Research And Improvement Of Fractional Order PI~?D~? Control System Based On ICA

Fractional calculus is a generation of integer calculus to the case of non-integer.Compared to integer calculus,fractional calculus is history memory and global.This characteristic enables that fractional calculus has been widely applied in signal processing,rheology and diffuse transmission etc.In the communication of automatic control,fractional calculus has received much attention from researchers and it has been used to improve the performance of control systems.Recently,it is a hot topic to design a fractional controller for a given controlled system.For fractional controller,the orders of controller as well as the parameters of controller should be designed.Currently,it is a difficult problem to design an ideal fractional controller.In this thesis,the fractional controller designing is studied from the view point of optimization based on imperialist competition algorithm.Our work are as follows:First,considering the problem that the ICA algorithm is easy to be early-maturing,a new Levy mutation based ICA algorithm,called LMICA is presented.The proposed method generates random number according to Levy distribution,then,the random number is viewed as disturbance and is added to the imperialist country to perform mutation.Since Levy distribution has the heavy trail characteristic,it can generate random number in a larger range.Therefore,it can seek the optimal solution in a larger range.Experimental results show that the ICA algorithm with Levy mutation can not only overcome the drawback of early-maturing,but also converges faster.Second,considering the difficult of tuning of fractional PID controller,a new method is proposed to tune the parameters of fractional PID controller based on imperialist completion algorithm with Levy mutation.The proposed algorithm constructs an optimization objective function according the overshoot,raised time,settle time and steady error.Then,the imperialist competition algorithm with Levymutation is adopted to minimize the objective function to obtain the optimal parameters and order of the controller.The proposed method is used to design fractional controller for automatic voltage regulator and satisfactory performance is obtained.Finally,we studied the fractional PI controller design of a class of fractional order system.In traditional fractional order controller design,only the performance specification in time domain or in frequency domain are considered,and it can't consider the time domain and frequency domain specification simultaneously.Therefore,a new design method is proposed,which can simultaneously satisfy the specification in frequency and time domain.In first step,the proposed method takes the phase margin and open loop gain variation as constrains,and derive the equations that the controller parameter should be satisfied.Then,the gain crossover frequency and the order of fractional PI controller is taken as the optimization variables,imperialist competition algorithm is used to search the ideal controller's parameter and order by minimizing the integral of time multiplied square error(ITSE).The controller design by the proposed method can satisfy the frequency and time specification with fastness and robustness.