commit 06cf168fab5aa11841600cfac2cc3638f95bda44 Author: Thomas Dehaeze Date: Thu Jan 30 15:10:45 2020 +0100 Initial commit diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..56946c3 --- /dev/null +++ b/.gitignore @@ -0,0 +1,48 @@ +figs/*.svg +*.autosave +*.original +old/ + +# Windows default autosave extension +*.asv + +# OSX / *nix default autosave extension +*.m~ + +# Compiled MEX binaries (all platforms) +*.mex* + +# Packaged app and toolbox files +*.mlappinstall +*.mltbx + +# Generated helpsearch folders +helpsearch*/ + +# Simulink code generation folders +slprj/ +sccprj/ + +# Matlab code generation folders +codegen/ + +# Simulink autosave extension +*.autosave + +# Simulink cache files +*.slxc + +# Octave session info +octave-workspace + +## Build tool auxiliary files: +*.fdb_latexmk +*.synctex +*.synctex(busy) +*.synctex.gz +*.synctex.gz(busy) +*.pdfsync + +# auto folder when using emacs and auctex +./auto/* +*.el diff --git a/css/htmlize.css b/css/htmlize.css new file mode 100644 index 0000000..0b32a03 --- /dev/null +++ b/css/htmlize.css @@ -0,0 +1,145 @@ +.org-bold { /* bold */ font-weight: bold; } +.org-bold-italic { /* bold-italic */ font-weight: bold; font-style: italic; } +.org-buffer-menu-buffer { /* buffer-menu-buffer */ font-weight: bold; } +.org-builtin { /* font-lock-builtin-face */ color: #7a378b; } +.org-button { /* button */ text-decoration: underline; } +.org-calendar-today { /* calendar-today */ text-decoration: underline; } +.org-change-log-acknowledgement { /* change-log-acknowledgement */ color: #b22222; } +.org-change-log-conditionals { /* change-log-conditionals */ color: #a0522d; } +.org-change-log-date { /* change-log-date */ color: #8b2252; } +.org-change-log-email { /* change-log-email */ color: #a0522d; } +.org-change-log-file { /* change-log-file */ color: #0000ff; } +.org-change-log-function { /* change-log-function */ color: #a0522d; } +.org-change-log-list { /* change-log-list */ color: #a020f0; } +.org-change-log-name { /* change-log-name */ color: #008b8b; } +.org-comint-highlight-input { /* comint-highlight-input */ font-weight: bold; } +.org-comint-highlight-prompt { /* comint-highlight-prompt */ color: #00008b; } +.org-comment { /* font-lock-comment-face */ color: #999988; font-style: italic; } +.org-comment-delimiter { /* font-lock-comment-delimiter-face */ color: #999988; font-style: italic; } +.org-completions-annotations { /* completions-annotations */ font-style: italic; } +.org-completions-common-part { /* completions-common-part */ color: #000000; background-color: #ffffff; } +.org-completions-first-difference { /* completions-first-difference */ font-weight: bold; } +.org-constant { /* font-lock-constant-face */ color: #008b8b; } +.org-diary { /* diary */ color: #ff0000; } +.org-diff-context { /* diff-context */ color: #7f7f7f; } +.org-diff-file-header { /* diff-file-header */ background-color: #b3b3b3; font-weight: bold; } +.org-diff-function { /* diff-function */ background-color: #cccccc; } +.org-diff-header { /* diff-header */ background-color: #cccccc; } +.org-diff-hunk-header { /* diff-hunk-header */ background-color: #cccccc; } +.org-diff-index { /* diff-index */ background-color: #b3b3b3; font-weight: bold; } +.org-diff-nonexistent { /* diff-nonexistent */ background-color: #b3b3b3; font-weight: bold; } +.org-diff-refine-change { /* diff-refine-change */ background-color: #d9d9d9; } +.org-dired-directory { /* dired-directory */ color: #0000ff; } +.org-dired-flagged { /* dired-flagged */ color: #ff0000; font-weight: bold; } +.org-dired-header { /* dired-header */ color: #228b22; } +.org-dired-ignored { /* dired-ignored */ color: #7f7f7f; } +.org-dired-mark { /* dired-mark */ color: #008b8b; } +.org-dired-marked { /* dired-marked */ color: #ff0000; font-weight: bold; } +.org-dired-perm-write { /* dired-perm-write */ color: #b22222; } +.org-dired-symlink { /* dired-symlink */ color: #a020f0; } +.org-dired-warning { /* dired-warning */ color: #ff0000; font-weight: bold; } +.org-doc { /* font-lock-doc-face */ color: #8b2252; } +.org-escape-glyph { /* escape-glyph */ color: #a52a2a; } +.org-file-name-shadow { /* file-name-shadow */ color: #7f7f7f; } +.org-flyspell-duplicate { /* flyspell-duplicate */ color: #cdad00; font-weight: bold; text-decoration: underline; } +.org-flyspell-incorrect { /* flyspell-incorrect */ color: #ff4500; font-weight: bold; text-decoration: underline; } +.org-fringe { /* fringe */ background-color: #f2f2f2; } +.org-function-name { /* font-lock-function-name-face */ color: teal; } +.org-header-line { /* header-line */ color: #333333; background-color: #e5e5e5; } +.org-help-argument-name { /* help-argument-name */ font-style: italic; } +.org-highlight { /* highlight */ background-color: #b4eeb4; } +.org-holiday { /* holiday */ background-color: #ffc0cb; } +.org-isearch { /* isearch */ color: #b0e2ff; background-color: #cd00cd; } +.org-isearch-fail { /* isearch-fail */ background-color: #ffc1c1; } +.org-italic { /* italic */ font-style: italic; } +.org-keyword { /* font-lock-keyword-face */ color: #0086b3; } +.org-lazy-highlight { /* lazy-highlight */ background-color: #afeeee; } +.org-link { /* link */ color: #0000ff; text-decoration: underline; } +.org-link-visited { /* link-visited */ color: #8b008b; text-decoration: underline; } +.org-log-edit-header { /* log-edit-header */ color: #a020f0; } +.org-log-edit-summary { /* log-edit-summary */ color: #0000ff; } +.org-log-edit-unknown-header { /* log-edit-unknown-header */ color: #b22222; } +.org-match { /* match */ background-color: #ffff00; } +.org-next-error { /* next-error */ background-color: #eedc82; } +.org-nobreak-space { /* nobreak-space */ color: #a52a2a; text-decoration: underline; } +.org-org-archived { /* org-archived */ color: #7f7f7f; } +.org-org-block { /* org-block */ color: #7f7f7f; } +.org-org-block-begin-line { /* org-block-begin-line */ color: #b22222; } +.org-org-block-end-line { /* org-block-end-line */ color: #b22222; } +.org-org-checkbox { /* org-checkbox */ font-weight: bold; } +.org-org-checkbox-statistics-done { /* org-checkbox-statistics-done */ color: #228b22; font-weight: bold; } +.org-org-checkbox-statistics-todo { /* org-checkbox-statistics-todo */ color: #ff0000; font-weight: bold; } +.org-org-clock-overlay { /* org-clock-overlay */ background-color: #ffff00; } +.org-org-code { /* org-code */ color: #7f7f7f; } +.org-org-column { /* org-column */ background-color: #e5e5e5; } +.org-org-column-title { /* org-column-title */ background-color: #e5e5e5; font-weight: bold; text-decoration: underline; } +.org-org-date { /* org-date */ color: #a020f0; text-decoration: underline; } +.org-org-document-info { /* org-document-info */ color: #191970; } +.org-org-document-info-keyword { /* org-document-info-keyword */ color: #7f7f7f; } +.org-org-document-title { /* org-document-title */ color: #191970; font-size: 144%; font-weight: bold; } +.org-org-done { /* org-done */ color: #228b22; font-weight: bold; } +.org-org-drawer { /* org-drawer */ color: #0000ff; } +.org-org-ellipsis { /* org-ellipsis */ color: #b8860b; text-decoration: underline; } +.org-org-footnote { /* org-footnote */ color: #a020f0; text-decoration: underline; } +.org-org-formula { /* org-formula */ color: #b22222; } +.org-org-headline-done { /* org-headline-done */ color: #bc8f8f; } +.org-org-hide { /* org-hide */ color: #ffffff; } +.org-org-latex-and-export-specials { /* org-latex-and-export-specials */ color: #8b4513; } +.org-org-level-1 { /* org-level-1 */ color: #0000ff; } +.org-org-level-2 { /* org-level-2 */ color: #a0522d; } +.org-org-level-3 { /* org-level-3 */ color: #a020f0; } +.org-org-level-4 { /* org-level-4 */ color: #b22222; } +.org-org-level-5 { /* org-level-5 */ color: #228b22; } +.org-org-level-6 { /* org-level-6 */ color: #008b8b; } +.org-org-level-7 { /* org-level-7 */ color: #7a378b; } +.org-org-level-8 { /* org-level-8 */ color: #8b2252; } +.org-org-link { /* org-link */ color: #0000ff; text-decoration: underline; } +.org-org-meta-line { /* org-meta-line */ color: #b22222; } +.org-org-mode-line-clock { /* org-mode-line-clock */ color: #000000; background-color: #bfbfbf; } +.org-org-mode-line-clock-overrun { /* org-mode-line-clock-overrun */ color: #000000; background-color: #ff0000; } +.org-org-quote { /* org-quote */ color: #7f7f7f; } +.org-org-scheduled { /* org-scheduled */ color: #006400; } +.org-org-scheduled-previously { /* org-scheduled-previously */ color: #b22222; } +.org-org-scheduled-today { /* org-scheduled-today */ color: #006400; } +.org-org-sexp-date { /* org-sexp-date */ color: #a020f0; } +.org-org-special-keyword { /* org-special-keyword */ color: #a020f0; } +.org-org-table { /* org-table */ color: #0000ff; } +.org-org-tag { /* org-tag */ font-weight: bold; } +.org-org-target { /* org-target */ text-decoration: underline; } +.org-org-time-grid { /* org-time-grid */ color: #b8860b; } +.org-org-todo { /* org-todo */ color: #ff0000; font-weight: bold; } +.org-org-upcoming-deadline { /* org-upcoming-deadline */ color: #b22222; } +.org-org-verbatim { /* org-verbatim */ color: #7f7f7f; } +.org-org-verse { /* org-verse */ color: #7f7f7f; } +.org-org-warning { /* org-warning */ color: #ff0000; font-weight: bold; } +.org-outline-1 { /* outline-1 */ color: #0000ff; } +.org-outline-2 { /* outline-2 */ color: #a0522d; } +.org-outline-3 { /* outline-3 */ color: #a020f0; } +.org-outline-4 { /* outline-4 */ color: #b22222; } +.org-outline-5 { /* outline-5 */ color: #228b22; } +.org-outline-6 { /* outline-6 */ color: #008b8b; } +.org-outline-7 { /* outline-7 */ color: #7a378b; } +.org-outline-8 { /* outline-8 */ color: #8b2252; } +.org-preprocessor { /* font-lock-preprocessor-face */ color: #7a378b; } +.org-query-replace { /* query-replace */ color: #b0e2ff; background-color: #cd00cd; } +.org-regexp-grouping-backslash { /* font-lock-regexp-grouping-backslash */ font-weight: bold; } +.org-regexp-grouping-construct { /* font-lock-regexp-grouping-construct */ font-weight: bold; } +.org-region { /* region */ background-color: #eedc82; } +.org-secondary-selection { /* secondary-selection */ background-color: #ffff00; } +.org-shadow { /* shadow */ color: #7f7f7f; } +.org-show-paren-match { /* show-paren-match */ background-color: #40e0d0; } +.org-show-paren-mismatch { /* show-paren-mismatch */ color: #ffffff; background-color: #a020f0; } +.org-string { /* font-lock-string-face */ color: #dd1144; } +.org-tool-bar { /* tool-bar */ color: #000000; background-color: #bfbfbf; } +.org-tooltip { /* tooltip */ color: #000000; background-color: #ffffe0; } +.org-trailing-whitespace { /* trailing-whitespace */ background-color: #ff0000; } +.org-type { /* font-lock-type-face */ color: #228b22; } +.org-underline { /* underline */ text-decoration: underline; } +.org-variable-name { /* font-lock-variable-name-face */ color: teal; } +.org-warning { /* font-lock-warning-face */ color: #ff0000; font-weight: bold; } +.org-widget-button { /* widget-button */ font-weight: bold; } +.org-widget-button-pressed { /* widget-button-pressed */ color: #ff0000; } +.org-widget-documentation { /* widget-documentation */ color: #006400; } +.org-widget-field { /* widget-field */ background-color: #d9d9d9; } +.org-widget-inactive { /* widget-inactive */ color: #7f7f7f; } +.org-widget-single-line-field { /* widget-single-line-field */ background-color: #d9d9d9; } diff --git a/css/readtheorg.css b/css/readtheorg.css new file mode 100644 index 0000000..1690bd0 --- /dev/null +++ b/css/readtheorg.css @@ -0,0 +1,1095 @@ +@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic|Roboto+Slab:400,700|Inconsolata:400,700); +@import