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bibliography: => #+BIBLIOGRAPHY: here

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Thomas Dehaeze
2021-05-02 22:18:30 +02:00
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content/zettels/fractional_order_transfer_functions.md
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@@ -15,16 +15,16 @@ The documentation for the toolbox is accessible [here](https://fomcon.net/fomcon
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
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);
G = oustafod(r,n,wb,wh);
```
```text
@@ -37,10 +37,8 @@ G =
Continuous-time transfer function.
```
Few examples of different slopes are shown in Figure [1](#orgaa7c066).
Few examples of different slopes are shown in Figure [1](#org9241d6d).
<a id="orgaa7c066"></a>
<a id="org9241d6d"></a>
{{< figure src="/ox-hugo/approximate_deriv_int.png" caption="Figure 1: Example of fractional approximations" >}}
<./biblio/references.bib>