Optimal Disturbance Rejection For Discrete-Time System With Time-Delay In Control Input

The discrete-time control system theory is more and more valued by people. Time delay phenomenon widespread exists in control systems which can decline performance of the control system. In addition, control systems sometimes have the influence by all kinds of exosystem exogenous disturbance. Time-delay systems are also called systems with aftereffect or dead-time, hereditary systems, equations with deviating argument or differential-difference equations. Many processes include time-delay phenomena in their inner dynamics, such as network congestion control and networked control system. Since the existence of time-delays usually deteriorates the performance of closed-loop systems and may be a source of instability, the control problem for systems with time-delays has received increasing attention.So it is a significative research task for discrete-time systems with control delay via output feedback.This paper research the optimal disturbance rejection via dynamic output feedback for discrete-time systems. Design optimal disturbance rejection control law for linear discrete-time system and linear discrete-time system with control delay which the output of the system can reject exogenous disturbance and achieve optimal performance index at the same time. Solve the physically realizable for the controller contained state of the exosystem by constructing disturbance observer. The main research content as follows:1. Summarize the characteristic of the discrete-time linear systems. Review the history of the time-delay system theory and introduce research method and status of this field. Introduce optimal control theory and correlation dominant research results. Development status and the important application field of the optimal control theory and the disturbance rejection problem is expatiated. The mainly results of the output feedback theory are analysed. 2. The objective of this paper is studying the disturbance rejection under external persistent disturbances with known dynamic characteristics but unknown initial conditions based on dynamic output feedback for linear discrete-time systems. Using a model transformation, the system with disturbances is transformed to an augmented system without disturbances. By constructing a reduced-order observer of the augmented system and designing a feedforward and feedback optimal control law, a dynamic output feedback control law approximating optimal control is presented. Then simulation results demonstrate the effectiveness of the designed control law.3. Research disturbance rejection under external persistent disturbances with known dynamic characteristics but unknown initial conditions based on for discrete-time systems with control delay via output feedback. Firstly, based on the model transformation, the system with control delay is transformed to a nondelayed system. Secondly transform the system with disturbance to an augmented system without disturbance. Then the feedforward and feedback optimal disturbance rejection control law is derived from a Riccati equation and a Stein equation. A reduced-order observer estimating state and disturbance variables is constructed to make feedforward control and state feedback physically realizable. And the dynamic output feedback disturbance rejection control law approximating the optimal one is obtained. Simulations demonstrate the effectiveness of the control law.