Initial commit
This commit is contained in:
commit
06cf168fab
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.gitignore
vendored
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48
.gitignore
vendored
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|||||||
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figs/*.svg
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||||||
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*.autosave
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||||||
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*.original
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||||||
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old/
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||||||
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||||||
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# Windows default autosave extension
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||||||
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*.asv
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||||||
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||||||
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# OSX / *nix default autosave extension
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||||||
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*.m~
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||||||
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||||||
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# Compiled MEX binaries (all platforms)
|
||||||
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*.mex*
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||||||
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||||||
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# Packaged app and toolbox files
|
||||||
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*.mlappinstall
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||||||
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*.mltbx
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||||||
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||||||
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# Generated helpsearch folders
|
||||||
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helpsearch*/
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||||||
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||||||
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# Simulink code generation folders
|
||||||
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slprj/
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||||||
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sccprj/
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||||||
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||||||
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# Matlab code generation folders
|
||||||
|
codegen/
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||||||
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||||||
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# Simulink autosave extension
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||||||
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*.autosave
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||||||
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||||||
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# Simulink cache files
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||||||
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*.slxc
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||||||
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|
||||||
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# Octave session info
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||||||
|
octave-workspace
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||||||
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||||||
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## Build tool auxiliary files:
|
||||||
|
*.fdb_latexmk
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||||||
|
*.synctex
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||||||
|
*.synctex(busy)
|
||||||
|
*.synctex.gz
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||||||
|
*.synctex.gz(busy)
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||||||
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*.pdfsync
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||||||
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||||||
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# auto folder when using emacs and auctex
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||||||
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./auto/*
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||||||
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*.el
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||||||
145
css/htmlize.css
Normal file
145
css/htmlize.css
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|||||||
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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; }
|
||||||
|
.org-builtin { /* font-lock-builtin-face */ color: #7a378b; }
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||||||
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.org-button { /* button */ text-decoration: underline; }
|
||||||
|
.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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||||||
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.org-change-log-conditionals { /* change-log-conditionals */ color: #a0522d; }
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||||||
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.org-change-log-date { /* change-log-date */ color: #8b2252; }
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||||||
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.org-change-log-email { /* change-log-email */ color: #a0522d; }
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||||||
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.org-change-log-file { /* change-log-file */ color: #0000ff; }
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||||||
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.org-change-log-function { /* change-log-function */ color: #a0522d; }
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||||||
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.org-change-log-list { /* change-log-list */ color: #a020f0; }
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||||||
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.org-change-log-name { /* change-log-name */ color: #008b8b; }
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||||||
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.org-comint-highlight-input { /* comint-highlight-input */ font-weight: bold; }
