Research On Rational Approximation Method Of Fractional Calculus Operator

In recent years,with the fractional calculus theory is applied to engineering fields, people’s research interests for the fractional calculus are promoted greatly. With the deepening of the theoretical research,Fractional Calculus Operators approximate discretization method has also got more and more attention of scholars.At present,The key issues of the methods about operator calculus digital realization is its discretization, The paper discusses the best rational approximation of the fractional calculus operator amplitude conditions, given construction methods and procedures of the rational approximation and to ensure that the fractional calculus operator the best rational approximation of a constructor method is effective. And procedures to determine the approximation error and approximation band structure best rational approximation function to the lowest order of the best approximation characteristics, and using MATLAB mathematical tools to write the fractional integral operator best rational approximation function, auxiliary analysis of the study.This paper studies the indirect discretization methods, focusing on the optimal rational approximation problem of the fractional calculus parameters s±α in S domain. In this paper fractional integral operator is taken as an example to discuss the conditions which meet the amplitude of the best rational approximation, and the structure of the rational approximation PIαDβ functions is given, and MATLAB simulation software is used to make the fractional integral paramator rational approximation function generation program. Research based on the Build fractional calculus operator best rational approximation. Also discussed the problem of fractional calculus operator best rational approximation PIαDβ based controller design. Due to the build controller digital implementation is relatively complex, difficult structural adjustment, in order to get a hold of the original controller frequency characteristics of the structure of the most simple controller model. And taking two-inertia motor drive system model in the case of neglecting damping as an example, simulated the test of controller performance based on MATLAB. The innovation of this paper is:proposed a fractional calculus operator rational approximation method, and applied this method in the fractional PIαDβ controller on theory level, with the verification using MATLAB, discussed the data simulation and provided a theory base for promoting the performance of fractional controller.