Add analysis, images, and explanations
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css/htmlize.css
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.org-bold { /* bold */ font-weight: bold; }
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.org-bold-italic { /* bold-italic */ font-weight: bold; font-style: italic; }
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.org-buffer-menu-buffer { /* buffer-menu-buffer */ font-weight: bold; }
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.org-builtin { /* font-lock-builtin-face */ color: #7a378b; }
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.org-button { /* button */ text-decoration: underline; }
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.org-calendar-today { /* calendar-today */ text-decoration: underline; }
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.org-change-log-acknowledgement { /* change-log-acknowledgement */ color: #b22222; }
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.org-change-log-conditionals { /* change-log-conditionals */ color: #a0522d; }
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.org-change-log-date { /* change-log-date */ color: #8b2252; }
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.org-change-log-email { /* change-log-email */ color: #a0522d; }
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.org-change-log-file { /* change-log-file */ color: #0000ff; }
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.org-change-log-function { /* change-log-function */ color: #a0522d; }
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.org-change-log-list { /* change-log-list */ color: #a020f0; }
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.org-change-log-name { /* change-log-name */ color: #008b8b; }
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.org-comint-highlight-input { /* comint-highlight-input */ font-weight: bold; }
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.org-comint-highlight-prompt { /* comint-highlight-prompt */ color: #00008b; }
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.org-comment { /* font-lock-comment-face */ color: #999988; font-style: italic; }
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.org-comment-delimiter { /* font-lock-comment-delimiter-face */ color: #999988; font-style: italic; }
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.org-completions-annotations { /* completions-annotations */ font-style: italic; }
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.org-completions-common-part { /* completions-common-part */ color: #000000; background-color: #ffffff; }
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.org-completions-first-difference { /* completions-first-difference */ font-weight: bold; }
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.org-constant { /* font-lock-constant-face */ color: #008b8b; }
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.org-diary { /* diary */ color: #ff0000; }
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.org-diff-context { /* diff-context */ color: #7f7f7f; }
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.org-diff-file-header { /* diff-file-header */ background-color: #b3b3b3; font-weight: bold; }
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.org-diff-function { /* diff-function */ background-color: #cccccc; }
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.org-diff-header { /* diff-header */ background-color: #cccccc; }
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.org-diff-hunk-header { /* diff-hunk-header */ background-color: #cccccc; }
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.org-diff-index { /* diff-index */ background-color: #b3b3b3; font-weight: bold; }
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.org-diff-nonexistent { /* diff-nonexistent */ background-color: #b3b3b3; font-weight: bold; }
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.org-diff-refine-change { /* diff-refine-change */ background-color: #d9d9d9; }
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.org-dired-directory { /* dired-directory */ color: #0000ff; }
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.org-dired-flagged { /* dired-flagged */ color: #ff0000; font-weight: bold; }
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.org-dired-header { /* dired-header */ color: #228b22; }
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.org-dired-ignored { /* dired-ignored */ color: #7f7f7f; }
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.org-dired-mark { /* dired-mark */ color: #008b8b; }
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.org-dired-marked { /* dired-marked */ color: #ff0000; font-weight: bold; }
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.org-dired-perm-write { /* dired-perm-write */ color: #b22222; }
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.org-dired-symlink { /* dired-symlink */ color: #a020f0; }
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.org-dired-warning { /* dired-warning */ color: #ff0000; font-weight: bold; }
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.org-doc { /* font-lock-doc-face */ color: #8b2252; }
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.org-escape-glyph { /* escape-glyph */ color: #a52a2a; }
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.org-file-name-shadow { /* file-name-shadow */ color: #7f7f7f; }
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.org-flyspell-duplicate { /* flyspell-duplicate */ color: #cdad00; font-weight: bold; text-decoration: underline; }
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.org-flyspell-incorrect { /* flyspell-incorrect */ color: #ff4500; font-weight: bold; text-decoration: underline; }
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.org-fringe { /* fringe */ background-color: #f2f2f2; }
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.org-function-name { /* font-lock-function-name-face */ color: teal; }
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.org-header-line { /* header-line */ color: #333333; background-color: #e5e5e5; }
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.org-help-argument-name { /* help-argument-name */ font-style: italic; }
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.org-highlight { /* highlight */ background-color: #b4eeb4; }
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.org-holiday { /* holiday */ background-color: #ffc0cb; }
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.org-isearch { /* isearch */ color: #b0e2ff; background-color: #cd00cd; }
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.org-isearch-fail { /* isearch-fail */ background-color: #ffc1c1; }
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.org-italic { /* italic */ font-style: italic; }
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.org-keyword { /* font-lock-keyword-face */ color: #0086b3; }
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.org-lazy-highlight { /* lazy-highlight */ background-color: #afeeee; }
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.org-link { /* link */ color: #0000ff; text-decoration: underline; }
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.org-link-visited { /* link-visited */ color: #8b008b; text-decoration: underline; }
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.org-log-edit-header { /* log-edit-header */ color: #a020f0; }
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.org-log-edit-summary { /* log-edit-summary */ color: #0000ff; }
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.org-log-edit-unknown-header { /* log-edit-unknown-header */ color: #b22222; }
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.org-match { /* match */ background-color: #ffff00; }
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.org-next-error { /* next-error */ background-color: #eedc82; }
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.org-nobreak-space { /* nobreak-space */ color: #a52a2a; text-decoration: underline; }
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.org-org-archived { /* org-archived */ color: #7f7f7f; }
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.org-org-block { /* org-block */ color: #7f7f7f; }
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.org-org-block-begin-line { /* org-block-begin-line */ color: #b22222; }
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.org-org-block-end-line { /* org-block-end-line */ color: #b22222; }
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.org-org-checkbox { /* org-checkbox */ font-weight: bold; }
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.org-org-checkbox-statistics-done { /* org-checkbox-statistics-done */ color: #228b22; font-weight: bold; }
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.org-org-checkbox-statistics-todo { /* org-checkbox-statistics-todo */ color: #ff0000; font-weight: bold; }
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.org-org-clock-overlay { /* org-clock-overlay */ background-color: #ffff00; }
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.org-org-code { /* org-code */ color: #7f7f7f; }
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.org-org-column { /* org-column */ background-color: #e5e5e5; }
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.org-org-column-title { /* org-column-title */ background-color: #e5e5e5; font-weight: bold; text-decoration: underline; }
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.org-org-date { /* org-date */ color: #a020f0; text-decoration: underline; }
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.org-org-document-info { /* org-document-info */ color: #191970; }
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.org-org-document-info-keyword { /* org-document-info-keyword */ color: #7f7f7f; }
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.org-org-document-title { /* org-document-title */ color: #191970; font-size: 144%; font-weight: bold; }
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.org-org-done { /* org-done */ color: #228b22; font-weight: bold; }
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.org-org-drawer { /* org-drawer */ color: #0000ff; }
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.org-org-ellipsis { /* org-ellipsis */ color: #b8860b; text-decoration: underline; }
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.org-org-footnote { /* org-footnote */ color: #a020f0; text-decoration: underline; }
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.org-org-formula { /* org-formula */ color: #b22222; }
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.org-org-headline-done { /* org-headline-done */ color: #bc8f8f; }
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.org-org-hide { /* org-hide */ color: #ffffff; }
