Study On Stability And Parameter Tuning Of Linear Active Disturbance Rejection Control For First Order Plus Time-Delay Systems

First order plus time-delay systems have received continuous attentions from control theory studies due to their playing important roles in process control,which mainly include the analysis of system's stability and the design method of controller.This paper studies the linear active disturbance rejection control for first order plus time-delay systems from the perspective of frequency domain,using Nyquist plot and Bode plot as analysis tools.And this paper has completed the following work:First,the stability of first order plus time-delay systems under first order linear active disturbance rejection control is analyzed.For stable systems with time-delay,the linear active disturbance rejection controller is designed by ignoring the time-delay plant,then the stability of closed systems is analyzed by Nyquist plot.The necessary and sufficient conditions for the stability of the closed systems and the upper bound of the time-delay are given.For unstable systems with time-delay,the linear active disturbance rejection controller is designed based on the reduced-order extended state observer.Then using the Nyquist plot and block diagram transformation to simplify the process of stability's analysis,and obtain the same stability conditions and upper bound of time-delay as the existing reference.Second,the parameter tuning of linear active disturbance rejection control for first order plus time-delay systems is studied.Based on the step response curve method of Ziegler-Nichols,the parameter tuning formula for the first order linear active disturbance control is given.Bode plot shows that the first order linear active disturbance rejection control obtained by the tuning formula have approximately the same gain crossing frequency and phase Margin as the PI controller obtained by the Ziegler-Nichols rules,and are better in suppressing overshoot and anti high frequency measurement noise.The above work show that the method of frequency domain is a powerful tool for studying linear active disturbance rejection control for first order plus time-delay systems.The results of this paper are expected to provide theoretical guidance for the further application of active disturbance rejection control in process control.