Input Delay Compensation For Linear Systems With Both Single Input And State Delays

Analysis and design of time-delay systems have received much attention on both control and applied mathematics communities during the past several decades.This is because,on the one hand,time-delay systems have very wide applications in engineering practice such as chemical process control,machining,combustion systems,networked systems,and biological system.On the other hand,time-delay systems as special cases of distributed parameter systems are infinite dimensional and thus are hard to be dealt with in both mathematics and in practice.Take stability and stabilization for example.For a linear time-invariant time-delay system,a main technical difficulty for stability and stabilization lies in that the system has infinitely many characteristic roots.Hence,it is not easy to analytically study the roots distribution.Although there have been plenty of results available in the literature dealing with the analysis and design of time-delay systems,there are still a lot of problems to be further studied,for example,there are many unsolved problems in the design of control system with both input and state delays,which needs to be further investigated.This dissertation will study the input delay compensation of control system with both input and state delays from some new perspectives,in particular,the state and input delays are point delays.Two delay compensation strategies based on nested predictor feedback and observer-predictor feedback are proposed,by these methods the systems will be transformed into new systems with only state delays whose sizes will not be enlarged.Effective methods will then be established to design controllers for the delay compensated systems with only state delays by using their special structures and properties.Finally,the proposed input delay compensation methods will be applied to retarded-type time-delay systems,discrete-time time-delay systems and neutral-type time-delay systems.Chapter 2 investigates input delay compensation of discrete-time linear systems with both state and input delays.Under the assumption that the original time-delay system without input delay can be stabilised by state feedback,a nested predictor feedback controller is established to predict the future states such that the arbitrarily large yet exactly known input delay in the original system is completely compensated.Consequently,it is shown that the closed-loop system consisting of the original time-delay system and the nested prediction feedback controller is asymptotically stable.Under an additional assumption,an explicit nested predictor feedback controller without involving any nested summations is also established.However,Chapter 3 studies the input delay compensation for neutral type time-delay systems with both state and input delays,where the input delay can be arbitrarily large yet bounded.A nested predictor is also established to predict the future states such that the input delays are compensated completely.It is shown that the compensated closed-loop system in the presence of input delay possesses the same characteristic equation as the closed-loop system in the absence of input delay.An implementation scheme by adding input filters is also proposed.Under an additional assumption,explicit nested predictor feedback controllers involving only 1-fold integrals are established.Chapter 4 considers input delay compensation of linear systems with both state and distinct input delays.Both continuous-time and discrete-time time-delay systems are studied in this chapter.Nested predictor feedback controllers are designed to predict the future states such that the distinct input delays that can be arbitrarily large yet bounded are compensated completely.It is shown that the compensated closed-loop system possesses the same characteristic equation as the closed-loop system without distinct input delays.Moreover,the safe implementation problem for the continuous-time nested predictor feedback controller is solved via adding input filters.Chapter 5 studies input delay compensation of retarded-type linear systems with both state and input delays,where the input delay can be arbitrarily large yet exactly known.Observer–predictor based controllers are designed to predict the future states so that the input delay can be properly compensated.Necessary and sufficient conditions guaranteeing the stability of the closed-loop system are provided in terms of the stability of some simple linear time-delay systems refereed to as observer-error systems,by which the separation principle is discovered.Moreover,approaches in terms of linear matrix inequalities are also provided to design both the state feedback gains and observer gains.Chapter 6 investigates the consensus and input delay compensation problem for high-order discrete-time multi-agent systems with state,input and communication delays,where the input and communication delays can be arbitrarily large yet exactly known.Moreover,the communication delays are different for different agents.Nested predictor based state feedback protocols and full-order/reduced-order observer based output feedback protocols are established to predict the future states so that the consensus is achieved.It is shown that both the input and communication delays can be compensated completely.Furthermore,linear matrix inequalities based approaches are provided to design state feedback gains and observer gains.