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.org-org-latex-and-export-specials { /* org-latex-and-export-specials */ color: #8b4513; }
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.org-org-level-1 { /* org-level-1 */ color: #0000ff; }
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.org-org-level-2 { /* org-level-2 */ color: #a0522d; }
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.org-org-level-3 { /* org-level-3 */ color: #a020f0; }
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.org-org-level-4 { /* org-level-4 */ color: #b22222; }
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.org-org-level-5 { /* org-level-5 */ color: #228b22; }
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.org-org-level-6 { /* org-level-6 */ color: #008b8b; }
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.org-org-level-7 { /* org-level-7 */ color: #7a378b; }
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.org-org-level-8 { /* org-level-8 */ color: #8b2252; }
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.org-org-link { /* org-link */ color: #0000ff; text-decoration: underline; }
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.org-org-meta-line { /* org-meta-line */ color: #b22222; }
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.org-org-mode-line-clock { /* org-mode-line-clock */ color: #000000; background-color: #bfbfbf; }
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.org-org-mode-line-clock-overrun { /* org-mode-line-clock-overrun */ color: #000000; background-color: #ff0000; }
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.org-org-quote { /* org-quote */ color: #7f7f7f; }
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.org-org-scheduled { /* org-scheduled */ color: #006400; }
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.org-org-scheduled-previously { /* org-scheduled-previously */ color: #b22222; }
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.org-org-scheduled-today { /* org-scheduled-today */ color: #006400; }
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.org-org-sexp-date { /* org-sexp-date */ color: #a020f0; }
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.org-org-special-keyword { /* org-special-keyword */ color: #a020f0; }
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.org-org-table { /* org-table */ color: #0000ff; }
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.org-org-tag { /* org-tag */ font-weight: bold; }
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.org-org-target { /* org-target */ text-decoration: underline; }
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.org-org-time-grid { /* org-time-grid */ color: #b8860b; }
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.org-org-todo { /* org-todo */ color: #ff0000; font-weight: bold; }
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.org-org-upcoming-deadline { /* org-upcoming-deadline */ color: #b22222; }
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.org-org-verbatim { /* org-verbatim */ color: #7f7f7f; }
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.org-org-verse { /* org-verse */ color: #7f7f7f; }
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.org-org-warning { /* org-warning */ color: #ff0000; font-weight: bold; }
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.org-outline-1 { /* outline-1 */ color: #0000ff; }
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.org-outline-2 { /* outline-2 */ color: #a0522d; }
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.org-outline-3 { /* outline-3 */ color: #a020f0; }
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.org-outline-4 { /* outline-4 */ color: #b22222; }
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.org-outline-5 { /* outline-5 */ color: #228b22; }
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.org-outline-6 { /* outline-6 */ color: #008b8b; }
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.org-outline-7 { /* outline-7 */ color: #7a378b; }
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.org-outline-8 { /* outline-8 */ color: #8b2252; }
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.org-preprocessor { /* font-lock-preprocessor-face */ color: #7a378b; }
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.org-query-replace { /* query-replace */ color: #b0e2ff; background-color: #cd00cd; }
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.org-regexp-grouping-backslash { /* font-lock-regexp-grouping-backslash */ font-weight: bold; }
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.org-regexp-grouping-construct { /* font-lock-regexp-grouping-construct */ font-weight: bold; }
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.org-region { /* region */ background-color: #eedc82; }
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.org-secondary-selection { /* secondary-selection */ background-color: #ffff00; }
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.org-shadow { /* shadow */ color: #7f7f7f; }
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.org-show-paren-match { /* show-paren-match */ background-color: #40e0d0; }
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.org-show-paren-mismatch { /* show-paren-mismatch */ color: #ffffff; background-color: #a020f0; }
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.org-string { /* font-lock-string-face */ color: #dd1144; }
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.org-tool-bar { /* tool-bar */ color: #000000; background-color: #bfbfbf; }
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.org-tooltip { /* tooltip */ color: #000000; background-color: #ffffe0; }
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.org-trailing-whitespace { /* trailing-whitespace */ background-color: #ff0000; }
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.org-type { /* font-lock-type-face */ color: #228b22; }
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.org-underline { /* underline */ text-decoration: underline; }
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.org-variable-name { /* font-lock-variable-name-face */ color: teal; }
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.org-warning { /* font-lock-warning-face */ color: #ff0000; font-weight: bold; }
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.org-widget-button { /* widget-button */ font-weight: bold; }
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.org-widget-button-pressed { /* widget-button-pressed */ color: #ff0000; }
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.org-widget-documentation { /* widget-documentation */ color: #006400; }
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.org-widget-field { /* widget-field */ background-color: #d9d9d9; }
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.org-widget-inactive { /* widget-inactive */ color: #7f7f7f; }
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.org-widget-single-line-field { /* widget-single-line-field */ background-color: #d9d9d9; }
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<?xml version="1.0" encoding="utf-8"?>
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<!-- 2020-10-23 ven. 23:04 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Encoder - Test Bench</title>
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<meta name="generator" content="Org mode" />
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<meta name="author" content="Dehaeze Thomas" />
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<link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
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<link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
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<link rel="stylesheet" type="text/css" href="./css/zenburn.css"/>
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<script type="text/javascript" src="./js/jquery.min.js"></script>
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<script type="text/javascript" src="./js/bootstrap.min.js"></script>
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<script type="text/javascript" src="./js/jquery.stickytableheaders.min.js"></script>
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<script type="text/javascript" src="./js/readtheorg.js"></script>
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<script>MathJax = {
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tex: {
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tags: 'ams',
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macros: {bm: ["\\boldsymbol{#1}",1],}
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}
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};
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</script>
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<script type="text/javascript" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
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</head>
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<body>
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<div id="content">
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<h1 class="title">Encoder - Test Bench</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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||||||
|
<li><a href="#org0d09252">1. Experimental Setup</a></li>
|
||||||
|
<li><a href="#org4c1706c">2. Huddle Test</a>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#org169c9b3">2.1. Load Data</a></li>
|
||||||
|
<li><a href="#org71d6eed">2.2. Time Domain Results</a></li>
|
||||||
|
<li><a href="#org526b687">2.3. Frequency Domain Noise</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li><a href="#org25a61fe">3. Comparison Interferometer / Encoder</a>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#orgb31234a">3.1. Load Data</a></li>
|
||||||
|
<li><a href="#org4fa5441">3.2. Time Domain Results</a></li>
|
||||||
|
<li><a href="#orge79e200">3.3. Difference between Encoder and Interferometer as a function of time</a></li>
|
||||||
|
<li><a href="#org625a811">3.4. Difference between Encoder and Interferometer as a function of position</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li><a href="#org2e4bf3b">4. Identification</a>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#org8a892bd">4.1. Load Data</a></li>
|
||||||
|
<li><a href="#org7e3c2ba">4.2. Identification</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org0d09252" class="outline-2">
|
||||||
|
<h2 id="org0d09252"><span class="section-number-2">1</span> Experimental Setup</h2>
|
||||||
|
<div class="outline-text-2" id="text-1">
|
||||||
|
<p>
|
||||||
|
The experimental Setup is schematically represented in Figure <a href="#org5bc9553">1</a>.
