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@book{taghirad13_paral,
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author = {Taghirad, Hamid},
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title = {Parallel robots : mechanics and control},
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year = 2013,
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publisher = {CRC Press},
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address = {Boca Raton, FL},
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isbn = 9781466555778,
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keywords = {favorite, parallel robot},
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}
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@article{preumont07_six_axis_singl_stage_activ,
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author = {A. Preumont and M. Horodinca and I. Romanescu and B. de
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Marneffe and M. Avraam and A. Deraemaeker and F. Bossens and
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A. Abu Hanieh},
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title = {A Six-Axis Single-Stage Active Vibration Isolator Based on
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Stewart Platform},
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journal = {Journal of Sound and Vibration},
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volume = 300,
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number = {3-5},
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pages = {644-661},
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year = 2007,
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doi = {10.1016/j.jsv.2006.07.050},
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url = {https://doi.org/10.1016/j.jsv.2006.07.050},
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keywords = {parallel robot},
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}
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@book{skogestad07_multiv_feedb_contr,
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author = {Skogestad, Sigurd and Postlethwaite, Ian},
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title = {Multivariable Feedback Control: Analysis and Design -
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Second Edition},
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year = 2007,
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publisher = {John Wiley},
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isbn = 978-0470011683,
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keywords = {favorite},
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}
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@article{preumont08_trans_zeros_struc_contr_with,
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author = {Preumont, Andr{\'e} and De Marneffe, Bruno and Krenk,
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Steen},
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title = {Transmission Zeros in Structural Control With Collocated
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Multi-Input/multi-Output Pairs},
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journal = {Journal of guidance, control, and dynamics},
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volume = 31,
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number = 2,
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pages = {428--432},
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year = 2008,
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}
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@ -365,16 +365,16 @@ Make well defined notations.
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** Kinematic Analysis
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<<ssec:nhexa_stewart_platform_kinematics>>
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*** Inverse Kinematics
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**** Inverse Kinematics
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*** Forward Kinematics
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**** Forward Kinematics
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*** Jacobian Matrix
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**** Jacobian Matrix
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- Velocity Loop Closure
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- Static Forces
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*** Singularities
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**** Singularities
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- Briefly mention singularities, and say that for small stroke, it is not an issue, the Jacobian matrix may be considered constant
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@ -1,8 +1,9 @@
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% Created 2024-03-19 Tue 11:06
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% Created 2025-02-05 Wed 17:49
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% Intended LaTeX compiler: pdflatex
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\documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt}
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\input{preamble.tex}
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\input{preamble_extra.tex}
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\bibliography{simscape-nano-hexapod.bib}
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\author{Dehaeze Thomas}
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\date{\today}
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@ -12,7 +13,7 @@
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pdftitle={Simscape Model - Nano Hexapod},
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pdfkeywords={},
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pdfsubject={},
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pdfcreator={Emacs 29.2 (Org mode 9.7)},
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pdfcreator={Emacs 29.4 (Org mode 9.6)},
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pdflang={English}}
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\usepackage{biblatex}
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@ -22,27 +23,311 @@
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\tableofcontents
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\clearpage
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Goal of this report is:
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Introduction:
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\begin{itemize}
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\item show what is an hexapod, how we can define its geometry, stiffness, etc\ldots{}
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\item Some kinematics: stiffness matrix, mass matrix, etc\ldots{}
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\item talk about cubic architecture?
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\item Choice of architecture to do 5DoF control (Section \ref{sec:nhexa_platform_review})
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\item Stewart platform (Section \ref{sec:nhexa_stewart_platform})
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Show what is an hexapod, how we can define its geometry, stiffness, etc\ldots{}
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Some kinematics: stiffness matrix, mass matrix, etc\ldots{}
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\item Need to model the active vibration platform: multi-body model (Section \ref{sec:nhexa_model})
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Explain what we want to capture with this model
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Key elements (plates, joints, struts): for now simplistic model (rigid body elements, perfect joints, \ldots{}), but in next section, FEM will be used
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\item Control (Section \ref{sec:nhexa_control})
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\end{itemize}
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\chapter{Active Vibration Platforms}
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\label{sec:nhexa_platform_review}
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\textbf{Goals}:
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\begin{itemize}
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\item Explain why Stewart platform architecture is chosen
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\item Explain what is a Stewart platform (quickly as it will be shown in details in the next section)
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\item Quick review of active vibration platforms (5 or 6DoF)
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\end{itemize}
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Active vibration platform with 5DoF or 6DoF?
