Acta mathematica scientia,Series B ›› 2000, Vol. 20 ›› Issue (2): 235-244.

• Articles • Previous Articles     Next Articles

STABILIZATION OF VIBRATING BEAM BY VELOCITY FEEDBACK CONTROL

 WANG Yao-Ting, LI Qing-Jia   

  1. Department of Mathematics, Shanxi University, Taiyuan 030006, China
  • Online:2000-04-18 Published:2000-04-18
  • Contact: LI Qing-Jia E-mail:sjli@mail.sxu.edu.cn
  • Supported by:

    Project 69674011 supported by NSFC

Abstract:

A flexible structure consisting of a Euler-Bernoulli beam with co-located sen-
sors and actuators is considered. The control is a shear force in proportion to velocity.
It is known that uniform exponential stability can be achieved with velocity feedback. A
sensitivity asymptotic analysis of the system’s eigenvalues and eigenfunctions is set up.
The authors prove that, for K1 2 [0, +1), all of the generalized eigenvectors of A form a
Riesz basis of H. It is also proved that the optimal exponential decay rate can be obtained
from the spectrum of the system for 0 < K1 < +1.

Key words: Beam eqution, velocity feedback control, optimal exponential decay rate,
exponential stabilization

CLC Number: 

  • 93D15
Trendmd