Modelling and Control Synthesis of Flexible Multibody Systems

  • J. Haug
  • W. Schiehlen
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 361)


In the last two decades, several models have been developed for the simulation of gross nonlinear motions of multibody systems which incorporate elastic members with small deformations. Although these models represent the real system sufficiently well for simulation, a closed-loop controller designed on the basis of such models may result in instability if applied to the real system.

In this paper, the value of a model consisting of superelements for control synthesis is investigated. The superelements approximating flexible bodies with beam like structures are composed of a series of rigid bodies interconnected by joints and springs. As an example, the nonlinear equations of motion of a plane flexible robot with two links are derived and linearized for control synthesis. A first controller is synthesized by using the pole placement method. Applied to the ‘real system’ represented by a highly accurate finite element model, the controller leads to instability. Therefore, a second robust controller is synthesized by using left coprime factorization and H minimization.


Multibody System Control Synthesis Robust Controller Open Loop Control Flexible Body 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Engell, S., Modelgüte und Regelgüte,VDI Berichte Nr. 925, VDI—Verlag, 1989.Google Scholar
  2. [2]
    Czaijkowski, E.A., and Preumont, A., and Hafka, R.T., “Spillover Stabilization of Large Space Structures”, Journal of Guidance and Control 13 (1990) 1000–1007.CrossRefGoogle Scholar
  3. [3]
    Kleemann, U., Regelung elastischer Roboter, VDI Fortschritt—Berichte, Reihe 8, Nr. 191, VDI—Verlag, 1989.Google Scholar
  4. [4]
    Schiehlen, W.O., Technische Dynamik, Teubner, 1986.Google Scholar
  5. [5]
    Rauh, J., Ein Beitrag zur Modellierung elastischer Balkensysteme, VDI Fortschritt—Berichte, Reihe 18, Nr. 37, VDI—Verlag, 1987.Google Scholar
  6. [6]
    Melzer F., “Semi—Symbolic Equations of Motion for Flexible Multibody Systems”, Proceedings of the 1993 ASME International Computers in Engineering Conference, San Diego, August 8–12, 1993.Google Scholar
  7. [7]
    The Math Works Inc., MATLAB User’s Guide, Natick, MA, 1992.Google Scholar
  8. [8]
    McFarlain D.C. and Glover K., Robust Controller Design Using Normalized Coprime Factor Plant Description,Springer-Verlag, 1990.Google Scholar

Copyright information

© Springer-Verlag Wien 1995

Authors and Affiliations

  • J. Haug
    • 1
  • W. Schiehlen
    • 1
  1. 1.University of StuttgartStuttgartGermany

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