url(https://maxcdn.bootstrapcdn.com/font-awesome/4.3.0/css/font-awesome.min.css); + +h1,h2,h3,h4,h5,h6,legend{ + font-family:"Roboto Slab","ff-tisa-web-pro","Georgia",Arial,sans-serif; + font-weight:700; + margin-top:0; +} + +h1{ + font-size:175%; +} + +.subtitle{ + font-size:95%; /* of h1 */ +} + +h2{ + font-size:150%; +} + +h3{ + font-size:125%; +} + +h4{ + font-size:115%; +} + +h5{ + font-size:110%; +} + +h6{ + font-size:100%; +} + +h4,h5,h6{ + color:#2980B9; + font-weight:300; +} + +html{ + -ms-text-size-adjust:100%; + -webkit-text-size-adjust:100%; + font-size:100%; + height:100%; + overflow-x:hidden; +} + +body{ + background:#edf0f2; + color:#404040; + font-family:"Lato","proxima-nova","Helvetica Neue",Arial,sans-serif; + font-weight:normal; + margin:0; + min-height:100%; + overflow-x:hidden; +} + +#content{ + background:#fcfcfc; + height:100%; + margin-left:300px; + /* margin:auto; */ + max-width:1200px; + min-height:100%; + padding:1.618em 3.236em; +} + +p{ + font-size:16px; + line-height:24px; + margin:0px 0px 24px 0px; +} + +b,strong{ + font-weight:bold} + +blockquote{ + background-color: #F0F0F0; + border-left:5px solid #CCCCCC; + font-style:italic; + line-height:24px; + margin:0px 0px 24px 0px; + /* margin-left:24px; */ + padding: 6px 20px; +} + +ul,ol,dl{ + line-height:24px; + list-style-image:none; + /* list-style:none; */ + margin:0px 0px 24px 0px; + padding:0; +} + +li{ + margin-left: 24px; +} + +dd{ + margin:0; +} + +#content .section ul,#content .toctree-wrapper ul,article ul{ + list-style:disc; + line-height:24px; + margin-bottom:24px} + +#content .section ul li,#content .toctree-wrapper ul li,article ul li{ + list-style:disc; + margin-left:24px} + +#content .section ul li p:last-child,#content .toctree-wrapper ul li p:last-child,article ul li p:last-child{ + margin-bottom:0} + +#content .section ul li ul,#content .toctree-wrapper ul li ul,article ul li ul{ + margin-bottom:0} + +#content .section ul li li,#content .toctree-wrapper ul li li,article ul li li{ + list-style:circle} + +#content .section ul li li li,#content .toctree-wrapper ul li li li,article ul li li li{ + list-style:square} + +#content .section ul li ol li,#content .toctree-wrapper ul li ol li,article ul li ol li{ + list-style:decimal} + +#content .section ol,#content ol,article ol{ + list-style:decimal; + line-height:24px; + margin-bottom:24px} + +#content .section ol li,#content ol li,article ol li{ + list-style:decimal; + margin-left:24px} + +#content .section ol li p:last-child,#content ol li p:last-child,article ol li p:last-child{ + margin-bottom:0} + +#content .section ol li ul,#content ol li ul,article ol li ul{ + margin-bottom:0} + +#content .section ol li ul li,#content ol li ul li,article ol li ul li{ + list-style:disc} + +dl dt{ + font-weight:bold; +} + +dl p,dl table,dl ul,dl ol{ + margin-bottom:12px !important; +} + +dl dd{ + margin:0 0 12px 24px; +} + +@media print{ + .codeblock,pre.src{ + white-space:pre.src-wrap} +} + +@media print{ + html,body,section{ + background:none !important} + + *{ + box-shadow:none !important; + text-shadow:none !important; + filter:none !important; + -ms-filter:none !important} + + a,a:visited{ + text-decoration:underline} + + pre.src,blockquote{ + page-break-inside:avoid} + + thead{ + display:table-header-group} + + tr,img{ + page-break-inside:avoid} + + img{ + max-width:100% !important} + + @page{ + margin:0.5cm} + + p,h2,h3{ + orphans:3; + widows:3} + + h2,h3{ + page-break-after:avoid} +} + +@media print{ + #postamble{ + display:none} + + #content{ + margin-left:0} +} + +@media print{ + #table-of-contents{ + display:none} + + @page{ + size: auto; + margin: 25mm 25mm 25mm 25mm;} + + body { + margin: 0px;} +} + +@media screen and (max-width: 768px){ +} + +@media only screen and (max-width: 480px){ +} + +@media screen and (max-width: 768px){ + .tablet-hide{ + display:none} +} + +@media screen and (max-width: 480px){ + .mobile-hide{ + display:none} +} + +@media screen and (max-width: 480px){ +} + +@media screen and (max-width: 768px){ + #content{ + margin-left:0} + + #content #content{ + padding:1.618em} + + #content.shift{ + position:fixed; + min-width:100%; + left:85%; + top:0; + height:100%; + overflow:hidden} +} + +@media screen and (min-width: 1400px){ + #content{ + background:rgba(0,0,0,0.05)} + + #content{ + background:#fcfcfc} +} + +@media screen and (max-width: 768px){ + #copyright{ + width:85%; + display:none} + + #copyright.shift{ + display:block} + + img{ + width:100%; + height:auto} +} + +@media screen and (max-width: 480px){ + #content .sidebar{ + width:100%} +} + +code{ + background:#fff; + border:solid 1px #e1e4e5; + /* color:#000; for clickable code */ + font-family:Consolas,"Andale Mono WT","Andale Mono","Lucida Console","Lucida Sans Typewriter","DejaVu Sans Mono","Bitstream Vera Sans Mono","Liberation Mono","Nimbus Mono L",Monaco,"Courier New",Courier,monospace; + font-size:75%; + max-width:100%; + overflow-x:auto; + padding:0 5px; + white-space:nowrap; +} + +.codeblock-example{ + border:1px solid #e1e4e5; + border-bottom:none; + padding:24px; + padding-top:48px; + font-weight:500; + background:#fff; + position:relative} + +.codeblock-example:after{ + content:"Example"; + position:absolute; + top:0px; + left:0px; + background:#9B59B6; + color:#fff; + padding:6px 12px} + +.codeblock-example.prettyprint-example-only{ + border:1px solid #e1e4e5; + margin-bottom:24px} + +.codeblock,pre.src,#content .literal-block{ + border:1px solid #e1e4e5; + padding:12px; + overflow-x:auto; + background:#fff; + margin:1px 0 24px 0} + +pre.src{ + /* color:#404040; */ + display:block; + font-family:Consolas,"Andale Mono WT","Andale Mono","Lucida Console","Lucida Sans Typewriter","DejaVu Sans Mono","Bitstream Vera Sans Mono","Liberation Mono","Nimbus Mono L",Monaco,"Courier New",Courier,monospace; + font-size:12px; + line-height:1.5; + margin:1px 0px 24px 0px; + overflow:auto; + padding:12px; + white-space:pre; +} + +.example{ + background:#f3f6f6; + border:1px solid #e1e4e5; + color:#404040; + font-size: 12px; + line-height: 1.5; + margin-bottom:24px; + padding:12px; +} + +table{ + border-collapse:collapse; + border-spacing:0; + empty-cells:show; + margin-bottom:24px; + border-bottom:1px solid #e1e4e5; +} + +td{ + vertical-align:top} + +table td,table th{ + font-size:90%; + margin:0; + overflow:visible; + padding:8px 16px; + background-color:white; + border:1px solid #e1e4e5; +} + +table thead th{ + font-weight:bold; + border-top:3px solid #e1e4e5; + border-bottom:1px solid #e1e4e5; +} + +table caption{ + color:#000; + font:italic 85%/1 arial,sans-serif; + padding:1em 0; +} + +table tr:nth-child(2n-1) td{ + background-color:#f3f6f6; +} + +table tr:nth-child(2n) td{ + background-color:white; +} + +.figure p{ + color:#000; + font:italic 85%/1 arial,sans-serif; + padding:1em 0; +} + +.rotate-90{ + -webkit-transform:rotate(90deg); + -moz-transform:rotate(90deg); + -ms-transform:rotate(90deg); + -o-transform:rotate(90deg); + transform:rotate(90deg); +} + +.rotate-270{ + -webkit-transform:rotate(270deg); + -moz-transform:rotate(270deg); + -ms-transform:rotate(270deg); + -o-transform:rotate(270deg); + transform:rotate(270deg); +} + +#toggle-sidebar, +#table-of-contents .close-sidebar { + display: none; +} + +@media screen and (max-width: 768px) { + #table-of-contents { + display: none; + width: 60%; + } + + #table-of-contents h2 a { + display: block; + } + + #table-of-contents:target { + display: block; + } + + #copyright, #postamble { + display: none; + } + + #toggle-sidebar { + background-color: #2980B9; + display: block; + margin-bottom: 1.6em; + padding: 0.6em; + text-align: center; + } + + #toggle-sidebar h2 { + background-color:#2980B9; + width:100%; + height:50px; + left:0; + top:0; + color: white; + font-size: 100%; + line-height: 50px; + position:fixed; + margin: 