Add CSS/JS. Add plant identification scripts
This commit is contained in:
parent
595d6c5188
commit
c2607b8218
145
css/htmlize.css
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145
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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1095
css/readtheorg.css
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1095
css/readtheorg.css
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Load Diff
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figs/frequency_response_matrix.png
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figs/frequency_response_matrix.png
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After Width: | Height: | Size: 180 KiB |
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figs/identification_coherence.png
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figs/identification_coherence.png
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After Width: | Height: | Size: 116 KiB |
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figs/identification_matrix_fit.png
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figs/identification_matrix_fit.png
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After Width: | Height: | Size: 186 KiB |
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figs/identification_ux.png
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figs/identification_ux.png
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After Width: | Height: | Size: 55 KiB |
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figs/identification_uy.png
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figs/identification_uy.png
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After Width: | Height: | Size: 58 KiB |
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figs/weights.png
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figs/weights.png
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After Width: | Height: | Size: 41 KiB |
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index.html
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index.html
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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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<!-- 2019-09-10 mar. 18:15 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<title>Cercalo 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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<style type="text/css">
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<!--/*--><![CDATA[/*><!--*/
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.title { text-align: center;
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margin-bottom: .2em; }
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.subtitle { text-align: center;
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font-size: medium;
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font-weight: bold;
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margin-top:0; }
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.todo { font-family: monospace; color: red; }
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.done { font-family: monospace; color: green; }
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.priority { font-family: monospace; color: orange; }
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.tag { background-color: #eee; font-family: monospace;
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padding: 2px; font-size: 80%; font-weight: normal; }
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.timestamp { color: #bebebe; }
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.timestamp-kwd { color: #5f9ea0; }
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.org-right { margin-left: auto; margin-right: 0px; text-align: right; }
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.org-left { margin-left: 0px; margin-right: auto; text-align: left; }
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.org-center { margin-left: auto; margin-right: auto; text-align: center; }
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.underline { text-decoration: underline; }
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#postamble p, #preamble p { font-size: 90%; margin: .2em; }
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p.verse { margin-left: 3%; }
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pre {
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border: 1px solid #ccc;
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box-shadow: 3px 3px 3px #eee;
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padding: 8pt;
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font-family: monospace;
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overflow: auto;
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margin: 1.2em;
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}
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pre.src {
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position: relative;
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overflow: visible;
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padding-top: 1.2em;
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}
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pre.src:before {
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display: none;
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position: absolute;
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background-color: white;
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top: -10px;
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right: 10px;
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padding: 3px;
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border: 1px solid black;
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}
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pre.src:hover:before { display: inline;}
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/* Languages per Org manual */
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pre.src-asymptote:before { content: 'Asymptote'; }
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pre.src-awk:before { content: 'Awk'; }
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pre.src-C:before { content: 'C'; }
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/* pre.src-C++ doesn't work in CSS */
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pre.src-clojure:before { content: 'Clojure'; }
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pre.src-css:before { content: 'CSS'; }
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pre.src-D:before { content: 'D'; }
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pre.src-ditaa:before { content: 'ditaa'; }
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pre.src-dot:before { content: 'Graphviz'; }
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pre.src-calc:before { content: 'Emacs Calc'; }
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pre.src-emacs-lisp:before { content: 'Emacs Lisp'; }
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pre.src-fortran:before { content: 'Fortran'; }
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pre.src-gnuplot:before { content: 'gnuplot'; }
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pre.src-haskell:before { content: 'Haskell'; }
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pre.src-hledger:before { content: 'hledger'; }
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pre.src-java:before { content: 'Java'; }
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pre.src-js:before { content: 'Javascript'; }
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pre.src-latex:before { content: 'LaTeX'; }
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pre.src-ledger:before { content: 'Ledger'; }
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pre.src-lisp:before { content: 'Lisp'; }
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pre.src-lilypond:before { content: 'Lilypond'; }
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pre.src-lua:before { content: 'Lua'; }
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pre.src-matlab:before { content: 'MATLAB'; }
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pre.src-mscgen:before { content: 'Mscgen'; }
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#org-div-home-and-up
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{ text-align: right; font-size: 70%; white-space: nowrap; }
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textarea { overflow-x: auto; }
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{ background-color: #ffff00; color: #000000; font-weight: bold; }
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/*]]>*/-->
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</style>
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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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/*
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@licstart The following is the entire license notice for the
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JavaScript code in this tag.
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||||||
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|
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|
Copyright (C) 2012-2019 Free Software Foundation, Inc.
|
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The JavaScript code in this tag is free software: you can
|
||||||
|
redistribute it and/or modify it under the terms of the GNU
|
||||||
|
General Public License (GNU GPL) as published by the Free Software
|
||||||
|
Foundation, either version 3 of the License, or (at your option)
|
||||||
|
any later version. The code is distributed WITHOUT ANY WARRANTY;
|
||||||
|
without even the implied warranty of MERCHANTABILITY or FITNESS
|
||||||
|
FOR A PARTICULAR PURPOSE. See the GNU GPL for more details.
|
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|
||||||
|
As additional permission under GNU GPL version 3 section 7, you
|
||||||
|
may distribute non-source (e.g., minimized or compacted) forms of
|
||||||
|
that code without the copy of the GNU GPL normally required by
|
||||||
|
section 4, provided you include this license notice and a URL
|
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|
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|
||||||
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@licend The above is the entire license notice
|
||||||
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for the JavaScript code in this tag.
