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Study on the Applications of Variational System Theory

Research Project

Project/Area Number 60550166
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 機械力学・制御工学
Research InstitutionHokkaido University

Principal Investigator

HIMA Masasuke  Professor, Faculty of Eng., Hokkaido University, 工学部, 教授 (10029457)

Co-Investigator(Kenkyū-buntansha) ISURUGI Yoshihisa  Lecturer, Faculty of Eng., Hokkaido University, 工学部, 講師 (00109480)
Project Period (FY) 1985 – 1986
Project Status Completed (Fiscal Year 1986)
Budget Amount *help
¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 1986: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1985: ¥1,200,000 (Direct Cost: ¥1,200,000)
KeywordsDesign methods of nonlinear system / Disturbance decoupled control system / Model following control system / Discretizing of continuous time control law / Approximate digital expressions / Control of robot / ロボットの制御 / 飛行体の制御
Research Abstract

In this project, we studied the nonlinear system theory based on the variational approach and named as a "Variational System Theory", and its applications to the real control processes. Applying the method introduced by L.I.Rozonoer to the nonlinear system with controls appearing linearly and the C -structure, we derived several equivalent necessary and sufficient conditions of complete invariance and output controllability. Combining these conditions with those of stability and functional independence, we have obtained the design procedures of canonical form, nonlinear observers, decoupling, disturbance decoupling, inverse systems, and model following control systems. Especially, our model following control system has enough flexibility for the further theoretical investigations and the practical applications.
In the different but related projects of our group, we studied the design of multistep discretizing controller for continuous time control law, approximate digital expressions of … More continuous time nonlinear systems, and carried out a preliminary investigation on the computer aided design of nonlinear control systems. Incorporating the results obtained in these projects with our design procedures of nonlinear systems, we studied the control problem of a robot Rhino XR-1 along the continuous path and obtained the expected results both in the numerical simulations and in the practical experiments, where the static and dynamic characteristics of the robot are identified experimentally for the three degrees of freedom. This result seems to show the applicability of our theory.
If the state space of a nonlinear system is a differentiable manifold, our invariance theory can be applied only to the local expressions of its dynamical behaviour. Therefore, it is necessary to study how to combine the control laws designed for each local expressions. With the aim of solving this difficulty, we studied the attitude control problem of an artificial satellite. Applying our design procedures and the expression via quarternion numbers, we obtained successful results in stabilizing problems, which gave us a hint to study the problem in general. Less

Report

(1 results)
  • 1986 Final Research Report Summary
  • Research Products

    (18 results)

All Other

All Publications (18 results)

  • [Publications] 島公脩: システムと制御. 29. 45-54 (1985)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] 石動善久: システムと制御. 29. 259-267 (1985)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] 石動善久: システムと制御. 29. 322-330 (1985)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] 石動善久: システムと制御. 29. 749-757 (1985)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] 石動善久: システムと制御. 30. 312-319 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] 山下裕: システムと制御. (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] 石動善久: 精密工学. (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] 山下裕: システムと制御. (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] 島公脩: システムと制御.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] SHIMA, Masasuke: "Theory of Invariance and its Applications - VII. Disturbance Decoupling -" Systems and Control. 29. 45-54 (1985)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] ISURUGI, Yoshihisa: "Digital Control Law of Continuous-time Systems" Systems and Control. 29. 259-267 (1985)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] ISURUGI, Yoshihisa: "Theory of Invariance and its Applications - VIII. Model Following Control Systems -" Systems and Control. 29. 322-330 (1985)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] ISURUGI, Yoshihisa: "Stability of Control Systems Using Digital Controller Based on Multi-Step Methods" Systems and Control. 29. 749-757 (1985)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] ISURUGI, Yoshihisa: "Discretization of Nonlinear Continuous-Time Control Law" Systems and Control. 30. 312-319 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] YAMASHITA, Yuu: "Theory of Invariance and its Applications - IX. Output Controllability of Multi-Input Multi-Output Nonlinear Systems -" Systems and Control.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] ISURUGI, Yoshihisa: "Dynamic Digital Control of a Multi-Articulated Robot" J.Japan Society of Precision Engineering.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] YAMASHITA, Yuu: "Attitude Control of an Artificial Sattelite via Nonlinear Control Theory" Systems and Control.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] SHIMA, Masasuke: "Discrete-Time Expressions of Nonlinear Control Systems" Systems and Control.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary

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Published: 1987-03-31   Modified: 2016-04-21  

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