Nonlinear extension of battery constrained predictive charging control with transmission of Jacobian matrix

Abstract

Battery charging operation limits can be considered systematically in the optimal constrained control framework of model predictive control (MPC). Hence, MPC-based battery charge control techniques are very promising for solving health-aware optimal charging problem. However, the battery’s nonlinear state of charge (SOC) - open circuit voltage (OCV) relationship prevents the direct application of standard MPC design process. Therefore, in this paper, we present a nonlinear extension of MPC charge control structure for lithium-ion batteries based on one of the most commonly used equivalent circuit models (ECMs). In the proposed charge control structure, extended Kalman filter (EKF) is adopted for battery state estimation. Furthermore, the Jacobian matrix obtained through first-order Taylor approximation in EKF is reused in MPC formulation. This can effectively handle the nonlinear battery charging control problem, while simultaneously make full use of the linearization result of EKF. Consequently, the linear assumption of SOC–OCV relationship in the literature is unlocked by embedding EKF into MPC formulation in a systematic way. Numerical validation with real experimental data has shown that the battery’s electrical constraints are respected during the whole charging process. Furthermore, the prediction horizon of MPC has much more impact on battery limit operation time reduction than the control horizon of MPC. The ratio between weighting factors λ and γ in MPC’s cost function is important to ensure the objective of controlling the minimum charging time.