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This paper uses the Continued Fraction Expansion (CFE) method for analogrealization of fractional order differ-integrator and few special classes offractional order (FO) controllers viz. Fractional OrderProportional-Integral-Derivative (FOPID) controller, FO[PD] controller and FOlead-lag compensator. Contemporary researchers have given several formulationsfor rational approximation of fractional order elements. However, approximationof the controllers studied in this paper, due to having fractional power of arational transfer function, is not available in analog domain; although itsdigital realization already exists. This motivates us for applying CFE basedanalog realization technique for complicated FO controller structures to getequivalent rational transfer functions in terms of the controller tuningparameters. The symbolic expressions for rationalized transfer function interms of the controller tuning parameters are especially important as readyreferences, without the need of running CFE algorithm every time and also helpsin the synthesis of analog circuits for such FO controllers.

Symbolic Representation for Analog Realization of A Family of Fractional Order Controller Structures via Continued Fraction Expansion