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Synchrotron applications?
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\begin{itemize}
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\item Literature review? (\textbf{maybe more suited for chapter 2})
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\begin{itemize}
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\item \url{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/bibliography.org}
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\item Talk about flexible joint? Maybe not so much as it should be topic of second chapter.
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Just say that we must of flexible joints that can be defined as 3 to 6DoF joints, and it will be optimize in chapter 2.
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\end{itemize}
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\item \cite{taghirad13_paral}
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\item For some systems, just XYZ control (stack stages), example: holler
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\item For other systems, Stewart platform (ID16a), piezo based
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\item Examples of Stewart platforms for general vibration control, some with Piezo, other with Voice coil. IFF, \ldots{}
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Show different geometry configuration
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\item DCM: tripod?
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\end{itemize}
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\section{Active vibration control of sample stages}
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\href{file:///home/thomas/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/A0-nass-introduction/nass-introduction.org}{Review of stages with online metrology for Synchrotrons}
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\begin{itemize}
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\item[{$\square$}] Talk about external metrology?
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\item[{$\square$}] Talk about control architecture?
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\item[{$\square$}] Comparison with the micro-station / NASS
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\end{itemize}
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\section{Serial and Parallel Manipulators}
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\textbf{Goal}:
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\begin{itemize}
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\item Explain why a parallel manipulator is here preferred
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\item Compact, 6DoF, higher control bandwidth, linear, simpler
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\item Show some example of serial and parallel manipulators
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\item A review of Stewart platform will be given in Chapter related to the detailed design of the Nano-Hexapod
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\end{itemize}
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\chapter{The Stewart platform}
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\label{sec:nhexa_stewart_platform}
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\begin{itemize}
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\item Some history about Stewart platforms
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\item What is so special and why it is so used in different fields: give examples
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Explain advantages compared to serial architecture
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\item Little review (very quick: two extreme sizes, piezo + voice coil)
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Complete review of Stewart platforms will be made in Chapter 2
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\item Presentation of tools used to analyze the properties of the Stewart platform => useful for design and control
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\end{itemize}
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\section{Mechanical Architecture}
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\label{ssec:nhexa_stewart_platform_architecture}
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\url{file:///home/thomas/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/stewart-architecture.org}
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Presentation of the typical architecture
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\begin{itemize}
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\item Explain the different frames, etc\ldots{}
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\item explain key elements:
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\begin{itemize}
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\item two plates
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\item joints
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\item actuators
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\end{itemize}
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\end{itemize}
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Make well defined notations.
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\begin{itemize}
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\item \{F\}, \{M\}
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\item si, li, ai, bi, etc.
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\item[{$\square$}] Make figure with defined frames, joints, etc\ldots{}
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Maybe can use this figure as an example:
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\begin{center}
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\includesvg[scale=1]{/home/thomas/Cloud/work-projects/ID31-NASS/phd-thesis-chapters/A0-nass-introduction/figs/introduction_stewart_du14}
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\end{center}
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\end{itemize}
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\section{Kinematic Analysis}
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\label{ssec:nhexa_stewart_platform_kinematics}
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\paragraph{Inverse Kinematics}
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\paragraph{Forward Kinematics}
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\paragraph{Jacobian Matrix}
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\begin{itemize}
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\item Velocity Loop Closure
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\item Static Forces
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\end{itemize}
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\paragraph{Singularities}
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\begin{itemize}
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\item Briefly mention singularities, and say that for small stroke, it is not an issue, the Jacobian matrix may be considered constant
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\end{itemize}
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\section{Static Analysis}
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\label{ssec:nhexa_stewart_platform_static}
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How stiffness varies with orientation of struts.
