Update Content - 2020-12-10

content/zettels/fractional_order_transfer_functions.md

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+title = "Fractional Order Transfer Functions"
+author = ["Thomas Dehaeze"]
+draft = false
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+
+Tags
+:
+
+
+## Example Using the FOMCON toolbox {#example-using-the-fomcon-toolbox}
+
+The documentation for the toolbox is accessible [here](https://fomcon.net/fomcon-toolbox/overview/).
+
+Here are the parameters that are used to define the wanted properties of the fractional model:
+
+```matlab
+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:
+
+```matlab
+G = oustafod(r,n,wb,wh);
+```
+
+Few examples of different slopes are shown in Figure [1](#orgb7e7209).
+
+<a id="orgb7e7209"></a>
+
+{{< figure src="/ox-hugo/approximate_deriv_int.png" caption="Figure 1: Example of fractional approximations" >}}
+
+<./biblio/references.bib>