Parameter Tuning Analysis Based On Fractional Order PID Controller

With the development of social productivity,traditional PID controllers can no longer meet higher production needs.Therefore,fractional-order PID controllers have become the focus of research in recent years.As we all know,the fractional-order PID controller with its two additional fractional-order parameters has been favored by scholars because of the integer-order PID and the infinite potential of fractional-order calculus in adjusting the flexibility of the parameters.However,fractional-order PID controllers also inherit some of the shortcomings of integer-order PID controllers.Due to the structural limitations of the first-order PID controller,the load disturbance suppression response and the set value response cannot be taken into account.This problem can be better solved with 2DOF(Two Degrees Of Freedom)PID.In terms of parameter tuning of 2DOF PID controllers,most of the existing methods currently have some problems.For example,common methods of controlled objects use integer order approximation,which is not only less accurate than the fractional order model,but also does not make the fractional order controller optimal Control performance.Secondly,due to the particularity of the fractional-order theory and the two-degree-of-freedom structure,the general tuning method is redundant in the derivation process.This article starts from the related theory of fractional calculus,briefly introduces the related content of fractional order system,and makes a detailed summary of the basic structure and main design methods of fractional order PID controller and 2DOF fractional-order PID controller,respectively.The main contents of this article are:1.Two-degree-of-freedom fractional-order PID/I-PD controllers are designed for two types of fractional-order controlled systems(type 1 system and type 2 system).In this paper,the integer-order approximation is not performed on the fractional-order controlled object.Processing to ensure the accuracy of the controlled object.First of all,the equivalent transformation is performed using the principle of automatic control without changing the essence of the entire control system.Second,the structure obtained by the transformation is subjected to pole-zero cancellation using the Bode ideal transfer function,which makes 7 unknowns to be set by the 2DOF fractional order controller The parameter(Kp,Ki,Kd,?,?, ?,?)is simplified to three(Kp,?,?),and this process also ensures that the controller has a good adaptability to the uncertainty of the controlled object.Finally,the optimal solution is obtained by multiplying time by the absolute error integral(ITAE)as a performance index within a reasonable range of parameters.At the same time,for the two types of controllers designed in this paper,the differences are analyzed in detail through simulation experiments.The small gain theorem is used to analyze the stability of the designed control system.The traditional parameter tuning method of 2DOF PID and particle swarm optimization(PSO)algorithm are used as references for comparative experiments.When using the traditional method,based on the nature of the two-degree-of-freedom controller structure(two types of equivalent transfer functions:set-point transfer function and disturbance transfer function),the correlation of unknown parameters and transfer function is used to first ensure the anti-interference performance of the system.On this basis,the tracking performance of the system is guaranteed;using particle swarm optimization,ITAE is used as a performance index to perform unknown parameter optimization directly within a reasonable range.The final simulation results verify the effectiveness,speed and stability of the method through specific data indicators such as overshoot and steady-state error.2.Based on the in-depth study of the two-degree-of-freedom fractional order PID controller,this paper also proposes a controller design method that uses D decomposition to dominate the pole placement.The basic idea is to configure the dominant pole based on the dynamic response index constraints,from which the linear function of the fractional order controller parameters K Ki with respect to Kd,?,? can be obtained.After the parameter ? is fixed,only Kd and ? are free parameter.The D decomposition method is used to determine Kd and ? to ensure the advantage of the selected pole.In this process,the differential evolution algorithm is introduced as a medium to determine the stable region of the parameters,so that the fractional PID controller can achieve the ideal system control performance.In addition,HM-MD2 motor-driven experimental platform is used for real-world simulation.The experimental process is based on Code Composer Studio and MATLAB/Simulink software development platform.Firstly,the motor model is identified by fractional-order system,and the fractional-order transfer function model is obtained.Then,the 2DOF PID designed in the paper is used for experimental testing.The classic one-degree-of-freedom fractional-order PID is used as a reference.Performance,from the experimental data obtained,its actual control performance and simulation experiment performance are consistent to achieve the expected goal,showing the higher robustness and practicability of the 2DOF PID controller.