0; + padding: 0; + opacity:0.7; + } + + #table-of-contents .close-sidebar { + color: rgba(255, 255, 255, 0.3); + display: inline-block; + margin: 0px 10px 0px 45px; + padding: 10px; + } +} + +*{ + -webkit-box-sizing:border-box; + -moz-box-sizing:border-box; + box-sizing:border-box; +} + +figcaption,figure,footer,header,hgroup,nav{ + display:block} + +ins{ + background:#ff9; + color:#000; + text-decoration:none} + +mark{ + background:#ff0; + color:#000; + font-style:italic; + font-weight:bold} + +small{ + font-size:85%} + +sub,sup{ + font-size:75%; + line-height:0; + position:relative; + vertical-align:baseline} + +sup{ + top:-0.5em} + +sub{ + bottom:-0.25em} + +img{ + -ms-interpolation-mode:bicubic; + vertical-align:middle; 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+ display: block; + float: right; + font-size: 80%; + font-weight: normal; + margin: 0 3px; + padding: 1px 2px; + border-radius: 10px; +} + +.tag .FLAGGED { + background-color: #DB2D27; + border: 1px solid #DB2D27; + color: white; + font-weight: bold; +} + +.timestamp { + font-family: Consolas,"Andale Mono WT","Andale Mono","Lucida Console","Lucida Sans Typewriter","DejaVu Sans Mono","Bitstream Vera Sans Mono","Liberation Mono","Nimbus Mono L",Monaco,"Courier New",Courier,monospace; + font-size: 90%; + color: navy; +} + +.nav .timestamp { + color: inherit; +} + +.inlinetask { + background: #FFF9E3; /* url(dialog-todo.png) no-repeat 10px 8px; */ + border: 3px solid #FFEB8E; + /* border-right-style: none; */ + /* border-left-style: none; */ + /* padding: 10px 20px 10px 60px; */ + padding: 9px 12px; + margin-bottom: 24px; + font-family:"Roboto Slab","ff-tisa-web-pro","Georgia",Arial,sans-serif} diff --git a/data/simscape_gravity.zip b/data/simscape_gravity.zip new file mode 100644 index 0000000..0c2ef52 Binary files /dev/null and b/data/simscape_gravity.zip differ diff --git a/figs/sim_add_external_force.pdf b/figs/sim_add_external_force.pdf new file mode 100644 index 0000000..1c0ccf2 Binary files /dev/null and b/figs/sim_add_external_force.pdf differ diff --git a/figs/sim_add_external_force.png b/figs/sim_add_external_force.png new file mode 100644 index 0000000..c963ace Binary files /dev/null and b/figs/sim_add_external_force.png differ diff --git a/figs/sim_change_eq_position.pdf b/figs/sim_change_eq_position.pdf new file mode 100644 index 0000000..9d40771 Binary files /dev/null and b/figs/sim_change_eq_position.pdf differ diff --git a/figs/sim_change_eq_position.png b/figs/sim_change_eq_position.png new file mode 100644 index 0000000..0b1517a Binary files /dev/null and b/figs/sim_change_eq_position.png differ diff --git a/figs/sim_change_initial_position.pdf b/figs/sim_change_initial_position.pdf new file mode 100644 index 0000000..7fa3e58 Binary files /dev/null and b/figs/sim_change_initial_position.pdf differ diff --git a/figs/sim_change_initial_position.png b/figs/sim_change_initial_position.png new file mode 100644 index 0000000..fe62ca9 Binary files /dev/null and b/figs/sim_change_initial_position.png differ diff --git a/figs/sim_init.pdf b/figs/sim_init.pdf new file mode 100644 index 0000000..8f17b10 Binary files /dev/null and b/figs/sim_init.pdf differ diff --git a/figs/sim_init.png b/figs/sim_init.png new file mode 100644 index 0000000..2bed7a6 Binary files /dev/null and b/figs/sim_init.png differ diff --git a/figs/simscape_model.png b/figs/simscape_model.png new file mode 100644 index 0000000..aa5db3d Binary files /dev/null and b/figs/simscape_model.png differ diff --git a/gravity_test.slx b/gravity_test.slx new file mode 100644 index 0000000..a9aca55 Binary files /dev/null and b/gravity_test.slx differ diff --git a/index.html b/index.html new file mode 100644 index 0000000..56db05c --- /dev/null +++ b/index.html @@ -0,0 +1,424 @@ + + + + + + + + +Gravity with Simscape Models + + + + + + + + + + + + + + + +
+ UP + | + HOME +
+

