Applied Mathematics and Optimization

, Volume 35, Issue 3, pp 331–351 | Cite as

An LQR-control problem for a multicomponent flexible structure



This paper is concerned with modeling and control of a multicomponent distributed-parameter structure. General results from the theory of infinitedimensional systems are used to pose an LQR-control problem for the structure. Different variations of the structure are considered and, in particular, approximation schemes for two forms of the structure are presented in detail. Responses of the system to an elastic initial condition are presented. It is shown that convergent state feedback control laws can be obtained which result in significant suppression of vibrations and unwanted displacements throughout the structure.

Key Words

Feedback control Functional gains Galerkin method 

AMS Classification

49 65 93 


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  1. 1.
    H.T. Banks, R.C. Smith, and Y. Wang. The modeling of piezoceramic patch interactions with shells, plates and beams. Quarterly of Applied Mathematics, to appear.Google Scholar
  2. 2.
    H.M. Chun, J.D. Turner, and V. Lupi. Distributed parameter multibody dynamics modeling. Advances in the Astronautical Sciences, 76:513–526, 1991.Google Scholar
  3. 3.
    J.S. Gibson and A. Adamian. Approximation theory for linear-quadratic-gqussian optimal control of flexible structure. SIAM Journal of Control and Optimization, 29:1–37, 1991.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    D.M. Gorinevsky. Galerkin approximation in modeling of controlled distributed parameter flexible systems. Computer Methods in Applied Mechanics and Engineering, 106:107–128, 1993.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    T. Kato. Perturbation of Linear Operators. Springer-Verlag, New York, 1981.Google Scholar
  6. 6.
    V.D. Lupi, H.M. Chun, and J.D. Turner. Distributed control and simulation of a Bernoulli-Euler beam. Journal of Guidance, Control and Dynamics, 15:727–734, 1992.zbMATHCrossRefGoogle Scholar
  7. 7.
    NASA. Proceedings of the Nasa Workshop on Distributed Parameter Modeling and Control of Flexible Aerospace Structures. NASA Conference Publication 3242, June 1994.Google Scholar
  8. 8.
    J.H. Prevost. DYNAFLOW. Department Civil Engineering and Operation Research, Princeton University, 1992.Google Scholar
  9. 9.
    M. Tadi. An optimal control problem for a Timoshenko beam. Ph.D. Dissertation. Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, 1991.Google Scholar
  10. 10.
    M. Tadi. Computational algorithms for controlling a Timoshenko beam. Computer Methods in Applied Mechanics and Engineering, submitted.Google Scholar
  11. 11.
    M. Tadi and J.A. Burns. Feedback controller for a flexible structure using piezoceramic actuators. Dynamics and Control, 5(4):401, 1995.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag New York Inc 1997

Authors and Affiliations

  • M. Tadi
    • 1
  1. 1.Frick LaboratoryPrinceton UniversityPrincetonUSA

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