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Same with stroke?
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Or maybe in the detailed chapter?
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\section{Dynamic Analysis}
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\label{ssec:nhexa_stewart_platform_dynamics}
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Very complex => multi-body model
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For instance, compute the plant for massless struts and perfect joints (will be compared with Simscape model).
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But say that if we want to model more complex cases, it becomes impractical (cite papers).
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\section*{Conclusion}
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All depends on the geometry.
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Reasonable choice of geometry is made in chapter 1.
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Optimization of the geometry will be made in chapter 2.
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\chapter{Multi-Body Model}
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\label{sec:nhexa_model}
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\textbf{Goal}:
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\begin{itemize}
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\item Study the dynamics of Stewart platform
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\item Instead of working with complex analytical models: a multi-body model is used.
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Complex because has to model the inertia of the struts.
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Cite papers that tries to model the stewart platform analytically
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Advantage: it will be easily included in the model of the NASS
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\item Mention the Toolbox (maybe make a DOI for that)
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\item[{$\square$}] Have a table somewhere that summarizes the main characteristics of the nano-hexapod model
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\begin{itemize}
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\item location of joints
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\item size / mass of platforms, etc\ldots{}
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\end{itemize}
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\end{itemize}
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\section{Model Definition}
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\label{ssec:nhexa_model_def}
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\begin{itemize}
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\item[{$\square$}] Make a schematic of the definition process (for instance knowing the ai, bi points + \{A\} and \{B\} allows to compute Jacobian, etc\ldots{})
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\item What is important for the model:
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\begin{itemize}
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\item Inertia of plates and struts
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\item Positions of joints / Orientation of struts
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\item Definition of frames (for Jacobian, stiffness analysis, etc\ldots{})
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\end{itemize}
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\end{itemize}
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Then, several things can be computed:
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\begin{itemize}
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\item Kinematics, stiffness, platform mobility, dynamics, etc\ldots{}
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\end{itemize}
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\begin{itemize}
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\item Joints: can be 2dof to 6dof
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\item Actuators: can be modelled as wanted
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\end{itemize}
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\section{Nano Hexapod}
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\label{ssec:nhexa_model_nano_hexapod}
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Start simple:
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\begin{itemize}
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\item Perfect joints, massless actuators
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\end{itemize}
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Joints: perfect 2dof/3dof (+ mass-less)
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Actuators: APA + Encoder (mass-less)
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\begin{itemize}
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\item k = 1N/um
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\item Force sensor
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\end{itemize}
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Definition of each part + Plant with defined inputs/outputs (force sensor, relative displacement sensor, etc\ldots{})
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\section{Model Dynamics}
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\label{ssec:nhexa_model_dynamics}
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\begin{itemize}
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\item If all is perfect (mass-less struts, perfect joints, etc\ldots{}), maybe compare analytical model with simscape model?
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\item Say something about the model order
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Model order is 12, and that we can compute modes from matrices M and K, compare with the Simscape model
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\item Compare with analytical formulas (see number of states)
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\end{itemize}
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\section*{Conclusion}
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\begin{itemize}
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\item Validation of multi-body model in a simple case
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\item Possible to increase the model complexity when required
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\begin{itemize}
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\item If considered 6dof joint stiffness, model order increases
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\item Can have an effect on IFF performances: \cite{preumont07_six_axis_singl_stage_activ}
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\item Conclusion: during the conceptual design, we consider a perfect, but will be taken into account later
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\item Optimization of the Flexible joint will be performed in Chapter 2.2
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\end{itemize}
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\item MIMO system: how to control? => next section
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\end{itemize}
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\chapter{Control of Stewart Platforms}
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\label{sec:nhexa_control}
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MIMO control: much more complex than SISO control because of interaction.
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Possible to ignore interaction when good decoupling is achieved.
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Important to have tools to study interaction
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Different ways to try to decouple a MIMO plant.
