Feedback Stabilization of a System of Rigid Bodies with a Flexible Beam

  • Alexander Zuyev
Conference paper
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 396)


Dynamical models of flexible-link robot manipulators are generally described by a set of coupled ordinary and partial differential equations, which gives rise to series of mathematical control problems in infinite dimensional spaces [1, 2, 3, 7]. However, finite dimensional approximate models obtained by the assumed modes and finite elements methods are used more frequently for solving the motion planning and stabilization problems [6]. It should be emphasized that the majority of publications in this area is concentrated on planar manipulator models with a free end. To study spatial manipulators with a tip mass, the mathematical model that describes the motion of a multi-link manipulator under the action of gravity and controls (torques and forces) was proposed in [8].


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Fattorini, H.O.: Infinite dimensional optimization and control theory. Cambridge University Press, Cambridge (1999)MATHGoogle Scholar
  2. 2.
    Lagnese, J.E., Leugering, G.: Controllability of Thin Elastic Beams and Plates. In: Levine, W.S. (ed.) The control handbook, pp. 1139–1156. CRC Press – IEEE Press, Boca Raton (1996)Google Scholar
  3. 3.
    Luo, Z.-H., Guo, B.-Z., Morgul, O.: Stability and stabilization of infinite dimensional systems with applications. Springer, London (1999)MATHGoogle Scholar
  4. 4.
    Mikhajlov, V.P.: Partial differential equations. Translated from the Russian by P.C. Sinha. Revised from the 1976 Russian ed. Mir Publishers, Moscow (1978)Google Scholar
  5. 5.
    Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, New York (1983)MATHGoogle Scholar
  6. 6.
    Talebi, H.A., Patel, R.V., Khorasani, K.: Control of Flexible-link Manipulators Using Neural Networks. Springer, London (2001)MATHGoogle Scholar
  7. 7.
    Zuyev, A.: Partial asymptotic stabilization of nonlinear distributed parameter systems. Automatica. 41, 1–10 (2005)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Zuyev, A.L.: Modeling of a spatial flexible manipulator with telescoping (in Russian). In: Proceedings of the Institute of Applied Mathematics and Mechanics (Tr. Inst. Prikl. Mat. Mekh.), vol. 10, pp. 51–58 (2005)Google Scholar

Copyright information

© Springer London 2009

Authors and Affiliations

  • Alexander Zuyev
    • 1
  1. 1.Alexander Zuyev Institute of Applied Mathematics and MechanicsNational Academy of Sciences of UkraineDonetskUkraine

Personalised recommendations