|
||||||
|
</p>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org5bc9553" class="figure">
|
||||||
|
<p><img src="figs/exp_setup_schematic.png" alt="exp_setup_schematic.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 1: </span>Schematic of the Experiment</p>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org7f3df10" class="figure">
|
||||||
|
<p><img src="figs/IMG_20201023_153905.jpg" alt="IMG_20201023_153905.jpg" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 2: </span>Side View of the encoder</p>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org71727ed" class="figure">
|
||||||
|
<p><img src="figs/IMG_20201023_153914.jpg" alt="IMG_20201023_153914.jpg" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 3: </span>Front View of the encoder</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org4c1706c" class="outline-2">
|
||||||
|
<h2 id="org4c1706c"><span class="section-number-2">2</span> Huddle Test</h2>
|
||||||
|
<div class="outline-text-2" id="text-2">
|
||||||
|
<p>
|
||||||
|
The goal in this section is the estimate the noise of both the encoder and the intereferometer.
|
||||||
|
</p>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org169c9b3" class="outline-3">
|
||||||
|
<h3 id="org169c9b3"><span class="section-number-3">2.1</span> Load Data</h3>
|
||||||
|
<div class="outline-text-3" id="text-2-1">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">load(<span class="org-string">'mat/int_enc_huddle_test.mat'</span>, <span class="org-string">'interferometer'</span>, <span class="org-string">'encoder'</span>, <span class="org-string">'t'</span>);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">interferometer = detrend(interferometer, 0);
|
||||||
|
encoder = detrend(encoder, 0);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org71d6eed" class="outline-3">
|
||||||
|
<h3 id="org71d6eed"><span class="section-number-3">2.2</span> Time Domain Results</h3>
|
||||||
|
<div class="outline-text-3" id="text-2-2">
|
||||||
|
|
||||||
|
<div id="org06a0d1c" class="figure">
|
||||||
|
<p><img src="figs/huddle_test_time_domain.png" alt="huddle_test_time_domain.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 4: </span>Huddle test - Time domain signals</p>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">G_lpf = 1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>10);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="orgee9ad22" class="figure">
|
||||||
|
<p><img src="figs/huddle_test_time_domain_filtered.png" alt="huddle_test_time_domain_filtered.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 5: </span>Huddle test - Time domain signals filtered with a LPF at 10Hz</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org526b687" class="outline-3">
|
||||||
|
<h3 id="org526b687"><span class="section-number-3">2.3</span> Frequency Domain Noise</h3>
|
||||||
|
<div class="outline-text-3" id="text-2-3">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">Ts = 1e<span class="org-type">-</span>4;
|
||||||
|
win = hann(ceil(10<span class="org-type">/</span>Ts));
|
||||||
|
|
||||||
|
[p_i, f] = pwelch(interferometer, win, [], [], 1<span class="org-type">/</span>Ts);
|
||||||
|
[p_e, <span class="org-type">~</span>] = pwelch(encoder, win, [], [], 1<span class="org-type">/</span>Ts);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org7e02bb2" class="figure">
|
||||||
|
<p><img src="figs/huddle_test_asd.png" alt="huddle_test_asd.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 6: </span>Amplitude Spectral Density of the signals during the Huddle test</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org25a61fe" class="outline-2">
|
||||||
|
<h2 id="org25a61fe"><span class="section-number-2">3</span> Comparison Interferometer / Encoder</h2>
|
||||||
|
<div class="outline-text-2" id="text-3">
|
||||||
|
<p>
|
||||||
|
The goal here is to make sure that the interferometer and encoder measurements are coherent.
|
||||||
|
We may see non-linearity in the interferometric measurement.
|
||||||
|
</p>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orgb31234a" class="outline-3">
|
||||||
|
<h3 id="orgb31234a"><span class="section-number-3">3.1</span> Load Data</h3>
|
||||||
|
<div class="outline-text-3" id="text-3-1">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">load(<span class="org-string">'mat/int_enc_comp.mat'</span>, <span class="org-string">'interferometer'</span>, <span class="org-string">'encoder'</span>, <span class="org-string">'u'</span>, <span class="org-string">'t'</span>);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">interferometer = detrend(interferometer, 0);
|
||||||
|
encoder = detrend(encoder, 0);
|
||||||
|
u = detrend(u, 0);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org4fa5441" class="outline-3">
|
||||||
|
<h3 id="org4fa5441"><span class="section-number-3">3.2</span> Time Domain Results</h3>
|
||||||
|
<div class="outline-text-3" id="text-3-2">
|
||||||
|
|
||||||
|
<div id="org486d613" class="figure">
|
||||||
|
<p><img src="figs/int_enc_one_cycle.png" alt="int_enc_one_cycle.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 7: </span>One cycle measurement</p>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org2bb119e" class="figure">
|
||||||
|
<p><img src="figs/int_enc_one_cycle_error.png" alt="int_enc_one_cycle_error.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 8: </span>Difference between the Encoder and the interferometer during one cycle</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orge79e200" class="outline-3">
|
||||||
|
<h3 id="orge79e200"><span class="section-number-3">3.3</span> Difference between Encoder and Interferometer as a function of time</h3>
|
||||||
|
<div class="outline-text-3" id="text-3-3">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">Ts = 1e<span class="org-type">-</span>4;
|
||||||
|
d_i_mean = reshape(interferometer, [2<span class="org-type">/</span>Ts floor(Ts<span class="org-type">/</span>2<span class="org-type">*</span>length(interferometer))]);
|
||||||
|
d_e_mean = reshape(encoder, [2<span class="org-type">/</span>Ts floor(Ts<span class="org-type">/</span>2<span class="org-type">*</span>length(encoder))]);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">w0 = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>5; <span class="org-comment">% [rad/s]</span>
|
||||||
|
xi = 0.7;
|
||||||
|
|
||||||
|
G_lpf = 1<span class="org-type">/</span>(1 <span class="org-type">+</span> 2<span class="org-type">*</span>xi<span class="org-type">/</span>w0<span class="org-type">*</span>s <span class="org-type">+</span> s<span class="org-type">^</span>2<span class="org-type">/</span>w0<span class="org-type">^</span>2);
|
||||||
|
|
||||||
|
d_err_mean = reshape(lsim(G_lpf, encoder <span class="org-type">-</span> interferometer, t), [2<span class="org-type">/</span>Ts floor(Ts<span class="org-type">/</span>2<span class="org-type">*</span>length(encoder))]);
|
||||||
|
d_err_mean = d_err_mean <span class="org-type">-</span> mean(d_err_mean);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="orgf0015d1" class="figure">
|
||||||
|
<p><img src="figs/int_enc_error_mean_time.png" alt="int_enc_error_mean_time.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 9: </span>Difference between the two measurement in the time domain, averaged for all the cycles</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org625a811" class="outline-3">
|
||||||
|
<h3 id="org625a811"><span class="section-number-3">3.4</span> Difference between Encoder and Interferometer as a function of position</h3>
|
||||||
|
<div class="outline-text-3" id="text-3-4">
|
||||||
|
<p>
|
||||||
|
Compute the mean of the interferometer measurement corresponding to each of the encoder measurement.
