Preview Control For Linear Delay Systems

Time delay systems are common in both theoretical and practical applications.Since time delay systems have infinite dimensionas,they are always difficult to design controller for delay systems than for delay-free systems.It is necessary to study particular methods in designing controllers for different kinds of delay systems.In this dissertation,the preview control for linear delay systems is studied,and some research results are obtained.(1)The preview control problem for continuous-time systems with input delay is studied by predictor method.Firstly,the tracking problem is transformed into a regulation one by constructing an augmented error system.Then,the time delay in control input is eliminated via variable substitution,and a delay-free augmented error system is obtained.Based on that,a controller for the augmented error system is derived by applying preview control theory.Finally,the future value of state vector in the controller is predicted using the known information,and a series of integral simplification is used to obtain the preview controller of the original system.(2)The predictor method is used to study the preview control problem of discrete-time input delay systems with disturbances.The tracking problem of time delay system is transformed into a regulation one without delay by the construction of augmented error system and variable substitution.The preview control theory and the predictor feedback method are used to obtain a controller with both time delay compensation and preview compensation.When the state vector of the system is not measurable,the design method of preview controller with full dimension state observer is given.(3)The preview control problem of discrete-time systems with both state delay and input delay is studied by lifting-predictor method.Discrete lifting technology and variable substitution method are used to eliminate the state delay and input delay,separately.The stabilizability and detectability of the augmented error system are discussed by PBH rank test.Based on that,a controller with state delay compensation,input delay compensation and preview compensation of the reference signal is designed.(4)The preview control problem for a type one linear continuous-time system with multiple input delays is studied by integral transformation.When the system has multiple input delays,it is impossible to eliminate the time delays completely by means of variable substitution method.In order to solve this problem,an integral transformation is used to the augmented error system.This transformation contains convolutions of input variables on different delay intervals.The stabilizability and detectability of the transformed system are analyzed,and the preview controller is designed.The preview controller of the original system is further obtained.(5)The preview control problem of continuous time input delay systems is studied by using Backstepping method.An augmented error system is constructed by introducing integrator,and the tracking problem is transformed into a regulation one.Furthermore,the augmented error system with time delay is transformed into a coupled one,and a tracking controller of the coupled system is designed.Finally,the preview controller of the original system is deduced.This method makes full use of the characteristics of infinite dimension of time delay system,and has more advantages than other methods in stability proof.