一阶时滞系统线性自抗扰控制器参数稳定域分析

当使用线性自抗扰控制器(linear active disturbance rejection controller,LADRC)控制时滞系统时,闭环系统的稳定性与控制器参数的选取有较大的关系.如何定量求取线性自抗扰针对时滞系统的参数稳定域还没有有效的方法.本文针对线性自抗扰控制器控制一阶时滞系统,利用双轨迹法精确求解出了线性自抗扰控制器参数的稳定域.该方法利用双轨迹的图形性质,有效地将求解具有时滞的控制系统闭环特征方程根的分布问题转化为求解双轨迹交点频率的问题,从而得到能够保证闭环系统稳定性的控制器参数稳定域.求得的稳定域为时滞系统线性自抗扰控制器的整定提供了理论依据.仿真结果验证了所提出方法的有效性.

Stability region analysis of linear active disturbance rejection controllers for first order systems with time delay

The selection of controller parameters plays an important role to the stability of the closed-loop system when a linear active disturbance rejection controller (LADRC) is used to control a time-delay system. Unfortunately, for timedelay systems, there is no effective way to quantificationally obtain the stability region of LADRC. In this paper, the stability region of LADRC parameters is accurately determined by the dual-locus diagram method for first order time-delay systems controlled by LADRC. Motivated by the dual-locus diagram property, the problem of solving characteristic equation root distribution of control systems with time delay is effectively transformed into the problem of finding the frequency of the dual-locus diagram intersection point. Thus, the stability region which can guarantee the stability of the closed-loop system can be obtained. The obtained stability region provides a theoretical basis for the LADRC tuning of system with time delay. Simulation results demonstrate the validity of the proposed method.