|
||||||
|
</p>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">[e_sorted, <span class="org-type">~</span>, e_ind] = unique(encoder);
|
||||||
|
|
||||||
|
i_mean = zeros(length(e_sorted), 1);
|
||||||
|
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(e_sorted)</span>
|
||||||
|
i_mean(<span class="org-constant">i</span>) = mean(interferometer(e_ind <span class="org-type">==</span> <span class="org-constant">i</span>));
|
||||||
|
<span class="org-keyword">end</span>
|
||||||
|
|
||||||
|
i_mean_error = (i_mean <span class="org-type">-</span> e_sorted);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="orgd4f6d77" class="figure">
|
||||||
|
<p><img src="figs/int_enc_error_mean_position.png" alt="int_enc_error_mean_position.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 10: </span>Difference between the two measurement as a function of the measured position by the encoder, averaged for all the cycles</p>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The period of the non-linearity seems to be \(1.53 \mu m\) which corresponds to the wavelength of the Laser.
|
||||||
|
</p>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">win_length = 1530; <span class="org-comment">% length of the windows (corresponds to 1.53 um)</span>
|
||||||
|
num_avg = floor(length(e_sorted)<span class="org-type">/</span>win_length); <span class="org-comment">% number of averaging</span>
|
||||||
|
|
||||||
|
i_init = ceil((length(e_sorted) <span class="org-type">-</span> win_length<span class="org-type">*</span>num_avg)<span class="org-type">/</span>2); <span class="org-comment">% does not start at the extremity</span>
|
||||||
|
|
||||||
|
e_sorted_mean_over_period = mean(reshape(i_mean_error(i_init<span class="org-type">:</span>i_init<span class="org-type">+</span>win_length<span class="org-type">*</span>num_avg<span class="org-type">-</span>1), [win_length num_avg]), 2);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="orgb5a621e" class="figure">
|
||||||
|
<p><img src="figs/int_non_linearity_period_wavelength.png" alt="int_non_linearity_period_wavelength.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 11: </span>Non-Linearity of the Interferometer over the period of the wavelength</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org2e4bf3b" class="outline-2">
|
||||||
|
<h2 id="org2e4bf3b"><span class="section-number-2">4</span> Identification</h2>
|
||||||
|
<div class="outline-text-2" id="text-4">
|
||||||
|
</div>
|
||||||
|
<div id="outline-container-org8a892bd" class="outline-3">
|
||||||
|
<h3 id="org8a892bd"><span class="section-number-3">4.1</span> Load Data</h3>
|
||||||
|
<div class="outline-text-3" id="text-4-1">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">load(<span class="org-string">'mat/int_enc_id_noise_bis.mat'</span>, <span class="org-string">'interferometer'</span>, <span class="org-string">'encoder'</span>, <span class="org-string">'u'</span>, <span class="org-string">'t'</span>);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">interferometer = detrend(interferometer, 0);
|
||||||
|
encoder = detrend(encoder, 0);
|
||||||
|
u = detrend(u, 0);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org7e3c2ba" class="outline-3">
|
||||||
|
<h3 id="org7e3c2ba"><span class="section-number-3">4.2</span> Identification</h3>
|
||||||
|
<div class="outline-text-3" id="text-4-2">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">Ts = 1e<span class="org-type">-</span>4; <span class="org-comment">% Sampling Time [s]</span>
|
||||||
|
win = hann(ceil(10<span class="org-type">/</span>Ts));
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">[tf_i_est, f] = tfestimate(u, interferometer, win, [], [], 1<span class="org-type">/</span>Ts);
|
||||||
|
[co_i_est, <span class="org-type">~</span>] = mscohere(u, interferometer, win, [], [], 1<span class="org-type">/</span>Ts);
|
||||||
|
|
||||||
|
[tf_e_est, <span class="org-type">~</span>] = tfestimate(u, encoder, win, [], [], 1<span class="org-type">/</span>Ts);
|
||||||
|
[co_e_est, <span class="org-type">~</span>] = mscohere(u, encoder, win, [], [], 1<span class="org-type">/</span>Ts);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org801d42d" class="figure">
|
||||||
|
<p><img src="figs/identification_dynamics_coherence.png" alt="identification_dynamics_coherence.png" />
|
||||||
|
</p>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org7f77bc5" class="figure">
|
||||||
|
<p><img src="figs/identification_dynamics_bode.png" alt="identification_dynamics_bode.png" />
|
||||||
|
</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div id="postamble" class="status">
|
||||||
|
<p class="author">Author: Dehaeze Thomas</p>
|
||||||
|
<p class="date">Created: 2020-10-23 ven. 23:04</p>
|
||||||
|
</div>
|
||||||
|
</body>
|
||||||
|
</html>
|
||||||
403
index.org
Normal file
403
index.org
Normal file
@ -0,0 +1,403 @@
|
|||||||
|
#+TITLE: Encoder - Test Bench
|
||||||
|
:DRAWER:
|
||||||
|
#+LANGUAGE: en
|
||||||
|
#+EMAIL: dehaeze.thomas@gmail.com
|
||||||
|
#+AUTHOR: Dehaeze Thomas
|
||||||
|
|
||||||
|
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
|
||||||
|
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
|
||||||
|
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/zenburn.css"/>
|
||||||
|
#+HTML_HEAD: <script type="text/javascript" src="./js/jquery.min.js"></script>
|
||||||
|
#+HTML_HEAD: <script type="text/javascript" src="./js/bootstrap.min.js"></script>
|
||||||
|
#+HTML_HEAD: <script type="text/javascript" src="./js/jquery.stickytableheaders.min.js"></script>
|
||||||
|
#+HTML_HEAD: <script type="text/javascript" src="./js/readtheorg.js"></script>
|
||||||
|
|
||||||
|
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/tikz/org/}{config.tex}")
|
||||||
|
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
|
||||||
|
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
|
||||||
|
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
|
||||||
|
#+PROPERTY: header-args:latex+ :results raw replace :buffer no
|
||||||
|
#+PROPERTY: header-args:latex+ :eval no-export
|
||||||
|
#+PROPERTY: header-args:latex+ :exports both
|
||||||
|
#+PROPERTY: header-args:latex+ :mkdirp yes
|
||||||
|
#+PROPERTY: header-args:latex+ :output-dir figs
|
||||||
|
#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
|
||||||
|
|
||||||
|
#+PROPERTY: header-args:matlab :session *MATLAB*
|
||||||
|
#+PROPERTY: header-args:matlab+ :tangle script.m
|
||||||
|
#+PROPERTY: header-args:matlab+ :comments org
|
||||||
|
#+PROPERTY: header-args:matlab+ :exports both
|
||||||
|
#+PROPERTY: header-args:matlab+ :results none
|
||||||
|
#+PROPERTY: header-args:matlab+ :eval no-export
|
||||||
|
#+PROPERTY: header-args:matlab+ :noweb yes
|
||||||
|
#+PROPERTY: header-args:matlab+ :mkdirp yes
|
||||||
|
#+PROPERTY: header-args:matlab+ :output-dir figs
|
||||||
|
:END:
|
||||||
|
|
||||||
|
* Experimental Setup
|
||||||
|
The experimental Setup is schematically represented in Figure [[fig:exp_setup_schematic]].
