digital-brain/content/zettels/fractional_order_transfer_functions.md

+++ title = "Fractional Order Transfer Functions" author = ["Thomas Dehaeze"] draft = false +++

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Example Using the FOMCON toolbox

The documentation for the toolbox is accessible here.

Here are the parameters that are used to define the wanted properties of the fractional model:

wb = 2*pi*0.1; % Lowest frequency bound
wh = 2*pi*1e3; % Highest frequency bound
n  = 8; % Approximation order
r = 0.5; % Wanted slope, The corresponding phase will be pi*r

Then, to create an approximation of a fractional-order operator \(s^r\) of order \(n\) which is valid in the frequency range \([\omega_b, \omega_h]\), the oustafod function can be used:

G = oustafod(r,n,wb,wh);

Few examples of different slopes are shown in Figure 1.

{{< figure src="/ox-hugo/approximate_deriv_int.png" caption="Figure 1: Example of fractional approximations" >}}

<./biblio/references.bib>