LMI-based robust observer design for battery state-of-charge estimation

Estimating the battery State-of-Charge (SoC) is often done using nonlinear extensions of the Kalman filter. These filters do not explicitly address convergence of the estimation error and robustness with respect to model uncertainty, and make nonrealistic assumptions on the noise. Therefore, these filters require extensive tuning of the covariance matrices, which is a non-intuitive and tedious task. In this paper, a robust Luenberger estimator is proposed that explicitly addresses the requirements on estimation-error convergence, robustness and noise attenuation and shows their inherent trade-off. Different observers are synthesised using polytopic embeddings of the nonlinear battery model and using linear matrix inequalities that provide bounds on the {ell-{2,infty}-, ell-{infty,infty}-} or the ell-{2,2}-gains between input and output (to accommodate for model uncertainty and sensor noise). This guarantees a robustly converging SoC observer and makes its design more intuitive. The proposed observers are validated and compared with an Extended Kalman Filter (EKF) using experimental data. The results show that the performance of two out of three proposed observers is similar to the EKF, while the implementation is simpler and tuning is more intuitive and more straightforward.