Research On The Passive Synthesis Method Of Fractional Order Immittance Functions In W-domain

In recent years,as a powerful tool,fractional calculus has been widely used in many engineering fields such as equipment modeling and system control.In the field of actual electrical engineering,many devices and equipment show fractional order nature.Considering the inherent fractional order characteristics of electrical equipment,fractional order modeling using fractional order circuit models can more simply and accurately describe actual physical systems.The actual design of fractional-order circuits is inseparable from the synthesis theory of fractional-order circuits,but at this stage,research on passive synthesis methods for fractional-order circuits is still in its infancy,and much work remains to be done in this area.This thesis mainly studies the passive synthesis method of the fractional-order two-element and three-element circuit immittance functions in W-domain.First,the W-domain equivalent positive real condition is improved,and the problem of W-domain positive real decomposition of the passive network immittance function is studied.Then,based on the s-W transformation,the fractional rational order immittance function is transformed into the W-domain integer-order immittance function,the partial fraction expansion is derived in W domain,and the properties of poles and zeros are studied.Based on this,the passive synthesis method of fractional order two-element circuits is given.Finally,taking the fractional-order RL_αC_βthree-element-kind circuit as an example,the W-domain minimum function definition of fractional-order RL_αC_βcircuit is proposed,and the W-domain Brune synthesis method to realize the minimum function is given.The method can be extended to any ractional-order three-element-kind networks by impedance scaling.