Attachment observability of a rotating body-beam

Deguenon, Judicael; Barbulescu, Alina

doi:10.2478/auom-2013-0045

Abstract

In this article we analyze the admissibility and the exact observability of a body-beam system when the output is taken in a point of attachment from the beam to the body. The single output case chosen here is the practical measurement of the strength, its velocity or its moment. We prove the exact observability for the moment and the admissibility for the other cases. These results are obtained by the spectral properties of rotating body beam system operator and Ingham's inequalities.

References

[1] B. D’Andrea - Novel and J. M. Coron, Stabilization of a rotating body- beam without damping, IEEE Transaction Automatic Control, 43 (1998), no.5 , 608 - 618.
Search in Google Scholar
[2] J. Bailleul and M. Levi, Rotational elastic dynamics, Physica D, 27 (1987), 43 - 62.10.1016/0167-2789(87)90004-2
Search in Google Scholar
[3] A. Bensoussan, G. D. Prato, M. Delfour and S.K. Mitter, Representation and control of infinite-dimensional systems, Vol. I, Birkhauser, Boston, Inc., Boston, MA, 1992.10.1007/978-1-4612-2750-2
Search in Google Scholar
[4] A.M. Bloch and E. S. Titi, On the dynamics of rotating elastic beams, Proceedings Conf. New Trends Syst. theory, Genoa, Italy, July 9-11, 1990, Conte, Perdon and Wyman (Eds.), Birkauser, Cambridge, 1990.
Search in Google Scholar
[5] H. Brezis, Analyse fonctionnelle, theorie et applications, Masson, Paris, 1983.
Search in Google Scholar
[6] B. Chentouf and J. F. Couchouron, Nonlinear feedback stabilization of a rotating body-beam system, ESAIM: Control, Optimization and Calculus of Variations, 4(1999), 515 - 535.10.1051/cocv:1999120
Search in Google Scholar
[7] R. F. Curtain and H. Zwart, An introduction to Infinite-Dimensional Linear Systems Theory, Texts Applied Math. 21, Springer-Verlag, New York, 199510.1007/978-1-4612-4224-6
Search in Google Scholar
[8] J. Deguenon, Observateurs des Systemes Anti-Adjoints de Dimension In- finie et Applications, These unique de doctorat, Universite de Metz - Metz, 2003.
Search in Google Scholar
[9] A. J. Deguenon, G. Sallet and C. Z. Xu, A Luenberger observer for infinite dimensional skew-symmetric systems with application to an elastic beam, Proc. 2nd Int. Symp on Comm. Control and Signal, Marrakech, 2006.
Search in Google Scholar
[10] A. J. Deguenon and A. Barbulescu, Theoretical Observers for Infinite Dimensional Skew-Symmetric Systems, 2012, submitted
Search in Google Scholar
[11] C.E. Hmelo-Silver, R. Jordan, L. Liu, S. Gray, M. Demeter, S. Ru- gaber, S. Vattam and S. Goel, Focusing on Function: Thinking below the Surface of Complex Natural Systems, 27- 35, <http://home.cc.gatech.edu/dil/uploads/Science-Scope-Paper.pdf
Search in Google Scholar
[12] A.E. Ingham, Some trigonometrical inequalities with applications to the theory of series, Math. Zeischrift, 41(1936), 367 - 379.10.1007/BF01180426
Search in Google Scholar
[13] A. El Jai and A.J. Pritchard, Capteurs et actionneurs dans l’analyse des systemes distribues, Recherche en Mathematiques Appliquees, Masson, 1986.
Search in Google Scholar
[14] H. Laousy, C.Z. Xu and G. Sallet, Boundary feedback stabilization of a rotating body-beam system, IEEE Transaction Automatic Control, 41 (1996), no.2, 241 - 245.
Search in Google Scholar
[15] X.-D. Li, C.-Z. Xu, Y.-J. Peng and M. Tucsnak, On the numerical investigation of a Luenberger type observer for infinite-dimensional vibrating systems, Proceedings of the 17th World Congress, The International Federation of Automatic Control (IFAC), Seoul, Korea, July 6-11, 2008, 7264-7269.
Search in Google Scholar
[16] L. Marsavina, A. D. Nurse, L. Braescu and E.M. Craciun, Stress singularity of symmetric free-edge joints with elasto-plastic behaviour, Comp. Mat. Sci., 52 (2012), No.1, 231-235.
Search in Google Scholar
[17] A. Pazy, Semigroups of linear operators and applications to partial differential equations, Springer Verlag, New York, 1983.10.1007/978-1-4612-5561-1
Search in Google Scholar
[18] T. W. Peterson, <http://esd.mit.edu/symp09/presentations/day1walkerlunch.peterson.pdf.
Search in Google Scholar
[19] D. L. Russell and G. Weiss, A general necessary conditions for exact observability, SIAM J. Control and Optimizations, 32 (1994), no.1 , 1 - 23.
Search in Google Scholar
[20] R. Selescu and A. Barbulescu, The bending of the nonprismatic bars, with constant section and the inertia moment variable periodic, Bull. Sci. Pitesti Univ., Mathematics and Informatics, 2 (1998), 209 - 222.
Search in Google Scholar
[21] J. Weidmann, Linear Operators in Hilbert Spaces, Springer-Verlag, Berlin, 1980.10.1007/978-1-4612-6027-1
Search in Google Scholar
[22] C. Z. Xu and J. Bailleul, Stabilizability and stabilization of a rotating body beam system with torque control, IEEE Transaction Automatic Control, 38 (1993), no.12 , 1754 - 1765.
Search in Google Scholar

Attachment observability of a rotating body-beam

Abstract

Paradigm

My account