Feedback Controller Design For One Dimensional Model With Time Delay

In the practical engineering problems,we have access to information and the system control ability is limited,so the ”time-delay” is a common and inevitable appearance.Time delay control problems in recent years become a hot control theory.The theoretical research results have important guidance and reference for practical engineering application.In this paper,we mainly study the controller design problem with control input delay,which is different from the existing design method of time delay controller.In this paper,a controller is designed according to the feedback equivalent principle of the system,which is used to guarantee the stability and attenuation rate of the closed-loop system.The main contents of this paper are as follows:In this chapter,the exponential stabilization of a time delay controller in one dimensional wave equation is studied.By transforming the time-delay system into a coupled system in series,an exponentially stable coupling system-called the target system which is constructed by using the known results.A singular kernel integral transformation is designed,and the relationship between the current control system and the target system is established by transformation,and the expression of the state feedback controller can be determined.The proof of the bounded invertibility of the transformation is proved.Then the closed-loop system is equivalent to the target system.Secondly,we consider the exponential stabilization problem of a time-delay controller in one dimensional weak coupling system.The time delay control system can be written as an abstract development equation,and the system is transformed into a cascade form by linear transformation.The target system with exponential stability is constructed by the feedback control and migration operator of the same bit.A function matrix transformation is designed to establish the relationship between the current control system and the target system,and the expression of the state feedback controller can be given.We also prove the bounded invertibility of the transformation,thus the feedback of the current control system is equivalent to the target system.The method used in this paper is universal,although this paper is aimed at the study of one dimensional system.The method can also be used in the design of time delay controllers for other systems.