Abstract

A flexible structure consisting of serially connected Euler–Bernoulli beams with co-located sensors and actuators is considered. Controls are point forces and point bending moments applied at the nodes. It is known that uniform exponential stability can be achieved with linear velocity feedback. A sensitivity analysis of the system’s spectrum with respect to feedback coefficients is set up. It is also proved that in a particular case exponential decay rate can be obtained from the spectrum of the system.

MSC codes

  1. 93D15
  2. 73K12
  3. 35P10

Keywords

  1. serially connected beams
  2. point control
  3. exponential stabilization

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
J. M. Ball, M. Slemrod, Nonharmonic Fourier series and the stabilization of distributed semilinear control systems, Comm. Pure Appl. Math., 32 (1979), 555–587
2.
G. Chen, M. Delfour, A. M. Krall, G. Payre, Modeling, stabilization and control of serially connected beams, SIAM J. Control Optim., 25 (1987), 526–546
3.
G. Chen, S. G. Krantz, D. W. Ma, C. E. Wayne, H. H. West, Sung J. Lee, The Euler-Bernoulli beam equation with boundary energy dissipationOperator methods for optimal control problems (New Orleans, La., 1986), Lecture Notes in Pure and Appl. Math., Vol. 108, Dekker, New York, 1987, 67–96
4.
G. Chen, S. G. Krantz, D. L. Russell, C. E. Wayne, H. H. West, M. P. Coleman, Analysis, designs, and behavior of dissipative joints for coupled beams, SIAM J. Appl. Math., 49 (1989), 1665–1693
5.
Steven G. Krantz, William H. Paulsen, Asymptotic eigenfrequency distributions for the N-beam Euler-Bernoulli coupled beam equation with dissipative joints, J. Symbolic Comput., 11 (1991), 369–418
6.
F. Conrad, A. V. Balakrishnan, J. P. Zolésio, Stabilization of vibrating beams by a specific feedbackCOMCON Workshop on Stabilization of Flexible Structures, Montpellier, France, 1987, in Stabilization of Flexible Structures, Optimization Software, New York, 1988, 36–51
7.
M. Delfour, M. P. Polis, On Issues Related to Stabilization of Large Flexible Structures, manuscript
8.
Denise Huet, Décomposition spectrale et opérateurs, Presses Universitaires de France, Paris, 1976, 148–
9.
J. Leblond, J. P. Marmorat, Stabilization of flexible structures with unbounded input and output operators, preprint
10.
P. Rideau, Masters Thesis, Contrôle d'un assemblage de poutres flexibles par des capteurs-actionneurs ponctuels, Thesis, Ecole des Mines de Paris, Sophia-Antipolis, France, 1985
11.
F. Riesz, B. Sz. Nagy, Leçons d'Analyse Fonctionnelle, Gauthiers-Villars, Paris, 1968
12.
David L. Russell, Linear stabilization of the linear oscillator in Hilbert space, J. Math. Anal. Appl., 25 (1969), 663–675
13.
Yoshiyuki Sakawa, Feedback control of second-order evolution equations with damping, SIAM J. Control Optim., 22 (1984), 343–361

Information & Authors

Information

Published In

cover image SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Pages: 423 - 437
ISSN (online): 1095-7138

History

Submitted: 31 May 1988
Accepted: 26 May 1989
Published online: 14 July 2006

MSC codes

  1. 93D15
  2. 73K12
  3. 35P10

Keywords

  1. serially connected beams
  2. point control
  3. exponential stabilization

Authors

Affiliations

Metrics & Citations

Metrics

Citations

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited By

View Options

View options

PDF

View PDF

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share on social media