Standard report format
This commit is contained in:
parent
2413fc641e
commit
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321
.gitignore
vendored
321
.gitignore
vendored
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# -*- mode: gitignore; -*-
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#
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.auctex-auto/
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_minted*
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*.slxc
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*.synctex.gz
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*~
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||||
\#*\#
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/.emacs.desktop
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/.emacs.desktop.lock
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*.elc
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auto-save-list
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tramp
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.\#*
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||||
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# Org-mode
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.org-id-locations
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*_archive
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||||
|
||||
# flymake-mode
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||||
*_flymake.*
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||||
|
||||
# eshell files
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||||
/eshell/history
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||||
/eshell/lastdir
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||||
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||||
# elpa packages
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||||
/elpa/
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||||
|
||||
# reftex files
|
||||
*.rel
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||||
|
||||
# AUCTeX auto folder
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||||
/auto/
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||||
|
||||
# cask packages
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||||
.cask/
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||||
dist/
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||||
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||||
# Flycheck
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||||
flycheck_*.el
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||||
# server auth directory
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/server/
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||||
|
||||
# projectiles files
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.projectile
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|
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# directory configuration
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.dir-locals.el
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||||
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||||
# network security
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||||
/network-security.data
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# bibtex
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*.aux
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*.bbl
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*.blg
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# Simulink
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*.autosave
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*.original
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mat/
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figures/
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ltximg/
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slprj/
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matlab/slprj/
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*.slxc
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# ============================================================
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# ============================================================
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# LATEX
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# ============================================================
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# ============================================================
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## Core latex/pdflatex auxiliary files:
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||||
*.aux
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||||
*.lof
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||||
*.log
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||||
*.lot
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||||
*.fls
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||||
*.out
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||||
*.toc
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||||
*.fmt
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||||
*.fot
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||||
*.cb
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||||
*.cb2
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||||
.*.lb
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||||
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## Intermediate documents:
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*.dvi
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*.xdv
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*-converted-to.*
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# these rules might exclude image files for figures etc.
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# *.ps
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# *.eps
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# *.pdf
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## Generated if empty string is given at "Please type another file name for output:"
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.pdf
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||||
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||||
## Bibliography auxiliary files (bibtex/biblatex/biber):
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*.bbl
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||||
*.bcf
|
||||
*.blg
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||||
*-blx.aux
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*-blx.bib
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*.run.xml
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||||
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## Build tool auxiliary files:
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*.fdb_latexmk
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*.synctex
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*.synctex(busy)
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*.synctex.gz
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*.synctex.gz(busy)
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*.pdfsync
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## Build tool directories for auxiliary files
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# latexrun
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latex.out/
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## Auxiliary and intermediate files from other packages:
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# algorithms
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*.alg
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*.loa
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# achemso
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acs-*.bib
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|
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# amsthm
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*.thm
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|
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# beamer
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||||
*.nav
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||||
*.pre
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*.snm
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*.vrb
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||||
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# changes
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||||
*.soc
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# cprotect
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*.cpt
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# elsarticle (documentclass of Elsevier journals)
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*.spl
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# endnotes
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*.ent
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# fixme
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*.lox
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||||
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# feynmf/feynmp
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*.mf
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*.mp
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*.t[1-9]
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*.t[1-9][0-9]
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*.tfm
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||||
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||||
#(r)(e)ledmac/(r)(e)ledpar
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*.end
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||||
*.?end
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*.[1-9]
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||||
*.[1-9][0-9]
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||||
*.[1-9][0-9][0-9]
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||||
*.[1-9]R
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||||
*.[1-9][0-9]R
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||||
*.[1-9][0-9][0-9]R
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||||
*.eledsec[1-9]
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||||
*.eledsec[1-9]R
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||||
*.eledsec[1-9][0-9]
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||||
*.eledsec[1-9][0-9]R
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||||
*.eledsec[1-9][0-9][0-9]
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||||
*.eledsec[1-9][0-9][0-9]R
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||||
|
||||
# glossaries
|
||||
*.acn
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||||
*.acr