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||||||
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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; }
|
||||||
|
.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; }
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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; }
|
||||||
|
.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; }
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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; }
|
||||||
|
.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; }
|
||||||
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.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; }
|
||||||
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.org-outline-2 { /* outline-2 */ color: #a0522d; }
|
||||||
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.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; }
|
||||||
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.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; }
|
||||||
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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; }
|
||||||
|
.org-string { /* font-lock-string-face */ color: #dd1144; }
|
||||||
|
.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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||||||
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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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||||||
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.org-widget-single-line-field { /* widget-single-line-field */ background-color: #d9d9d9; }
|
||||||
1095
css/readtheorg.css
Normal file
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css/readtheorg.css
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File diff suppressed because it is too large
Load Diff
BIN
data/simscape_gravity.zip
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data/simscape_gravity.zip
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figs/sim_add_external_force.pdf
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figs/sim_add_external_force.pdf
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figs/sim_add_external_force.png
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figs/sim_add_external_force.png
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After Width: | Height: | Size: 36 KiB |
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figs/sim_change_eq_position.pdf
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figs/sim_change_eq_position.pdf
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figs/sim_change_eq_position.png
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figs/sim_change_eq_position.png
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figs/sim_change_initial_position.pdf
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figs/sim_change_initial_position.pdf
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figs/sim_change_initial_position.png
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figs/sim_change_initial_position.png
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After Width: | Height: | Size: 97 KiB |
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figs/sim_init.pdf
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figs/sim_init.png
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figs/sim_init.png
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After Width: | Height: | Size: 44 KiB |
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figs/simscape_model.png
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After Width: | Height: | Size: 55 KiB |
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gravity_test.slx
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|||||||
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<?xml version="1.0" encoding="utf-8"?>
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||||||
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<?xml version="1.0" encoding="utf-8"?>
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||||||
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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||||||
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||||
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||||
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<head>
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||||||
|
<!-- 2020-01-30 jeu. 15:07 -->
|
||||||
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||||
|
<meta name="viewport" content="width=device-width, initial-scale=1" />
|
||||||
|
<title>Gravity with Simscape Models</title>
|
||||||
|
<meta name="generator" content="Org mode" />
|
||||||
|
<meta name="author" content="Dehaeze Thomas" />
|
||||||
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<style type="text/css">
|
||||||
|
<!--/*--><![CDATA[/*><!--*/
|
||||||
|
.title { text-align: center;
|
||||||
|
margin-bottom: .2em; }
|
||||||
|
.subtitle { text-align: center;
|
||||||
|
font-size: medium;
|
||||||
|
font-weight: bold;
|
||||||
|
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; }
|
||||||
|
.timestamp-kwd { color: #5f9ea0; }
|
||||||
|
.org-right { margin-left: auto; margin-right: 0px; text-align: right; }
|
||||||
|
.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; }
|
||||||
|
.underline { text-decoration: underline; }
|
||||||
|
#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;
|
||||||
|
padding: 8pt;
|
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|
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<a accesskey="h" href="./index.html"> UP </a>
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|
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<a accesskey="H" href="./index.html"> HOME </a>
|
||||||
|
</div><div id="content">
|
||||||
|
<h1 class="title">Gravity with Simscape Models</h1>
|
||||||
|
<div id="table-of-contents">
|
||||||
|
<h2>Table of Contents</h2>
|
||||||
|
<div id="text-table-of-contents">
|
||||||
|
<ul>
|
||||||
|
<li><a href="#org7dc51cd">1. Simulink</a></li>
|
||||||
|
<li><a href="#org8d21a55">2. Initial Simulation</a></li>
|
||||||
|
<li><a href="#org308b7c9">3. Change the equilibrium position</a></li>
|
||||||
|
<li><a href="#orgf4b9c9b">4. Add external force</a></li>
|
||||||
|
<li><a href="#org93c1a6d">5. Change initial position</a></li>
|
||||||
|
<li><a href="#org4f1210f">6. Conclusion</a></li>
|
||||||
|
</ul>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We would like to include gravity in a Simscape multi-body model while starting the simulation at the equilibrium.
|
||||||
|
</p>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
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.
|
||||||
|
</p>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
