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Thomas Dehaeze
2021-08-24 16:00:27 +02:00
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content/article/stein03_respec_unstab.md
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@@ -9,7 +9,7 @@ Tags
Reference
: ([Stein 2003](#org50b7ac8))
: ([Stein 2003](#orge299f80))
Author(s)
: Stein, G.
@@ -73,15 +73,15 @@ It is here proposed to call it **dirt**
</div>
The job of a serious control designer is then to more dirt from one place to another, using appropriate tools, without being able to get rid of any of it (illustrated in Figure [1](#org956e0bf)).
The job of a serious control designer is then to more dirt from one place to another, using appropriate tools, without being able to get rid of any of it (illustrated in Figure [1](#orgf166bde)).
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{{< figure src="/ox-hugo/stein03_serious_design.png" caption="Figure 1: Sensitivity reduction at low frequency unavoidably leads to sensitivity increase at higher frequencies" >}}
In the same spirit, the job of a more academic control designer with more abstract tools such as LQG, \\(\mathcal{H}\_\infty\\), is to set parameters (weights) of a synthesis machine to adjust the contours of the machine's digging blades to get just the right shape for the sensitivity function (Figure [2](#org73c6dd3)).
In the same spirit, the job of a more academic control designer with more abstract tools such as LQG, \\(\mathcal{H}\_\infty\\), is to set parameters (weights) of a synthesis machine to adjust the contours of the machine's digging blades to get just the right shape for the sensitivity function (Figure [2](#org29aa88f)).
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{{< figure src="/ox-hugo/stein03_formal_design.png" caption="Figure 2: Sensitivity shaping automated by modern control tools" >}}
@@ -89,9 +89,9 @@ In the same spirit, the job of a more academic control designer with more abstra
## Available bandwidth {#available-bandwidth}
An argument is sometimes made that the Bode integrals are not really restrictive because we only seek to dig holes over finite frequency bands.
We then have an infinite frequency range left over into which to dump the dirt, so we can make the layer arbitrarily thin (Figure [3](#orgb2839fe)).
We then have an infinite frequency range left over into which to dump the dirt, so we can make the layer arbitrarily thin (Figure [3](#orgf23d7a5)).
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{{< figure src="/ox-hugo/stein03_spreading_it_thin.png" caption="Figure 3: It is possible to spead the increase of the sensitivity function over a larger frequency band" >}}
@@ -121,6 +121,7 @@ All the action of the feedback design, the sensitivity improvements as well as t
Only a small error \\(\delta\\) occurs outside that range, associated with the tail of the complete integrals.
## Bibliography {#bibliography}
<a id="org50b7ac8"></a>Stein, Gunter. 2003. “Respect the Unstable.” _IEEE Control Systems Magazine_ 23 (4). IEEE:12–25.
<a id="orge299f80"></a>Stein, Gunter. 2003. “Respect the Unstable.” _IEEE Control Systems Magazine_ 23 (4). IEEE:12–25.