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||||
*.glg
|
||||
*.glo
|
||||
*.gls
|
||||
*.glsdefs
|
||||
|
||||
# gnuplottex
|
||||
*-gnuplottex-*
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||||
|
||||
# gregoriotex
|
||||
*.gaux
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||||
*.gtex
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||||
|
||||
# htlatex
|
||||
*.4ct
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||||
*.4tc
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||||
*.idv
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||||
*.lg
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||||
*.trc
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||||
*.xref
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||||
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||||
# hyperref
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||||
*.brf
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||||
|
||||
# knitr
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*-concordance.tex
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||||
# TODO Comment the next line if you want to keep your tikz graphics files
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*.tikz
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||||
*-tikzDictionary
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||||
|
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# listings
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||||
*.lol
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||||
|
||||
# makeidx
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||||
*.idx
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*.ilg
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*.ind
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||||
*.ist
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||||
|
||||
# minitoc
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||||
*.maf
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||||
*.mlf
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||||
*.mlt
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||||
*.mtc[0-9]*
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||||
*.slf[0-9]*
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||||
*.slt[0-9]*
|
||||
*.stc[0-9]*
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||||
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||||
# minted
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||||
_minted*
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||||
*.pyg
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||||
|
||||
# morewrites
|
||||
*.mw
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||||
|
||||
# nomencl
|
||||
*.nlg
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||||
*.nlo
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||||
*.nls
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||||
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||||
# pax
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||||
*.pax
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||||
|
||||
# pdfpcnotes
|
||||
*.pdfpc
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||||
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# sagetex
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||||
*.sagetex.sage
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||||
*.sagetex.py
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||||
*.sagetex.scmd
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||||
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||||
# scrwfile
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||||
*.wrt
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||||
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||||
# sympy
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||||
*.sout
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||||
*.sympy
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||||
sympy-plots-for-*.tex/
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||||
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||||
# pdfcomment
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||||
*.upa
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||||
*.upb
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||||
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||||
# pythontex
|
||||
*.pytxcode
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||||
pythontex-files-*/
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||||
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||||
# thmtools
|
||||
*.loe
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||||
|
||||
# TikZ & PGF
|
||||
*.dpth
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||||
*.md5
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||||
*.auxlock
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||||
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||||
# todonotes
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||||
*.tdo
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||||
|
||||
# easy-todo
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||||
*.lod
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||||
|
||||
# xmpincl
|
||||
*.xmpi
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||||
|
||||
# xindy
|
||||
*.xdy
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||||
|
||||
# xypic precompiled matrices
|
||||
*.xyc
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||||
|
||||
# endfloat
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||||
*.ttt
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||||
*.fff
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||||
|
||||
# Latexian
|
||||
TSWLatexianTemp*
|
||||
|
||||
## Editors:
|
||||
# WinEdt
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||||
*.bak
|
||||
*.sav
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||||
|
||||
# Texpad
|
||||
.texpadtmp
|
||||
|
||||
# LyX
|
||||
*.lyx~
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||||
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||||
# Kile
|
||||
*.backup
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||||
|
||||
# KBibTeX
|
||||
*~[0-9]*
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||||
|
||||
# auto folder when using emacs and auctex
|
||||
./auto/*
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||||
*.el
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||||
|
||||
# expex forward references with \gathertags
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||||
*-tags.tex
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||||
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||||
# standalone packages
|
||||
*.sta
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||||
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||||
111
.latexmkrc
Normal file
111
.latexmkrc
Normal file
@ -0,0 +1,111 @@
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#!/bin/env perl
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||||
# Shebang is only to get syntax highlighting right across GitLab, GitHub and IDEs.
|
||||
# This file is not meant to be run, but read by `latexmk`.
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||||
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||||
# ======================================================================================
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||||
# Perl `latexmk` configuration file
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||||
# ======================================================================================
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||||
|
||||
# ======================================================================================
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||||
# PDF Generation/Building/Compilation
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||||
# ======================================================================================
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||||
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||||
@default_files=('nass-rotating-3dof-model.tex');
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||||
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||||
# PDF-generating modes are:
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||||
# 1: pdflatex, as specified by $pdflatex variable (still largely in use)
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||||
# 2: postscript conversion, as specified by the $ps2pdf variable (useless)
|
||||
# 3: dvi conversion, as specified by the $dvipdf variable (useless)
|
||||
# 4: lualatex, as specified by the $lualatex variable (best)
|
||||
# 5: xelatex, as specified by the $xelatex variable (second best)
|
||||
$pdf_mode = 1;
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||||
|
||||
# Treat undefined references and citations as well as multiply defined references as
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||||
# ERRORS instead of WARNINGS.
|
||||
# This is only checked in the *last* run, since naturally, there are undefined references
|
||||
# in initial runs.
|
||||
# This setting is potentially annoying when debugging/editing, but highly desirable
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||||
# in the CI pipeline, where such a warning should result in a failed pipeline, since the
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||||
# final document is incomplete/corrupted.
|
||||
#
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||||
# However, I could not eradicate all warnings, so that `latexmk` currently fails with
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||||
# this option enabled.
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||||
# Specifically, `microtype` fails together with `fontawesome`/`fontawesome5`, see:
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||||
# https://tex.stackexchange.com/a/547514/120853
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||||
# The fix in that answer did not help.
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||||
# Setting `verbose=silent` to mute `microtype` warnings did not work.
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||||
# Switching between `fontawesome` and `fontawesome5` did not help.
|
||||
$warnings_as_errors = 0;
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||||
|
||||
# Show used CPU time. Looks like: https://tex.stackexchange.com/a/312224/120853
|
||||
$show_time = 1;
|
||||
|
||||
# Default is 5; we seem to need more owed to the complexity of the document.
|
||||
# Actual documents probably don't need this many since they won't use all features,
|
||||
# plus won't be compiling from cold each time.
|
||||
$max_repeat=7;
|
||||
|
||||
# --shell-escape option (execution of code outside of latex) is required for the
|
||||
#'svg' package.
