Fractional Order System Identification And Controller Design Based On Chebyshev Wavelets

Establishing an accurate mathematical model is the basis for achieving complex process control,optimization and prediction.Many industrial processes not only have the characteristics of nonlinearity and multivariate coupling,but also their dynamic behavior is related to historical information.Fractional calculus has historical memory and globality,which can better describe the historical dependence of system evolution.Fractional calculus theory has shown great advantages in the system modeling and controller design because of this unique feature.The calculation of fractional order is not easy to deal with and the computational complexity is large in the fractional order system identification and the controller optimization design.In this paper,the fractional calculus operator of the Chebyshev wavelet are studied for the fractional order system identification and the fractional order controller design.The fractional calculus operation matrix of Chebyshev wavelet is deduced,and the parametric representation of fractional calculus operator is realized.The fractional order system identification and fractional order controller are transformed into parameter optimization problem.Specific research work is as follows:Firstly,a method of parameter identification and order identification for linear fractional order system is given based on the computational matrix of fractional integral of Chebyshev wavelet.This method obtains the matrix of fractional integral of Chebyshev wavelet by means of the base transformation.Using the operation matrix,the linear fractional order system is transformed into an algebraic equation,and the parametric representation of the calculus order is realized.Finally,the parameters and order are estimated by minimizing the error between the output of the actual system and the output of the identified system.The experimental results confirm the effectiveness of the method.Secondly,a class of nonlinear fractional order systems is studied,which is the parameter identification of fractional Hammerstein system.The fractional Hammerstein system is composed of a polynomial nonlinear function followed by a linear fractional order system.The fractional order Hammerstein system is transformed into an algebraic equation by using the calculus integral of the Chebyshev wavelet,and the parameters and orders identification of the nonlinear and fractional dynamic subsystem are realized.Finally,this paper presents a parameter optimization design method for fractional order PI~?D~? mcontroller of automatic voltage regulation system based on fractional integral operational matrix of Chebyshev wavelet.The fractional transfer function of the whole closed loop system is transformed into an algebraic equation by using the operational matrix.According to the idea of optimization,the particle swarm optimization algorithm is used to optimize the controller parameters.Compared with other controllers,the designed fractional order controller exhibits good control performance.