Research On Active Disturbance Rejection Control Strategy For Fractional Order Systems

There are mainly integer-order calculus and fractional-order calculus in the field of mathematics.As an important branch,fractional-order calculus can provide a more accurate mathematical model for objects with memory.As scholars continue to study in the field of fractional calculus,fractional calculus are used to describe more and more traditional controllers.This application can not only retain the original control effect based on the system but also have a characteristic of fast response.Non-model-based active disturbance rejection controls are more suitable for fractional systems due to the fact that Lyapunov functions are difficult to construct and that non-linear methods are not easy to introduce to fractional systems and that there are uncertainties and disturbances in system,The single integer order active disturbance rejection controller will increase the systematic observation error.In view of the above problems,this paper focuses on the strategy of fractional-order systems active disturbance rejection control.The main research contents are as follows:Firstly,the fractional order is introduced into the traditional tracking differentiator by using the Oustaloup algorithm.And then the traditional tracking differentiator is extended to fractional order tracking differentiator.The most important thing is to get the input containing fractional transitions.The same Oustaloup algorithm is also used to improve the fractional order extended state observer.The fractional extended state observer can measure the system state and disturbance state more accurately.At the same time,the improved fractional expansion state observer also improves the robustness of the system effectively.Secondly,the design of fractional order PID controller is studied in depth which is an important part of fractional order active disturbance rejection control.The influence of five parameters in fractional order PID controller on the dynamic performance of the system is analyzed emphatically.The stability of fractional order active disturbance rejection control is verified by root locus and Byrd diagram.At the same time,the universality of the controller is analyzed by the simulation of non-proportional system,third-order system and nonlinear system.Thirdly,we study the discretization of fractional systems.First,the discrete approximation of fractional calculus operator is verified by the Bode diagram.Then the discretization method is applied to the discrete approximation of fractional extended state observer by simulating the method of integer order discretization.Finally,the simulation of the observed object shows that the discretized observer has a very good observational effect.Finally,the paper summarizes the research work and puts forward the direction for further study.