Research Papers

Model-Based State-of-Charge Estimation for a Valve-Regulated Lead-Acid Battery Using Linear Matrix Inequalities

[+] Author and Article Information
Zheng Shen

e-mail: zus120@psu.edu

Christopher D. Rahn

Fellow ASME
e-mail: cdrahn@psu.edu
Department of Mechanical and Nuclear Engineering,
Mechatronics Research Laboratory,
The Pennsylvania State University,
University Park, PA 16802

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 4, 2012; final manuscript received February 15, 2013; published online May 22, 2013. Assoc. Editor: Luis Alvarez.

J. Dyn. Sys., Meas., Control 135(4), 041015 (May 22, 2013) (8 pages) Paper No: DS-12-1169; doi: 10.1115/1.4023766 History: Received June 04, 2012; Revised February 15, 2013

State-of-charge (SOC) estimation for valve-regulated lead-acid (VRLA) batteries is complicated by the switched linear nature of the underlying dynamics. A first principles nonlinear model is simplified to provide two switched linear models and linearized to produce charge, discharge, and averaged models. Luenberger and switched SOC estimators are developed based on these models and propagated using experimental data. A design methodology based on linear matrix inequalities (LMIs) is used in the switched SOC estimator design to obtain a switched Luenberger observer with guaranteed exponential stability. The results show that estimation errors are halved by including switching in the observer design.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Pop, V., Bergveld, H., Danilov, D., Regtien, P., and Notten, P., 2008, Battery Management Systems: Accurate State-of-Charge Indication for Battery Powered Applications, Springer, New York.
Piller, S., Perrin, M., and Jossen, A., 2001, “Methods for State-of-Charge Determination and Their Applications,” J. Power Sources, 96(1), pp. 113–120. [CrossRef]
Pop, V., Bergveld, H. J., Notten, P. H. L., and Regtien, P. P. L., 2005, “State-of-the-Art of Battery State-of-Charge Determination,” Measure. Sci. Technol., 16(12), p. R93. [CrossRef]
Ng, K. S., Moo, C.-S., Chen, Y.-P., and Hsieh, Y.-C., 2009, “Enhanced Coulomb Counting Method for Estimating State-of-Charge and State-of-Health of Lithium-Ion Batteries,” Appl. Energy, 86(9), pp. 1506–1511. [CrossRef]
Plett, G. L., 2004, “Extended Kalman Filtering for Battery Management Systems of LIPB-Based HEV Battery Packs: Part 1. Background,” J. Power Sources, 134(2), pp. 252–261. [CrossRef]
Plett, G. L., 2004, “Extended Kalman Filtering for Battery Management Systems of LIPB-Based HEV Battery Packs: Part 2. Modeling and Identification,” J. Power Sources, 134(2), pp. 262–276. [CrossRef]
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. [CrossRef]
Vasebi, A., Partovibakhsh, M., and Bathaee, S. M. T., 2007, “A Novel Combined Battery Model for State-of-Charge Estimation in Lead-Acid Batteries Based on Extended Kalman Filter for Hybrid Electric Vehicle Applications,” J. Power Sources, 174(1), pp. 30–40. [CrossRef]
Vasebi, A., Bathaee, S., and Partovibakhsh, M., 2008, “Predicting State of Charge of Lead-Acid Batteries for Hybrid Electric Vehicles by Extended Kalman Filter,” Energy Convers. Manage., 49(1), pp. 75–82. [CrossRef]
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. [CrossRef]
Santhanagopalan, S., and White, R., 2008, “State of Charge Estimation for Electrical Vehicle Batteries,” IEEE International Conference on Control Applications, pp. 690–695. [CrossRef]
Santhanagopalan, S., and White, R. E., 2010, “State of Charge Estimation Using an Unscented Filter for High Power Lithium Ion Cells,” Int. J. Energy Res., 34(2), pp. 152–163. [CrossRef]
Shen, Z., Gou, J., Rahn, C. D., and Wang, C.-Y., 2011, “Ritz Model of a Lead-Acid Battery With Application to Electric Locomotives,” ASME Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control, Vol. 1, pp. 713–720. [CrossRef]
Ge, S., and Sun, Z., 2005, Switched Linear Systems: Control and Design, Springer, New York.
Lin, H., and Antsaklis, P., 2009, “Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results,” IEEE Trans. Auto. Control, 54(2), pp. 308–322. [CrossRef]
Alessandri, A., Baglietto, M., and Battistelli, G., 2005, “Luenberger Observers for Switching Discrete-Time Linear Systems,” 44th IEEE Conference on Decision and Control (CDC-ECC `05), pp. 7014–7019. [CrossRef]
Boyd, S., Ghaoul, L., Feron, E., and Balakrishnan, V., 1994, Linear Matrix Inequalities in System and Control Theory (Applied Mathematics), Society for Industrial and Applied Mathematics, Philadelphia.
Srinivasan, V., Wang, G. Q., and Wang, C. Y., 2003, “Mathematical Modeling of Current-Interrupt and Pulse Operation of Valve-Regulated Lead Acid Cells,” J. Electrochem. Soc., 150(3), pp. A316–A325. [CrossRef]
Gu, W. B., Wang, C. Y., and Liaw, B. Y., 1997, “Numerical Modeling of Coupled Electrochemical and Transport Processes in Lead-Acid Batteries,” J. Electrochem. Soc., 144(6), pp. 2053–2061. [CrossRef]
Bode, H., 1977, Lead-Acid Batteries, Wiley, New York.
Polyak, B. T., and Shcherbakov, P. S., 2002, “Superstable Linear Control Systems. II. Design,” Auto. Remote Control, 63, pp. 1745–1763. [CrossRef]
Alessandri, A., and Coletta, P., 2001, “Switching Observers for Continuous-Time and Discrete-Time Linear Systems,” Proceedings of the American Control Conference (ACC), Vol. 3, pp. 2516–2521. [CrossRef]
Zhang, F., 2005, The Schur Complement and Its Applications, Springer, New York.
Connors, K., 1990, Chemical Kinetics: The Study of Reaction Rates in Solution, VCH, Berlin.


