Steady-state system analysis of a proton exchange membrane fuel cell nonlinear mathematical model

Verica Radisavljevic-Gajic; Kyle Graham

doi:10.1115/DSCC2017-5388

Steady-state system analysis of a proton exchange membrane fuel cell nonlinear mathematical model

Verica Radisavljevic-Gajic
, Kyle Graham

Villanova University College of Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this paper we analyze the steady state dynamic behavior of a nonlinear model of a Proton Exchange Membrane (PEM) fuel cell. This model is used in several theoretical studies and application papers of PEM fuel cells. We indicate limitations and discuss potential constraints of this mathematical model. We establish conditions for the asymptotic stability at steady state by using the first stability method of Lyapunov. We find that the linearized model at steady state is uncontrollable. Specifically, the state variable corresponding to the hydrogen pressure is not controllable. This means that dynamics deviations of the state space variable corresponding to the hydrogen pressure around the steady state equilibrium point cannot be controlled. Due to its stability, the hydrogen pressure we go to the equilibrium point according to its internal (uncontrolled) dynamics so that the model is still applicable for theoretical and practical studies.

Original language	English
Title of host publication	Vibration in Mechanical Systems; Modeling and Validation; Dynamic Systems and Control Education; Vibrations and Control of Systems; Modeling and Estimation for Vehicle Safety and Integrity; Modeling and Control of IC Engines and Aftertreatment Systems;Unmanned Aerial Vehicles (UAVs) and Their Applications; Dynamics and Control of Renewable Energy Systems; Energy Harvesting; Control of Smart Buildings and Microgrids; Energy Systems
Publisher	American Society of Mechanical Engineers
ISBN (Electronic)	9780791858295
DOIs	https://doi.org/10.1115/DSCC2017-5388
State	Published - 2017
Externally published	Yes
Event	ASME 2017 Dynamic Systems and Control Conference, DSCC 2017 - Tysons, United States Duration: 11 Oct 2017 → 13 Oct 2017

Publication series

Name	ASME 2017 Dynamic Systems and Control Conference, DSCC 2017
Volume	3

Conference

Conference	ASME 2017 Dynamic Systems and Control Conference, DSCC 2017
Country/Territory	United States
City	Tysons
Period	11/10/17 → 13/10/17

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 7 Affordable and Clean Energy

Access to Document

10.1115/DSCC2017-5388

Cite this

Radisavljevic-Gajic, V., & Graham, K. (2017). Steady-state system analysis of a proton exchange membrane fuel cell nonlinear mathematical model. In Vibration in Mechanical Systems; Modeling and Validation; Dynamic Systems and Control Education; Vibrations and Control of Systems; Modeling and Estimation for Vehicle Safety and Integrity; Modeling and Control of IC Engines and Aftertreatment Systems;Unmanned Aerial Vehicles (UAVs) and Their Applications; Dynamics and Control of Renewable Energy Systems; Energy Harvesting; Control of Smart Buildings and Microgrids; Energy Systems (ASME 2017 Dynamic Systems and Control Conference, DSCC 2017; Vol. 3). American Society of Mechanical Engineers. https://doi.org/10.1115/DSCC2017-5388

Radisavljevic-Gajic, Verica ; Graham, Kyle. / Steady-state system analysis of a proton exchange membrane fuel cell nonlinear mathematical model. Vibration in Mechanical Systems; Modeling and Validation; Dynamic Systems and Control Education; Vibrations and Control of Systems; Modeling and Estimation for Vehicle Safety and Integrity; Modeling and Control of IC Engines and Aftertreatment Systems;Unmanned Aerial Vehicles (UAVs) and Their Applications; Dynamics and Control of Renewable Energy Systems; Energy Harvesting; Control of Smart Buildings and Microgrids; Energy Systems. American Society of Mechanical Engineers, 2017. (ASME 2017 Dynamic Systems and Control Conference, DSCC 2017).

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title = "Steady-state system analysis of a proton exchange membrane fuel cell nonlinear mathematical model",

abstract = "In this paper we analyze the steady state dynamic behavior of a nonlinear model of a Proton Exchange Membrane (PEM) fuel cell. This model is used in several theoretical studies and application papers of PEM fuel cells. We indicate limitations and discuss potential constraints of this mathematical model. We establish conditions for the asymptotic stability at steady state by using the first stability method of Lyapunov. We find that the linearized model at steady state is uncontrollable. Specifically, the state variable corresponding to the hydrogen pressure is not controllable. This means that dynamics deviations of the state space variable corresponding to the hydrogen pressure around the steady state equilibrium point cannot be controlled. Due to its stability, the hydrogen pressure we go to the equilibrium point according to its internal (uncontrolled) dynamics so that the model is still applicable for theoretical and practical studies.",

author = "Verica Radisavljevic-Gajic and Kyle Graham",

note = "Publisher Copyright: Copyright {\textcopyright} 2017 ASME.; ASME 2017 Dynamic Systems and Control Conference, DSCC 2017 ; Conference date: 11-10-2017 Through 13-10-2017",

year = "2017",

doi = "10.1115/DSCC2017-5388",

language = "English",

series = "ASME 2017 Dynamic Systems and Control Conference, DSCC 2017",

publisher = "American Society of Mechanical Engineers",

booktitle = "Vibration in Mechanical Systems; Modeling and Validation; Dynamic Systems and Control Education; Vibrations and Control of Systems; Modeling and Estimation for Vehicle Safety and Integrity; Modeling and Control of IC Engines and Aftertreatment Systems;Unmanned Aerial Vehicles (UAVs) and Their Applications; Dynamics and Control of Renewable Energy Systems; Energy Harvesting; Control of Smart Buildings and Microgrids; Energy Systems",