|
||||
# It converts raw SVG files to the PDF+PDF_TEX combo using InkScape.
|
||||
#
|
||||
# SyncTeX allows to jump between source (code) and output (PDF) in IDEs with support
|
||||
# (many have it). A value of `1` is enabled (gzipped), `-1` is enabled but uncompressed,
|
||||
# `0` is off.
|
||||
# Testing in VSCode w/ LaTeX Workshop only worked for the compressed version.
|
||||
# Adjust this as needed. Of course, only relevant for local use, no effect on a remote
|
||||
# CI pipeline (except for slower compilation, probably).
|
||||
#
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||||
# %O and %S will forward Options and the Source file, respectively, given to latexmk.
|
||||
#
|
||||
# `set_tex_cmds` applies to all *latex commands (latex, xelatex, lualatex, ...), so
|
||||
# no need to specify these each. This allows to simply change `$pdf_mode` to get a
|
||||
# different engine. Check if this works with `latexmk --commands`.
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set_tex_cmds("--shell-escape -interaction=nonstopmode --synctex=1 %O %S");
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||||
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# Use default pdf viewer
|
||||
$pdf_previewer = 'zathura';
|
||||
|
||||
# option 2 is same as 1 (run biber when necessary), but also deletes the
|
||||
# regeneratable bbl-file in a clenaup (`latexmk -c`). Do not use if original
|
||||
# bib file is not available!
|
||||
$bibtex_use = 2; # default: 1
|
||||
|
||||
# Change default `biber` call, help catch errors faster/clearer. See
|
||||
# https://web.archive.org/web/20200526101657/https://www.semipol.de/2018/06/12/latex-best-practices.html#database-entries
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||||
$biber = "biber --validate-datamodel %O %S";
|
||||
|
||||
# Glossaries
|
||||
add_cus_dep('glo', 'gls', 0, 'run_makeglossaries');
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||||
add_cus_dep('acn', 'acr', 0, 'run_makeglossaries');
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||||
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||||
sub run_makeglossaries {
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if ( $silent ) {
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system "makeglossaries -q -s '$_[0].ist' '$_[0]'";
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||||
}
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||||
else {
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system "makeglossaries -s '$_[0].ist' '$_[0]'";
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||||
};
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||||
}
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||||
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||||
# ======================================================================================
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||||
# Auxiliary Files
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||||
# ======================================================================================
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||||
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||||
# Let latexmk know about generated files, so they can be used to detect if a
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||||
# rerun is required, or be deleted in a cleanup.
|
||||
# loe: List of Examples (KOMAScript)
|
||||
# lol: List of Listings (`listings` and `minted` packages)
|
||||
# run.xml: biber runs
|
||||
# glg: glossaries log
|
||||
# glstex: generated from glossaries-extra
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||||
push @generated_exts, 'loe', 'lol', 'run.xml', 'glstex', 'glo', 'gls', 'glg', 'acn', 'acr', 'alg';
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||||
|
||||
# Also delete the *.glstex files from package glossaries-extra. Problem is,
|
||||
# that that package generates files of the form "basename-digit.glstex" if
|
||||
# multiple glossaries are present. Latexmk looks for "basename.glstex" and so
|
||||
# does not find those. For that purpose, use wildcard.
|
||||
# Also delete files generated by gnuplot/pgfplots contour plots
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||||
# (.dat, .script, .table).
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||||
$clean_ext = "%R-*.glstex %R_contourtmp*.*";
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||||
@ -3,7 +3,6 @@
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title = {Sensor Fusion Methods for High Performance Active Vibration Isolation Systems},
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||||
journal = {Journal of Sound and Vibration},
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||||
volume = {342},
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||||
number = {nil},
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||||
pages = {1-21},
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||||
year = {2015},
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||||
doi = {10.1016/j.jsv.2015.01.006},
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||||
@ -139,7 +138,6 @@
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||||
publisher = {Springer International Publishing},
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||||
url = {https://doi.org/10.1007/978-3-319-72296-2},
|
||||
doi = {10.1007/978-3-319-72296-2},
|
||||
pages = {nil},
|
||||
series = {Solid Mechanics and Its Applications},
|
||||
}
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||||
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||||
@ -281,8 +279,6 @@
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||||
Systems},
|
||||
journal = {Frontiers in Mechanical Engineering},
|
||||
volume = 1,
|
||||
number = {nil},
|
||||
pages = {nil},
|
||||
year = 2015,
|
||||
doi = {10.3389/fmech.2015.00014},
|
||||
url = {https://doi.org/10.3389/fmech.2015.00014},
|
||||
@ -13,16 +13,18 @@
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||||
#+BIND: org-latex-image-default-option "scale=1"
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||||
#+BIND: org-latex-image-default-width ""
|
||||
|
||||
#+LaTeX_CLASS: scrreprt
|
||||
#+LaTeX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12, parskip=full]
|
||||
#+LaTeX_HEADER: \usepackage{siunitx}
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||||
#+LaTeX_HEADER: \usepackage{tikz}
|
||||
#+LaTeX_HEADER: \usetikzlibrary{shapes.misc,arrows,arrows.meta}
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||||
#+LaTeX_HEADER: \usepackage{bm}
|
||||
#+LaTeX_HEADER: \usepackage{amsmath}
|
||||
#+LaTeX_HEADER_EXTRA: \usepackage{amssymb}
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||||
#+LaTeX_HEADER_EXTRA: \input{preamble.tex}
|
||||
#+LaTeX_HEADER_EXTRA: \addbibresource{ref.bib}
|
||||
#+LATEX_CLASS: scrreprt
|
||||
#+LATEX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]
|
||||
#+LATEX_HEADER: \usepackage{siunitx}
|
||||
#+LATEX_HEADER: \usepackage{tikz}
|
||||
#+LATEX_HEADER: \usetikzlibrary{shapes.misc,arrows,arrows.meta}
|
||||
#+LATEX_HEADER: \usepackage{bm}
|
||||
#+LATEX_HEADER: \usepackage{amsmath}
|
||||
#+LATEX_HEADER_EXTRA: \usepackage{amssymb}
|
||||
#+LATEX_HEADER_EXTRA: \input{preamble.tex}
|
||||
#+LATEX_HEADER_EXTRA: \bibliography{nass-rotating-3dof-model.bib}
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||||
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||||
#+BIND: org-latex-bib-compiler "biber"
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||||
|
||||
#+PROPERTY: header-args:matlab :session *MATLAB*
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||||
#+PROPERTY: header-args:matlab+ :comments org
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||||
@ -56,6 +58,49 @@
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||||
#+latex: \clearpage
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||||
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||||
* Build :noexport:
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||||
#+NAME: startblock
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||||
#+BEGIN_SRC emacs-lisp :results none :tangle no
|
||||
(add-to-list 'org-latex-classes
|
||||
'("scrreprt"
|
||||
"\\documentclass{scrreprt}"
|
||||
("\\chapter{%s}" . "\\chapter*{%s}")
|
||||
("\\section{%s}" . "\\section*{%s}")
|
||||
("\\subsection{%s}" . "\\subsection*{%s}")
|
||||
("\\paragraph{%s}" . "\\paragraph*{%s}")
|
||||
))
|
||||
|
||||
|
||||
;; Remove automatic org heading labels
|
||||
(defun my-latex-filter-removeOrgAutoLabels (text backend info)
|
||||
"Org-mode automatically generates labels for headings despite explicit use of `#+LABEL`. This filter forcibly removes all automatically generated org-labels in headings."
