Design Of Linear Active Disturbance Rejection Controller Based On Performance Index

Active Disturbance Rejection Control(ADRC)is a new type of control scheme with strong anti-interference ability and no requirement for accurate mathematical model of the plant.The main idea is to construct the extended state observer(ESO)to observe the total of the controlled system except the series integral.Disturb and compensate for the total disturbance through the feedback channel.However,blindly compensating the system into a series integral form without fully utilizing the known information of the system may not fully exploit the potential of the system.Since ESO is the core structure of ADRC,the original ESO uses a special nonlinear function,so the relationship between its observation performance and parameters is not intuitive,and the parameter configuration is very complicated.In addition,in actual engineering,due to high frequency noise and other reasons,the ESO bandwidth limitation cannot be achieved relatively large,which seriously affects the ESO’s disturbance estimation accuracy and cannot be applied to some scenarios where the control precision is very high.In this paper,aiming at the expansion of observer performance and system dynamic performance optimization,the ESO parameters are correlated with the frequency domain index and the system pole region and system dynamic performance respectively,and the corresponding ESO parameter configuration and controller parameter configuration method are given.For the ESO bandwidth limitation problem,the corresponding control strategy is given in combination with the output feedback.The main content of this paper is divided into the following sections.Firstly,for the second-order controlled system with known structure and variable parameters,the ESO is constructed by introducing the model information,and the transfer function of the system total disturbance to the ESO output is derived,and the expected frequency domain performance index is given.By analyzing the phase-frequency characteristics and amplitude-frequency characteristics of the transfer function,an ESO parameter configuration method that satisfies the desired frequency domain performance index is given.Then the system is compensated to the nominal system by disturbance compensation,and the controller parameter configuration method based on the classical linear controller method is given.The simulation results verify the feasibility and effectiveness of the theoretical results.Then,from the perspective of dynamic performance optimization of the system output,considering the second-order controlled object given above and the ESO design and parameter configuration,the controller design is improved.Firstly,the correspondence between the pole configuration of the system area and the dynamic performance index is given.On this basis,the range of controller parameters satisfying the pole configuration in the specified area is obtained by coordinate transformation,so as to ensure the dynamic performance of the system output meets the expected requirements,and the effectiveness is verified by simulation experiments.Finally,considering the limited ESO bandwidth used by the ADRC controller,the disturbance observation error is large,so the combination of ADRC and output feedback is proposed.The tracking problem of the original system is first converted into the origin stabilization problem of the error closed-loop system,and then the ESO observation is used to estimate and compensate the total disturbance.Then the pole of the whole closed-loop system is configured by the designed output feedback subsystem,and the ESO compensation error,the system tracking error and the mathematical expression between the configuration poles are given,which proves that the system tracking error is about the convergence of the configuration pole index.Simulation results verify the feasibility of the method.