Robust procedures for the estimation of operating conditions of lithium-ion battery cells

The estimation of both the state of charge and the state of health is a basic requirement for the implementation of reliable operating procedures for battery systems in hybrid and electric vehicles as well as for other mobile applications. However, typical battery models describing the dynamics for charging and discharging are characterized by non-negligible nonlinearities. These nonlinearities result from a strong state of charge dependency of the open circuit voltage and the battery time constants. Hence, estimators for a dynamic operation of batteries have to deal with such phenomena. In previous work, different approaches were investigated to cope with this problem. The available strategies range from neural networks and gain-scheduled Luenberger-type observers to the implementation of Extended Kalman Filters. Especially, the two latter approaches make use of equivalent circuit models for the implementation of the corresponding estimators. However, an asymptotic stability proof for the error dynamics of these estimators is typically not performed. This problem can be solved by an observer design that makes use of Linear Matrix Inequalities (LMIs) in combination with a polytopic uncertainty model. Corresponding modeling and design procedures as well as numerical simulation results are presented in this paper to highlight the efficiency of the LMI-based observer design.