|
||||
(when (org-export-derived-backend-p backend 'latex)
|
||||
(replace-regexp-in-string "\\\\label{sec:org[a-f0-9]+}\n" "" text)))
|
||||
(add-to-list 'org-export-filter-headline-functions
|
||||
'my-latex-filter-removeOrgAutoLabels)
|
||||
|
||||
;; Remove all org comments in the output LaTeX file
|
||||
(defun delete-org-comments (backend)
|
||||
(loop for comment in (reverse (org-element-map (org-element-parse-buffer)
|
||||
'comment 'identity))
|
||||
do
|
||||
(setf (buffer-substring (org-element-property :begin comment)
|
||||
(org-element-property :end comment))
|
||||
"")))
|
||||
(add-hook 'org-export-before-processing-hook 'delete-org-comments)
|
||||
|
||||
;; Use no package by default
|
||||
(setq org-latex-packages-alist nil)
|
||||
(setq org-latex-default-packages-alist nil)
|
||||
|
||||
;; Do not include the subtitle inside the title
|
||||
(setq org-latex-subtitle-separate t)
|
||||
(setq org-latex-subtitle-format "\\subtitle{%s}")
|
||||
|
||||
(setq org-export-before-parsing-hook '(org-ref-glossary-before-parsing
|
||||
org-ref-acronyms-before-parsing))
|
||||
#+END_SRC
|
||||
|
||||
* Introduction :ignore:
|
||||
|
||||
An important aspect of the Nano Active Stabilization System (NASS) is that the nano-hexapod is continuously rotating around a vertical axis while the external metrology is not.
|
||||
@ -4878,7 +4923,7 @@ Results show that the two proposed IFF modifications can be applied for the NASS
|
||||
| Frequency | $\omega$ | =w= | [rad/s] |
|
||||
|
||||
* Bibliography :ignore:
|
||||
#+latex: \printbibliography
|
||||
#+latex: \printbibliography[heading=bibintoc,title={Bibliography}]
|
||||
|
||||
* Helping Functions :noexport:
|
||||
** Initialize Path
|
||||
|
||||
Binary file not shown.
@ -1,6 +1,6 @@
|
||||
% Created 2023-02-28 Tue 14:05
|
||||
% Created 2023-07-03 Mon 17:38
|
||||
% Intended LaTeX compiler: pdflatex
|
||||
\documentclass[a4paper, 10pt, DIV=12, parskip=full]{scrreprt}
|
||||
\documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt}
|
||||
|
||||
\usepackage{siunitx}
|
||||
\usepackage{tikz}
|
||||
@ -9,7 +9,7 @@
|
||||
\usepackage{amsmath}
|
||||
\usepackage{amssymb}
|
||||
\input{preamble.tex}
|
||||
\addbibresource{ref.bib}
|
||||
\bibliography{nass-rotating-3dof-model.bib}
|
||||
\author{Dehaeze Thomas}
|
||||
\date{\today}
|
||||
\title{NASS - Effect of rotation}
|
||||
@ -58,6 +58,7 @@ Section \ref{sec:rotating_system_description} & \texttt{rotating\_1\_system\_des
|
||||
Section \ref{sec:rotating_iff_pure_int} & \texttt{rotating\_2\_iff\_pure\_int.m}\\
|
||||
Section \ref{sec:rotating_iff_pseudo_int} & \texttt{rotating\_3\_iff\_hpf.m}\\
|
||||
Section \ref{sec:rotating_iff_parallel_stiffness} & \texttt{rotating\_4\_iff\_kp.m}\\
|
||||
Section \ref{sec:rotating_relative_damp_control} & \texttt{rotating\_5\_rdc.m}\\
|
||||
Section \ref{sec:rotating_comp_act_damp} & \texttt{rotating\_5\_act\_damp\_comparison.m}\\
|
||||
Section \ref{sec:rotating_nano_hexapod} & \texttt{rotating\_6\_nano\_hexapod.m}\\
|
||||
Section \ref{sec:rotating_nass} & \texttt{rotating\_6\_nass.m}\\
|
||||
@ -66,7 +67,6 @@ Section \ref{sec:rotating_nass} & \texttt{rotating\_6\_nass.m}\\
|
||||
\end{table}
|
||||
|
||||
\chapter{System Description and Analysis}
|
||||
\label{sec:org057d64e}
|
||||
\label{sec:rotating_system_description}
|
||||
The studied system consists of a 2 degree of freedom translation stage on top of a rotating stage (Figure \ref{fig:rotating_3dof_model_schematic}).
