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Synthesis of gain scheduled control systems based on nonlinear affine basis

Research Project

Project/Area Number 18K04209
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 21040:Control and system engineering-related
Research InstitutionTokyo Metropolitan University

Principal Investigator

Kojima Akira  東京都立大学, システムデザイン研究科, 教授 (80234756)

Project Period (FY) 2018-04-01 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2018: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywordsゲインスケジュールド制御 / 線形パラメータ変動システム / ロバスト制御 / 線形行列不等式 / 非線形アファイン基底
Outline of Final Research Achievements

Parameter-dependent LMIs (linear matrix inequalities) have been playing a crucial role in characterizing the controller design for parameter varying systems, and comprehensive design methods have been established for linear parameter varying systems. However, the parameter-dependent LMIs are generally difficult to compute, and efficient computation methods have been required in order to broaden the practical application fields.
In this research, we propose a computation method for polynomial parameter-dependent LMIs based on the Bernstein basis with parameter region partitioning. Furthermore, it is shown that the conservativeness of the proposed method is characterized in terms of the parameter region partitioning, and the solution accuracy is recovered at the 2nd order of the maximal region size. The proposed methods are applied to the gain scheduled control for mechatronics and power grid systems, and the features of the resulting systems are discussed.

Academic Significance and Societal Importance of the Research Achievements

制御システムを構成する上で重要な課題は,広い動作範囲で適切な動きを保証することであり,このような課題を克服するために,ゲインスケジュールド制御法が広く用いられてきた.しかしながら,その設計には負荷の高い計算を要し,また性能の検証が容易でないという課題があった.本研究は,これらの設計に利用可能な計算法を,Bernstein基底とよぶ非線形基底を導入することにより導き,原問題を任意の精度で解き,設計上達成できる性能を検証できることを示した.そして提案法を,自然エネルギー大量導入時の系統制御問題,機械系の制御問題に適用し,その特徴を明らかにした.

Report

(5 results)
  • 2021 Annual Research Report   Final Research Report ( PDF )
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (17 results)

All 2022 2021 2020 2019 2018 Other

All Journal Article (6 results) (of which Peer Reviewed: 6 results) Presentation (8 results) Remarks (3 results)

  • [Journal Article] A characterization of preview load frequency control in terms of power system inertia2021

    • Author(s)
      Shogo Ikekawa, Kotaro Hashikura, Akira Kojima
    • Journal Title

      Proc. of SICE Annual Conference 2021

      Volume: 1 Pages: 184-187

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Gain scheduled control of a parallelogram linkage robot manipulator considering nonlinearity due to mechanical properties2021

    • Author(s)
      Hitomu Saito, Akira Kojima
    • Journal Title

      Proc. of SICE Annual Conference 2021

      Volume: 1 Pages: 1305-1308

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 区間むだ時間系に対する有界実補題の導出2020

    • Author(s)
      児島 晃, 端倉 弘太郎
    • Journal Title

      計測自動制御学会論文集

      Volume: 56 Issue: 10 Pages: 475-482

    • DOI

      10.9746/sicetr.56.475

    • NAID

      130007925074

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] A Calculation Method of Parameter-dependent LMIs on Nonlinear Affine Basis2019

    • Author(s)
      児島 晃
    • Journal Title

      Transactions of the Society of Instrument and Control Engineers

      Volume: 55 Issue: 7 Pages: 429-438

    • DOI

      10.9746/sicetr.55.429

    • NAID

      130007679326

    • ISSN
      0453-4654, 1883-8189
    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] A calculation method of parameter-dependent LMIs on Bernstein polynomial basis: polytopic representation case2019

    • Author(s)
      Akira Kojima
    • Journal Title

      Proc. of 2019 IEEE 58th Conference on Decision and Control

      Volume: 1 Pages: 2850-2857

    • DOI

      10.1109/cdc40024.2019.9028962

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] A characterization of parameter-dependent LMIs on Bernstein polynomial basis2018

    • Author(s)
      Akira Kojima
    • Journal Title

      Proc. of 2018 IEEE Conference on Decision and Control

      Volume: 1 Pages: 4687-4694

    • DOI

      10.1109/cdc.2018.8619253

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Presentation] H2制御性能に着目したゲイン調整法とその負荷周波数制御への応用2022

    • Author(s)
      池川聖悟,児島 晃
    • Organizer
      第9回 計測自動制御学会制御部門マルチシンポジウム,神奈川(Online)
    • Related Report
      2021 Annual Research Report
  • [Presentation] 機構的特性を考慮した3自由度マニピュレータの追従制御2022

    • Author(s)
      門司 達也 ,齊藤 仁夢 ,児島 晃
    • Organizer
      第66回システム制御情報学会研究発表講演会 (SCI’22),京都
    • Related Report
      2021 Annual Research Report
  • [Presentation] 予測誤差を考慮した予見負荷周波数制御と慣性定数の評価2020

    • Author(s)
      池川 聖悟, 宮本 楓雅, 端倉 弘太郎, 児島 晃, 益田 泰輔
    • Organizer
      第63回 自動制御連合講演会
    • Related Report
      2020 Research-status Report
  • [Presentation] 機構的特性を考慮したゲインスケジュールド制御法の開発2020

    • Author(s)
      齊藤 仁夢, 児島 晃
    • Organizer
      第63回 自動制御連合講演会
    • Related Report
      2020 Research-status Report
  • [Presentation] 系統慣性の変化を考慮したゲインスケジュールド負荷周波数制御法の検討2020

    • Author(s)
      池川聖悟,端倉弘太郎,児島 晃
    • Organizer
      第8回 計測自動制御学会制御部門マルチシンポジウム
    • Related Report
      2020 Research-status Report
  • [Presentation] 多項式非線形基底を用いたロボットマニピュレータのゲインスケジュールド制御2019

    • Author(s)
      石友真, 花房健多, 児島晃
    • Organizer
      第62回自動制御連合講演会
    • Related Report
      2019 Research-status Report
  • [Presentation] Bernstein基底を用いたパラメータ依存LMIの解法 -ポリトープ型パラメータを扱う場合-2019

    • Author(s)
      児島 晃
    • Organizer
      第6回 計測自動制御学会制御部門マルチシンポジウム
    • Related Report
      2018 Research-status Report
  • [Presentation] 非線形特性を考慮したマニピュレータのゲインスケジュールド制御2018

    • Author(s)
      村﨑智文,児島 晃
    • Organizer
      第19 回計測自動制御学会システムインテグレーション部門講演会
    • Related Report
      2018 Research-status Report
  • [Remarks] 東京都立大学システムデザイン研究科 児島研究室HP

    • URL

      http://www.comp.sd.tmu.ac.jp/akojima-lab/

    • Related Report
      2021 Annual Research Report 2019 Research-status Report
  • [Remarks] 東京都立大学システムデザイン研究科 児島研究室HP

    • URL

      http://www.comp.sd.tmu.ac.jp/akojima-lab/index.html

    • Related Report
      2020 Research-status Report
  • [Remarks] 首都大学東京システムデザイン研究科 児島研究室HP

    • URL

      http://www.comp.sd.tmu.ac.jp/akojima-lab/index.html

    • Related Report
      2018 Research-status Report

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Published: 2018-04-23   Modified: 2023-01-30  

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