Stability test for a parabolic partial differential equation

Miklos Vajta

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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    Abstract

    The paper describes a stability test applied to coupled parabolic partial differential equations. The PDE's describe the temperature distribution of composite structures with linear inner heat sources. The distributed transfer functions are developed based on the transmission matrix of each layer. To analyse the stability of the system we define a virtual feedback-loop. We give the virtual feedback transfer functions for different boundary conditions. Given an open-loop linear system (the virtual feedback-loop) we can apply the Nyquist stability test to determine the critical gains of the inner heat sources. The method described is easy to use and avoids numerical problems arising from locating the infinite number of system poles by numerical approximation.
    Original languageEnglish
    Title of host publication9th Mediterranean Conference on Control and Automation: Book of abstracts
    Place of PublicationZagreb, Croatia
    PublisherKoREMA Secretariat
    Pages151-151
    Number of pages4
    ISBN (Print)953-6037-34-3
    Publication statusPublished - 27 Jun 2001
    Event9th IEEE Mediterranean Conference on Control and Automation, MED 2001 - Hotel Excelsior, Dubrovnik, Croatia
    Duration: 27 Jun 200129 Jun 2001
    Conference number: 9

    Conference

    Conference9th IEEE Mediterranean Conference on Control and Automation, MED 2001
    Abbreviated titleMED
    CountryCroatia
    CityDubrovnik
    Period27/06/0129/06/01

    Fingerprint

    Partial differential equations
    Feedback
    Transfer functions
    Composite structures
    Linear systems
    Poles
    Temperature distribution
    Boundary conditions
    Hot Temperature

    Keywords

    • Distributed-parameter systems
    • Nyquist stability test
    • Partial differential equations

    Cite this

    Vajta, M. (2001). Stability test for a parabolic partial differential equation. In 9th Mediterranean Conference on Control and Automation: Book of abstracts (pp. 151-151). Zagreb, Croatia: KoREMA Secretariat.
    Vajta, Miklos. / Stability test for a parabolic partial differential equation. 9th Mediterranean Conference on Control and Automation: Book of abstracts. Zagreb, Croatia : KoREMA Secretariat, 2001. pp. 151-151
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    author = "Miklos Vajta",
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    Vajta, M 2001, Stability test for a parabolic partial differential equation. in 9th Mediterranean Conference on Control and Automation: Book of abstracts. KoREMA Secretariat, Zagreb, Croatia, pp. 151-151, 9th IEEE Mediterranean Conference on Control and Automation, MED 2001, Dubrovnik, Croatia, 27/06/01.

    Stability test for a parabolic partial differential equation. / Vajta, Miklos.

    9th Mediterranean Conference on Control and Automation: Book of abstracts. Zagreb, Croatia : KoREMA Secretariat, 2001. p. 151-151.

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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    Vajta M. Stability test for a parabolic partial differential equation. In 9th Mediterranean Conference on Control and Automation: Book of abstracts. Zagreb, Croatia: KoREMA Secretariat. 2001. p. 151-151