Performance Output Tracking For Distributed Parameter Systems With Input Delay

In engineering practice,many mathematical and physical models of control problems require partial differential equations to accurately describe.Such control systems are called distributed parameter control systems.With the development of modern industry and the perfection of mathematical and physical theories,the theory of distributed parameter control has made great progress.In distributed parameter control theory,stability theory has always been a focus of research.However,with the development of science and technology,the performance output tracking of distributed parameter system has attracted the attention of many scholars at home and abroad in recent years.In this thesis,we study the performance output tracking problem for a class partial differential equation control system with input delay.The equations we study include reaction diffusion equation,wave equation,the transfer equation and three of the cascade system.Through the analysis of a given control object,the thesis reveals the system performance output tracking mechanism in spite of the delay input.It makes the output regulation theory of distributed parameter systems has a further progress and development.This thesis studies and analyzes the performance output tracking problem of a class of partial differential equation control systems with input delay.The main research contents are divided into the following four parts:In the first part is Chapter 2 of the dissertation,and the performance tracking problem for one-dimensional wave equation with input delay is studied.In a given control system,the control not only has input delay,but also is not on the same system boundary with the disturbance and tracking signal,which brings great difficulties to the tracking problem.Different from the existing control problem,in this chapter,we designs an auxiliary trajectory and servomechanism to reject the external disturbance and transform the control and the reference signal into the same channel such that the output signal can track the reference signal.At the same time,we design the state observer and prove the convergence of the observer by using the regulation error signal only.Finally,in a closed loop system,we prove that all subsystems are uniformly bounded.In particular,we not only study the tracking problem with input delay,but also analyze and solve the problem that the input signal and the reference signal are not in the same channel,extending the results of the existing literature.Finally,the effectiveness of the proposed control scheme is verified by numerical simulation.The second part is Chapter 3 of the dissertation,and we mainly analyze performance output tracking problem for one-dimensional heat-wave cascade system with unmatched disturbance.For the output tracking of PDE-PDE cascaded system,there are few available literature results.The main problem of this chapter is that the control input and disturbance are located in two different systems.At the same time,the control input and performance output signal are located on the boundary of two different systems.Firstly,by applying auxiliary trajectory and servomechanism twice,the external interference is rejected and the control signal and the reference signal are transformed to the same channel,so as to obtain the state feedback controller.Then,the state observer of the cascade system is designed by using the regulation error and the convergence of the observer is obtained by using the Lyapunov function method.Finally,we prove the uniform boundedness of the closed-loop system.Compared with the existing literatures,we consider that the control and performance output are located on the boundary of the two subsystems of the cascade system,which are more complex than the single system.It enriches and generalizes the results of the existing literatures.Moreover,it develops the output regulation theory of the infinite dimensional system.At the end of this chapter,relevant numerical simulation is carried out to verify the feasibility and effectiveness of the controller and observer proposed in this chapter.The third part is Chapter 4 of the dissertation and we study the performance output tracking problem for one dimensional heat-wave cascade equation with input delay.Different from the cascade system studied in chapter 3,the cascade system studied in this chapter is driven by a wave system as input.First,without considering delay,we reject the disturbance and obtain a state feedback controller that can complete the output tracking task.Then the state observer of the cascade system is designed and the exponential convergence of the observer is proved.At the same time,we prove the uniform boundedness of all subsystems.Furthermore,when the input delay exists,the delay is transformed into a first order hyperbolic equation,and a new controller is obtained by applying auxiliary trajectory and servomechanism despite delay.At the end of this chapter,we numerically simulate the tracking effect despite input delay,and obtain the effectiveness of the signal tracking,disturbance rejected and delay compensation.All simulation verify the effectiveness of the control scheme proposed in this chapter.The last part is Chapter 5 of the dissertation,and discusses the output tracking problems of other PDE systems.The output tracking of heat equation and schr?dinger equation are analyzed in detail.Then,the feasibility of the proposed method is simply explained.At the end of the dissertation,the problems in dealing with the output tracking of cascade system are put forward,and the direction of future efforts is pointed out.