|
||||||
|
|
||||||
|
The mass can be vertically moved using the amplified piezoelectric actuator.
|
||||||
|
The displacement of the mass (relative to the mechanical frame) is measured both by the interferometer and by the encoder.
|
||||||
|
|
||||||
|
#+name: fig:exp_setup_schematic
|
||||||
|
#+caption: Schematic of the Experiment
|
||||||
|
[[file:figs/exp_setup_schematic.png]]
|
||||||
|
|
||||||
|
#+name: fig:encoder_side_view
|
||||||
|
#+caption: Side View of the encoder
|
||||||
|
[[file:figs/IMG_20201023_153905.jpg]]
|
||||||
|
|
||||||
|
#+name: fig:encoder_front_view
|
||||||
|
#+caption: Front View of the encoder
|
||||||
|
[[file:figs/IMG_20201023_153914.jpg]]
|
||||||
|
|
||||||
|
* Huddle Test
|
||||||
|
** Introduction :ignore:
|
||||||
|
The goal in this section is the estimate the noise of both the encoder and the intereferometer.
|
||||||
|
|
||||||
|
** Matlab Init :noexport:ignore:
|
||||||
|
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||||
|
<<matlab-dir>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none :results silent :noweb yes
|
||||||
|
<<matlab-init>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
** Load Data
|
||||||
|
#+begin_src matlab
|
||||||
|
load('mat/int_enc_huddle_test.mat', 'interferometer', 'encoder', 't');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab
|
||||||
|
interferometer = detrend(interferometer, 0);
|
||||||
|
encoder = detrend(encoder, 0);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
** Time Domain Results
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
plot(t, encoder, 'DisplayName', 'Encoder')
|
||||||
|
plot(t, interferometer, 'DisplayName', 'Interferometer')
|
||||||
|
hold off;
|
||||||
|
xlabel('Time [s]'); ylabel('Displacement [m]');
|
||||||
|
legend('location', 'northeast');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :tangle no :exports results :results file replace
|
||||||
|
exportFig('figs/huddle_test_time_domain.pdf', 'width', 'wide', 'height', 'normal');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+name: fig:huddle_test_time_domain
|
||||||
|
#+caption: Huddle test - Time domain signals
|
||||||
|
#+RESULTS:
|
||||||
|
[[file:figs/huddle_test_time_domain.png]]
|
||||||
|
|
||||||
|
#+begin_src matlab
|
||||||
|
G_lpf = 1/(1 + s/2/pi/10);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
plot(t, lsim(G_lpf, encoder, t), 'DisplayName', 'Encoder')
|
||||||
|
plot(t, lsim(G_lpf, interferometer, t), 'DisplayName', 'Interferometer')
|
||||||
|
hold off;
|
||||||
|
xlabel('Time [s]'); ylabel('Displacement [m]');
|
||||||
|
legend('location', 'northeast');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :tangle no :exports results :results file replace
|
||||||
|
exportFig('figs/huddle_test_time_domain_filtered.pdf', 'width', 'wide', 'height', 'normal');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+name: fig:huddle_test_time_domain_filtered
|
||||||
|
#+caption: Huddle test - Time domain signals filtered with a LPF at 10Hz
|
||||||
|
#+RESULTS:
|
||||||
|
[[file:figs/huddle_test_time_domain_filtered.png]]
|
||||||
|
|
||||||
|
** Frequency Domain Noise
|
||||||
|
#+begin_src matlab
|
||||||
|
Ts = 1e-4;
|
||||||
|
win = hann(ceil(10/Ts));
|
||||||
|
|
||||||
|
[p_i, f] = pwelch(interferometer, win, [], [], 1/Ts);
|
||||||
|
[p_e, ~] = pwelch(encoder, win, [], [], 1/Ts);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
plot(f, sqrt(p_i), 'DisplayName', 'Interferometer');
|
||||||
|
plot(f, sqrt(p_e), 'DisplayName', 'Encoder');
|
||||||
|
hold off;
|
||||||
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||||
|
ylabel('ASD [$m/\sqrt{Hz}$]'); xlabel('Frequency [Hz]');
|
||||||
|
legend();
|
||||||
|
xlim([1e-1, 5e3]);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :tangle no :exports results :results file replace
|
||||||
|
exportFig('figs/huddle_test_asd.pdf', 'width', 'wide', 'height', 'tall');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+name: fig:huddle_test_asd
|
||||||
|
#+caption: Amplitude Spectral Density of the signals during the Huddle test
|
||||||
|
#+RESULTS:
|
||||||
|
[[file:figs/huddle_test_asd.png]]
|
||||||
|
|
||||||
|
* Comparison Interferometer / Encoder
|
||||||
|
** Introduction :ignore:
|
||||||
|
The goal here is to make sure that the interferometer and encoder measurements are coherent.
|
||||||
|
We may see non-linearity in the interferometric measurement.
