“Passivity Analysis of Nonlinear Euler-Bernoulli Beams”

Authors: Mehrdad P. Fard,
Affiliation: Norsk Hydro
Reference: 2002, Vol 23, No 4, pp. 239-258.

Keywords: Vibration control, distributed parameter systems, passivity

Abstract: The Lagrangian equations for distributed-parameter systems based on HamiltonĀ“s principle are developed. These equations are subsequently used to derive nonlinear models for beams. The passivity properties of the flexible mechanical systems based on their distributed-parameter models are then investigated and direct output feedback control laws for control purposes are proposed. Finite gain L2 stability and passivity of closed-loop systems are proven. Illustrative cases with simulation of the nonlinear beams and stabilizing feedback control laws are included in the text.

PDF PDF (1707 Kb)        DOI: 10.4173/mic.2002.4.1

DOI forward links to this article:
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[1] AAMO, O.M. FOSSEN, T.I. (1999). Controlling line tension in thruster assisted mooring systems, In Proc. 1999 IEEE Conf. on Control Applications, Hawaii, 22-26.
[2] AMES W.E (1965). Nonlinear Partial Equations in Engineering, Academic Press.
[3] KHALIL, H.K. (1996). Nonlinear Systems, Sec. Ed., Prentice Hall, New York.
[4] MATSUNO K. MURATA, K. (1999). Passivity and PDS control of flexible mechanical systems on the basis of distributed parameter systems, In Proc. 1999 IEEE Int. Conf. on Systems. Man, and Cybernetics, Tokyo, Japan, 51-56.
[5] MITCHELL, A.R. GRIFFTHS, D.F. (1980). The Finite Difference Method in Partial Differential Equations, John Wiley and Sons, UK.
[6] RICHTMYER, R.D. MORTONON, K.W. (1967). Difference Methods for Initial-Value Problems, Sec. ed., John Wiley and Sons, New York.
[7] SMITH. G.D. (1978). Numerical Solution of Partial Differential Equations: Finite Difference Methods, Sec. ed., Clarendon Press, Oxford, UK.
[8] VAN DER SCHAFT, A.J. (1996). L2-Gain and Passivity Techniques in Nonlinear Control, In Lecture Notes in control and Information Sciences, Springer Verlag, Heidberg, vol. 218.

  title={{Passivity Analysis of Nonlinear Euler-Bernoulli Beams}},
  author={Fard, Mehrdad P.},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}