vault backup: 2024-08-29 16:05:36

This commit is contained in:
Dane Sabo 2024-08-29 16:05:36 -04:00
parent 6b1a85cf5e
commit 42fc8bbed3
5 changed files with 514 additions and 6 deletions

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"obsidian-admonition",
"obsidian-git",
"obsidian-full-calendar",
"highlightr-plugin"
"highlightr-plugin",
"obsidian-footnotes"
]

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],
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{
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"Mod"
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}

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{
"id": "obsidian-footnotes",
"name": "Footnote Shortcut",
"version": "0.1.3",
"minAppVersion": "0.12.0",
"description": "Insert and write footnotes faster",
"author": "Alexis Rondeau, Micha Brugger, Jason Qin",
"authorUrl": "https://publish.obsidian.md/alexisrondeau",
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<mark style="background: #FFB86CA6;">Examining the robustness of a <mark style="background: #FFF3A3A6;">controller</mark> requires additional mathematical formalism of a system, and analysis of perturbations to a nominal plant model.</mark>
<mark style="background: #FF5582A6;">Perturbations can be considered as two forms--structured and unstructured perturbation.</mark>
<mark style="background: #ADCCFFA6;">Unstructured perturbation in particular allows the perturbation to take on any transfer function (or transfer matrix), such that the gain of the transfer function remains less than one.</mark>
If a <mark style="background: #FFB86CA6;">controlled system</mark> remains stable for the ~~nominal plant and all possible perturbations~~ all possible perturbations within the set, it is considered robust.
To actually validate this statement with actual perturbations is a difficult problem.
Generating perturbations is not trivial because there is so much possibility for the form of an unstructured perturbation.
For an engineer to accomplish this task today one of two things happens:
If a <mark style="background: #FFB86CA6;">controlled system</mark> remains stable for the ~~nominal plant and all possible perturbations~~ all possible perturbations within the set[^1], it is considered robust.
To <mark style="background: #FF5582A6;">actually</mark> validate this statement with <mark style="background: #FFB86CA6;">actual</mark> perturbations is a difficult problem.
Generating perturbations is not trivial <mark style="background: #FFB86CA6;">because there is so much possibility for the form of an unstructured perturbation.</mark>
<mark style="background: #FFB86CA6;">For an engineer to accomplish this task today one of two things happens: </mark>
1. An engineer can randomly generate transfer functions as a perturbation and evaluate if their gain is less than one, or
2. An engineer creates a structured perturbation instead using some parameters (transfer function order, physical attributes, etc.)
@ -23,4 +23,6 @@ This method of perturbation generation can be very powerful for robust controlle
**STATS: 407 words. 157 too many.**
[[QE Abstract Take 1 Edits]]
[[QE Abstract Take 1 Edits]]
[^1]:Likely need to introduce what the fuck the set is