Gravity with Simscape Models

+ + +

+We would like to include gravity in a Simscape multi-body model while starting the simulation at the equilibrium. +

+ +

+The basic idea is to first perform a simulation of the system until it goes at it rest position and save the rest position forces and deflection in each joint. +

+ +

+We can then think of three solutions to start a new simulation directly at the steady state position: +

+ + +

+The three solutions are tested below. +

+ +
+

1 Simulink

+
+
+
open 'gravity_test.slx'
+
+
+ + +
+

simscape_model.png +

+

Figure 1: Simscape model used for the simulations

+
+
+
+ +
+

2 Initial Simulation

+
+
+
g = -10; % [m/s^2]
+
+k = 1e3; % Stiffness [N/m]
+c = 10; % Damping [N/(m/s)]
+
+l0 = 0; % Initial wanted position [m]
+leq = 0; % equilibrium position [m]
+
+F_ext = 0; % External force [N]
+F_act = 0; % Actuator force [N]
+
+
+ + +
+

sim_init.png +

+

Figure 2: Initial Simulation (png, pdf)

+
+
+
+ +
+

3 Change the equilibrium position

+
+
+
l0 = 0; % Initial wanted position [m]
+leq = -out_init.Fm.Data(end)/k; % equilibrium position [m]
+
+F_ext = 0; % External force [N]
+F_act = 0; % Actuator force [N]
+
+
+ + +
+

sim_change_eq_position.png +

+

Figure 3: Simulation after changing the equilibrium position of the joint (png, pdf)

+
+
+
+ +
+

4 Add external force

+
+
+
l0 = 0; % Initial wanted position [m]
+leq = 0; % equilibrium position [m]
+
+F_ext = -out_init.Fm.Data(end); % External force [N]
+F_act = 0; % Actuator force [N]
+
+
+ + +
+

sim_add_external_force.png +

+

Figure 4: Simulater after adding an external force applied to the solid (png, pdf)

+
+
+
+
+

5 Change initial position

+
+
+
l0 = out_init.d.Data(end); % Initial wanted position [m]
+leq = 0; % equilibrium position [m]
+
+F_ext = 0; % External force [N]
+F_act = 0; % Actuator force [N]
+
+
+ + +
+

sim_change_initial_position.png +

+

Figure 5: Simulation after changing the initial position of the joint (png, pdf)

+
+
+
+
+

6 Conclusion

+
+

+Changing the equilibrium position of each joint seem the most practical solution. +

