An Extended Differential Flatness Approach for the Health-Conscious Nonlinear Model Predictive Control of Lithium-Ion Batteries

This brief paper examines the problem of optimizing lithium-ion battery management online, in a health-conscious manner. This is a computationally intensive problem. Previous work by the authors addresses this challenge by exploiting the differential flatness of Fick's law of diffusion to improve computational efficiency, but is limited by the fact that the dynamics of a full battery cell are not differentially flat, even when the individual battery electrode dynamics are. The brief paper addresses this challenge by extending the application of differential flatness to a full single particle model. In particular, we use the conservation of charge to express the flat output trajectory of one electrode as an affine function of the other electrode's flat output trajectory. In this way, we enforce differential flatness for the full battery model. This makes it possible to express the battery charge/discharge trajectory in terms of one flat output trajectory. We optimize this trajectory using a pseudospectral method. This reduces the computational cost of the optimization by about a factor of 5 compared with pseudospectral optimization alone. In addition, the robustness of the nonlinear model predictive control strategy is demonstrated in simulation by adding state-of-health parameter uncertainties.