We can then think of three solutions to start a new simulation directly at the steady state position:
|
||||||
|
</p>
|
||||||
|
<ul class="org-ul">
|
||||||
|
<li>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.</li>
|
||||||
|
<li>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.</li>
|
||||||
|
<li>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”.</li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The three solutions are tested below.
|
||||||
|
</p>
|
||||||
|
|
||||||
|
<div id="outline-container-org7dc51cd" class="outline-2">
|
||||||
|
<h2 id="org7dc51cd"><span class="section-number-2">1</span> Simulink</h2>
|
||||||
|
<div class="outline-text-2" id="text-1">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">open <span class="org-string">'gravity_test.slx'</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org3b3589c" class="figure">
|
||||||
|
<p><img src="figs/simscape_model.png" alt="simscape_model.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 1: </span>Simscape model used for the simulations</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org8d21a55" class="outline-2">
|
||||||
|
<h2 id="org8d21a55"><span class="section-number-2">2</span> Initial Simulation</h2>
|
||||||
|
<div class="outline-text-2" id="text-2">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">g = <span class="org-type">-</span>10; <span class="org-comment">% [m/s^2]</span>
|
||||||
|
|
||||||
|
k = 1e3; <span class="org-comment">% Stiffness [N/m]</span>
|
||||||
|
c = 10; <span class="org-comment">% Damping [N/(m/s)]</span>
|
||||||
|
|
||||||
|
l0 = 0; <span class="org-comment">% Initial wanted position [m]</span>
|
||||||
|
leq = 0; <span class="org-comment">% equilibrium position [m]</span>
|
||||||
|
|
||||||
|
F_ext = 0; <span class="org-comment">% External force [N]</span>
|
||||||
|
F_act = 0; <span class="org-comment">% Actuator force [N]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org8a4e1c7" class="figure">
|
||||||
|
<p><img src="figs/sim_init.png" alt="sim_init.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 2: </span>Initial Simulation (<a href="./figs/sim_init.png">png</a>, <a href="./figs/sim_init.pdf">pdf</a>)</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org308b7c9" class="outline-2">
|
||||||
|
<h2 id="org308b7c9"><span class="section-number-2">3</span> Change the equilibrium position</h2>
|
||||||
|
<div class="outline-text-2" id="text-3">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">l0 = 0; <span class="org-comment">% Initial wanted position [m]</span>
|
||||||
|
leq = <span class="org-type">-</span>out_init.Fm.Data(end)<span class="org-type">/</span>k; <span class="org-comment">% equilibrium position [m]</span>
|
||||||
|
|
||||||
|
F_ext = 0; <span class="org-comment">% External force [N]</span>
|
||||||
|
F_act = 0; <span class="org-comment">% Actuator force [N]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="orgace9d61" class="figure">
|
||||||
|
<p><img src="figs/sim_change_eq_position.png" alt="sim_change_eq_position.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 3: </span>Simulation after changing the equilibrium position of the joint (<a href="./figs/sim_change_eq_position.png">png</a>, <a href="./figs/sim_change_eq_position.pdf">pdf</a>)</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orgf4b9c9b" class="outline-2">
|
||||||
|
<h2 id="orgf4b9c9b"><span class="section-number-2">4</span> Add external force</h2>
|
||||||
|
<div class="outline-text-2" id="text-4">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">l0 = 0; <span class="org-comment">% Initial wanted position [m]</span>
|
||||||
|
leq = 0; <span class="org-comment">% equilibrium position [m]</span>
|
||||||
|
|
||||||
|
F_ext = <span class="org-type">-</span>out_init.Fm.Data(end); <span class="org-comment">% External force [N]</span>
|
||||||
|
F_act = 0; <span class="org-comment">% Actuator force [N]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="orge24bd38" class="figure">
|
||||||
|
<p><img src="figs/sim_add_external_force.png" alt="sim_add_external_force.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 4: </span>Simulater after adding an external force applied to the solid (<a href="./figs/sim_add_external_force.png">png</a>, <a href="./figs/sim_add_external_force.pdf">pdf</a>)</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div id="outline-container-org93c1a6d" class="outline-2">
|
||||||
|
<h2 id="org93c1a6d"><span class="section-number-2">5</span> Change initial position</h2>
|
||||||
|
<div class="outline-text-2" id="text-5">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">l0 = out_init.d.Data(end); <span class="org-comment">% Initial wanted position [m]</span>
|
||||||
|
leq = 0; <span class="org-comment">% equilibrium position [m]</span>
|
||||||
|
|
||||||
|
F_ext = 0; <span class="org-comment">% External force [N]</span>
|
||||||
|
F_act = 0; <span class="org-comment">% Actuator force [N]</span>
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="orgdedf3a7" class="figure">
|
||||||
|
<p><img src="figs/sim_change_initial_position.png" alt="sim_change_initial_position.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 5: </span>Simulation after changing the initial position of the joint (<a href="./figs/sim_change_initial_position.png">png</a>, <a href="./figs/sim_change_initial_position.pdf">pdf</a>)</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div id="outline-container-org4f1210f" class="outline-2">
|
||||||
|
<h2 id="org4f1210f"><span class="section-number-2">6</span> Conclusion</h2>
|
||||||
|
<div class="outline-text-2" id="text-6">
|
||||||
|
<p>
|
||||||
|
Changing the equilibrium position of each joint seem the most practical solution.
|
||||||
|
</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div id="postamble" class="status">
|
||||||
|
<p class="author">Author: Dehaeze Thomas</p>
|
||||||
|
<p class="date">Created: 2020-01-30 jeu. 15:07</p>
|
||||||
|
</div>
|
||||||
|
</body>
|
||||||
|
</html>
|
||||||
224
index.org
Normal file
224
index.org
Normal file
@ -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: <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>
|
||||||
|
|
||||||
|
#+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)
|
||||||
|
<<matlab-dir>>
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none :results silent :noweb yes
|
||||||
|
<<matlab-init>>
|
||||||
|
#+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")
|
||||||
|
<<plt-matlab>>
|
||||||
|
#+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")
|
||||||
|
<<plt-matlab>>
|
||||||
|
#+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")
|
||||||
|
<<plt-matlab>>
|
||||||
|
#+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")
|
||||||
|
<<plt-matlab>>
|
||||||
|
#+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 joint seem the most practical solution.