|
||||||
|
|
||||||
|
** Matlab Init :noexport:ignore:
|
||||||
|
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||||
|
<<matlab-dir>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none :results silent :noweb yes
|
||||||
|
<<matlab-init>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
** Load Data
|
||||||
|
#+begin_src matlab
|
||||||
|
load('mat/int_enc_comp.mat', 'interferometer', 'encoder', 'u', 't');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab
|
||||||
|
interferometer = detrend(interferometer, 0);
|
||||||
|
encoder = detrend(encoder, 0);
|
||||||
|
u = detrend(u, 0);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
** Time Domain Results
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
plot(t, encoder, '-', 'DisplayName', 'Encoder')
|
||||||
|
plot(t, interferometer, '--', 'DisplayName', 'Interferometer')
|
||||||
|
hold off;
|
||||||
|
xlabel('Time [s]'); ylabel('Displacement [m]');
|
||||||
|
legend('location', 'northeast');
|
||||||
|
xlim([50, 52])
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :tangle no :exports results :results file replace
|
||||||
|
exportFig('figs/int_enc_one_cycle.pdf', 'width', 'wide', 'height', 'normal');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+name: fig:int_enc_one_cycle
|
||||||
|
#+caption: One cycle measurement
|
||||||
|
#+RESULTS:
|
||||||
|
[[file:figs/int_enc_one_cycle.png]]
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
plot(t, encoder - interferometer, 'DisplayName', 'Difference')
|
||||||
|
hold off;
|
||||||
|
xlabel('Time [s]'); ylabel('Displacement [m]');
|
||||||
|
legend('location', 'northeast');
|
||||||
|
xlim([50, 52])
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :tangle no :exports results :results file replace
|
||||||
|
exportFig('figs/int_enc_one_cycle_error.pdf', 'width', 'wide', 'height', 'normal');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+name: fig:int_enc_one_cycle_error
|
||||||
|
#+caption: Difference between the Encoder and the interferometer during one cycle
|
||||||
|
#+RESULTS:
|
||||||
|
[[file:figs/int_enc_one_cycle_error.png]]
|
||||||
|
|
||||||
|
** Difference between Encoder and Interferometer as a function of time
|
||||||
|
#+begin_src matlab
|
||||||
|
Ts = 1e-4;
|
||||||
|
d_i_mean = reshape(interferometer, [2/Ts floor(Ts/2*length(interferometer))]);
|
||||||
|
d_e_mean = reshape(encoder, [2/Ts floor(Ts/2*length(encoder))]);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab
|
||||||
|
w0 = 2*pi*5; % [rad/s]
|
||||||
|
xi = 0.7;
|
||||||
|
|
||||||
|
G_lpf = 1/(1 + 2*xi/w0*s + s^2/w0^2);
|
||||||
|
|
||||||
|
d_err_mean = reshape(lsim(G_lpf, encoder - interferometer, t), [2/Ts floor(Ts/2*length(encoder))]);
|
||||||
|
d_err_mean = d_err_mean - mean(d_err_mean);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
for i_i = 1:size(d_err_mean, 2)
|
||||||
|
plot(t(1:size(d_err_mean, 1)), d_err_mean(:, i_i), 'k-')
|
||||||
|
end
|
||||||
|
plot(t(1:size(d_err_mean, 1)), mean(d_err_mean, 2), 'r-')
|
||||||
|
hold off;
|
||||||
|
xlabel('Time [s]'); ylabel('Displacement [m]');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :tangle no :exports results :results file replace
|
||||||
|
exportFig('figs/int_enc_error_mean_time.pdf', 'width', 'wide', 'height', 'normal', 'pdf', false);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+name: fig:int_enc_error_mean_time
|
||||||
|
#+caption: Difference between the two measurement in the time domain, averaged for all the cycles
|
||||||
|
#+RESULTS:
|
||||||
|
[[file:figs/int_enc_error_mean_time.png]]
|
||||||
|
|
||||||
|
** Difference between Encoder and Interferometer as a function of position
|
||||||
|
Compute the mean of the interferometer measurement corresponding to each of the encoder measurement.
|
||||||
|
|
||||||
|
#+begin_src matlab
|
||||||
|
[e_sorted, ~, e_ind] = unique(encoder);
|
||||||
|
|
||||||
|
i_mean = zeros(length(e_sorted), 1);
|
||||||
|
for i = 1:length(e_sorted)
|
||||||
|
i_mean(i) = mean(interferometer(e_ind == i));
|
||||||
|
end
|
||||||
|
|
||||||
|
i_mean_error = (i_mean - e_sorted);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
% plot(encoder, interferometer - encoder, 'k.', 'DisplayName', 'Difference')
|
||||||
|
plot(1e6*(e_sorted), 1e9*(i_mean_error))
|
||||||
|
hold off;
|
||||||
|
xlabel('Encoder Measurement [$\mu m$]'); ylabel('Measrement Error [nm]');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :tangle no :exports results :results file replace
|
||||||
|
exportFig('figs/int_enc_error_mean_position.pdf', 'width', 'wide', 'height', 'normal');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+name: fig:int_enc_error_mean_position
|
||||||
|
#+caption: Difference between the two measurement as a function of the measured position by the encoder, averaged for all the cycles
|
||||||
|
#+RESULTS:
|
||||||
|
[[file:figs/int_enc_error_mean_position.png]]
|
||||||
|
|
||||||
|
The period of the non-linearity seems to be $1.53 \mu m$ which corresponds to the wavelength of the Laser.
|
||||||
|
|
||||||
|
#+begin_src matlab
|
||||||
|
win_length = 1530; % length of the windows (corresponds to 1.53 um)
|
||||||
|
num_avg = floor(length(e_sorted)/win_length); % number of averaging
|
||||||
|
|
||||||
|
i_init = ceil((length(e_sorted) - win_length*num_avg)/2); % does not start at the extremity
|
||||||
|
|
||||||
|
e_sorted_mean_over_period = mean(reshape(i_mean_error(i_init:i_init+win_length*num_avg-1), [win_length num_avg]), 2);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
plot(1e-3*(0:win_length-1), e_sorted_mean_over_period)
|
||||||
|
hold off;
|
||||||
|
xlabel('Displacement [$\mu m$]'); ylabel('Measurement Non-Linearity [nm]');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :tangle no :exports results :results file replace
|
||||||
|
exportFig('figs/int_non_linearity_period_wavelength.pdf', 'width', 'wide', 'height', 'tall');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+name: fig:int_non_linearity_period_wavelength
|
||||||
|
#+caption: Non-Linearity of the Interferometer over the period of the wavelength
|
||||||
|
#+RESULTS:
|
||||||