|
||||
|
||||
@ -85,7 +85,6 @@ The position of the payload is represented by \((d_u, d_v, 0)\) expressed in the
|
||||
\end{figure}
|
||||
|
||||
\section{Equations of motion}
|
||||
\label{sec:org32cf2f6}
|
||||
To obtain the equations of motion for the system represented in Figure \ref{fig:rotating_3dof_model_schematic}, the Lagrangian equations are used:
|
||||
\begin{equation}
|
||||
\label{eq:lagrangian_equations}
|
||||
@ -120,7 +119,6 @@ The uniform rotation of the system induces \textbf{two gyroscopic effects} as sh
|
||||
One can verify that without rotation (\(\Omega = 0\)) the system becomes equivalent to two uncoupled one degree of freedom mass-spring-damper systems.
|
||||
|
||||
\section{Transfer Functions in the Laplace domain}
|
||||
\label{sec:org8130277}
|
||||
To study the dynamics of the system, the differential equations of motions \eqref{eq:eom_coupled} are converted into the Laplace domain and the \(2 \times 2\) transfer function matrix \(\mathbf{G}_d\) from \(\begin{bmatrix}F_u & F_v\end{bmatrix}\) to \(\begin{bmatrix}d_u & d_v\end{bmatrix}\) in equation \eqref{eq:Gd_mimo_tf} is obtained.
|
||||
Its elements are shown in equation \eqref{eq:Gd_indiv_el}.
|
||||
|
||||
@ -153,7 +151,6 @@ The elements of transfer function matrix \(\mathbf{G}_d\) are now described by e
|
||||
\end{subequations}
|
||||
|
||||
\section{System Poles: Campbell Diagram}
|
||||
\label{sec:org7485ccd}
|
||||
The poles of \(\mathbf{G}_d\) are the complex solutions \(p\) of equation \eqref{eq:poles}.
|
||||
|
||||
\begin{equation}
|
||||
@ -183,7 +180,6 @@ Physically, the negative stiffness term \(-m\Omega^2\) induced by centrifugal fo
|
||||
\end{figure}
|
||||
|
||||
\section{System Dynamics: Effect of rotation}
|
||||
\label{sec:orgb1d33ee}
|
||||
The system dynamics from actuator forces \([F_u, F_v]\) to the relative motion \([d_u, d_v]\) is identified for several rotating velocities.
|
||||
|
||||
Looking at the transfer function matrix \(\mathbf{G}_d\) in equation \eqref{eq:Gd_w0_xi_k}, one can see that the two diagonal (direct) terms are equal and that the two off-diagonal (coupling) terms are opposite.
|
||||
@ -198,7 +194,6 @@ For \(\Omega > \omega_0\), the low frequency pair of complex conjugate poles \(p
|
||||
\end{figure}
|
||||
|
||||
\chapter{Integral Force Feedback}
|
||||
\label{sec:org8602056}
|
||||
\label{sec:rotating_iff_pure_int}
|
||||
In order to further decrease the residual vibrations, active damping can be used for reducing the magnification of the response in the vicinity of the resonances \cite{collette11_review_activ_vibrat_isolat_strat}.
|
||||
|
||||
@ -217,7 +212,6 @@ However, none of these study have been applied to a rotating system.
|
||||
In this section, Integral Force Feedback strategy is applied on the rotating suspended platform, and it is shown that gyroscopic effects alters the system dynamics and that IFF cannot be applied as is.
|
||||
|
||||
\section{System and Equations of motion}
|
||||
\label{sec:orgd805948}
|
||||
In order to apply Integral Force Feedback, two force sensors are added in series with the actuators (Figure \ref{fig:rotating_3dof_model_schematic_iff}).
|
||||
Two identical controllers \(K_F\) are then used to feedback each of the sensed force to its associated actuator:
|
||||
\begin{equation}
|
||||
@ -283,7 +277,6 @@ This can be explained as follows: a constant actuator force \(F_u\) induces a sm
|
||||
This small displacement then increases the centrifugal force \(m\Omega^2d_u = \frac{\Omega^2}{{\omega_0}^2 - \Omega^2} F_u\) which is then measured by the force sensors.
|
||||
|
||||
\section{Effect of the rotation speed on the IFF plant dynamics}
|
||||
\label{sec:orgcebce06}
|
||||
The transfer functions from actuator forces \([F_u,\ F_v]\) to the measured force sensors \([f_u,\ f_v]\) are identified for several rotating velocities and shown in Figure \ref{fig:rotating_iff_bode_plot_effect_rot}.