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Radisavljevic-Gajic, V & Graham, K 2017, Steady-state system analysis of a proton exchange membrane fuel cell nonlinear mathematical model. in Vibration in Mechanical Systems; Modeling and Validation; Dynamic Systems and Control Education; Vibrations and Control of Systems; Modeling and Estimation for Vehicle Safety and Integrity; Modeling and Control of IC Engines and Aftertreatment Systems;Unmanned Aerial Vehicles (UAVs) and Their Applications; Dynamics and Control of Renewable Energy Systems; Energy Harvesting; Control of Smart Buildings and Microgrids; Energy Systems. ASME 2017 Dynamic Systems and Control Conference, DSCC 2017, vol. 3, American Society of Mechanical Engineers, ASME 2017 Dynamic Systems and Control Conference, DSCC 2017, Tysons, United States, 11/10/17. https://doi.org/10.1115/DSCC2017-5388

Steady-state system analysis of a proton exchange membrane fuel cell nonlinear mathematical model. / Radisavljevic-Gajic, Verica; Graham, Kyle.
Vibration in Mechanical Systems; Modeling and Validation; Dynamic Systems and Control Education; Vibrations and Control of Systems; Modeling and Estimation for Vehicle Safety and Integrity; Modeling and Control of IC Engines and Aftertreatment Systems;Unmanned Aerial Vehicles (UAVs) and Their Applications; Dynamics and Control of Renewable Energy Systems; Energy Harvesting; Control of Smart Buildings and Microgrids; Energy Systems. American Society of Mechanical Engineers, 2017. (ASME 2017 Dynamic Systems and Control Conference, DSCC 2017; Vol. 3).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Steady-state system analysis of a proton exchange membrane fuel cell nonlinear mathematical model

AU - Radisavljevic-Gajic, Verica

AU - Graham, Kyle

PY - 2017

Y1 - 2017

N2 - In this paper we analyze the steady state dynamic behavior of a nonlinear model of a Proton Exchange Membrane (PEM) fuel cell. This model is used in several theoretical studies and application papers of PEM fuel cells. We indicate limitations and discuss potential constraints of this mathematical model. We establish conditions for the asymptotic stability at steady state by using the first stability method of Lyapunov. We find that the linearized model at steady state is uncontrollable. Specifically, the state variable corresponding to the hydrogen pressure is not controllable. This means that dynamics deviations of the state space variable corresponding to the hydrogen pressure around the steady state equilibrium point cannot be controlled. Due to its stability, the hydrogen pressure we go to the equilibrium point according to its internal (uncontrolled) dynamics so that the model is still applicable for theoretical and practical studies.

AB - In this paper we analyze the steady state dynamic behavior of a nonlinear model of a Proton Exchange Membrane (PEM) fuel cell. This model is used in several theoretical studies and application papers of PEM fuel cells. We indicate limitations and discuss potential constraints of this mathematical model. We establish conditions for the asymptotic stability at steady state by using the first stability method of Lyapunov. We find that the linearized model at steady state is uncontrollable. Specifically, the state variable corresponding to the hydrogen pressure is not controllable. This means that dynamics deviations of the state space variable corresponding to the hydrogen pressure around the steady state equilibrium point cannot be controlled. Due to its stability, the hydrogen pressure we go to the equilibrium point according to its internal (uncontrolled) dynamics so that the model is still applicable for theoretical and practical studies.

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M3 - Conference contribution

AN - SCOPUS:85036633664

T3 - ASME 2017 Dynamic Systems and Control Conference, DSCC 2017

BT - Vibration in Mechanical Systems; Modeling and Validation; Dynamic Systems and Control Education; Vibrations and Control of Systems; Modeling and Estimation for Vehicle Safety and Integrity; Modeling and Control of IC Engines and Aftertreatment Systems;Unmanned Aerial Vehicles (UAVs) and Their Applications; Dynamics and Control of Renewable Energy Systems; Energy Harvesting; Control of Smart Buildings and Microgrids; Energy Systems

PB - American Society of Mechanical Engineers

T2 - ASME 2017 Dynamic Systems and Control Conference, DSCC 2017

Y2 - 11 October 2017 through 13 October 2017

ER -

Radisavljevic-Gajic V, Graham K. Steady-state system analysis of a proton exchange membrane fuel cell nonlinear mathematical model. In Vibration in Mechanical Systems; Modeling and Validation; Dynamic Systems and Control Education; Vibrations and Control of Systems; Modeling and Estimation for Vehicle Safety and Integrity; Modeling and Control of IC Engines and Aftertreatment Systems;Unmanned Aerial Vehicles (UAVs) and Their Applications; Dynamics and Control of Renewable Energy Systems; Energy Harvesting; Control of Smart Buildings and Microgrids; Energy Systems. American Society of Mechanical Engineers. 2017. (ASME 2017 Dynamic Systems and Control Conference, DSCC 2017). doi: 10.1115/DSCC2017-5388

Steady-state system analysis of a proton exchange membrane fuel cell nonlinear mathematical model

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