On Some Properties of Padé Approximations for Fractional Order Transfer Function (FOTF)

The issue of identifying and designing control systems of fractional order models involves the necessity of their approximation to integer order. The most popular techniques include: Oustaloup’s method, Matsuda’s method, CFE (Continued Fraction Expansion) method, M-SBL method and different more. It is also possible to use the Padé approximation. The article examines some properties of this method. The case of the fractional power term (complex variable transfer function raised to a fractional power) is the main focus since it serves as a basis for approximating more intricate fractional order systems. The article’s innovation is in using the nonlinear least squares method to obtain a mathematical description of the behavior of the zeros and poles of the chosen component after approximation. Relying on the gathered statistics, it was found that a very good fit was produced. The approximation of the behaviour of zeros and poles also allowed for the presentation of a new, alternative notation for the Padé approximation.