|
[[file:figs/int_non_linearity_period_wavelength.png]]
|
||||||
|
|
||||||
|
* Identification
|
||||||
|
** Matlab Init :noexport:ignore:
|
||||||
|
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||||
|
<<matlab-dir>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none :results silent :noweb yes
|
||||||
|
<<matlab-init>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
** Load Data
|
||||||
|
#+begin_src matlab
|
||||||
|
load('mat/int_enc_id_noise_bis.mat', 'interferometer', 'encoder', 'u', 't');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab
|
||||||
|
interferometer = detrend(interferometer, 0);
|
||||||
|
encoder = detrend(encoder, 0);
|
||||||
|
u = detrend(u, 0);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
** Identification
|
||||||
|
#+begin_src matlab
|
||||||
|
Ts = 1e-4; % Sampling Time [s]
|
||||||
|
win = hann(ceil(10/Ts));
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab
|
||||||
|
[tf_i_est, f] = tfestimate(u, interferometer, win, [], [], 1/Ts);
|
||||||
|
[co_i_est, ~] = mscohere(u, interferometer, win, [], [], 1/Ts);
|
||||||
|
|
||||||
|
[tf_e_est, ~] = tfestimate(u, encoder, win, [], [], 1/Ts);
|
||||||
|
[co_e_est, ~] = mscohere(u, encoder, win, [], [], 1/Ts);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
plot(f, co_i_est, '-')
|
||||||
|
plot(f, co_e_est, '-')
|
||||||
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
|
||||||
|
ylabel('Coherence'); xlabel('Frequency [Hz]');
|
||||||
|
hold off;
|
||||||
|
xlim([0.5, 5e3]);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :tangle no :exports results :results file replace
|
||||||
|
exportFig('figs/identification_dynamics_coherence.pdf', 'width', 'normal', 'height', 'normal');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+name: fig:identification_dynamics_coherence
|
||||||
|
#+caption:
|
||||||
|
#+RESULTS:
|
||||||
|
[[file:figs/identification_dynamics_coherence.png]]
|
||||||
|
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
figure;
|
||||||
|
tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||||
|
|
||||||
|
ax1 = nexttile;
|
||||||
|
hold on;
|
||||||
|
plot(f, abs(tf_i_est), '-', 'DisplayName', 'Int')
|
||||||
|
plot(f, abs(tf_e_est), '-', 'DisplayName', 'Enc')
|
||||||
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||||
|
ylabel('Amplitude'); set(gca, 'XTickLabel',[]);
|
||||||
|
hold off;
|
||||||
|
ylim([1e-7, 3e-4]);
|
||||||
|
|
||||||
|
ax2 = nexttile;
|
||||||
|
hold on;
|
||||||
|
plot(f, 180/pi*angle(tf_i_est), '-')
|
||||||
|
plot(f, 180/pi*angle(tf_e_est), '-')
|
||||||
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
|
||||||
|
ylabel('Phase'); xlabel('Frequency [Hz]');
|
||||||
|
hold off;
|
||||||
|
yticks(-360:90:360);
|
||||||
|
axis padded 'auto x'
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2], 'x');
|
||||||
|
xlim([0.5, 5e3]);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :tangle no :exports results :results file replace
|
||||||
|
exportFig('figs/identification_dynamics_bode.pdf', 'width', 'wide', 'height', 'tall');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+name: fig:identification_dynamics_bode
|
||||||
|
#+caption:
|
||||||
|
#+RESULTS:
|
||||||
|
[[file:figs/identification_dynamics_bode.png]]
|
||||||
7
js/bootstrap.min.js
vendored
Normal file
7
js/bootstrap.min.js
vendored
Normal file
File diff suppressed because one or more lines are too long
4
js/jquery.min.js
vendored
Normal file
4
js/jquery.min.js
vendored
Normal file
File diff suppressed because one or more lines are too long
1
js/jquery.stickytableheaders.min.js
vendored
Normal file
1
js/jquery.stickytableheaders.min.js
vendored
Normal file
@ -0,0 +1 @@
|
|||||||
|
!function(a,b){"use strict";function c(c,g){var h=this;h.$el=a(c),h.el=c,h.id=e++,h.$window=a(b),h.$document=a(document),h.$el.bind("destroyed",a.proxy(h.teardown,h)),h.$clonedHeader=null,h.$originalHeader=null,h.isSticky=!1,h.hasBeenSticky=!1,h.leftOffset=null,h.topOffset=null,h.init=function(){h.$el.each(function(){var b=a(this);b.css("padding",0),h.$originalHeader=a("thead:first",this),h.$clonedHeader=h.$originalHeader.clone(),b.trigger("clonedHeader."+d,[h.$clonedHeader]),h.$clonedHeader.addClass("tableFloatingHeader"),h.$clonedHeader.css("display","none"),h.$originalHeader.addClass("tableFloatingHeaderOriginal"),h.$originalHeader.after(h.$clonedHeader),h.$printStyle=a('<style type="text/css" media="print">.tableFloatingHeader{display:none !important;}.tableFloatingHeaderOriginal{position:static !important;}</style>'),a("head").append(h.$printStyle)}),h.setOptions(g),h.updateWidth(),h.toggleHeaders(),h.bind()},h.destroy=function(){h.$el.unbind("destroyed",h.teardown),h.teardown()},h.teardown=function(){h.isSticky&&h.$originalHeader.css("position","static"),a.removeData(h.el,"plugin_"+d),h.unbind(),h.$clonedHeader.remove(),h.$originalHeader.removeClass("tableFloatingHeaderOriginal"),h.$originalHeader.css("visibility","visible"),h.$printStyle.remove(),h.el=null,h.$el=null},h.bind=function(){h.$scrollableArea.on("scroll."+d,h.toggleHeaders),h.isWindowScrolling||(h.$window.on("scroll."+d+h.id,h.setPositionValues),h.$window.on("resize."+d+h.id,h.toggleHeaders)),h.$scrollableArea.on("resize."+d,h.toggleHeaders),h.$scrollableArea.on("resize."+d,h.updateWidth)},h.unbind=function(){h.$scrollableArea.off("."+d,h.toggleHeaders),h.isWindowScrolling||(h.$window.off("."+d+h.id,h.setPositionValues),h.$window.off("."+d+h.id,h.toggleHeaders)),h.$scrollableArea.off("."+d,h.updateWidth)},h.toggleHeaders=function(){h.$el&&h.$el.each(function(){var b,c=a(this),d=h.isWindowScrolling?isNaN(h.options.fixedOffset)?h.options.fixedOffset.outerHeight():h.options.fixedOffset:h.$scrollableArea.offset().top+(isNaN(h.options.fixedOffset)?0:h.options.fixedOffset),e=c.offset(),f=h.$scrollableArea.scrollTop()+d,g=h.$scrollableArea.scrollLeft(),i=h.isWindowScrolling?f>e.top:d>e.top,j=(h.isWindowScrolling?f:0)<e.top+c.height()-h.$clonedHeader.height()-(h.isWindowScrolling?0:d);i&&j?(b=e.left-g+h.options.leftOffset,h.$originalHeader.css({position:"fixed","margin-top":h.options.marginTop,left:b,"z-index":3}),h.leftOffset=b,h.topOffset=d,h.