|
||||
|
||||
As was expected from the derived equations of motion:
|
||||
@ -301,7 +294,6 @@ A pair of (minimum phase) complex conjugate zeros appears between the two comple
|
||||
\end{figure}
|
||||
|
||||
\section{Decentralized Integral Force Feedback}
|
||||
\label{sec:orge2c5479}
|
||||
The control diagram for decentralized Integral Force Feedback is shown in Figure \ref{fig:rotating_iff_diagram}.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
@ -337,7 +329,6 @@ The control system is thus canceling the spring forces which makes the suspended
|
||||
\end{figure}
|
||||
|
||||
\chapter{Integral Force Feedback with an High Pass Filter}
|
||||
\label{sec:orgfb40773}
|
||||
\label{sec:rotating_iff_pseudo_int}
|
||||
As was explained in the previous section, the instability of the IFF controller applied on the rotating system comes in part from the high gain at low frequency caused by the pure integrators.
|
||||
|
||||
@ -354,7 +345,6 @@ This modification of the IFF controller is typically done to avoid saturation as
|
||||
This is however not why this high pass filter is added here.
|
||||
|
||||
\section{Modified Integral Force Feedback Controller}
|
||||
\label{sec:orgdadd42f}
|
||||
The Integral Force Feedback Controller is modified such that instead of using pure integrators, pseudo integrators (i.e. low pass filters) are used:
|
||||
\begin{equation}
|
||||
K_{\text{IFF}}(s) = g\frac{1}{\omega_i + s} \begin{bmatrix}
|
||||
@ -400,7 +390,6 @@ It is interesting to note that \(g_{\text{max}}\) also corresponds to the contro
|
||||
\end{figure}
|
||||
|
||||
\section{Optimal IFF with HPF parameters \(\omega_i\) and \(g\)}
|
||||
\label{sec:org021fb11}
|
||||
Two parameters can be tuned for the modified controller in equation \eqref{eq:iff_lhf}: the gain \(g\) and the pole's location \(\omega_i\).
|
||||
The optimal values of \(\omega_i\) and \(g\) are here considered as the values for which the damping of all the closed-loop poles are simultaneously maximized.
|
||||
|
||||
@ -430,7 +419,6 @@ Three regions can be observed:
|
||||
\end{figure}
|
||||
|
||||
\section{Obtained Damped Plant}
|
||||
\label{sec:orgb6771f0}
|
||||
|
||||
Let's choose \(\omega_i = 0.1 \cdot \omega_0\) and compute the damped plant.
|
||||
The undamped and damped plants are compared in Figure \ref{fig:rotating_iff_hpf_damped_plant} in blue and red respectively.
|
||||
@ -464,7 +452,6 @@ The same trade-off can be seen between achievable damping and loss of compliance
|
||||
\end{figure}
|
||||
|
||||
\chapter{IFF with a stiffness in parallel with the force sensor}
|
||||
\label{sec:org5641ff7}
|
||||
\label{sec:rotating_iff_parallel_stiffness}
|
||||
In this section it is proposed to add springs in parallel with the force sensors to counteract the negative stiffness induced by the gyroscopic effects.
|
||||
|
||||
@ -477,7 +464,6 @@ Such springs are schematically shown in Figure \ref{fig:rotating_3dof_model_sche
|
||||
\end{figure}
|
||||
|
||||
\section{Equations}
|
||||
\label{sec:org3a4d6b3}
|
||||
The forces measured by the two force sensors represented in Figure \ref{fig:rotating_3dof_model_schematic_iff_parallel_springs} are described by Eq. \eqref{eq:measured_force_kp}.
|
||||
|
||||
\begin{equation}
|
||||
@ -525,7 +511,6 @@ Thus, if the added \textbf{parallel stiffness} \(k_p\) is \textbf{higher than th
|
||||
\end{important}
|
||||
|
||||
\section{Effect of the parallel stiffness on the IFF plant}
|
||||
\label{sec:org7a5fe58}
|
||||
The IFF plant (transfer function from \([F_u, F_v]\) to \([f_u, f_v]\)) is identified in three different cases:
|
||||
\begin{itemize}
|
||||
\item without parallel stiffness \(k_p = 0\)
|
||||
@ -552,7 +537,6 @@ It is shown that if the added stiffness is higher than the maximum negative stif
|
||||
\end{figure}
|
||||
|
||||
\section{Effect of \(k_p\) on the attainable damping}
|
||||
\label{sec:orgaa16b8e}
|
||||
|
||||
Even though the parallel stiffness \(k_p\) has no impact on the open-loop poles (as the overall stiffness \(k\) is kept constant), it has a large impact on the transmission zeros.
|
||||
Moreover, as the attainable damping is generally proportional to the distance between poles and zeros \cite{preumont18_vibrat_contr_activ_struc_fourt_edition}, the parallel stiffness \(k_p\) is foreseen to have some impact on the attainable damping.
|
||||
@ -579,7 +563,6 @@ This is confirmed by the Figure \ref{fig:rotating_iff_kp_optimal_gain} where the
|
||||
\end{figure}
|
||||
|
||||
\section{Damped plant}
|
||||
\label{sec:org3b9852c}
|
||||
Let's choose a parallel stiffness equal to \(k_p = 2 m \Omega^2\) and compute the damped plant.
|
||||
The damped and undamped transfer functions from \(F_u\) to \(d_u\) are compared in Figure \ref{fig:rotating_iff_kp_damped_plant}.
