Study On The Stability Of Linear Active Disturbance Rejection Control

Active Disturbance Rejection Control(ADRC)is a general controller proposed by Prof.Jingqing Han,which combines the essence of PID technology and the application of modern control theory.It has the advantages of simple structure,convenient pa-rameters adjustment.Also,it can overcome the effects of unmodeled system dynamics and external disturbance.Linear Active Disturbance Rejection Control(LADRC)is an improved version of Active Disturbance Rejection Control.It changes the Extended State Observer(ESO)and feedback control law in the ADRC to linearity.Convenient for theoretical research,while reducing the number of parameters to be adjusted.In this paper,the stability of Linear Active Disturbance Rejection Control is studied.The specific research contents are as follows:Firstly,the mechanism of anti-disturbing for Linear Active Disturbance Rejection Control is studied for a second-order system with unknown parameters.There is no external disturbance and the internal uncertainty of system is linear.A necessary and sufficient condition for the second-order object of Linear Active Disturbance Rejection Control is given.And the Nyquist stability criterion in the classical control theory is used to prove the reason why the method of“Bandwidth",which is widely used in practice,can overcome the influence of object parameter uncertainty and find the right parameters for Linear Active Disturbance Rejection Controller to ensure the stability of systems.Then,on the basis of the above work,the stability of the LADRC sampling control problem for the second-order system is investigated.It pointed out that the method of designing a continuous-time controller by adjusting the bandwidth is also suitable for the design of sampled-data controllers when the sampling period is appropriate enough.Finally,for the n-order linear system with unknown parameters,the Small-Gain theorem is used to explain the robustness of Linear Active Disturbance Rejection Con-trol.With the conditions that the internal uncertainty of system is linear and it contains external disturbance,the LADRC can be decomposed into two interconnected structures with state feedback subsystems and observer error subsystems.If the gain product of the two subsystems decomposed is less than 1,then the LADRC is stable,according to the Small-Gain theorem.Although the state feedback subsystem can not obtain the ex-act gain value due to the unknown parameters,the gain of the observer error subsystem can be reduced so that the gain of the two subsystems satisfy the Small-Gain theorem,thus ensuring the stability of the LADRC.