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Engineering Application of Fractional Calculus

Research Project

Project/Area Number 23560076
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Engineering fundamentals
Research InstitutionUniversity of Hyogo (2013-2014)
National Institute of Advanced Industrial Science and Technology (2011-2012)

Principal Investigator

KURODA Masaharu  兵庫県立大学, 大学院工学研究科, 教授 (60344222)

Research Collaborator ARAKI Nozomu  
MATSUBUCHI Hiroki  
YOSHITANI Naoki  
Project Period (FY) 2011-04-28 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥5,460,000 (Direct Cost: ¥4,200,000、Indirect Cost: ¥1,260,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2011: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Keywords微積分 / 振動 / 制御 / PID制御 / 柔軟構造物 / ロバスト性 / 制御工学 / 振動制御 / フィードバック制御 / 実験 / 1センサ法 / 複数センサ法 / Grunwald-Letnikovの定義 / 1/2階微分 / 粘弾性体 / 物理数学 / ダイナミクス / 運動方程式 / 安定判別
Outline of Final Research Achievements

Fractional calculus in which the order of the differentiation/integration is expanded to a non-integer value is applied to vibration control engineering. First, the definition of the fractional differentiation/integration is discretized. Then its algorithm is downloaded to a digital signal processor (DSP). The output signal from one sensor can be differentiated/integrated to a fractional order with the DSP. Furthermore, a technique is developed by which a linear combination of the output signals from multiple displacement and velocity sensors is converted into a fractional differentiation/integration response. Finally, vibration control experiments of a flexible cantilevered beam are conducted using fractional PID feedback control. In contrast to conventional PID feedback control, the fractional PID feedback control can achieve not only the equivalent vibration-suppression effect, but also better robust stability against parameter variation.

Report

(5 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (18 results)

All 2015 2014 2013 2011 Other

All Journal Article (3 results) (of which Peer Reviewed: 3 results,  Acknowledgement Compliant: 2 results) Presentation (14 results) Remarks (1 results)

  • [Journal Article] Vibration Control Using Fractional Derivative Feedback2014

    • Author(s)
      Kuroda, M.
    • Journal Title

      Congress Abstracts of 17th U.S. National Congress on Theoretical and Applied Mechanics

      Volume: 1

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Vibration Control Using Fractional Derivative Feedback2014

    • Author(s)
      Kuroda, M. and Matsubuchi, H.
    • Journal Title

      Proc. of 8th European Nonlinear Dynamics Conference (ENOC 2014)

      Volume: 1

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] THE FRACTIONAL DERIVATIVE AS A COMPLEX EIGENVALUE PROBLEM2011

    • Author(s)
      Masaharu Kuroda
    • Journal Title

      Proc. IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments

      Volume: - Pages: 109-117

    • DOI

      10.1007/978-94-007-1643-8_13

    • ISBN
      9789400716421, 9789400716438
    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] 非整数階微分を用いた振動制御(第2報:PD制御の拡張とその制御効果の検証)2015

    • Author(s)
      松淵博基,吉谷尚樹,黒田雅治
    • Organizer
      日本機械学会 D&D 2015
    • Place of Presentation
      弘前大学(青森)
    • Year and Date
      2015-08-25 – 2015-08-28
    • Related Report
      2014 Annual Research Report
  • [Presentation] 非整数階微分を用いた振動制御(第3報:柔軟構造物の変位・速度情報を用いた分数階微分応答の計測)2015

    • Author(s)
      吉谷尚樹,松淵博基,黒田雅治
    • Organizer
      日本機械学会 D&D 2015
    • Place of Presentation
      弘前大学(青森)
    • Year and Date
      2015-08-25 – 2015-08-28
    • Related Report
      2014 Annual Research Report
  • [Presentation] Vibration Control Experiment using Fractional PID Feedback2015

    • Author(s)
      Kuroda, M., Matsubuchi, H. and Yoshitani, N.
    • Organizer
      ASME 2015 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE 2015)
    • Place of Presentation
      Boston (USA)
    • Year and Date
      2015-08-02 – 2015-08-05
    • Related Report
      2014 Annual Research Report
  • [Presentation] 非整数階PID制御による振動制御実験2015

