scholarly journals Riesz basis generation, eigenvalues distribution, and exponential stability for a euler-bernoulli beam with joint feedback control

2001 ◽  
Vol 14 (1) ◽  
Author(s):  
Bao-Zhu Guo ◽  
K.Y. Chan
Keyword(s):  
Feedback Control ◽  
Exponential Stability ◽  
Riesz Basis ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam ◽  
Eigenvalues Distribution

scholarly journals Stabilization of Variable Coefficients Euler-Bernoulli Beam with Viscous Damping under a Force Control in Rotation and Velocity Rotation

2017 ◽  
Vol 9 (6) ◽  
pp. 1
Author(s):  
Bomisso G. Jean Marc ◽  
Tour\'{e} K. Augustin ◽  
Yoro Gozo
Keyword(s):  
Exponential Stability ◽  
Force Control ◽  
Riesz Basis ◽  
Closed Loop ◽  
Variable Coefficients ◽  
Viscous Damping ◽  
Closed Loop System ◽  
Bernoulli Beam ◽  
Spectral System ◽  
Euler Bernoulli Beam

This paper investigates the problem of exponential stability for a damped Euler-Bernoulli beam with variable coefficients clamped at one end and subjected to a force control in rotation and velocity rotation. We adopt the Riesz basis approach for show that the closed-loop system is a Riesz spectral system. Therefore, the exponential stability and the spectrum-determined growth condition are obtained.

Optimal Vibration Feedback Control of an Euler-Bernoulli Beam: Toward Realization of the Active Sink Method

1999 ◽  
Vol 121 (2) ◽  
pp. 174-182 ◽  
Author(s):  
N. Tanaka ◽  
Y. Kikushima
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Control Point ◽  
Control Law ◽  
Bernoulli Beam ◽  
Control Laws ◽  
Reflected Waves ◽  
Feedback Control Systems ◽  
Active Wave ◽  
Euler Bernoulli Beam

This paper discusses the optimal vibration feedback control of an Euler-Bernoulli beam from a viewpoint of active wave control making all structural modes inactive (more than suppressed). Using a transfer matrix method, the paper derives two kinds of optimal control laws termed “active sink” which inactivates all structural modes; one obtained by eliminating reflected waves and the other by transmitted waves at a control point. Moreover, the characteristic equation of the active sink system is derived, the fundamental properties being investigated. Towards the goal of implementing the optimal control law that is likely to be non-causal, a “classical” velocity feedback control law (Balas, 1979) widely used in a vibration control engineering is applied, revealing a substantial shortcoming. Introduction of a “classical” displacement feedback to the velocity is found to realize the optimal control law in a restricted frequency range. Finally, two kinds of stability verification for closed feedback control systems are presented for distributed parameter structures.

scholarly journals The Exponential Stability Result of an Euler-Bernoulli Beam Equation with Interior Delays and Boundary Damping

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Peng-cheng Han ◽  
Yan-fang Li ◽  
Gen-qi Xu ◽  
Dan-hong Liu
Keyword(s):  
Exponential Stability ◽  
Semigroup Theory ◽  
Stability Result ◽  
Beam Equation ◽  
Bernoulli Beam ◽  
Boundary Damping ◽  
Exponentially Stable ◽  
Stability Issue ◽  
Euler Bernoulli Beam ◽  
The Relationship

We study the exponential stability of Euler-Bernoulli beam with interior time delays and boundary damping. At first, we prove the well-posedness of the system by the C0 semigroup theory. Next we study the exponential stability of the system by constructing appropriate Lyapunov functionals. We transform the exponential stability issue into the solvability of inequality equations. By analyzing the relationship between delays parameters α and damping parameters β, we describe (β,α)-region for which the system is exponentially stable. Furthermore, we obtain an estimation of the decay rate λ⁎.

Riesz Basis Generation of the Euler-Bernoulli Beam Equation with Boundary Energy Dissipation

2012 ◽  
Vol 433-440 ◽  
pp. 123-127
Author(s):  
Cui Lian Zhou
Keyword(s):  
Energy Dissipation ◽  
Boundary Conditions ◽  
Riesz Basis ◽  
Boundary Energy ◽  
Basis Property ◽  
Beam Equation ◽  
Bernoulli Beam ◽  
Riesz Basis Property ◽  
Euler Bernoulli Beam ◽  
Regular Property

In this paper, the Riesz basis generation of the Euler-Bernoulli beam equation with with boundary energy dissipation is studied. Using the regular property of the boundary conditions, it is shown that the Riesz basis property holds

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