|
||||
|
||||
@ -621,7 +604,6 @@ The added high pass filter gives almost the same damping properties while giving
|
||||
\end{figure}
|
||||
|
||||
\chapter{Relative Damping Control}
|
||||
\label{sec:orgd8405fb}
|
||||
\label{sec:rotating_relative_damp_control}
|
||||
In order to apply a ``relative damping control strategy'', relative motion sensors are added in parallel with the actuators as shown in Figure \ref{fig:rotating_3dof_model_schematic_rdc}.
|
||||
|
||||
@ -644,7 +626,6 @@ K_d(s) = \frac{s}{s + \omega_d}
|
||||
\end{figure}
|
||||
|
||||
\section{Equations of motion}
|
||||
\label{sec:org5975c6a}
|
||||
Let's note \(\bm{G}_d\) the transfer function between actuator forces and measured relative motion in parallel with the actuators:
|
||||
\begin{equation}
|
||||
\begin{bmatrix} d_u \\ d_v \end{bmatrix} = \mathbf{G}_d \begin{bmatrix} F_u \\ F_v \end{bmatrix}
|
||||
@ -672,7 +653,6 @@ Which are between the two pairs of complex conjugate poles at:
|
||||
Therefore, for \(\Omega < \sqrt{k/m}\) (i.e. stable system), the transfer functions for Relative Damping Control have \textbf{alternating complex conjugate poles and zeros}.
|
||||
|
||||
\section{Decentralized Relative Damping Control}
|
||||
\label{sec:orgd96d997}
|
||||
The transfer functions from \([F_u,\ F_v]\) to \([d_u,\ d_v]\) is identified and shown in Figure \ref{fig:rotating_rdc_plant_effect_rot} for several rotating velocities.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
@ -691,7 +671,6 @@ The closed-loop system is unconditionally stable and the poles can be damped as
|
||||
\end{figure}
|
||||
|
||||
\section{Damped Plant}
|
||||
\label{sec:org4b65581}
|
||||
Let's select a reasonable ``Relative Damping Control'' gain, and compute the closed-loop damped system.
|
||||
The open-loop and damped plants are compared in Figure \ref{fig:rotating_rdc_damped_plant}.
|
||||
|
||||
@ -705,7 +684,6 @@ It does not increase the low frequency coupling as compared to Integral Force Fe
|
||||
\end{figure}
|
||||
|
||||
\chapter{Comparison of Active Damping Techniques}
|
||||
\label{sec:orgb99bbdc}
|
||||
\label{sec:rotating_comp_act_damp}
|
||||
These two proposed IFF modifications as well as relative damping control are now compared in terms of added damping and closed-loop behavior.
|
||||
|
||||
@ -713,7 +691,6 @@ For the following comparisons, the cut-off frequency for the added HPF is set to
|
||||
These values are chosen based on previous discussion about optimal parameters.
|
||||
|
||||
\section{Root Locus}
|
||||
\label{sec:orga1f0863}
|
||||
|
||||
Figure \ref{fig:rotating_comp_techniques_root_locus} shows the Root Locus plots for the two proposed IFF modifications as well as for relative damping control.
|
||||
While the two pairs of complex conjugate open-loop poles are identical for both IFF modifications, the transmission zeros are not.
|
||||
@ -731,7 +708,6 @@ It is interesting to note that the maximum added damping is very similar for bot
|
||||
\end{figure}
|
||||
|
||||
\section{Obtained Damped Plant}
|
||||
\label{sec:org9f20150}
|
||||
The actively damped plants are computed for the three techniques and compared in Figure \ref{fig:rotating_comp_techniques_dampled_plants}.
|
||||
|
||||
\begin{important}
|
||||
@ -747,7 +723,6 @@ Integral Force Feedback strategy is adding some coupling at low frequency which
|
||||
|
||||
|
||||
\section{Transmissibility And Compliance}
|
||||
\label{sec:orgdf971c5}
|
||||
The proposed active damping techniques are now compared in terms of closed-loop transmissibility and compliance.
|
||||
|
||||
The transmissibility is here defined as the transfer function from a displacement of the rotating stage along \(\vec{i}_x\) to the displacement of the payload along the same direction.
|
||||
@ -771,7 +746,6 @@ This is very well known characteristics of these common active damping technique
|
||||
\end{figure}
|
||||
|
||||
\chapter{Rotating Nano-Hexapod}
|
||||
\label{sec:org69b6cd1}
|
||||
\label{sec:rotating_nano_hexapod}
|
||||
The current analysis is now applied on a model representing the rotating nano-hexapod.
|
||||
|
||||
@ -779,7 +753,6 @@ Three nano-hexapod stiffnesses are tested: \(k_n = \SI{0.01}{\N\per\mu\m}\), \(k
|
||||
|
||||
Only the maximum rotating velocity is considered (\(\Omega = \SI{60}{rpm}\)) with the light sample (\(m_s = \SI{1}{kg}\)) as this is the worst identified case scenario.
|
||||
\section{Nano-Active-Stabilization-System - Plant Dynamics}
|
||||
\label{sec:org83bcdf5}
|
||||
For the NASS, the maximum rotating velocity is \(\Omega = \SI[parse-numbers=false]{2\pi}{\radian\per\s}\) for a suspended mass on top of the nano-hexapod's actuators equal to \(m_n + m_s = \SI{16}{\kilo\gram}\).
