| In the field of electrical engineering,most devices exhibit fractional order nature.The introduction of fractional-order components to model electrical equipment with fractional-order characteristics can make the model describing the actual physical system more concise and accurate.Considering that the structure of actual devices and equipment is relatively complex,in practical applications,more people use the black box modeling method for modeling.Fractional black-box modeling is inseparable from fractional fitting and fractio nal circuit synthesis of electrical equipment.But at this stage,both the research on fractional-order fitting methods and fractional-order synthesis methods are still in their infancy,and there is still a lot of work to be done in fractional-order modeling.In this thesis,the W-domain fitting method and passive synthesis method are studied mainly for the stability and positive realness of the Two element fractional order impedance function.Firstly,the fitting method based on rational function is given,the stability of fitting results is analyzed by s-W transformation,and the unstable fitting results are treated with genetic algorithm and least square method to make them meet the stability requirements.Then,referring to the integer-order vector matching method,a fitting method based on partial fraction expansion is given.By improving the integer-order Hamilton matrix,a practical positive real criterion for a class of W domain impedance functions is given.Finally,the union positive real method of the non-positive real term of the two element fractional order impedance function in the W domain is given.By synthesizing the merged positive real terms and the remaining positive real terms respectively,a passive synthesis method in the W domain of the two element fractional order impedance function is given.The fitting method and comprehensive method proposed in this thesis are verified by examples. |
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