Stabilization of Euler-bernoulli Beam Equations with Variable Coefficients under Delayed Boundary Output Feedback
نویسندگان
چکیده
In this article, we study the stabilization of an Euler-Bernoulli beam equation with variable coefficients where boundary observation is subject to a time delay. To resolve the mathematical complexity of variable coefficients, we design an observer-predictor based on the well-posed open-loop system: the state of system is estimated with available observation and then predicted without observation. We show that the closed-loop system is stable exponentially under estimated state feedback by a numerical simulation illustrating our results.
منابع مشابه
Riesz Basis Property and Exponential Stability of Controlled Euler--Bernoulli Beam Equations with Variable Coefficients
This paper studies the basis property and the stability of a distributed system described by a nonuniform Euler–Bernoulli beam equation under linear boundary feedback control. It is shown that there is a sequence of generalized eigenfunctions of the system, which forms a Riesz basis for the state Hilbert space. The asymptotic distribution of eigenvalues, the spectrumdetermined growth condition,...
متن کاملWell-posedness and regularity for an Euler-Bernoulli plate with variable coefficients and boundary control and observation
The open loop system of an Euler–Bernoulli plate with variable coefficients and partial boundary Neumann control and collocated observation is considered. Using the geometric multiplier method on Riemannian manifolds, we show that the system is well-posed in the sense of D. Salamon and regular in the sense of G. Weiss. Moreover, we determine that the feedthrough operator of this system is zero....
متن کاملDynamic stabilization of an Euler-Bernoulli beam under boundary control and non-collocated observation
We study the dynamic stabilization of an Euler–Bernoulli beam system using boundary force control at the free end and bending strain observation at the clamped end. We construct an infinite-dimensional observer to track the state exponentially. A proportional output feedback control based on the estimated state is designed. The closed-loop system is shown to be non-dissipative but admits a set ...
متن کاملDynamic stabilization of an Euler-Bernoulli beam equation with time delay in boundary observation
An Euler–Bernoulli beam equation under boundary control and delayed observation is considered. An observer–predictor based scheme is developed to stabilize the equation. On a time interval where the observation is available, the state is tracked by the observer; when the observation is not available due to the delay, the state is estimated by the predictor. The estimation is then used in propor...
متن کاملEnergy Harvesting Electrical from Nano Beam with Layer Piezoelectric under Random Vibration
In the present paper, electrical energy harvesting from random vibrations of an Euler-Bernoulli nano-beam with two piezoelectric layers is investigated. The beam is composed of an aluminum layer together with two piezoelectric ceramic layers (PZT 5A) serving as energy harvesting sensors. In the proposed method, the equations governing the bimorph nano-beam will be analytically derived using cla...
متن کامل