This paper develops an adaptive partial differential equation (PDE) observer for battery state-of-charge (SOC) and state-of-health (SOH) estimation. Real-time state and parameter information enables operation near physical limits without compromising durability, thereby unlocking the full potential of battery energy storage. SOC/SOH estimation is technically challenging because battery dynamics are governed by electrochemical principles, mathematically modeled by PDEs. We cast this problem as a simultaneous state (SOC) and parameter (SOH) estimation design for a linear PDE with a nonlinear output mapping. Several new theoretical ideas are developed, integrated together, and tested. These include a backstepping PDE state estimator, a Padé-based parameter identifier, nonlinear parameter sensitivity analysis, and adaptive inversion of nonlinear output functions. The key novelty of this design is a combined SOC/SOH battery estimation algorithm that identifies physical system variables, from measurements of voltage and current only.

References

References
1.
Chaturvedi
,
N. A.
,
Klein
,
R.
,
Christensen
,
J.
,
Ahmed
,
J.
, and
Kojic
,
A.
,
2010
, “
Algorithms for Advanced Battery-Management Systems
,”
IEEE Control Systems Magazine
,
30
(
3
), pp.
49
68
.10.1109/MCS.2010.936293
2.
Moura
,
S.
,
Fathy
,
H.
,
Callaway
,
D.
, and
Stein
,
J.
,
2011
, “
A Stochastic Optimal Control Approach for Power Management in Plug-in Hybrid Electric Vehicles
,”
IEEE Trans. Control Syst. Technol.
,
19
(
3
), pp.
545
555
.10.1109/TCST.2010.2043736
3.
Siegel
,
J. B.
,
Lin
,
X.
,
Stefanopoulou
,
A. G.
,
Hussey
,
D. S.
,
Jacobson
,
D. L.
, and
Gorsich
,
D.
,
2011
, “
Neutron Imaging of Lithium Concentration in LFP Pouch Cell Battery
,”
J. Electrochem. Soc.
,
158
(
5
), pp.
A523
A529
.10.1149/1.3566341
4.
Liu
,
P.
,
Wang
,
J.
,
Hicks-Garner
,
J.
,
Sherman
,
E.
,
Soukiazian
,
S.
,
Verbrugge
,
M.
,
Tataria
,
H.
,
Musser
,
J.
, and
Finamore
,
P.
,
2010
, “
Aging Mechanisms of LiFePO4 Batteries Deduced by Electrochemical and Structural Analyses
,”
J. Electrochem. Soc.
,
157
(
4
), pp.
A499
A507
.10.1149/1.3294790
5.
Thomas
,
K.
,
Newman
,
J.
, and
Darling
,
R.
,
2002
,
Advances in Lithium-Ion Batteries
,
Mathematical Modeling of Lithium Batteries
,
Kluwer Academic/Plenum Publishers
,
New York
, Chap. XII, pp.
345
392
.
6.
Plett
,
G. L.
,
2004
, “
Extended Kalman Filtering for Battery Management Systems of LiPB-Based HEV Battery Packs. Part 3. State and Parameter Estimation
,”
J. Power Sources
,
134
(
2
), pp.
277
292
.10.1016/j.jpowsour.2004.02.033
7.
Verbrugge
,
M.
, and
Tate
,
E.
,
2004
, “
Adaptive State of Charge Algorithm for Nickel Metal Hydride Batteries Including Hysteresis Phenomena
,”
J. Power Sources
,
126
(
1–2
), pp.
236
249
.10.1016/j.jpowsour.2003.08.042
8.
Verbrugge
,
M.
,
2007
, “
Adaptive, Multi-Parameter Battery State Estimator With Optimized Time-Weighting Factors
,”
J. Appl. Electrochem.
,
37
(
5
), pp.
605
616
.10.1007/s10800-007-9291-7
9.
Hu
,
Y.
, and
Yurkovich
,
S.
,
2012
, “
Battery Cell State-of-Charge Estimation Using Linear Parameter Varying System Techniques
,”
J. Power Sources
,
198
, pp.
338
350
.10.1016/j.jpowsour.2011.09.058
10.
Santhanagopalan
,
S.
, and
White
,
R. E.
,
2006
, “
Online Estimation of the State of Charge of a Lithium Ion Cell
,”
J. Power Sources
,
161
(
2
), pp.
1346
1355
.10.1016/j.jpowsour.2006.04.146
11.
Domenico
,
D. D.
,
Stefanopoulou
,
A.
, and
Fiengo
,
G.
,
2010
, “
Lithium-Ion Battery State of Charge and Critical Surface Charge Estimation Using an Electrochemical Model-Based Extended Kalman Filter
,”
ASME J. Dyn. Syst., Meas., Control
,
132
(
6
), p.
061302
.10.1115/1.4002475
12.
Smith
,
K. A.
,
Rahn
,
C. D.
, and
Wang
,
C.-Y.
,
2008
, “
Model-Based Electrochemical Estimation of Lithium-Ion Batteries
,”
2008 IEEE International Conference on Control Applications
, pp.
