vault backup: 2024-08-29 16:05:36
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.obsidian/community-plugins.json
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.obsidian/community-plugins.json
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@ -11,5 +11,6 @@
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"obsidian-admonition",
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"obsidian-git",
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"obsidian-full-calendar",
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"highlightr-plugin"
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"highlightr-plugin",
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"obsidian-footnotes"
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]
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.obsidian/hotkeys.json
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.obsidian/hotkeys.json
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@ -167,5 +167,13 @@
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],
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"key": "-"
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}
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],
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"obsidian-footnotes:insert-autonumbered-footnote": [
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{
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"modifiers": [
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"Mod"
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],
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"key": "0"
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}
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]
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}
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.obsidian/plugins/obsidian-footnotes/main.js
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.obsidian/plugins/obsidian-footnotes/main.js
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.obsidian/plugins/obsidian-footnotes/manifest.json
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.obsidian/plugins/obsidian-footnotes/manifest.json
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@ -0,0 +1,10 @@
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{
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"id": "obsidian-footnotes",
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"name": "Footnote Shortcut",
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"version": "0.1.3",
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"minAppVersion": "0.12.0",
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"description": "Insert and write footnotes faster",
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"author": "Alexis Rondeau, Micha Brugger, Jason Qin",
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"authorUrl": "https://publish.obsidian.md/alexisrondeau",
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"isDesktopOnly": false
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}
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@ -4,10 +4,10 @@
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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>
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<mark style="background: #FF5582A6;">Perturbations can be considered as two forms--structured and unstructured perturbation.</mark>
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<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>
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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.
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To actually validate this statement with actual perturbations is a difficult problem.
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Generating perturbations is not trivial because there is so much possibility for the form of an unstructured perturbation.
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For an engineer to accomplish this task today one of two things happens:
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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.
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To <mark style="background: #FF5582A6;">actually</mark> validate this statement with <mark style="background: #FFB86CA6;">actual</mark> perturbations is a difficult problem.
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Generating perturbations is not trivial <mark style="background: #FFB86CA6;">because there is so much possibility for the form of an unstructured perturbation.</mark>
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<mark style="background: #FFB86CA6;">For an engineer to accomplish this task today one of two things happens: </mark>
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1. An engineer can randomly generate transfer functions as a perturbation and evaluate if their gain is less than one, or
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2. An engineer creates a structured perturbation instead using some parameters (transfer function order, physical attributes, etc.)
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@ -23,4 +23,6 @@ This method of perturbation generation can be very powerful for robust controlle
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**STATS: 407 words. 157 too many.**
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[[QE Abstract Take 1 Edits]]
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[[QE Abstract Take 1 Edits]]
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[^1]:Likely need to introduce what the fuck the set is
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