0
Research Papers

Absolute Stability Analysis Using the Liénard Equation: A Study Derived From Control of Fuel Cell Ultracapacitor Hybrids

[+] Author and Article Information
William Nowak

Rochester Institute of Technology,
Rochester, NY 14623

Daniel Geiyer

Department of Mechanical and Aerospace Engineering,
University of Central Florida,
Orlando, FL 32816

Tuhin Das

Department of Mechanical and Aerospace Engineering,
University of Central Florida,
Orlando, FL 32816
e-mail: Tuhin.Das@ucf.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 4, 2015; final manuscript received December 9, 2015; published online January 12, 2016. Assoc. Editor: Junmin Wang.

J. Dyn. Sys., Meas., Control 138(3), 031007 (Jan 12, 2016) (10 pages) Paper No: DS-15-1152; doi: 10.1115/1.4032318 History: Received April 04, 2015; Revised December 09, 2015

Load-following in solid oxide fuel cells (SOFCs), hybridized with an ultracapacitor for energy storage, refers to an operating mode where the fuel cell's generated power follows the variable power demand, delivering the total demanded power at steady-state. Implementing this operating mode presents a rich set of problems in dynamical systems and control. This paper focuses on state-of-charge (SOC) control of the ultracapacitor during load-following, under transient constraints, and in the presence of an unknown nonlinearity. The problem is generalized to stabilization of a plant containing a cascaded connection of a driver and a driven dynamics, where the former is nonlinear and largely unknown. Closed-loop stability of the system is studied as a Lur'e problem and via energy-based Lyapunov equations, but both impose conservative conditions on the nonlinearity. An alternate approach is developed, where the closed-loop dynamics are formulated as a class of Liénard equations. The corresponding analysis, which is based on the nonlinear characteristics of the Liénard equation, yields more definitive and less conservative stability criteria. Additional conditions that lead to limit cycles are also derived, and a bifurcation pattern is revealed. The generality of the proposed approach indicates applicability to a variety of nonlinear systems.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Larminie, J. , and Dicks, A. , 2003, Fuel Cell Systems Explained, Wiley, Chichester, UK.
Lazzaretto, A. , Toffolo, A. , and Zanon, F. , 2004, “ Parameter Setting for a Tubular SOFC Simulation Model,” ASME J. Energy Resour. Technol., 126(1), pp. 40–46. [CrossRef]
Sedghisigarchi, K. , and Feliachi, A. , 2002, “ Control of Grid-Connected Fuel Cell Power Plant for Transient Stability Enhancement,” IEEE Power Engineering Society Winter Meeting, Vol. 1, pp. 383–388, Cat. No.02CH37309.
Campanari, S. , 2001, “ Thermodynamic Model and Parametric Analysis of a Tubular SOFC Module,” J. Power Sources, 92(1–2), pp. 26–34. [CrossRef]
Das, T. , and Weisman, R. , 2009, “ A Feedback Based Load Shaping Strategy for Fuel Utilization Control in SOFC Systems,” American Control Conference (ACC-09), St. Louis, MO, June 10–12, pp. 2767–2772.
Allag, T. , and Das, T. , 2012, “ Robust Nonlinear Control of Solid Oxide Fuel Cell Ultra-Capacitor Hybrid Systems,” IEEE Trans. Control Syst. Technol., 20(1), pp. 1–10. [CrossRef]
Das, T. , and Snyder, S. , 2013, “ Adaptive Control of a Solid Oxide Fuel Cell Ultra-Capacitor Hybrid System,” IEEE Trans. Control Syst. Technol., 21(2), pp. 372–383. [CrossRef]
Khalil, H. , 2002, Nonlinear Systems, 3rd ed., Prentice-Hall, Inc., Upper Saddle River, NJ.
Davis, H. T. , 2010, Introduction to Nonlinear Differential and Integral Equations, Dover Publications, Inc., New York.
Strogatz, S. H. , 2001, Nonlinear Dynamics and Chaos, 1st ed., Westview Press, Cambridge, MA.
Das, T. , Narayanan, S. , and Mukherjee, R. , 2010, “ Steady-State and Transient Analysis of a Steam-Reformer Based Solid Oxide Fuel Cell System,” ASME J. Fuel Cell Sci. Technol., 7(1), p. 011022.
Sedghisigarchi, K. , and Feliachi, A. , 2002, “ Control of Grid-Connected Fuel Cell Power Plant for Transient Stability Enhancement,” IEEE Power Engineering Society Transmission and Distribution Conference, Vol. 1, pp. 383–388.
Stiller, C. , Thorud, B. , Bolland, O. , Kandepu, R. , and Imsland, L. , 2006, “ Control Strategy for a Solid Oxide Fuel Cell and Gas Turbine Hybrid System,” J. Power Sources, 158(1), pp. 303–315. [CrossRef]
Nehrir, M. H. , and Wang, C. , 2006, Modeling and Control of Fuel Cells–Distributed Generation Applications, Wiley, Hoboken, NJ.
Murshed, A. M. , Huang, B. , and Nandakumar, K. , 2010, “ Estimation and Control of Solid Oxide Fuel Cell System,” Comput. Chem. Eng., 34(1), pp. 96–111. [CrossRef]
Gaynor, R. , Mueller, F. , Jabbari, F. , and Brouwer, J. , 2008, “ On Control Concepts to Prevent Fuel Starvation in Solid Oxide Fuel Cells,” J. Power Sources, 180(1), pp. 330–342. [CrossRef]
Sastry, S. , 1999, Nonlinear Systems: Analysis, Stability and Control, Springer-Verlag, New York.
Slotine, J. , and Weiping, L. , 1991, Applied Nonlinear Control, Prentice-Hall, Inc., Upper Saddle River, NJ.
Vidyasagar, M. , 2002, Nonlinear Systems Analysis, 2nd ed., Society for Industrial and Applied Mathematics, Philadelphia, PA.
Franklin, G. F. , Powell, J. D. , and Emami-Naeini, A. , 2014, Feedback Control of Dynamic Systems, 7th ed. Prentice Hall, Upper Saddle River, NJ.

Figures

Grahic Jump Location
Fig. 1

Schematic diagram of the hybrid SOFC system

Grahic Jump Location
Fig. 2

SOFC/UC hybrid as a cascaded system

Grahic Jump Location
Fig. 3

Generalized form of Fig. 2

Grahic Jump Location
Fig. 4

A Lur'e problem formulation derived from Fig. 3

Grahic Jump Location
Fig. 5

Circle criterion simulations: (b) with fb(e) and (c) with fc(e)

Grahic Jump Location
Fig. 6

Feedback system with driven dynamic equation generalized to Eq. (38)

Grahic Jump Location
Fig. 7

Variation OF λ1,2 with a, indicating Hopf bifurcation

Grahic Jump Location
Fig. 8

Simulations to verify Theorems 3 and 4

Grahic Jump Location
Fig. 9

Simulation verifying the stability result of Eq. (55)

Grahic Jump Location
Fig. 10

HIL test stand and experimental results

Tables

Errata

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