|
||||
The parallel stiffness corresponding to the centrifugal forces is \(m \Omega^2 \approx \SI{0.6}{\newton\per\mm}\).
|
||||
|
||||
@ -800,7 +773,6 @@ It is shown that the rotation has the largest effect on the soft nano-hexapod:
|
||||
\end{figure}
|
||||
|
||||
\section{Optimal IFF with High Pass Filter}
|
||||
\label{sec:org12ad94d}
|
||||
Let's apply Integral Force Feedback with an added High Pass Filter to the three nano-hexapods.
|
||||
|
||||
First, let's find the parameters of the IFF controller that yield best simultaneous damping.
|
||||
@ -846,7 +818,6 @@ The Root Locus for all three nano-hexapods are shown in Figure \ref{fig:rotating
|
||||
\end{figure}
|
||||
|
||||
\section{Optimal IFF with Parallel Stiffness}
|
||||
\label{sec:org1fa3213}
|
||||
For each considered nano-hexapod stiffness, the parallel stiffness \(k_p\) is varied from \(k_{p,\text{min}} = m\Omega^2\) (the minimum stiffness to have unconditional stability) to \(k_{p,\text{max}} = k_n\) (the total nano-hexapod stiffness).
|
||||
In order to keep the overall stiffness constant, the actuator stiffness \(k_a\) is decreased when \(k_p\) is increased:
|
||||
\begin{equation}
|
||||
@ -906,7 +877,6 @@ Similarly to what was found with the IFF and added High Pass Filter:
|
||||
\end{figure}
|
||||
|
||||
\section{Optimal Relative Motion Control}
|
||||
\label{sec:org7b55b79}
|
||||
|
||||
For each considered nano-hexapod stiffness, relative damping control is applied and the achievable damping ratio as a function of the controller gain is shown in Figure \ref{fig:rotating_rdc_optimal_gain}.
|
||||
|
||||
@ -931,7 +901,6 @@ It can be easily applied on the nano-hexapod with and without rotation without m
|
||||
\end{figure}
|
||||
|
||||
\section{Comparison of the obtained damped plants}
|
||||
\label{sec:orgb53c4fc}
|
||||
Let's now compare the obtained damped plants for the three active damping techniques applied on the three nano-hexapod stiffnesses (Figure \ref{fig:rotating_nass_damped_plant_comp}).
|
||||
|
||||
\begin{important}
|
||||
@ -950,7 +919,6 @@ Similarly to what was concluded in previous analysis:
|
||||
\end{figure}
|
||||
|
||||
\chapter{Nano-Active-Stabilization-System with rotation}
|
||||
\label{sec:orga4c7572}
|
||||
\label{sec:rotating_nass}
|
||||
Up until now, the model used consisted of an infinitely stiff vertical rotating stage with a X-Y suspended stage.
|
||||
|
||||
@ -958,7 +926,6 @@ While quite simplistic, this allowed to study the effects of rotation and the as
|
||||
|
||||
In this section, the limited compliance of the micro-station is taken into account as well as the rotation of the spindle.
|
||||
\section{NASS model}
|
||||
\label{sec:org9bfd222}
|
||||
|
||||
In order to be a bit closer to the NASS application, the 2DoF nano-hexapod (modelled as shown in Figure \ref{fig:rotating_3dof_model_schematic}) is now located on top of a model of the micro-station including (see Figure \ref{fig:rotating_nass_model} for a 3D view):
|
||||
\begin{itemize}
|
||||
@ -978,7 +945,6 @@ A payload is rigidly fixed to the nano-hexapod and the \(x,y\) motion of the pay
|
||||
\end{figure}
|
||||
|
||||
\section{System dynamics}
|
||||
\label{sec:org08abf57}
|
||||
|
||||
The dynamics of the undamped and damped plants are identified.
|
||||
The active damping parameters used are the optimal ones previously identified (i.e. for the rotating nano-hexapod fixed on a rigid platform).
|
||||
@ -1012,7 +978,6 @@ To confirm that the coupling is smaller when the stiffness of the nano-hexapod i
|
||||
\end{figure}
|
||||
|
||||
\section{Effect of disturbances}
|
||||
\label{sec:org9170a64}
|
||||
|
||||
The effect of three disturbances are considered:
|
||||
\begin{itemize}
|
||||
@ -1055,7 +1020,6 @@ Conclusions are similar than with the uniaxial (non-rotating) model:
|
||||
\end{figure}
|
||||
|
||||
\chapter{Conclusion}
|
||||
\label{sec:orgecb53c9}
|
||||
|
||||
In this study, the gyroscopic effects induced by the spindle's rotation have been studied using a spindle model (Section \ref{sec:rotating_system_description}).
|
||||
Decentralized IFF with pure integrators was shown to be unstable when applied to rotating platforms (Section \ref{sec:rotating_iff_pure_int}).
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@ -1076,5 +1040,5 @@ Then, this study has been applied to a rotating system that corresponds to the n
|
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To be closer to the real system dynamics, the limited compliance of the micro-station has been taken into account.
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||||
Results show that the two proposed IFF modifications can be applied for the NASS even in the presence of spindle rotation.
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||||
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||||
\printbibliography
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\printbibliography[heading=bibintoc,title={Bibliography}]
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\end{document}
|
||||
|
||||
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Reference in New Issue
Block a user