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Thomas Dehaeze 2021-01-07 09:53:00 +01:00
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content/zettels/fractional_order_transfer_functions.md
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@ -27,9 +27,19 @@ Then, to create an approximation of a fractional-order operator \\(s^r\\) of ord
G = oustafod(r,n,wb,wh); G = oustafod(r,n,wb,wh);
``` ```
Few examples of different slopes are shown in Figure [1](#orgb7e7209). ```text
G =
<a id="orgb7e7209"></a> 79.27 s^17 + 7.93e05 s^16 + 2.918e09 s^15 + 5.143e12 s^14 + 4.782e15 s^13 + 2.453e18 s^12 + 7.103e20 s^11 + 1.175e23 s^10 + 1.119e25 s^9 + 6.138e26 s^8 + 1.942e28 s^7 + 3.534e29 s^6 + 3.675e30 s^5 + 2.157e31 s^4 + 6.984e31 s^3 + 1.193e32 s^2 + 9.764e31 s + 2.939e31
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
s^17 + 1.312e04 s^16 + 6.327e07 s^15 + 1.462e11 s^14 + 1.783e14 s^13 + 1.199e17 s^12 + 4.553e19 s^11 + 9.877e21 s^10 + 1.232e24 s^9 + 8.866e25 s^8 + 3.678e27 s^7 + 8.775e28 s^6 + 1.196e30 s^5 + 9.208e30 s^4 + 3.909e31 s^3 + 8.755e31 s^2 + 9.395e31 s + 3.707e31
Continuous-time transfer function.
```
Few examples of different slopes are shown in Figure [1](#orgaa7c066).
<a id="orgaa7c066"></a>
{{< figure src="/ox-hugo/approximate_deriv_int.png" caption="Figure 1: Example of fractional approximations" >}} {{< figure src="/ox-hugo/approximate_deriv_int.png" caption="Figure 1: Example of fractional approximations" >}}