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.

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Fig. 1

Schematic diagram of a lead-acid cell

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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

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Fig. 3

Switched Luenberger observer diagram

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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).

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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

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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)



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