|
||||||
|
*/
|
||||||
|
<!--/*--><![CDATA[/*><!--*/
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function CodeHighlightOn(elem, id)
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{
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function CodeHighlightOff(elem, id)
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{
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|
var target = document.getElementById(id);
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if(elem.cacheClassElem)
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elem.className = elem.cacheClassElem;
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if(elem.cacheClassTarget)
|
||||||
|
target.className = elem.cacheClassTarget;
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}
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|
/*]]>*///-->
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||||||
|
</script>
|
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|
<script type="text/x-mathjax-config">
|
||||||
|
MathJax.Hub.Config({
|
||||||
|
displayAlign: "center",
|
||||||
|
displayIndent: "0em",
|
||||||
|
|
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|
"HTML-CSS": { scale: 100,
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|
linebreaks: { automatic: "false" },
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webFont: "TeX"
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},
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SVG: {scale: 100,
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|
linebreaks: { automatic: "false" },
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|
font: "TeX"},
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NativeMML: {scale: 100},
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TeX: { equationNumbers: {autoNumber: "AMS"},
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|
MultLineWidth: "85%",
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TagIndent: ".8em"
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|
}
|
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|
});
|
||||||
|
</script>
|
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|
<script type="text/javascript"
|
||||||
|
src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS_HTML"></script>
|
||||||
|
</head>
|
||||||
|
<body>
|
||||||
|
<div id="content">
|
||||||
|
<h1 class="title">Cercalo Test Bench</h1>
|
||||||
|
<div id="table-of-contents">
|
||||||
|
<h2>Table of Contents</h2>
|
||||||
|
<div id="text-table-of-contents">
|
||||||
|
<ul>
|
||||||
|
<li><a href="#org25712dd">1. Identification</a>
|
||||||
|
<ul>
|
||||||
|
<li><a href="#orgc595eec">1.1. Excitation Data</a></li>
|
||||||
|
<li><a href="#orgd0be9c1">1.2. Input / Output data</a></li>
|
||||||
|
<li><a href="#org6ef1d0f">1.3. Estimation of the Frequency Response Function Matrix</a></li>
|
||||||
|
<li><a href="#orgb893c50">1.4. Coherence</a></li>
|
||||||
|
<li><a href="#org57d6ee3">1.5. Extraction of a transfer function matrix</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li><a href="#org6115789">2. Plant Analysis</a></li>
|
||||||
|
<li><a href="#orgcdff0c9">3. Control</a></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="outline-container-org25712dd" class="outline-2">
|
||||||
|
<h2 id="org25712dd"><span class="section-number-2">1</span> Identification</h2>
|
||||||
|
<div class="outline-text-2" id="text-1">
|
||||||
|
</div>
|
||||||
|
<div id="outline-container-orgc595eec" class="outline-3">
|
||||||
|
<h3 id="orgc595eec"><span class="section-number-3">1.1</span> Excitation Data</h3>
|
||||||
|
<div class="outline-text-3" id="text-1-1">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">fs = <span class="org-highlight-numbers-number">1e4</span>;
|
||||||
|
Ts = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>fs;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We generate white noise with the "random number" simulink block, and we filter that noise.
|
||||||
|
</p>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">Gi = <span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">+</span>s<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">c2d<span class="org-rainbow-delimiters-depth-1">(</span>Gi, Ts, <span class="org-string">'tustin'</span><span class="org-rainbow-delimiters-depth-1">)</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<pre class="example">
|
||||||
|
c2d(Gi, Ts, 'tustin')
|
||||||
|
|
||||||
|
ans =
|
||||||
|
|
||||||
|
0.030459 (z+1)
|
||||||
|
--------------
|
||||||
|
(z-0.9391)
|
||||||
|
|
||||||
|
Sample time: 0.0001 seconds
|
||||||
|
Discrete-time zero/pole/gain model.
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orgd0be9c1" class="outline-3">
|
||||||
|
<h3 id="orgd0be9c1"><span class="section-number-3">1.2</span> Input / Output data</h3>
|
||||||
|
<div class="outline-text-3" id="text-1-2">
|
||||||
|
<p>
|
||||||
|
The identification data is loaded
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">ux = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_001.mat', 't', 'ux', 'yx', 'yy'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
uy = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_002.mat', 't', 'uy', 'yx', 'yy'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We remove the first seconds where the Cercalo is turned on.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">i0x = <span class="org-highlight-numbers-number">20</span><span class="org-type">*</span>fs;
|
||||||
|
|
||||||
|
i0y = <span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>fs;
|
||||||
|
|
||||||
|
ux.t = ux.t<span class="org-rainbow-delimiters-depth-1">(</span> i0x<span class="org-type">:</span>end<span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> ux.t<span class="org-rainbow-delimiters-depth-1">(</span>i0x<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
ux.ux = ux.ux<span class="org-rainbow-delimiters-depth-1">(</span>i0x<span class="org-type">:</span>end<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
ux.yx = ux.yx<span class="org-rainbow-delimiters-depth-1">(</span>i0x<span class="org-type">:</span>end<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
ux.yy = ux.yy<span class="org-rainbow-delimiters-depth-1">(</span>i0x<span class="org-type">:</span>end<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
|
||||||
|
uy.t = uy.t<span class="org-rainbow-delimiters-depth-1">(</span> i0y<span class="org-type">:</span>end<span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> uy.t<span class="org-rainbow-delimiters-depth-1">(</span>i0x<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
uy.uy = uy.uy<span class="org-rainbow-delimiters-depth-1">(</span>i0y<span class="org-type">:</span>end<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
uy.yx = uy.yx<span class="org-rainbow-delimiters-depth-1">(</span>i0y<span class="org-type">:</span>end<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
uy.yy = uy.yy<span class="org-rainbow-delimiters-depth-1">(</span>i0y<span class="org-type">:</span>end<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">ux.ux = ux.ux<span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-1">(</span>ux.ux<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
ux.yx = ux.yx<span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-1">(</span>ux.yx<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
ux.yy = ux.yy<span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-1">(</span>ux.yy<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
|
||||||
|
uy.ux = uy.ux<span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-1">(</span>uy.ux<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
uy.yx = uy.yx<span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-1">(</span>uy.yx<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
uy.yy = uy.yy<span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-1">(</span>uy.yy<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="orgdd27b44" class="figure">
|
||||||
|
<p><img src="figs/identification_ux.png" alt="identification_ux.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 1: </span>Identification signals when exciting the \(x\) axis (<a href="./figs/identification_ux.png">png</a>, <a href="./figs/identification_ux.pdf">pdf</a>)</p>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
<div id="orgc1aa49f" class="figure">
|
||||||
|
<p><img src="figs/identification_uy.png" alt="identification_uy.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 2: </span>Identification signals when exciting the \(y\) axis (<a href="./figs/identification_uy.png">png</a>, <a href="./figs/identification_uy.pdf">pdf</a>)</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org6ef1d0f" class="outline-3">
|
||||||
|
