From 86eb3b2a1316143200fe8e6adab9a63ea1440d2f Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Thu, 10 Dec 2020 16:00:20 +0100 Subject: [PATCH] Update Content - 2020-12-10 --- .../fractional_order_transfer_functions.md | 36 ++++++++++++++++++ static/ox-hugo/approximate_deriv_int.png | Bin 0 -> 173873 bytes 2 files changed, 36 insertions(+) create mode 100644 content/zettels/fractional_order_transfer_functions.md create mode 100644 static/ox-hugo/approximate_deriv_int.png diff --git a/content/zettels/fractional_order_transfer_functions.md b/content/zettels/fractional_order_transfer_functions.md new file mode 100644 index 0000000..9d016cf --- /dev/null +++ b/content/zettels/fractional_order_transfer_functions.md @@ -0,0 +1,36 @@ ++++ +title = "Fractional Order Transfer Functions" +author = ["Thomas Dehaeze"] +draft = false ++++ + +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). + + + +{{< figure src="/ox-hugo/approximate_deriv_int.png" caption="Figure 1: Example of fractional approximations" >}} + +<./biblio/references.bib> diff --git a/static/ox-hugo/approximate_deriv_int.png b/static/ox-hugo/approximate_deriv_int.png new file mode 100644 index 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