+
+
+
+
+

Author: Dehaeze Thomas

+

Created: 2020-01-30 jeu. 15:07

+
+ + diff --git a/index.org b/index.org new file mode 100644 index 0000000..a6ab7b5 --- /dev/null +++ b/index.org @@ -0,0 +1,224 @@ +#+TITLE: Gravity with Simscape Models +:DRAWER: +#+STARTUP: overview + +#+LANGUAGE: en +#+EMAIL: dehaeze.thomas@gmail.com +#+AUTHOR: Dehaeze Thomas + +#+HTML_LINK_HOME: ./index.html +#+HTML_LINK_UP: ./index.html + +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: + +#+HTML_MATHJAX: align: center tagside: right font: TeX + +#+PROPERTY: header-args:matlab :session *MATLAB* +#+PROPERTY: header-args:matlab+ :comments org +#+PROPERTY: header-args:matlab+ :results none +#+PROPERTY: header-args:matlab+ :exports org +#+PROPERTY: header-args:matlab+ :tangle matlab/simscape_gravity.m +#+PROPERTY: header-args:matlab+ :eval no-export +#+PROPERTY: header-args:matlab+ :output-dir figs +#+PROPERTY: header-args:matlab+ :mkdirp yes +:END: + +* Introduction :ignore: +We would like to include gravity in a Simscape multi-body model while starting the simulation at the equilibrium. + +The basic idea is to first perform a simulation of the system until it goes at it rest position and save the rest position forces and deflection in each joint. + +We can then think of three solutions to start a new simulation directly at the steady state position: +- Change the equilibrium position $l_0$ of each joint such that at $t=0$, $k \times l_0$ is equal to the previously measured force in the joint. + Here, it is suppose that we constrain the initial position of the joint to be equal to zero. + Then, these forces cancel each other and the simulation starts at equilibrium. +- Add an External force (or maybe the "Internal Force") in the direction of the joint (the "resolution frame" is fixed to the solids) equal to the opposite of the previously measured force. +- After the first simulation, measure the final change of position of each joint, then set the initial position to be the measured static position. + Then, the simulation will start at equilibrium, but all the elements will be "deflected". + +The three solutions are tested below. + +* ZIP file containing the data and matlab files :ignore: +#+begin_src bash :exports none :results none + if [ matlab/simscape_gravity.m -nt data/simscape_gravity.zip ]; then + cp matlab/simscape_gravity.m simscape_gravity.m; + zip data/simscape_gravity \ + gravity_test.slx \ + simscape_gravity.m + rm simscape_gravity.m; + fi +#+end_src + +#+begin_note +All the files (data and Matlab scripts) are accessible [[file:data/simscape_gravity.zip][here]]. +#+end_note + +* Matlab Init :noexport:ignore: +#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) +<> +#+end_src + +#+begin_src matlab :exports none :results silent :noweb yes +<> +#+end_src + +* Simulink +#+begin_src matlab + open 'gravity_test.slx' +#+end_src + +#+name: fig:simscape_model +#+caption: Simscape model used for the simulations +[[file:figs/simscape_model.png]] + +* Initial Simulation +#+begin_src matlab + g = -10; % [m/s^2] + + k = 1e3; % Stiffness [N/m] + c = 10; % Damping [N/(m/s)] + + l0 = 0; % Initial wanted position [m] + leq = 0; % equilibrium position [m] + + F_ext = 0; % External force [N] + F_act = 0; % Actuator force [N] +#+end_src + +#+begin_src matlab :exports none + out_init = sim('gravity_test.slx') + + out_init.d.Name = 'Displacement'; + out_init.Fm.Name = 'Force Sensor'; +#+end_src + +#+begin_src matlab :exports none + figure; + subplot(1,2,1) + plot(out_init.d) + title(''); + subplot(1,2,2) + plot(out_init.Fm) + title(''); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/sim_init.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:sim_init +#+CAPTION: Initial Simulation ([[./figs/sim_init.png][png]], [[./figs/sim_init.pdf][pdf]]) +[[file:figs/sim_init.png]] + +* Change the equilibrium position +#+begin_src matlab + l0 = 0; % Initial wanted position [m] + leq = -out_init.Fm.Data(end)/k; % equilibrium position [m] + + F_ext = 0; % External force [N] + F_act = 0; % Actuator force [N] +#+end_src + +#+begin_src matlab :exports none + out = sim('gravity_test.slx'); + + out.d.Name = 'Displacement'; + out.Fm.Name = 'Force Sensor'; +#+end_src + +#+begin_src matlab :exports none + figure; + subplot(1,2,1) + plot(out.d) + title(''); + subplot(1,2,2) + plot(out.Fm) + title(''); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/sim_change_eq_position.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:sim_change_eq_position +#+CAPTION: Simulation after changing the equilibrium position of the joint ([[./figs/sim_change_eq_position.png][png]], [[./figs/sim_change_eq_position.pdf][pdf]]) +[[file:figs/sim_change_eq_position.png]] + +* Add external force +#+begin_src matlab + l0 = 0; % Initial wanted position [m] + leq = 0; % equilibrium position [m] + + F_ext = -out_init.Fm.Data(end); % External force [N] + F_act = 0; % Actuator force [N] +#+end_src + +#+begin_src matlab :exports none + out = sim('gravity_test.slx'); + + out.d.Name = 'Displacement'; + out.Fm.Name = 'Force Sensor'; +#+end_src + +#+begin_src matlab :exports none + figure; + subplot(1,2,1) + plot(out.d) + title(''); + subplot(1,2,2) + plot(out.Fm) + title(''); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/sim_add_external_force.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:sim_add_external_force +#+CAPTION: Simulater after adding an external force applied to the solid ([[./figs/sim_add_external_force.png][png]], [[./figs/sim_add_external_force.pdf][pdf]]) +[[file:figs/sim_add_external_force.png]] +* Change initial position +#+begin_src matlab + l0 = out_init.d.Data(end); % Initial wanted position [m] + leq = 0; % equilibrium position [m] + + F_ext = 0; % External force [N] + F_act = 0; % Actuator force [N] +#+end_src + +#+begin_src matlab :exports none + out = sim('gravity_test.slx'); + + out.d.Name = 'Displacement'; + out.Fm.Name = 'Force Sensor'; +#+end_src + +#+begin_src matlab :exports none + figure; + subplot(1,2,1) + plot(out.d) + title(''); + subplot(1,2,2) + plot(out.Fm) + title(''); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/sim_change_initial_position.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:sim_change_initial_position +#+CAPTION: Simulation after changing the initial position of the joint ([[./figs/sim_change_initial_position.png][png]], [[./figs/sim_change_initial_position.pdf][pdf]]) +[[file:figs/sim_change_initial_position.png]] +* Conclusion +Changing the equilibrium position of each 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