<h3 id="org6ef1d0f"><span class="section-number-3">1.3</span> Estimation of the Frequency Response Function Matrix</h3>
|
||||||
|
<div class="outline-text-3" id="text-1-3">
|
||||||
|
<p>
|
||||||
|
We compute an estimate of the transfer functions.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>tf_ux_yx, f<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>ux.ux, ux.yx, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>fs<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
<span class="org-rainbow-delimiters-depth-1">[</span>tf_ux_yy, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>ux.ux, ux.yy, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>fs<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
<span class="org-rainbow-delimiters-depth-1">[</span>tf_uy_yx, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>uy.uy, uy.yx, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>fs<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
<span class="org-rainbow-delimiters-depth-1">[</span>tf_uy_yy, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>uy.uy, uy.yy, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>fs<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org26ecff4" class="figure">
|
||||||
|
<p><img src="figs/frequency_response_matrix.png" alt="frequency_response_matrix.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 3: </span>Frequency Response Matrix (<a href="./figs/frequency_response_matrix.png">png</a>, <a href="./figs/frequency_response_matrix.pdf">pdf</a>)</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orgb893c50" class="outline-3">
|
||||||
|
<h3 id="orgb893c50"><span class="section-number-3">1.4</span> Coherence</h3>
|
||||||
|
<div class="outline-text-3" id="text-1-4">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>coh_ux_yx, f<span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>ux.ux, ux.yx, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>fs<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
<span class="org-rainbow-delimiters-depth-1">[</span>coh_ux_yy, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>ux.ux, ux.yy, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>fs<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
<span class="org-rainbow-delimiters-depth-1">[</span>coh_uy_yx, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>uy.uy, uy.yx, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>fs<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
<span class="org-rainbow-delimiters-depth-1">[</span>coh_uy_yy, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>uy.uy, uy.yy, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>fs<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org2a5d4ff" class="figure">
|
||||||
|
<p><img src="figs/identification_coherence.png" alt="identification_coherence.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 4: </span>Coherence (<a href="./figs/identification_coherence.png">png</a>, <a href="./figs/identification_coherence.pdf">pdf</a>)</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="outline-container-org57d6ee3" class="outline-3">
|
||||||
|
<h3 id="org57d6ee3"><span class="section-number-3">1.5</span> Extraction of a transfer function matrix</h3>
|
||||||
|
<div class="outline-text-3" id="text-1-5">
|
||||||
|
<p>
|
||||||
|
First we define the initial guess for the resonance frequencies and the weights associated.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">freqs_res = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">410</span>, <span class="org-highlight-numbers-number">250</span><span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% [Hz]</span>
|
||||||
|
freqs_res_weights = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">10</span>, <span class="org-highlight-numbers-number">10</span><span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% [Hz]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
From the number of resonance frequency we want to fit, we define the order <code>N</code> of the system we want to obtain.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">N = <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>length<span class="org-rainbow-delimiters-depth-1">(</span>freqs_res<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We then make an initial guess on the complex values of the poles.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">xi = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">001</span>; <span class="org-comment">% Approximate modal damping</span>
|
||||||
|
poles = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>freqs_res<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-2">(</span>xi <span class="org-type">+</span> <span class="org-highlight-numbers-number">1i</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>freqs_res<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-2">(</span>xi <span class="org-type">-</span> <span class="org-highlight-numbers-number">1i</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">]</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We then define the weight that will be used for the fitting.
|
||||||
|
Basically, we want more weight around the resonance and at low frequency (below the first resonance).
|
||||||
|
Also, we want more importance where we have a better coherence.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">weight = ones<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, length<span class="org-rainbow-delimiters-depth-2">(</span>f<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
<span class="org-comment">% weight = G_coh';</span>
|
||||||
|
|
||||||
|
% alpha = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>;
|
||||||
|
|
||||||
|
% <span class="org-keyword">for</span> <span class="org-variable-name">freq_i</span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:length(freqs_res)</span>
|
||||||
|
% weight(f<span class="org-type">></span>(<span class="org-highlight-numbers-number">1</span><span class="org-type">-</span>alpha)<span class="org-type">*</span>freqs_res(freq_i) <span class="org-type">&</span> omega<span class="org-type"><</span>(<span class="org-highlight-numbers-number">1</span> <span class="org-type">+</span> alpha)<span class="org-type">*</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>freqs_res(freq_i)) = freqs_res_weights(freq_i);
|
||||||
|
<span class="org-comment">% end</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
Ignore data above some frequency.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">weight<span class="org-rainbow-delimiters-depth-1">(</span>f<span class="org-type">></span><span class="org-highlight-numbers-number">1000</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-highlight-numbers-number">0</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="orgd766a83" class="figure">
|
||||||
|
<p><img src="figs/weights.png" alt="weights.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 5: </span>Weights amplitude (<a href="./figs/weights.png">png</a>, <a href="./figs/weights.pdf">pdf</a>)</p>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
When we set some options for <code>vfit3</code>.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">opts = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
|
||||||
|
|
||||||
|
opts.stable = <span class="org-highlight-numbers-number">1</span>; <span class="org-comment">% Enforce stable poles</span>
|
||||||
|
opts.asymp = <span class="org-highlight-numbers-number">1</span>; <span class="org-comment">% Force D matrix to be null</span>
|
||||||
|
opts.relax = <span class="org-highlight-numbers-number">1</span>; <span class="org-comment">% Use vector fitting with relaxed non-triviality constraint</span>
|
||||||
|
opts.skip_pole = <span class="org-highlight-numbers-number">0</span>; <span class="org-comment">% Do NOT skip pole identification</span>
|
||||||
|
opts.skip_res = <span class="org-highlight-numbers-number">0</span>; <span class="org-comment">% Do NOT skip identification of residues (C,D,E)</span>
|
||||||
|
opts.cmplx_ss = <span class="org-highlight-numbers-number">0</span>; <span class="org-comment">% Create real state space model with block diagonal A</span>
|
||||||
|
|
||||||
|
opts.spy1 = <span class="org-highlight-numbers-number">0</span>; <span class="org-comment">% No plotting for first stage of vector fitting</span>
|
||||||
|
opts.spy2 = <span class="org-highlight-numbers-number">0</span>; <span class="org-comment">% Create magnitude plot for fitting of f(s)</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We define the number of iteration.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">Niter = <span class="org-highlight-numbers-number">5</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
An we run the <code>vectfit3</code> algorithm.
