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

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], ],
"key": "-" "key": "-"
} }
],
"obsidian-footnotes:insert-autonumbered-footnote": [
{
"modifiers": [
"Mod"
],
"key": "0"
}
] ]
} }

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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",
"isDesktopOnly": false
}

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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: #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: #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> <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. 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 actually validate this statement with actual perturbations is a difficult problem. 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 because there is so much possibility for the form of an unstructured perturbation. Generating perturbations is not trivial <mark style="background: #FFB86CA6;">because there is so much possibility for the form of an unstructured perturbation.</mark>
For an engineer to accomplish this task today one of two things happens: <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 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.) 2. An engineer creates a structured perturbation instead using some parameters (transfer function order, physical attributes, etc.)
@ -24,3 +24,5 @@ This method of perturbation generation can be very powerful for robust controlle
**STATS: 407 words. 157 too many.** **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