Application of the newton method to first-order implicit fractional transfer function approximation

In this paper, a method for approximating a first-order implicit fractional transfer function, that corresponds to a frequency-bounded fractional differentiator or integrator, is presented. The proposed method is based on the well-known Newton´s method for iterative root approximation. First-order implicit fractional transfer functions have several applications in modeling and control. This type of transfer function is the basis for the fractional lead-lag compensator. In the following, we provide the description of our algorithm, that enhances the existing technique, and illustrate its use in modeling and control with relevant comments.