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab"><span class="org-keyword">for</span> <span class="org-variable-name">iter</span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:Niter</span>
|
||||||
|
<span class="org-rainbow-delimiters-depth-1">[</span>SER_ux_yx, poles, <span class="org-type">~</span>, fit_ux_yx<span class="org-rainbow-delimiters-depth-1">]</span> = vectfit3<span class="org-rainbow-delimiters-depth-1">(</span>tf_ux_yx<span class="org-type">.'</span>, <span class="org-highlight-numbers-number">1i</span><span class="org-type">*</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f, poles, weight, opts<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
<span class="org-keyword">end</span>
|
||||||
|
<span class="org-keyword">for</span> <span class="org-variable-name">iter</span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:Niter</span>
|
||||||
|
<span class="org-rainbow-delimiters-depth-1">[</span>SER_uy_yx, poles, <span class="org-type">~</span>, fit_uy_yx<span class="org-rainbow-delimiters-depth-1">]</span> = vectfit3<span class="org-rainbow-delimiters-depth-1">(</span>tf_uy_yx<span class="org-type">.'</span>, <span class="org-highlight-numbers-number">1i</span><span class="org-type">*</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f, poles, weight, opts<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
<span class="org-keyword">end</span>
|
||||||
|
<span class="org-keyword">for</span> <span class="org-variable-name">iter</span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:Niter</span>
|
||||||
|
<span class="org-rainbow-delimiters-depth-1">[</span>SER_ux_yy, poles, <span class="org-type">~</span>, fit_ux_yy<span class="org-rainbow-delimiters-depth-1">]</span> = vectfit3<span class="org-rainbow-delimiters-depth-1">(</span>tf_ux_yy<span class="org-type">.'</span>, <span class="org-highlight-numbers-number">1i</span><span class="org-type">*</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f, poles, weight, opts<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
<span class="org-keyword">end</span>
|
||||||
|
<span class="org-keyword">for</span> <span class="org-variable-name">iter</span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:Niter</span>
|
||||||
|
<span class="org-rainbow-delimiters-depth-1">[</span>SER_uy_yy, poles, <span class="org-type">~</span>, fit_uy_yy<span class="org-rainbow-delimiters-depth-1">]</span> = vectfit3<span class="org-rainbow-delimiters-depth-1">(</span>tf_uy_yy<span class="org-type">.'</span>, <span class="org-highlight-numbers-number">1i</span><span class="org-type">*</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f, poles, weight, opts<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
<span class="org-keyword">end</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="orgc6407a4" class="figure">
|
||||||
|
<p><img src="figs/identification_matrix_fit.png" alt="identification_matrix_fit.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 6: </span>Transfer Function Extraction of the FRF matrix (<a href="./figs/identification_matrix_fit.png">png</a>, <a href="./figs/identification_matrix_fit.pdf">pdf</a>)</p>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
And finally, we create the identified state space model:
|
||||||
|
</p>
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">G_ux_yx = minreal<span class="org-rainbow-delimiters-depth-1">(</span>ss<span class="org-rainbow-delimiters-depth-2">(</span>full<span class="org-rainbow-delimiters-depth-3">(</span>SER_ux_yx.A<span class="org-rainbow-delimiters-depth-3">)</span>,SER_ux_yx.B,SER_ux_yx.C,SER_ux_yx.D<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
G_uy_yx = minreal<span class="org-rainbow-delimiters-depth-1">(</span>ss<span class="org-rainbow-delimiters-depth-2">(</span>full<span class="org-rainbow-delimiters-depth-3">(</span>SER_uy_yx.A<span class="org-rainbow-delimiters-depth-3">)</span>,SER_uy_yx.B,SER_uy_yx.C,SER_uy_yx.D<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
G_ux_yy = minreal<span class="org-rainbow-delimiters-depth-1">(</span>ss<span class="org-rainbow-delimiters-depth-2">(</span>full<span class="org-rainbow-delimiters-depth-3">(</span>SER_ux_yy.A<span class="org-rainbow-delimiters-depth-3">)</span>,SER_ux_yy.B,SER_ux_yy.C,SER_ux_yy.D<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
G_uy_yy = minreal<span class="org-rainbow-delimiters-depth-1">(</span>ss<span class="org-rainbow-delimiters-depth-2">(</span>full<span class="org-rainbow-delimiters-depth-3">(</span>SER_uy_yy.A<span class="org-rainbow-delimiters-depth-3">)</span>,SER_uy_yy.B,SER_uy_yy.C,SER_uy_yy.D<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
|
||||||
|
G = <span class="org-rainbow-delimiters-depth-1">[</span>G_ux_yx, G_uy_yx;
|
||||||
|
G_ux_yy, G_uy_yy<span class="org-rainbow-delimiters-depth-1">]</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/plant.mat', 'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div id="outline-container-org6115789" class="outline-2">
|
||||||
|
<h2 id="org6115789"><span class="section-number-2">2</span> Plant Analysis</h2>
|
||||||
