  This paper uses the Continued Fraction Expansion (CFE) method for analog
realization of fractional order differ-integrator and few special classes of
fractional order (FO) controllers viz. Fractional Order
Proportional-Integral-Derivative (FOPID) controller, FO[PD] controller and FO
lead-lag compensator. Contemporary researchers have given several formulations
for rational approximation of fractional order elements. However, approximation
of the controllers studied in this paper, due to having fractional power of a
rational transfer function, is not available in analog domain; although its
digital realization already exists. This motivates us for applying CFE based
analog realization technique for complicated FO controller structures to get
equivalent rational transfer functions in terms of the controller tuning
parameters. The symbolic expressions for rationalized transfer function in
terms of the controller tuning parameters are especially important as ready
references, without the need of running CFE algorithm every time and also helps
in the synthesis of analog circuits for such FO controllers.
