Optimal control for fast acquisition of equilibrium voltage for Li-ion batteries

Motivated by the recent electrode health diagnosis method that requires selective open-circuit voltage data, this paper presents a novel approach for the fast acquisition of battery equilibrium voltage using bidirectional current pulses. The proposed method was found by solving a minimum-time optimal control problem. Unlike the conventional pulse-relaxation method which requires a long relaxation period, the use of charge and discharge pulses reduces the testing time by 69%. The given problem is studied numerically and analytically. Analysis based on Pontryagin's minimum principle (PMP) demonstrates that the solution is either bang-bang or bang-off-bang control, depending on the constraints. Furthermore, the optimal control problem is reformulated into a finite-dimensional switching-time optimization problem, making it computationally tractable for onboard applications. Finally, experimental validation is presented for a 4.5 Ah NMC/graphite cell showing a 73% time reduction to reach a new equilibrium voltage.