Designing The Disturbance Observer And Interferometer And Applying It To Stabilize Euler-Bernoulli Beam

In past three decades,the study of control problem of the elastic systems has been a hot topic in mathematics control theory and engineering,in which the Euler-Bernoulli beam is a center model due to its extensive application.Firstly,assuming that there is one signal associated with disturbance,we considered the stability for a Euler-Bernoulli system with external disturbances.This process is composed of two parts: one is that,applying high gain method to design the extended state observer which is used to observe and estimate the disturbance.Another is that,we apply the feedback control law to the system based on the estimate of the disturbance,prove the closed-loop system is exponential stabilization based on the Lyapunov function method and semigroup theory.Secondly,if there is not one signal associated with disturbance,we analyzed the boundary control problem of a cantilever Euler-Bernoulli with disturbance.In order to stabilize this kind of system,we give three steps.Firstly,we introduce a new method which is supposed to select one eigenfunction to filter the disturbance.Hence,a timevarying high gain estimator is designed,where the idea of active disturbance rejection control is adopted.Secondly,we propose a boundary feedback controller to exponentially stabilize the system,which is based on the estimate of disturbance.Finally,the Lyapounov function method and semigroup theory are applied to prove the closed-loop error system is exponential stabilization.