$clonedHeader.css("display",""),h.isSticky||(h.isSticky=!0,h.updateWidth()),h.setPositionValues()):h.isSticky&&(h.$originalHeader.css("position","static"),h.$clonedHeader.css("display","none"),h.isSticky=!1,h.resetWidth(a("td,th",h.$clonedHeader),a("td,th",h.$originalHeader)))})},h.setPositionValues=function(){var a=h.$window.scrollTop(),b=h.$window.scrollLeft();!h.isSticky||0>a||a+h.$window.height()>h.$document.height()||0>b||b+h.$window.width()>h.$document.width()||h.$originalHeader.css({top:h.topOffset-(h.isWindowScrolling?0:a),left:h.leftOffset-(h.isWindowScrolling?0:b)})},h.updateWidth=function(){if(h.isSticky){h.$originalHeaderCells||(h.$originalHeaderCells=a("th,td",h.$originalHeader)),h.$clonedHeaderCells||(h.$clonedHeaderCells=a("th,td",h.$clonedHeader));var b=h.getWidth(h.$clonedHeaderCells);h.setWidth(b,h.$clonedHeaderCells,h.$originalHeaderCells),h.$originalHeader.css("width",h.$clonedHeader.width())}},h.getWidth=function(c){var d=[];return c.each(function(c){var e,f=a(this);if("border-box"===f.css("box-sizing"))e=f[0].getBoundingClientRect().width;else{var g=a("th",h.$originalHeader);if("collapse"===g.css("border-collapse"))if(b.getComputedStyle)e=parseFloat(b.getComputedStyle(this,null).width);else{var i=parseFloat(f.css("padding-left")),j=parseFloat(f.css("padding-right")),k=parseFloat(f.css("border-width"));e=f.outerWidth()-i-j-k}else e=f.width()}d[c]=e}),d},h.setWidth=function(a,b,c){b.each(function(b){var d=a[b];c.eq(b).css({"min-width":d,"max-width":d})})},h.resetWidth=function(b,c){b.each(function(b){var d=a(this);c.eq(b).css({"min-width":d.css("min-width"),"max-width":d.css("max-width")})})},h.setOptions=function(c){h.options=a.extend({},f,c),h.$scrollableArea=a(h.options.scrollableArea),h.isWindowScrolling=h.$scrollableArea[0]===b},h.updateOptions=function(a){h.setOptions(a),h.unbind(),h.bind(),h.updateWidth(),h.toggleHeaders()},h.init()}var d="stickyTableHeaders",e=0,f={fixedOffset:0,leftOffset:0,marginTop:0,scrollableArea:b};a.fn[d]=function(b){return this.each(function(){var e=a.data(this,"plugin_"+d);e?"string"==typeof b?e[b].apply(e):e.updateOptions(b):"destroy"!==b&&a.data(this,"plugin_"+d,new c(this,b))})}}(jQuery,window);
|
||||||
85
js/readtheorg.js
Normal file
85
js/readtheorg.js
Normal file
@ -0,0 +1,85 @@
|
|||||||
|
$(function() {
|
||||||
|
$('.note').before("<p class='admonition-title note'>Note</p>");
|
||||||
|
$('.seealso').before("<p class='admonition-title seealso'>See also</p>");
|
||||||
|
$('.warning').before("<p class='admonition-title warning'>Warning</p>");
|
||||||
|
$('.caution').before("<p class='admonition-title caution'>Caution</p>");
|
||||||
|
$('.attention').before("<p class='admonition-title attention'>Attention</p>");
|
||||||
|
$('.tip').before("<p class='admonition-title tip'>Tip</p>");
|
||||||
|
$('.important').before("<p class='admonition-title important'>Important</p>");
|
||||||
|
$('.hint').before("<p class='admonition-title hint'>Hint</p>");
|
||||||
|
$('.error').before("<p class='admonition-title error'>Error</p>");
|
||||||
|
$('.danger').before("<p class='admonition-title danger'>Danger</p>");
|
||||||
|
});
|
||||||
|
|
||||||
|
$( document ).ready(function() {
|
||||||
|
|
||||||
|
// Shift nav in mobile when clicking the menu.
|
||||||
|
$(document).on('click', "[data-toggle='wy-nav-top']", function() {
|
||||||
|
$("[data-toggle='wy-nav-shift']").toggleClass("shift");
|
||||||
|
$("[data-toggle='rst-versions']").toggleClass("shift");
|
||||||
|
});
|
||||||
|
// Close menu when you click a link.
|
||||||
|
$(document).on('click', ".wy-menu-vertical .current ul li a", function() {
|
||||||
|
$("[data-toggle='wy-nav-shift']").removeClass("shift");
|
||||||
|
$("[data-toggle='rst-versions']").toggleClass("shift");
|
||||||
|
});
|
||||||
|
$(document).on('click', "[data-toggle='rst-current-version']", function() {
|
||||||
|
$("[data-toggle='rst-versions']").toggleClass("shift-up");
|
||||||
|
});
|
||||||
|
// Make tables responsive
|
||||||
|
$("table.docutils:not(.field-list)").wrap("<div class='wy-table-responsive'></div>");
|
||||||
|
});
|
||||||
|
|
||||||
|
$( document ).ready(function() {
|
||||||
|
$('#text-table-of-contents ul').first().addClass('nav');
|
||||||
|
// ScrollSpy also requires that we use
|
||||||
|
// a Bootstrap nav component.
|
||||||
|
$('body').scrollspy({target: '#text-table-of-contents'});
|
||||||
|
|
||||||
|
// add sticky table headers
|
||||||
|
$('table').stickyTableHeaders();
|
||||||
|
|
||||||
|
// set the height of tableOfContents
|
||||||
|
var $postamble = $('#postamble');
|
||||||
|
var $tableOfContents = $('#table-of-contents');
|
||||||
|
$tableOfContents.css({paddingBottom: $postamble.outerHeight()});
|
||||||
|
|
||||||
|
// add TOC button
|
||||||
|
var toggleSidebar = $('<div id="toggle-sidebar"><a href="#table-of-contents"><h2>Table of Contents</h2></a></div>');
|
||||||
|
$('#content').prepend(toggleSidebar);
|
||||||
|
|
||||||
|
// add close button when sidebar showed in mobile screen
|
||||||
|
var closeBtn = $('<a class="close-sidebar" href="#">Close</a>');
|
||||||
|
var tocTitle = $('#table-of-contents').find('h2');
|
||||||
|
tocTitle.append(closeBtn);
|
||||||
|
});
|
||||||
|
|
||||||
|
window.SphinxRtdTheme = (function (jquery) {
|
||||||
|
var stickyNav = (function () {
|
||||||
|
var navBar,
|
||||||
|
win,
|
||||||
|
stickyNavCssClass = 'stickynav',
|
||||||
|
applyStickNav = function () {
|
||||||
|
if (navBar.height() <= win.height()) {
|
||||||
|
navBar.addClass(stickyNavCssClass);
|
||||||
|
} else {
|
||||||
|
navBar.removeClass(stickyNavCssClass);
|
||||||
|
}
|
||||||
|
},
|
||||||
|
enable = function () {
|
||||||
|
applyStickNav();
|
||||||
|
win.on('resize', applyStickNav);
|
||||||
|
},
|
||||||
|
init = function () {
|
||||||
|
navBar = jquery('nav.wy-nav-side:first');
|
||||||
|
win = jquery(window);
|
||||||
|
};
|
||||||
|
jquery(init);
|
||||||
|
return {
|
||||||
|
enable : enable
|
||||||
|
};
|
||||||
|
}());
|
||||||
|
return {
|
||||||
|
StickyNav : stickyNav
|
||||||
|
};
|
||||||
|
}($));
|
||||||
Loading…
Reference in New Issue
Block a user