Feedback Control Design Of Euler-Bernoulli Beam Equation With Pure Time Delay Control

The controllability,exact controllability,observability,stabilization and optimal control of the systems are the main research contents in the practical problems.In recent years,stabilization has become a hot issue.In this paper,we consider the problem of the control with time delay.Especially,taking the Euler-Bernoulli beam as the research object,we discuss the problem of rapid stabilization with internal control delay.Different from previous studies,we propose a new control design method in this paper–system equivalence method,which can also be applied to the study of other models.The details of this paper are as follows:We study the problem of rapid stabilization of an Euler-Bernoulli beam with internal time-delay control.Firstly,we construct a target system of the desired stability.Secondly,we select a suitable integral transform that transforms the present system to the target system.In this procedure,one can get a corresponding feedback control.Thirdly,we determine the inverse transform of the transformation that converts the target system to the original system,which provides the equivalence of both systems.Finally,we prove that the two transforms are bounded linear operators in an appropriate Hilbert space.