a polytopic representation of the system matrix. The TNL observer was successfully extended to the time-varying system model of a lithium-ion battery. The polytopic representation of the system matrix leads to more accurate estimation results in comparison to the nominal approach.