A Study For Identification Of Fractional Order System Parameters And Orders Based On Operational Matrix

Fractional calculus means that the order of differentiation or integration of a function is “non integer” or “any real number”.Different from integer calculus,fractional order is global and has historical memory.That is,fractional calculus at the current time of a function is related not only to the value of the current time,but also to the value of the historical time.Therefore,the fractional order model based on fractional calculus can more accurately describe the dynamic behavior of a system.A fractional order model of a system is the basis for analyzing the system behavior and implementing the system control.At present,system identification is the main method of fractional order model modeling,many scholars have studied fractional order system identification and proposed many identification methods.However,if the input and output signals of the system are polluted by noise with unknown statistical characteristics,the system parameters change with time,and the order is unknown or disproportionate,the existing fractional order identification theories and methods can not give accurate and effective identification results.Therefore,based on the operational matrix theory,the fractional order system is transformed into an algebraic system.On this basis,the order identification and time-varying parameter identification of the fractional order system under the condition of noise pollution are studied.The main research work is as follows:Aiming at the problem that the existing literature can not identify the order of the system,both Gauss-Newton auxiliary variable algorithm and optimal boundary ellipsoidinterior-point method are proposed to simultaneously identify the orders and parameters of the fractional order systems polluted by noise.In the two algorithms,the fractional order systems are transformed into algebraic systems by using the operational matrix of Blockpulse function,and then the parametric regression equations are written.For white noise environments,the Gauss-Newton auxiliary variable algorithm is used to identify the coefficient parameters and differentiation order of the system.For unknown but bounded noise,the optimal boundary ellipsoid-interior point method is used to identify the parameters and differentiation order of the system.The identification examples is used to verify the effectiveness of the proposed identification methods.Aiming at the problem that the parameters of the actual systems will change with time due to the change of working environment and other factors,the existing identification methods for fractional order constant systems are difficult to accurately identify time-varying parameters,in this thesis,a repeated auxiliary variable algorithm is proposed to identify the time-varying parameters of fractional order systems based on the Block pulse function operational matrix.The fractional time-varying systems are transformed into algebraic regression equations by using Block-pulse function operational matrix.The fractional timevarying system is transformed into an algebraic regression equation by using the Block pulse function operation matrix,on this basis,using the principle of repeated operation of the system,the repeated recursive least squares algorithm and repeated auxiliary variable recursive least squares algorithm are designed along the iterative axis when the system is not polluted by noise and colored noise.Identification experiments show that the algorithms have strong time-varying parameter tracking ability.Aiming at the problem that the Block-pulse function is a constant function on its definition,in the identification process,too few Block-pulse functions lead to low identification accuracy,too many Block-pulse functions will increase the computational burden.To solve this problem.In this thesis,an identification method of hybrid function operational matrix based on Bernoulli polynomial and Block-pulse function is proposed to identify the parameters and non proportional order of the system,and the identification method is applied to the fractional order modeling of boost switching converter.The simulation examples are given to verify the effectiveness of the proposed identification method.