|
||||||
7
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vendored
Normal file
7
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vendored
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4
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vendored
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vendored
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vendored
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vendored
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@ -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 = $('#table-of-contents').find('h2');
|
||||||
|
tocTitle.append(closeBtn);
|
||||||
|
});
|
||||||
|
|
||||||
|
window.SphinxRtdTheme = (function (jquery) {
|
||||||
|
var stickyNav = (function () {
|
||||||
|
var navBar,
|
||||||
|
win,
|
||||||
|
stickyNavCssClass = 'stickynav',
|
||||||
|
applyStickNav = function () {
|
||||||
|
if (navBar.height() <= win.height()) {
|
||||||
|
navBar.addClass(stickyNavCssClass);
|
||||||
|
} else {
|
||||||
|
navBar.removeClass(stickyNavCssClass);
|
||||||
|
}
|
||||||
|
},
|
||||||
|
enable = function () {
|
||||||
|
applyStickNav();
|
||||||
|
win.on('resize', applyStickNav);
|
||||||
|
},
|
||||||
|
init = function () {
|
||||||
|
navBar = jquery('nav.wy-nav-side:first');
|
||||||
|
win = jquery(window);
|
||||||
|
};
|
||||||
|
jquery(init);
|
||||||
|
return {
|
||||||
|
enable : enable
|
||||||
|
};
|
||||||
|
}());
|
||||||
|
return {
|
||||||
|
StickyNav : stickyNav
|
||||||
|
};
|
||||||
|
}($));
|
||||||
98
matlab/simscape_gravity.m
Normal file
98
matlab/simscape_gravity.m
Normal file
@ -0,0 +1,98 @@
|
|||||||
|
%% Clear Workspace and Close figures
|
||||||
|
clear; close all; clc;
|
||||||
|
|
||||||
|
%% Intialize Laplace variable
|
||||||
|
s = zpk('s');
|
||||||
|
|
||||||
|
% Simulink
|
||||||
|
|
||||||
|
open 'gravity_test.slx'
|
||||||
|
|
||||||
|
% 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]
|
||||||
|
|
||||||
|
out_init = sim('gravity_test.slx')
|
||||||
|
|
||||||
|
out_init.d.Name = 'Displacement';
|
||||||
|
out_init.Fm.Name = 'Force Sensor';
|
||||||
|
|
||||||
|
figure;
|
||||||
|
subplot(1,2,1)
|
||||||
|
plot(out_init.d)
|
||||||
|
title('');
|
||||||
|
subplot(1,2,2)
|
||||||
|
plot(out_init.Fm)
|
||||||
|
title('');
|
||||||
|
|
||||||
|
% 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]
|
||||||
|
|
||||||
|
out = sim('gravity_test.slx');
|
||||||
|
|
||||||
|
out.d.Name = 'Displacement';
|
||||||
|
out.Fm.Name = 'Force Sensor';
|
||||||
|
|
||||||
|
figure;
|
||||||
|
subplot(1,2,1)
|
||||||
|
plot(out.d)
|
||||||
|
title('');
|
||||||
|
subplot(1,2,2)
|
||||||
|
plot(out.Fm)
|
||||||
|
title('');
|
||||||
|
|
||||||
|
% 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]
|
||||||
|
|
||||||
|
out = sim('gravity_test.slx');
|
||||||
|
|
||||||
|
out.d.Name = 'Displacement';
|
||||||
|
out.Fm.Name = 'Force Sensor';
|
||||||
|
|
||||||
|
figure;
|
||||||
|
subplot(1,2,1)
|
||||||
|
plot(out.d)
|
||||||
|
title('');
|
||||||
|
subplot(1,2,2)
|
||||||
|
plot(out.Fm)
|
||||||
|
title('');
|
||||||
|
|
||||||
|
% 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]
|
||||||
|
|
||||||
|
out = sim('gravity_test.slx');
|
||||||
|
|
||||||
|
out.d.Name = 'Displacement';
|
||||||
|
out.Fm.Name = 'Force Sensor';
|
||||||
|
|
||||||
|
figure;
|
||||||
|
subplot(1,2,1)
|
||||||
|
plot(out.d)
|
||||||
|
title('');
|
||||||
|
subplot(1,2,2)
|
||||||
|
plot(out.Fm)
|
||||||
|
title('');
|
||||||
Loading…
Reference in New Issue
Block a user