Grahic Jump Location
Fig. 1

Schematic diagram of a lead-acid cell

Grahic Jump Location
Fig. 2

Battery voltage response: (a) models 3 (dash-dotted) and 4 (dashed) and experiment (solid); (b) models 1 (dashed), 2 (dash-dotted), and 5 (dotted) and experiment (solid); and (c) current applied to the battery

Grahic Jump Location
Fig. 3

Switched Luenberger observer diagram

Grahic Jump Location
Fig. 6

SOC estimation during 0.065 C discharge from 70% to 40% SOC: (a) actual SOC (solid) and SOC estimation based on the model 2 (dash-dotted) and averaged model (dashed). (b) Voltage tracking to experimental voltage data (solid) of SOC estimators based on the model 2 (dash-dotted) and averaged model (dashed).

Grahic Jump Location
Fig. 5

SOC estimation results: (a) SOC estimators based on models 3 (dash-dotted) and 4 (dashed) and calculated SOC (solid); (b) simulated battery voltage of models 3 (dash-dotted) and 4 (dashed) and the nonlinear model (solid); and (c) simulated current

Grahic Jump Location
Fig. 4

SOC estimation results: (a) estimated SOC based on switched linear models 3 (dash-dotted) and 4 (dashed) and experimentally calculated SOC (solid); (b) estimated SOC based on linear models 1 (dashed), 2 (dash-dotted), and 5 (dotted), voltage lookup method (solid) and experimental data (solid); (c) estimated voltage based on switched linear models 3 (dash-dotted) and 4 (dashed) and measured voltage (solid); and (d) estimated voltage based on linear models 1 (dashed), 2 (dash-dotted), and 5 (dotted) and measured voltage (solid)




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In