Optimal control for lithium‐ion batteries

Abstract

Modelling, simulation and optimal control for a lithium-ion battery cell is discussed. The model involves ionic concentrations, currents and potentials in the electrodes and the separator together with the battery temperature as state variables. The resulting system is a nonlinear PDAE system with 10 partial, 1 ordinary differential and 4 algebraic equations involving the ButlerVolmer kinetics for describing the interaction of ionic currents and potentials. Time-optimal charging of the battery subject to age-preventing leads to a state-constrained optimal control problem which is solved in two ways. A first-discretize-thenoptimize approach leads to a high-dimensional nonlinear optimization problem which is solved by an efficient solver. As an alternative, a feedback control law along an active arc of the state constraint of order 1 is derived to formulate and solve the corresponding so-called induced optimization problem.