Exploiting Differential Flatness and Pseudospectral Optimization to Improve the Computational Efficiency of Health-Conscious Lithium-Ion Battery Control
The paper demonstrates the above ideas using the SPM. The optimization problem is formulated by equation [1-6] and the SPM with film growth model. The cost function in Equation  aims to track the reference state of charge (SOC) and at the same time minimize the film growth rate, which is defined by equation - in Ramadass’s paper7. The weight β represents a tradeoff/balance between aggressive charging and battery degradation. Constraints [2-6] place limits on battery charge/discharge current, reflecting battery management hardware capabilities. Furthermore, these constraints limit battery SOC to prevent over-charging and over-discharging. Finally, these constraints also place bounds on battery state variables contributing to damage phenomena such as lithium plating and mechanical degradation. For instance, we bound the concentration gradients in the battery cell and the overpotentials driving the lithium plating side reaction8–10. The optimization approach presented in this paper transforms these equations and constraints from a dynamic programming problem to a nonlinear programming (NLP) problem. Solving this NLP problem using traditional optimization methods leads to a health-conscious battery management policy. The value of this paper lies not in this policy, but rather in the computational efficiency with which it is obtained. Specifically, to the best of the authors’ knowledge, this paper represents the first attempt to exploit lithium-ion battery model structure for more efficient solution of the health-conscious optimal management problem.
The research was funded by ARPA-E AMPED program grant # 0675-1565. The authors gratefully acknowledge this support.
1. M. FLIESS, J. LÉVINE, P. MARTIN, and P. ROUCHON, Int. J. Control, 61, 1327–1361 (1995).
2. B. Laroche, P. Martin, and P. Rouchon, Int. J. Robust Nonlinear Control, 10, 629–643 (2000).
3. M. Fliess and R. Marquez, Int. J. Control, 73, 606–623 (2000).
4. T. Meurer, Automatica, 47, 935–949 (2011).
5. R. Klein and N. Chaturvedi, Am. Control … (2011).
6. V. Boovaragavan and V. R. Subramanian, J. Power Sources, 173, 1006–1011 (2007).
7. P. Ramadass, B. Haran, P. M. Gomadam, R. White, and B. N. Popov, J. Electrochem. Soc., 151, A196 (2004).
8. J. Christensen and J. Newman, J. Solid State Electrochem., 10, 293–319 (2006).
9. X. Zhang, A. M. Sastry, and W. Shyy, J. Electrochem. Soc., 155, A542 (2008).