    • Author(s)
      黒田雅治
    • Organizer
      2014年度力学系の応用研究集会
    • Place of Presentation
      京都大学(京都)
    • Year and Date
      2015-03-28 – 2015-03-29
    • Related Report
      2014 Annual Research Report
  • [Presentation] 非整数階微分を用いた振動制御(第1報:理論解析および数値計算による検討)2014

    • Author(s)
      松淵博基,荒木 望,黒田雅治
    • Organizer
      日本機械学会 D&D 2014
    • Place of Presentation
      上智大学(東京)
    • Year and Date
      2014-08-26 – 2014-08-29
    • Related Report
      2014 Annual Research Report
  • [Presentation] Vibration Control Using Fractional Derivative Feedback2014

    • Author(s)
      Kuroda, M., Matsubuchi, H. and Araki, N.
    • Organizer
      ASME 2014 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE 2014)
    • Place of Presentation
      Buffalo (USA)
    • Year and Date
      2014-08-17 – 2014-08-20
    • Related Report
      2014 Annual Research Report
  • [Presentation] Vibration Control Using Fractional Derivative Feedback2014

    • Author(s)
      Kuroda, M. and Matsubuchi, H.
    • Organizer
      8th European Nonlinear Dynamics Conference (ENOC 2014)
    • Place of Presentation
      Vienna (Austria)
    • Year and Date
      2014-07-06 – 2014-07-11
    • Related Report
      2014 Annual Research Report
  • [Presentation] Vibration Control Using Fractional Derivative Feedback2014

    • Author(s)
      Kuroda, M.
    • Organizer
      17th U.S. National Congress on Theoretical and Applied Mechanics
    • Place of Presentation
      Michigan (USA)
    • Year and Date
      2014-06-15 – 2014-06-20
    • Related Report
      2014 Annual Research Report
  • [Presentation] 非整数階微分を用いた振動制御(第1報:理論解析および数値計算による検討)2014

    • Author(s)
      松淵博基、荒木望、黒田雅治
    • Organizer
      日本機械学会Dynamics and Design Conference 2014(D&D2014)
    • Place of Presentation
      上智大学 四谷キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] Vibration Control Using Fractional Derivative Feedback2014

    • Author(s)
      Masaharu Kuroda
    • Organizer
      17th U.S. National Congress on Theoretical and Applied Mechanics (USNCTAM 2014)
    • Place of Presentation
      Michigan State University(米国)
    • Related Report
      2013 Research-status Report
  • [Presentation] Vibration Control Using Fractional Derivative Feedback2014

    • Author(s)
      Masaharu Kuroda, Hiroki Matsubuchi
    • Organizer
      The 8th European Nonlinear Dynamics Conference (ENOC 2014)
    • Place of Presentation
      Vienna University of Technology(オーストリア)
    • Related Report
      2013 Research-status Report
  • [Presentation] Vibration Control Using Fractional Derivative Feedback2014

    • Author(s)
      Masaharu Kuroda, Hiroki Matsubuchi, Nozomu Araki
    • Organizer
      ASME 2014 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE 2014)
    • Place of Presentation
      Buffalo Niagara Convention Center(米国)
    • Related Report
      2013 Research-status Report
  • [Presentation] ある分数階微分方程式の解き方2013

    • Author(s)
      黒田雅治
    • Organizer
      力学系理論の応用に関する研究会
    • Place of Presentation
      早稲田大学西早稲田キャンパス(理工)
    • Related Report
      2012 Research-status Report
  • [Presentation] 分数階微積分を応用した機械構造物の振動制御2011

    • Author(s)
      黒田雅治
    • Organizer
      第54回自動制御連合講演会
    • Place of Presentation
      愛知県、豊橋技術科学大学
    • Related Report
      2011 Research-status Report
  • [Remarks] 非整数階微積分の工学応用、非線形工学に関する基礎的研究

    • URL

      http://www.eng.u-hyogo.ac.jp/outline/faculty/kuroda/index.html

    • Related Report
      2014 Annual Research Report

URL: 

Published: 2011-08-05   Modified: 2023-03-16  

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