Design And Stability Region Analysis Of Active Disturbance Rejection Control For Time-delay Systems

In most industrial processes,e.g.petroleum,chemical,pharmacy and waste water treatment,limited by devices,surroundings and human factors,time delay widely exists between the control variables and the controlled variables.Because of the time delay,control variables cannot react to the variation of system dynamics in time,which leads to harmful effects,e.g.high overshoot,long response time and instability.As a novel controller,active disturbance rejection controller(ADRC)inherits from PID the quality of error driven and rather than model-based.It realizes compensating disturbance by introducing the extended state observer(ESO)that estimates the disturbance.Besides,ADRC achieves the goal of disturbance rejection.Because ADRC has both the advantages of PID and the function of disturbance rejection,it has been widely used in process control.Hence,it has profound influence to explore how ADRC can overcome bad effects caused by time delay or time-varying delay on the premise that disturbance rejection is guaranteed.Meanwhile,in the closed-loop which consists of ADRC and the time delay process,it also has significance to determine the parameters stability region of ADRC for engineering tuning and theoretical analysis.For the problems above,based on the previous works,this paper makes the following research:On the one hand,as far as the structure of ADRC,a modified ADRC with adaptive delayed input is proposed for a class of processes with time-varying delay.This method identifies the time-varying delay via correlation technique and then sends this delay information to the delay module located before the input of ESO.This modification realizes the synchronization of time delay for both control loop and observer loop so as to reduce the bad effects of time delay.The effectiveness and robustness are verified by a process simulation of boiler combustion.On the other hand,as far as the theoretical analysis of ADRC,for the closed-loop consists of first order linear ADRC and first order time-delay system,the characteristic equation is firstly derived.Then the stability region of ADRC is determined by using the dual-locus diagram method to place all poles in the left half plane.The stability region obtained by this way can assuredly guarantee the stability and hopefully offer a theoretical foundation for ADRC tuning and analysis.Numerical simulation demonstrates the accuracy of the obtained stability region and the validity of the proposed method.