714
719
.
13.
Klein
,
R.
,
Chaturvedi
,
N. A.
,
Christensen
,
J.
,
Ahmed
,
J.
,
Findeisen
,
R.
, and
Kojic
,
A.
,
2012
, “
Electrochemical Model Based Observer Design for a Lithium-Ion Battery
,”
IEEE Trans. Control Syst. Technol.
, pp.
1
13
.
14.
Moura
,
S. J.
,
Chaturvedi
,
N.
, and
Krstic
,
M.
,
2012
, “
PDE Estimation Techniques for Advanced Battery Management Systems—Part I: SOC Estimation
,”
Proceedings of the 2012 American Control Conference
.
15.
Moura
,
S. J.
,
Chaturvedi
,
N.
, and
Krstic
,
M.
,
2012
, “
PDE Estimation Techniques for Advanced Battery Management Systems—Part II: SOH Identification
,”
Proceedings of the 2012 American Control Conference
.
16.
Moura
,
S. J.
,
Chaturvedi
,
N.
, and
Krstic
,
M.
,
2012
, “
Adaptive PDE Observer for Battery SOC/SOH Estimation
,”
2012 ASME Dynamic Systems and Control Conference
.
17.
Santhanagopalan
,
S.
,
Guo
,
Q.
,
Ramadass
,
P.
, and
White
,
R. E.
,
2006
, “
Review of Models for Predicting the Cycling Performance of Lithium Ion Batteries
,”
J. Power Sources
,
156
(
2
), pp.
620
628
.10.1016/j.jpowsour.2005.05.070
18.
Newman
,
J.
,
2008
,
Fortran Programs for the Simulation of Electrochemical Systems
, University of California, Berkley, CA.
19.
Chen
,
C.
,
1998
,
Linear System Theory and Design
,
Oxford University Press, Inc.
, Oxford, UK.
20.
Krstic
,
M.
, and
Smyshlyaev
,
A.
,
2008
,
Boundary Control of PDEs: A Course on Backstepping Designs
,
Society for Industrial and Applied Mathematics, Philadelphia, PA
.
21.
Delacourt
,
C.
,
Poizot
,
P.
,
Levasseur
,
S.
, and
Masquelier
,
C.
,
2006
, “
Size Effects on Carbon-Free LiFePO4 Powders
,”
Electrochem. Solid-State Lett.
,
9
(
7
), pp.
A352
A355
.10.1149/1.2201987
22.
Derrien
,
G.
,
Hassoun
,
J.
,
Panero
,
S.
, and
Scrosati
,
B.
,
2007
, “
Nanostructured Sn-C Composite as an Advanced Anode Material in High-Performance Lithium-Ion Batteries
,”
Adv. Mater.
,
19
(
17
), pp.
2336
–2340.10.1002/adma.200700748
23.
Forman
,
J. C.
,
Moura
,
S. J.
,
Stein
,
J. L.
, and
Fathy
,
H. K.
,
2012
, “
Genetic Identification and Fisher Identifiability Analysis of the Doyle-Fuller-Newman Model From Experimental Cycling of a LiFePO4 Cells
,”
J. Power
,
210
, pp.
263
275
.
24.
Khalil
,
H. K.
,
2002
,
Nonlinear Systems
,
3rd ed.
,
Prentice Hall
,
Englewood Cliffs, NJ
.
25.
Ioannou
,
P.
, and
Sun
,
J.
,
1996
,
Robust Adaptive Control
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
26.
Smyshlyaev
,
A.
, and
Krstic
,
M.
,
2010
,
Adaptive Control of Parabolic PDEs
,
Princeton University
,
Princeton, NJ
.
27.
Lund
,
B. F.
, and
Foss
,
B. A.
,
2008
, “
Parameter Ranking by Orthogonalization—Applied to Nonlinear Mechanistic Models
,”
Automatica
,
44
(
1
), pp.
278
281
.10.1016/j.automatica.2007.04.006
28.
Moura
,
S. J.
,
Stein
,
J. L.
, and
Fathy
,
H. K.
,
2012
, “
Battery-Health Conscious Power Management in Plug-In Hybrid Electric Vehicles Via Electrochemical Modeling and Stochastic Control
,”
IEEE Trans. Control Syst. Technol.
,
21
, pp. 679–694.10.1109/TCST.2012.2189773
29.
Morozovska
,
A.
,
Eliseev
,
E.
,
Balke
,
N.
, and
Kalinin
,
S.
,
2010
, “
Local Probing of Ionic Diffusion by Electrochemical Strain Microscopy: Spatial Resolution and Signal Formation Mechanisms
,”
J. Appl. Phys.
,
108
(
5
), p. 053712.10.1063/1.3460637
30.
Fang
,
W.
,
Kwon
,
O. J.
, and
Wang
,
C.-Y.
,
2010
, “
Electrochemical-Thermal Modeling of Automotive Li-Ion Batteries and Experimental Validation Using a Three-Electrode Cell
,”
Int. J. Energy Res.
,
34
(
2
), pp.
107
115
.10.1002/er.1652
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