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1 International Journal of Microelectronics and Computer Science

1 2012

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Application of Newton's Method to Analog and Digital Realization of Fractional-order Controllers

Tepljakov A., Petlenkov E., Belikov J.

International Journal of Microelectronics and Computer Science

2012

Vol. 3, nr 2

45-52

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 a modification of 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 analog and digital implementations of fractional-order systems and controllers with relevant examples and comments.