Research On Optimization And Application Of Digital Fractional PID Controller Based On Improved PSO

In recent years,the fractional calculus has been introduced into the study of control theory and made great progress with the efforts of experts and scholars.By applying the fractional calculus into the design of classical PID controller,the generated fractional PI?D?,controller outperforms the traditional PID controller and could satisfy the requirement of high-performance controller in current industrial fields.This thesis mainly studies the optimization and application of fractional PI?D?controller based on improved particle swarm optimization.The main contents are divided into the following four parts:In the first part,the particle swarm optimization algorithm and its developmenta are introduced firstly,and then considering the influence of inertia weight and learning factor on the PSO velocity model,an improved strategy for dynamic inertia weights and dynamic learning factors is presented in this thesis,by which the search performance is improved and it is not easy to fall into the local optimum.In the second part,the basic theory of fractional calculus and fractional order controllers are introduced firstly,and then the discrete implementation of the fractional-order controllers is analysed in detail,and meanwhile a generating function with variable parameter ? is presented in this thesis.Furthermore,the simulation experiments arc implemented based on the direct and indirect discretization method.The simulation results show that the value of the variable parameter ? and the orders will greatly affect the discretization results of different discretization methods.In the third part,the approaches of tuning the parameters for the fractional-order controllers based on the dominant pole method and the phase margin-amplitude margin method are introduced briefly,and then a parameter tuning algorithm is proposed for the fractional-order PI?D? controller based on improved PSO algorithm.Furthermore,a controller parameter optimization toolbox is designed based on the MATLAB/GUI,and the parameter tuning experiment is carried out for the fractional order PI?D? controller based on the direct and indirect discretization methods by using the optimization toolbox.The experiments of step response,gain robustness and anti-disturbing are carried out by selecting several typical simulation examples.The experimental results could verify the effectiveness of the proposed method and the optimized PI?D? controller has better control performance in comparison with the integer order controller.In the fourth part,the model of the double closed-loop brushless DC motor system is selected as the application object to test the effectiveness of the proposed method in this thesis.Then the optimization strategy in this thesis is used to optimize the design of integer-order PI speed regulator,fractional-order PI? speed regulator based on direct discretization and fractional-order PI? speed regulator based on indirect discretization.The simulation results verify that the fractional PI?speed regulator designed by using the method of this thesis has better speed tracking performance and robustness than other methods.