|
</div>
|
||||||
|
<div id="outline-container-orgcdff0c9" class="outline-2">
|
||||||
|
<h2 id="orgcdff0c9"><span class="section-number-2">3</span> Control</h2>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div id="postamble" class="status">
|
||||||
|
<p class="author">Author: Dehaeze Thomas</p>
|
||||||
|
<p class="date">Created: 2019-09-10 mar. 18:15</p>
|
||||||
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
|
</div>
|
||||||
|
</body>
|
||||||
|
</html>
|
||||||
403
index.org
403
index.org
@ -6,6 +6,14 @@
|
|||||||
#+EMAIL: dehaeze.thomas@gmail.com
|
#+EMAIL: dehaeze.thomas@gmail.com
|
||||||
#+AUTHOR: Dehaeze Thomas
|
#+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:matlab :session *MATLAB*
|
#+PROPERTY: header-args:matlab :session *MATLAB*
|
||||||
#+PROPERTY: header-args:matlab+ :comments org
|
#+PROPERTY: header-args:matlab+ :comments org
|
||||||
#+PROPERTY: header-args:matlab+ :results none
|
#+PROPERTY: header-args:matlab+ :results none
|
||||||
@ -17,7 +25,8 @@
|
|||||||
:END:
|
:END:
|
||||||
|
|
||||||
|
|
||||||
* Matlab Init :noexport:ignore:
|
* 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)
|
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||||
<<matlab-dir>>
|
<<matlab-dir>>
|
||||||
#+end_src
|
#+end_src
|
||||||
@ -26,7 +35,7 @@
|
|||||||
<<matlab-init>>
|
<<matlab-init>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
* Identification of the Plant
|
** Excitation Data
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
fs = 1e4;
|
fs = 1e4;
|
||||||
Ts = 1/fs;
|
Ts = 1/fs;
|
||||||
@ -56,35 +65,377 @@ Sample time: 0.0001 seconds
|
|||||||
Discrete-time zero/pole/gain model.
|
Discrete-time zero/pole/gain model.
|
||||||
#+end_example
|
#+end_example
|
||||||
|
|
||||||
|
** Input / Output data
|
||||||
|
The identification data is loaded
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
load('mat/data_001.mat', 't', 'ux')
|
ux = load('mat/data_001.mat', 't', 'ux', 'yx', 'yy');
|
||||||
|
uy = load('mat/data_002.mat', 't', 'uy', 'yx', 'yy');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
We remove the first seconds where the Cercalo is turned on.
|
||||||
|
#+begin_src matlab
|
||||||
|
i0x = 20*fs;
|
||||||
|
|
||||||
|
i0y = 10*fs;
|
||||||
|
|
||||||
|
ux.t = ux.t( i0x:end) - ux.t(i0x);
|
||||||
|
ux.ux = ux.ux(i0x:end);
|
||||||
|
ux.yx = ux.yx(i0x:end);
|
||||||
|
ux.yy = ux.yy(i0x:end);
|
||||||
|
|
||||||
|
uy.t = uy.t( i0y:end) - uy.t(i0x);
|
||||||
|
uy.uy = uy.uy(i0y:end);
|
||||||
|
uy.yx = uy.yx(i0y:end);
|
||||||
|
uy.yy = uy.yy(i0y:end);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
figure; plot(t, ux)
|
ux.ux = ux.ux-mean(ux.ux);
|
||||||
|
ux.yx = ux.yx-mean(ux.yx);
|
||||||
|
ux.yy = ux.yy-mean(ux.yy);
|
||||||
|
|
||||||
|
uy.ux = uy.ux-mean(uy.ux);
|
||||||
|
uy.yx = uy.yx-mean(uy.yx);
|
||||||
|
uy.yy = uy.yy-mean(uy.yy);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
figure;
|
||||||
|
ax1 = subplot(1, 2, 1);
|
||||||
|
plot(ux.t, ux.ux);
|
||||||
|
xlabel('Time [s]');
|
||||||
|
ylabel('Amplitude [V]');
|
||||||
|
legend({'$u_x$'});
|
||||||
|
|
||||||
|
ax2 = subplot(1, 2, 2);
|
||||||
|
hold on;
|
||||||
|
plot(ux.t, ux.yx, 'DisplayName', '$y_x$');
|
||||||
|
plot(ux.t, ux.yy, 'DisplayName', '$y_y$');
|
||||||
|
hold off;
|
||||||
|
xlabel('Time [s]');
|
||||||
|
ylabel('Amplitude [V]');
|
||||||
|
legend()
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
xlim([ux.t(1), ux.t(end)])
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||||
|
#+begin_src matlab :var filepath="figs/identification_ux.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
|
||||||
|
<<plt-matlab>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+NAME: fig:identification_ux
|
||||||
|
#+CAPTION: Identification signals when exciting the $x$ axis ([[./figs/identification_ux.png][png]], [[./figs/identification_ux.pdf][pdf]])
|
||||||
|
[[file:figs/identification_ux.png]]
|
||||||
|
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
figure;
|
||||||
|
ax1 = subplot(1, 2, 1);
|
||||||
|
plot(uy.t, uy.uy);
|
||||||
|
xlabel('Time [s]');
|
||||||
|
ylabel('Amplitude [V]');
|
||||||
|
legend({'$u_y$'});
|
||||||
|
|
||||||
|
ax2 = subplot(1, 2, 2);
|
||||||
|
hold on;
|
||||||
|
plot(uy.t, uy.yy, 'DisplayName', '$y_y$');
|
||||||
|
plot(uy.t, uy.yx, 'DisplayName', '$y_x$');
|
||||||
|
hold off;
|
||||||
|
xlabel('Time [s]');
|
||||||
|
ylabel('Amplitude [V]');
|
||||||
|
legend()
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
xlim([uy.t(1), uy.t(end)])
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||||
|
#+begin_src matlab :var filepath="figs/identification_uy.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
|
||||||
|
<<plt-matlab>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+NAME: fig:identification_uy
|
||||||
|
#+CAPTION: Identification signals when exciting the $y$ axis ([[./figs/identification_uy.png][png]], [[./figs/identification_uy.pdf][pdf]])
|
||||||
|
[[file:figs/identification_uy.png]]
|
||||||
|
|
||||||
|
** Estimation of the Frequency Response Function Matrix
|
||||||
|
We compute an estimate of the transfer functions.
