Construction of the Control Realizing the Rotation of a Timoshenko Beam

  • V. I. Kororbov
  • W. Krabs
  • G. M. Skylar

Abstract

We consider the linear model of a slowly rotating Timoshenko beam in a horizontal plane whose moment is controlled by the angular acceleration of the disk of the driving motor into which the beam is clamped. This work complements our previous results on the controllability of the beam from a position of rest into another position of rest; we give a method of construction of a piecewise constant control solving the problem.

Timoshenko beam controllability moment problem piecewise constant control 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Sakava, Y., Ito, R., and Fuji, N., Optimal Control of a Flexible Arm, Control Theory for Distributed Parameter Systems and Applications, Lecture Notes in Control and Information Sciences, Springer Verlag, Berlin, Germany, Vol. 54, pp. 175–187, 1983.Google Scholar
  2. 2.
    Delfour, M. C., Kern, M., Passeron, L., and Sevenne, B., Modelling of a Rotating Flexible Beam, Control of Distributed Parameter Systems, Edited by H. E. Rauch, Pergamon Press, Los Angeles, California, pp. 383–387, 1986.Google Scholar
  3. 3.
    Leugering, G., Control and Stabilization of a Flexible Arm, Dynamics and Stability of Systems, Vol. 5, pp. 37–42, 1990.Google Scholar
  4. 4.
    Leugering, G., On Control and Stabilization of a Rotating Beam by Applying Moments at the Base Only, Optimal Control of Partial Differential Equations, Edited by K. N. Hoffman and W. Krabs, Lecture Notes in Control and Information Sciences, Springer Verlag, Berlin, Germany, Vol. 149, pp. 182–191, 1991.Google Scholar
  5. 5.
    Krabs, W., Controllability of a Rotating Beam, Analysis and Optimization, State and Frequency Domain Approaches for Infinite—Dimensional Systems, Edited by R. F. Curtain, Lecture Notes in Control and Information Sciences, Springer Verlag, Berlin, Germany, Vol. 185, pp. 447–458, 1993.Google Scholar
  6. 6.
    Ballas, K., Steuerung eines rotierenden, flexiblen Balkens mit einem Drehmoment von minimaler L 2 -Norm, Diplomarbeit, Technical University Dormstadt, 1994.Google Scholar
  7. 7.
    Krabs, W., On the Controllability of the Rotation of a Flexible Arm, Control and Estimation of Distributed Parameter Systems, Nonlinear Phenomena, Edited by W. Desch et al., International Series on Numerical Mathematics, Birkhaüser Verlag, Basel, Switzerland, Vol. 118, pp. 267–269, 1994.Google Scholar
  8. 8.
    Krabs, W., and Nguen, C. L., On the Controllability of a Robot Arm, Mathematical Methods of Applied Science, Vol. 21, pp. 25–42, 1998.Google Scholar
  9. 9.
    Xiong, X. J., Modelling, Control, and Computer Simulation of a Rotating Timoshenko Beam, PhD Thesis, McGill University, Montreal, Canada, 1997.Google Scholar
  10. 10.
    Krabs, W., and Sklyar, G. M., On the Controllability of a Slowly Rotating Timoshenko Beam, Zeitschrift für Analysis und Ihre Anwendungen, Vol. 18, pp. 437–448, 1999.Google Scholar
  11. 11.
    Krabs, W., and Sklyar, G. M., On the Stabilizability of a Slowly Rotating Timoshenko Beam, Zeitschrift für Analysis und Ihre Anwendungen (to appear).Google Scholar
  12. 12.
    Krabs, W., On Moment Theory and Controllability of One-Dimensional Vibrating Systems and Heating Processes, Lecture Notes in Control and Information Sciences, Springer Verlag, Berlin, Germany, Vol. 173, 1992.Google Scholar

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • V. I. Kororbov
    • 1
    • 2
  • W. Krabs
    • 3
  • G. M. Skylar
    • 1
    • 4
  1. 1.Institute of MathematicsSzczecin UniversitySzczecinPoland
  2. 2.Department of Differential Equations and ControlKharkov State UniversityKharkovUkraine
  3. 3.Technische Universität DarmstadtDarmstadtGermany
  4. 4.Department of Mathematical AnalysisKharkov State UniversityKharkovUkraine

Personalised recommendations