Design And Implementation Of Fractional PID Controller

The concept of fractional calculus appeared around for many years,but researchers have long focused more on integral calculus.The research on Fractional Order Control Theory has been gradually progressed in recent years.Therefore,the research of Fractional Calculus and Fractional Order Control Systems has become a new research direction in the field of control.Through the unremitting efforts of the researchers,many important achievements have been achieved in the theoretical aspects of fractional calculus.This paper will further study the design of fractional order PID controllers,and use Matlab GUI technology to design the fractional order controller interface,so as to simplify the design steps of fractional order controller.The paper focuses on the design of fractional-order controller with controlled object with delay,improves the numerical solution of Laplace inverse transform,and draws the closed-loop step response curve of fractional-order system with delayed controlled object.This paper first introduces several commonly used functions in fractional calculus and the mainstream definition of fractional calculus,and also analyzes the properties of fractional calculus and the stability of fractional order system.In addition,Laplace transform of fractional calculus is introduced in this paper as Laplace inverse transform of fractional order system is involved in paper.Because of the frequent use of fractional-order control system Matlab toolbox in the research,Necessary to briefly describe the project team prepared fractional control system Matlab toolbox.The integer order controller before contact with only three adjustable parameters,and the fractional order controller on the basis of increased and two parameters,so here the fractional order PID controller in the influence of adjustable parameters on the system respectively were analyzed and demonstrated through examples of fractional order PID controller parameters and the change of fractional order respectively the closed-loop system step response curve of the effect.In addition,in the actual industrial control,the problem of parameter uncertainty and unpredictable interference is often encountered.The robustness of the system has become an index to evaluate the control performance of the system.Therefore,in this paper,Fractional Order Robust Controller PI?,PI?,PD? for gain variation are designed by using the formula derivation method,The order PID(IOPID)robust controller compares with it.Then,the method of derivation of fractional order controller parameters is too complex,it is not practical in reality,so the design of fractional order controller based on numerical optimization method in this paper to find,Therefore,the design of Fractional Order Controller based on numerical optimization method is presented.The three integral performance indexes(ISE,IAE,ITAE)to verify the design of the controller under various indicators.In order to solve the problem that it is difficult for the system to get a closed-loop response,a reduced order approximation of Pade' and a numerical inverse Laplace transform with a controlled object with delay are discussed.The approximate method of Oustaloup filter is studied.The fractional order transfer function is transformed to the higher order integer order model.Moreover,the Matlab function is simplified to the higher order approximation method of transfer function with fractional order to integer order.Finally,the fractional order controller is designed for the time domain and frequency domain performance indexes,and the design of the fractional order controller under different controlled objects is studied.Finally,in order to further simplify the design process of Fractional order controller,the design interface of Fractional order controller based on time domain and frequency domain performance index is programmed respectively by using Matlab GUI technology,and the parameters of Fractional order controller are added Search optimization algorithm,compare the optimization results of various algorithms.In the interface,the closed-loop step response curve of the system and the system crossover frequency can be drawn directly by clicking the button,and the rationality of the interface design is verified in the interface.The design of this interface greatly simplifies the design of controllers for fractional order controllers,making the design of fractional controllers based on time domain and frequency domain more intuitive and effective.