|
||||||
|
#+begin_src matlab
|
||||||
|
[tf_ux_yx, f] = tfestimate(ux.ux, ux.yx, hanning(ceil(1*fs)), [], [], fs);
|
||||||
|
[tf_ux_yy, ~] = tfestimate(ux.ux, ux.yy, hanning(ceil(1*fs)), [], [], fs);
|
||||||
|
[tf_uy_yx, ~] = tfestimate(uy.uy, uy.yx, hanning(ceil(1*fs)), [], [], fs);
|
||||||
|
[tf_uy_yy, ~] = tfestimate(uy.uy, uy.yy, hanning(ceil(1*fs)), [], [], fs);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
figure;
|
||||||
|
ax11 = subplot(2, 2, 1);
|
||||||
|
hold on;
|
||||||
|
plot(f, abs(tf_ux_yx))
|
||||||
|
title('Frequency Response Function $\frac{y_x}{u_x}$')
|
||||||
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||||
|
ylabel('Amplitude')
|
||||||
|
hold off;
|
||||||
|
|
||||||
|
ax12 = subplot(2, 2, 2);
|
||||||
|
hold on;
|
||||||
|
plot(f, abs(tf_ux_yy))
|
||||||
|
title('Frequency Response Function $\frac{y_x}{u_y}$')
|
||||||
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||||
|
hold off;
|
||||||
|
|
||||||
|
ax21 = subplot(2, 2, 3);
|
||||||
|
hold on;
|
||||||
|
plot(f, abs(tf_uy_yx))
|
||||||
|
title('Frequency Response Function $\frac{y_y}{u_x}$')
|
||||||
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||||
|
ylabel('Amplitude')
|
||||||
|
xlabel('Frequency [Hz]')
|
||||||
|
hold off;
|
||||||
|
|
||||||
|
ax22 = subplot(2, 2, 4);
|
||||||
|
hold on;
|
||||||
|
plot(f, abs(tf_uy_yy))
|
||||||
|
title('Frequency Response Function $\frac{y_y}{u_y}$')
|
||||||
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||||
|
xlabel('Frequency [Hz]')
|
||||||
|
hold off;
|
||||||
|
|
||||||
|
linkaxes([ax11,ax12,ax21,ax22],'x');
|
||||||
|
xlim([10, 1000]);
|
||||||
|
linkaxes([ax11,ax12,ax21,ax22],'y');
|
||||||
|
ylim([1e-2, 1e3])
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||||
|
#+begin_src matlab :var filepath="figs/frequency_response_matrix.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||||
|
<<plt-matlab>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+NAME: fig:frequency_response_matrix
|
||||||
|
#+CAPTION: Frequency Response Matrix ([[./figs/frequency_response_matrix.png][png]], [[./figs/frequency_response_matrix.pdf][pdf]])
|
||||||
|
[[file:figs/frequency_response_matrix.png]]
|
||||||
|
|
||||||
|
** Coherence
|
||||||
|
#+begin_src matlab
|
||||||
|
[coh_ux_yx, f] = mscohere(ux.ux, ux.yx, hanning(ceil(1*fs)), [], [], fs);
|
||||||
|
[coh_ux_yy, ~] = mscohere(ux.ux, ux.yy, hanning(ceil(1*fs)), [], [], fs);
|
||||||
|
[coh_uy_yx, ~] = mscohere(uy.uy, uy.yx, hanning(ceil(1*fs)), [], [], fs);
|
||||||
|
[coh_uy_yy, ~] = mscohere(uy.uy, uy.yy, hanning(ceil(1*fs)), [], [], fs);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
figure;
|
||||||
|
ax11 = subplot(2, 2, 1);
|
||||||
|
hold on;
|
||||||
|
plot(f, coh_ux_yx)
|
||||||
|
set(gca, 'Xscale', 'log');
|
||||||
|
title('Coherence $\frac{y_x}{u_x}$')
|
||||||
|
ylabel('Coherence')
|
||||||
|
hold off;
|
||||||
|
|
||||||
|
ax12 = subplot(2, 2, 2);
|
||||||
|
hold on;
|
||||||
|
plot(f, coh_ux_yy)
|
||||||
|
set(gca, 'Xscale', 'log');
|
||||||
|
title('Coherence $\frac{y_x}{u_y}$')
|
||||||
|
hold off;
|
||||||
|
|
||||||
|
ax21 = subplot(2, 2, 3);
|
||||||
|
hold on;
|
||||||
|
plot(f, coh_uy_yx)
|
||||||
|
set(gca, 'Xscale', 'log');
|
||||||
|
title('Coherence $\frac{y_y}{u_x}$')
|
||||||
|
ylabel('Coherence')
|
||||||
|
xlabel('Frequency [Hz]')
|
||||||
|
hold off;
|
||||||
|
|
||||||
|
ax22 = subplot(2, 2, 4);
|
||||||
|
hold on;
|
||||||
|
plot(f, coh_uy_yy)
|
||||||
|
set(gca, 'Xscale', 'log');
|
||||||
|
title('Coherence $\frac{y_y}{u_y}$')
|
||||||
|
xlabel('Frequency [Hz]')
|
||||||
|
hold off;
|
||||||
|
|
||||||
|
linkaxes([ax11,ax12,ax21,ax22],'x');
|
||||||
|
xlim([10, 1000]);
|
||||||
|
linkaxes([ax11,ax12,ax21,ax22],'y');
|
||||||
|
ylim([0, 1])
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||||
|
#+begin_src matlab :var filepath="figs/identification_coherence.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||||
|
<<plt-matlab>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+NAME: fig:identification_coherence
|
||||||
|
#+CAPTION: Coherence ([[./figs/identification_coherence.png][png]], [[./figs/identification_coherence.pdf][pdf]])
|
||||||
|
[[file:figs/identification_coherence.png]]
|
||||||
|
|
||||||
|
|
||||||
|
** Extraction of a transfer function matrix
|
||||||
|
First we define the initial guess for the resonance frequencies and the weights associated.
