Study On Adjustment Method Of Linear Active Disturbance Rejection Control For Second-order System

Active Disturbance Rejection Control(ADRC)is a new practical control tech-nology which combines the essence of classical PID and modern control theory.It is proposed by Prof.Jingqing Han.The controller has several excellent advantages,such as simple structure,a few parameters to be adjusted and effective estimation of system disturbance.Linear ADRC(LADRC)is a simplified linear version of ADRC which has less parameters.It is more popular in practice.This paper mainly studies the method of parameter adjustment on second-order stable objects.Also,we will discuss the relationship between PID and LADRC.The details are as follows:First,based on the LADRC standard transfer function block diagram,the root locus method,which is only used in classical cybernetics,is prop osed to study the sta-bility of LADRC.For the second-order system without zeros,we can design a second-order LADRC.And for the second-order system with a zero,we use Rlocus explain that both first-order LADRC and second-order LADRC can stabilize the system.In addition,By analyzing the LADRC with the root locus method,it is found that nominal value of b can be adjusted as a parameter to improve system performance.Then,the LADRC separation block diagram is proposed to completely decouple the system into a feedback subsystem and an error subsystem.Based on this,a series of adjustment methods are proposed.The first one is for double integrator system.If the controller bandwidth equals to the observer bandwidth,this system has a constant phase angle margin.Also,the crossover frequency of system can be arbitrarily de-signed.Futher,for second-order objects,the method can combine system steady state margin with adjustment parameter.And the method can ensure the system reaches the corresponding phase angle margin with a given crossover frequency.Finally,by analyzing the second-order LADRC structure,we suggest that LADRC can be interpreted as a modified PID control.LADRC filters the PID feedback com-pensator with a second-order low-pass filter;it also adds a pre-filter.Simultaneously,each given PID controller can be viewed as a special case of a second-order LADRC feedback compensator whose observer bandwidth is positive infinity.By comparing the Bode plots of PID and LADRC under different parameters,it is further verified that the low frequency band of LADRC and PID are almost coincident.LADRC' s middle and high frequency performance are better than PID.Also,if the observer bandwidth is infinity,two Bode plots are almost coincident.