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Reference book: \cite{skogestad07_multiv_feedb_contr}
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\section{Centralized and Decentralized Control}
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\label{ssec:nhexa_control_centralized_decentralized}
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\begin{itemize}
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\item Explain what is centralized and decentralized:
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\begin{itemize}
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\item linked to the sensor position relative to the actuators
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\item linked to the fact that sensors and actuators pairs are ``independent'' or each other (related to the control architecture, not because there is no coupling)
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\end{itemize}
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\item When can decentralized control be used and when centralized control is necessary?
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Study of interaction: RGA
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\end{itemize}
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\section{Choice of the control space}
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\label{ssec:nhexa_control_space}
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\begin{itemize}
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\item[{$\square$}] \url{file:///home/thomas/Cloud/research/matlab/decoupling-strategies/svd-control.org}
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\item Jacobian matrices, CoK, CoM, control in the frame of the struts, SVD, Modal, \ldots{}
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\item Combined CoM and CoK => Discussion of cubic architecture ? (quick, as it is going to be in detailed in chapter 2)
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\item Explain also the link with the setpoint: it is interesting to have the controller in the frame of the performance variables
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Also speak about disturbances? (and how disturbances can be mixed to different outputs due to control and interaction)
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\item Table that summarizes the trade-off for each strategy
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\item Say that in this study, we will do the control in the frame of the struts for simplicity (even though control in the cartesian frame was also tested)
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\end{itemize}
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\section{Active Damping with Decentralized IFF}
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\label{ssec:nhexa_control_iff}
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Guaranteed stability: \cite{preumont08_trans_zeros_struc_contr_with}
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\begin{itemize}
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\item[{$\square$}] I think there is another paper about that
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\end{itemize}
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For decentralized control: ``MIMO root locus'' can be used to estimate the damping / optimal gain
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Poles and converging towards \emph{transmission zeros}
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How to optimize the added damping to all modes?
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\begin{itemize}
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\item[{$\square$}] Add some papers citations
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\end{itemize}
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Compute:
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\begin{itemize}
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\item[{$\square$}] Plant dynamics
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\item[{$\square$}] Root Locus
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\end{itemize}
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\section{MIMO High-Authority Control - Low-Authority Control}
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\label{ssec:nhexa_control_hac_lac}
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Compute:
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\begin{itemize}
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\item[{$\square$}] compare open-loop and damped plant (outputs are the encoders)
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\item[{$\square$}] Implement decentralized control?
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\item[{$\square$}] Check stability:
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\begin{itemize}
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\item Characteristic Loci: Eigenvalues of \(G(j\omega)\) plotted in the complex plane
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\item Generalized Nyquist Criterion: If \(G(s)\) has \(p_0\) unstable poles, then the closed-loop system with return ratio \(kG(s)\) is stable if and only if the characteristic loci of \(kG(s)\), taken together, encircle the point \(-1\), \(p_0\) times anti-clockwise, assuming there are no hidden modes
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\end{itemize}
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\item[{$\square$}] Show some performance metric? For instance compliance?
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\end{itemize}
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\section*{Conclusion}
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\chapter*{Conclusion}
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\label{sec:nhexa_conclusion}
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\begin{itemize}
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\item Configurable Stewart platform model
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\item Will be included in the multi-body model of the micro-station => nass multi body model
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\item Control: complex problem, try to use simplest architecture
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\end{itemize}
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\begin{table}[htbp]
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\caption{\label{tab:simscape_nhexapod_section_matlab_code}Report sections and corresponding Matlab files}
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\centering
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\begin{tabularx}{0.6\linewidth}{lX}
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\toprule
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\textbf{Sections} & \textbf{Matlab File}\\
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\midrule
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Section \ref{sec}: & \texttt{simscape\_nhexapod\_1\_.m}\\
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\bottomrule
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\end{tabularx}
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\end{table}
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\chapter{Nano-Hexapod Kinematics}
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\label{sec:simscape_nhexapod_kinematics}
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\chapter{Conclusion}
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\label{sec:simscape_nhexapod_conclusion}
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\printbibliography[heading=bibintoc,title={Bibliography}]
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\end{document}
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