|
||||||
|
#+begin_src matlab
|
||||||
|
freqs_res = [410, 250]; % [Hz]
|
||||||
|
freqs_res_weights = [10, 10]; % [Hz]
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
From the number of resonance frequency we want to fit, we define the order =N= of the system we want to obtain.
|
||||||
|
#+begin_src matlab
|
||||||
|
N = 2*length(freqs_res);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
We then make an initial guess on the complex values of the poles.
|
||||||
|
#+begin_src matlab
|
||||||
|
xi = 0.001; % Approximate modal damping
|
||||||
|
poles = [2*pi*freqs_res*(xi + 1i), 2*pi*freqs_res*(xi - 1i)];
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
We then define the weight that will be used for the fitting.
|
||||||
|
Basically, we want more weight around the resonance and at low frequency (below the first resonance).
|
||||||
|
Also, we want more importance where we have a better coherence.
|
||||||
|
#+begin_src matlab
|
||||||
|
weight = ones(1, length(f));
|
||||||
|
% weight = G_coh';
|
||||||
|
|
||||||
|
% alpha = 0.1;
|
||||||
|
|
||||||
|
% for freq_i = 1:length(freqs_res)
|
||||||
|
% weight(f>(1-alpha)*freqs_res(freq_i) & omega<(1 + alpha)*2*pi*freqs_res(freq_i)) = freqs_res_weights(freq_i);
|
||||||
|
% end
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
Ignore data above some frequency.
|
||||||
|
#+begin_src matlab
|
||||||
|
weight(f>1000) = 0;
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
plot(f, weight);
|
||||||
|
plot(freqs_res, ones(size(freqs_res)), 'rx');
|
||||||
|
hold off;
|
||||||
|
xlabel('Frequency [Hz]');
|
||||||
|
xlabel('Weight Amplitude');
|
||||||
|
set(gca, 'xscale', 'log');
|
||||||
|
xlim([f(1), f(end)]);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||||
|
#+begin_src matlab :var filepath="figs/weights.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
|
||||||
|
<<plt-matlab>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+NAME: fig:weights
|
||||||
|
#+CAPTION: Weights amplitude ([[./figs/weights.png][png]], [[./figs/weights.pdf][pdf]])
|
||||||
|
[[file:figs/weights.png]]
|
||||||
|
|
||||||
|
When we set some options for =vfit3=.
|
||||||
|
#+begin_src matlab
|
||||||
|
opts = struct();
|
||||||
|
|
||||||
|
opts.stable = 1; % Enforce stable poles
|
||||||
|
opts.asymp = 1; % Force D matrix to be null
|
||||||
|
opts.relax = 1; % Use vector fitting with relaxed non-triviality constraint
|
||||||
|
opts.skip_pole = 0; % Do NOT skip pole identification
|
||||||
|
opts.skip_res = 0; % Do NOT skip identification of residues (C,D,E)
|
||||||
|
opts.cmplx_ss = 0; % Create real state space model with block diagonal A
|
||||||
|
|
||||||
|
opts.spy1 = 0; % No plotting for first stage of vector fitting
|
||||||
|
opts.spy2 = 0; % Create magnitude plot for fitting of f(s)
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
We define the number of iteration.
|
||||||
|
#+begin_src matlab
|
||||||
|
Niter = 5;
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
An we run the =vectfit3= algorithm.
