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Theoretical and Numerical Study on Sampled-Data Control of Parabolic Distributed Parameter Systems

Research Project

Project/Area Number 16540111
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKagoshima University

Principal Investigator

SANO Hideki  Kagoshima University, Computing and Communications Center, Associate Professor, 学術情報基盤センター, 助教授 (70278737)

Project Period (FY) 2004 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 2005: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2004: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywordsparabolic system / unbounded output operator / sampled-data H∞ control / finite-dimensional controller / residual mode filter / hyperbolic system / exponential stability / observability, reachability / 並流型熱交換器 / 境界フィードバック / 強連続半群 / スペクトル / 可観測性 / 可到達性 / 非負錐 / 線形放物型システム
Research Abstract

This research is concerned with sampled-data H_∞ control of parabolic systems with unbounded output operators. Especially, the output operator is assumed to be (-L)^γ-bounded, where 0<γ<1/2. For example, diffusion systems with boundary control can be formulated as parabolic systems with output operators of such a type. For the parabolic system with an ideal sampler and a zero-order hold, the aim is to construct a finite-dimensional discrete-time stabilizing controller that makes the L^2 -induced norm of the feedback sampled-data system less than a given positive number. For that purpose, the infinite-dimensional continuous-time system is formulated as an infinite-dimensional discrete-time system by using a lifting technique and a variable transformation. Based on a reduced-order model with a finite-dimensional state space for the infinite-dimensional discrete-time system, a finite-dimensional controller containing a residual mode filter is designed to provide the desirable performance.
Moreover, systems whose axial dispersion coefficients are sufficiently small and can be neglected are treated as control objects. A parallel-flow heat exchanger with boundary inputs is described by two parabolic equations when the axial dispersion is taken into consideration. On the other hand, the parabolic equations become hyperbolic equations in the case where the axial dispersion can be neglected. In this research, the stability analysis is carried out, for the closed-loop system which consists of the hyperbolic system and an output feedback law. In addition, the dynamical analysis such as observability and reachability is performed for the hyperbolic system.

Report

(3 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • Research Products

    (9 results)

All 2005 2004 Other

All Journal Article (9 results)

  • [Journal Article] 境界フィードバックを伴う並流型熱交換方程式の指数安定性について2005

    • Author(s)
      佐野 英樹
    • Journal Title

      システム制御情報学会論文誌 Vol.18, No.6

      Pages: 222-228

    • NAID

      10016147956

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Journal Article] On the stability of a linear bioprocess model with recycle loop2005

    • Author(s)
      Hideki Sano
    • Journal Title

      IEEE Transactions on Automatic Control Vol.50, No.8

      Pages: 1200-1205

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Journal Article] On exponential stability of parallel-flow heat exchanger equations with boundary feedback2005

    • Author(s)
      H.Sano, N.Kunimatsu
    • Journal Title

      Transactions of the Institute of Systems, Control and Information Engineers (in Japanese) Vol.18, No.6

      Pages: 222-228

    • NAID

      10016147956

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On the stability of a linear bioprocess model with recycle loop2005

    • Author(s)
      H.Sano, N.Kunimatsu
    • Journal Title

      IEEE Transactions on Automatic Control Vol.50, No.8

      Pages: 1200-1205

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] 非有界出力作用素をもつ線形放物型システムのサンプル値H∞制御2004

    • Author(s)
      佐野 英樹
    • Journal Title

      計測自動制御学会論文集 Vol.40, No.9

      Pages: 915-924

    • NAID

      130003971408

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Sampled-data H∞ control of linear parabolic systems with unbounded output operators2004

    • Author(s)
      H.Sano
    • Journal Title

      SICE Transactions (in Japanese) Vol.40, No.9

      Pages: 915-924

    • NAID

      130003971408

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] 非有界出力作用素をもつ線形放物型システムのサンプル値H∞制御2004

    • Author(s)
      佐野 英樹
    • Journal Title

      計測自動制御学会論文集 Vol.40,No.9

      Pages: 915-924

    • NAID

      130003971408

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Observability and reachability for parallel-flow heat exchanger equations

    • Author(s)
      Hideki Sano
    • Journal Title

      IMA Journal of Mathematical Control and Information 印刷中

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Observability and reachability for parallel-flow heat exchanger equations

    • Author(s)
      H.Sano
    • Journal Title

      IMA Journal of Mathematical Control and Information (in press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary

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Published: 2004-04-01   Modified: 2016-04-21  

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