|
||||||
|
#+begin_src matlab
|
||||||
|
for iter = 1:Niter
|
||||||
|
[SER_ux_yx, poles, ~, fit_ux_yx] = vectfit3(tf_ux_yx.', 1i*2*pi*f, poles, weight, opts);
|
||||||
|
end
|
||||||
|
for iter = 1:Niter
|
||||||
|
[SER_uy_yx, poles, ~, fit_uy_yx] = vectfit3(tf_uy_yx.', 1i*2*pi*f, poles, weight, opts);
|
||||||
|
end
|
||||||
|
for iter = 1:Niter
|
||||||
|
[SER_ux_yy, poles, ~, fit_ux_yy] = vectfit3(tf_ux_yy.', 1i*2*pi*f, poles, weight, opts);
|
||||||
|
end
|
||||||
|
for iter = 1:Niter
|
||||||
|
[SER_uy_yy, poles, ~, fit_uy_yy] = vectfit3(tf_uy_yy.', 1i*2*pi*f, poles, weight, opts);
|
||||||
|
end
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
figure;
|
||||||
|
ax11 = subplot(2, 2, 1);
|
||||||
|
hold on;
|
||||||
|
plot(f, abs(tf_ux_yx))
|
||||||
|
plot(f, abs(fit_ux_yx))
|
||||||
|
title('Frequency Response Function $\frac{y_x}{u_x}$')
|
||||||
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||||
|
ylabel('Amplitude')
|
||||||
|
hold off;
|
||||||
|
|
||||||
|
ax12 = subplot(2, 2, 2);
|
||||||
|
hold on;
|
||||||
|
plot(f, abs(tf_ux_yy))
|
||||||
|
plot(f, abs(fit_ux_yy))
|
||||||
|
title('Frequency Response Function $\frac{y_x}{u_y}$')
|
||||||
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||||
|
hold off;
|
||||||
|
|
||||||
|
ax21 = subplot(2, 2, 3);
|
||||||
|
hold on;
|
||||||
|
plot(f, abs(tf_uy_yx))
|
||||||
|
plot(f, abs(fit_uy_yx))
|
||||||
|
title('Frequency Response Function $\frac{y_y}{u_x}$')
|
||||||
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||||
|
ylabel('Amplitude')
|
||||||
|
xlabel('Frequency [Hz]')
|
||||||
|
hold off;
|
||||||
|
|
||||||
|
ax22 = subplot(2, 2, 4);
|
||||||
|
hold on;
|
||||||
|
plot(f, abs(tf_uy_yy))
|
||||||
|
plot(f, abs(fit_uy_yy))
|
||||||
|
title('Frequency Response Function $\frac{y_y}{u_y}$')
|
||||||
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||||
|
xlabel('Frequency [Hz]')
|
||||||
|
hold off;
|
||||||
|
|
||||||
|
linkaxes([ax11,ax12,ax21,ax22],'x');
|
||||||
|
xlim([10, 1000]);
|
||||||
|
linkaxes([ax11,ax12,ax21,ax22],'y');
|
||||||
|
ylim([1e-2, 1e3])
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||||
|
#+begin_src matlab :var filepath="figs/identification_matrix_fit.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||||
|
<<plt-matlab>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+NAME: fig:identification_matrix_fit
|
||||||
|
#+CAPTION: Transfer Function Extraction of the FRF matrix ([[./figs/identification_matrix_fit.png][png]], [[./figs/identification_matrix_fit.pdf][pdf]])
|
||||||
|
[[file:figs/identification_matrix_fit.png]]
|
||||||
|
|
||||||
|
And finally, we create the identified state space model:
|
||||||
|
#+begin_src matlab
|
||||||
|
G_ux_yx = minreal(ss(full(SER_ux_yx.A),SER_ux_yx.B,SER_ux_yx.C,SER_ux_yx.D));
|
||||||
|
G_uy_yx = minreal(ss(full(SER_uy_yx.A),SER_uy_yx.B,SER_uy_yx.C,SER_uy_yx.D));
|
||||||
|
G_ux_yy = minreal(ss(full(SER_ux_yy.A),SER_ux_yy.B,SER_ux_yy.C,SER_ux_yy.D));
|
||||||
|
G_uy_yy = minreal(ss(full(SER_uy_yy.A),SER_uy_yy.B,SER_uy_yy.C,SER_uy_yy.D));
|
||||||
|
|
||||||
|
G = [G_ux_yx, G_uy_yx;
|
||||||
|
G_ux_yy, G_uy_yy];
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
[tf_est, freqs] = tfestimate(ux, yx, hanning(ceil(length(ux)/10)), [], [], fs);
|
save('mat/plant.mat', 'G');
|
||||||
|
|
||||||
% h = idfrd(tf_est, freqs*2*pi, Ts);
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+begin_src matlab
|
|
||||||
figure;
|
|
||||||
ax1 = subplot(2, 1, 1);
|
|
||||||
hold on;
|
|
||||||
plot(freqs, abs(tf_est),'--')
|
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
||||||
ylabel('Amplitude [m/N]');
|
|
||||||
hold off;
|
|
||||||
|
|
||||||
ax2 = subplot(2, 1, 2);
|
|
||||||
hold on;
|
|
||||||
plot(freqs, mod(180+180/pi*phase(tf_est), 360)-180,'--')
|
|
||||||
set(gca,'xscale','log');
|
|
||||||
ylim([-180, 180]);
|
|
||||||
yticks([-180, -90, 0, 90, 180]);
|
|
||||||
xlabel('Frequency [$Hz$]'); ylabel('Phase [deg]');
|
|
||||||
hold off;
|
|
||||||
#+end_src
|
#+end_src
|
||||||
|
* Plant Analysis
|
||||||
|
* Control
|
||||||
|
|||||||
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 = $('#table-of-contents').find('h2');
|
||||||
|
tocTitle.append(closeBtn);
|
||||||
|
});
|
||||||
|
|
||||||
|
window.SphinxRtdTheme = (function (jquery) {
|
||||||
|
var stickyNav = (function () {
|
||||||
|
var navBar,
|
||||||
|
win,
|
||||||
|
stickyNavCssClass = 'stickynav',
|
||||||
|
applyStickNav = function () {
|
||||||
|
if (navBar.height() <= win.height()) {
|
||||||
|
navBar.addClass(stickyNavCssClass);
|
||||||
|
} else {
|
||||||
|
navBar.removeClass(stickyNavCssClass);
|
||||||
|
}
|
||||||
|
},
|
||||||
|
enable = function () {
|
||||||
|
applyStickNav();
|
||||||
|
win.on('resize', applyStickNav);
|
||||||
|
},
|
||||||
|
init = function () {
|
||||||
|
navBar = jquery('nav.wy-nav-side:first');
|
||||||
|
win = jquery(window);
|
||||||
|
};
|
||||||
|
jquery(init);
|
||||||
|
return {
|
||||||
|
enable : enable
|
||||||
|
};
|
||||||
|
}());
|
||||||
|
return {
|
||||||
|
StickyNav : stickyNav
|
||||||
|
};
|
||||||
|
}($));
|
||||||
BIN
mat/plant.mat
Normal file
BIN
mat/plant.mat
Normal file
Binary file not shown.
Loading…
Reference in New Issue
Block a user