#+TITLE: Mechatronic approach for the design of a Nano Active Stabilization System
:DRAWER:
#+SUBTITLE: PhD Thesis

#+LANGUAGE: en
#+EMAIL: dehaeze.thomas@gmail.com
#+AUTHOR: Dehaeze Thomas

#+STARTUP: overview
#+DATE: {{{time(%Y-%m-%d)}}}

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#+PROPERTY: header-args:latex+ :exports results
#+PROPERTY: header-args:latex+ :mkdirp yes
#+PROPERTY: header-args:latex+ :output-dir figs
#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
:END:

* Build                                                             :noexport:
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(add-to-list 'org-export-filter-headline-functions
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        do
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#+END_SRC

* Useful snippets                                                   :noexport:
- acronyms acrshort:nass acrshort:mimo acrshort:lti [[acrfull:siso][Single-Input Single-Output (SISO)]]
- glossary terms gls:ka, gls:phi.
- Footnote[fn:1]

* Glossary and Acronyms - Tables                                      :ignore:

#+name: glossary
| label | name              | description           |
|-------+-------------------+-----------------------|
| ka    | \ensuremath{k_a}  | Actuator Stiffness in |
| phi   | \ensuremath{\phi} | A woody bush          |

#+name: acronyms
| key  | abbreviation | full form                        |
|------+--------------+----------------------------------|
| mimo | MIMO         | Multiple-Inputs Multiple-Outputs |
| siso | SISO         | Single-Input Single-Output       |
| nass | NASS         | Nano Active Stabilization System |
| lti  | LTI          | Linear Time Invariant            |

* Title Page                                                          :ignore:

#+begin_export latex
\begin{titlepage}
  \vspace*{5cm}
  \makeatletter
  \begin{center}
    \begin{Huge}
      \@title
    \end{Huge}\\[0.1cm]
    %
    \begin{Large}
      \@subtitle
    \end{Large}\\
    %
    \emph{by}\\
    \@author
    %
    \vfill
    A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (PhD) in Engineering Science\\
    at\\
    \textsc{Liège Université}
  \end{center}
  \makeatother
\end{titlepage}

\newpage
\null
\thispagestyle{empty}
\newpage
#+end_export

* Abstract
:PROPERTIES:
:UNNUMBERED: notoc
:END:

* Résumé
:PROPERTIES:
:UNNUMBERED: notoc
:END:

* Acknowledgments
:PROPERTIES:
:UNNUMBERED: notoc
:END:

* Table of Contents                                                   :ignore:

#+begin_export latex
\dominitoc
\tableofcontents

\listoftables
\listoffigures
#+end_export

* Introduction
** Context of this thesis / Background and Motivation

- ESRF (Figure [[fig:esrf_picture]])

#+name: fig:esrf_picture
#+caption: European Synchrotron Radiation Facility
#+attr_latex: :width 0.7\linewidth
[[file:figs/esrf_picture.jpg]]

- ID31 and Micro Station (Figure [[fig:id31_microstation_picture]])

#+begin_src latex :file id31_microstation_picture.pdf
\begin{tikzpicture}
  \node[inner sep=0pt, anchor=south west] (photo) at (0,0)
  {\includegraphics[width=0.39\textwidth]{/home/thomas/Cloud/documents/reports/phd-thesis/figs/exp_setup_photo.png}};

  \coordinate[] (aheight) at (photo.north west);
  \coordinate[] (awidth)  at (photo.south east);

  \coordinate[] (granite) at ($0.1*(aheight)+0.1*(awidth)$);
  \coordinate[] (trans)   at ($0.5*(aheight)+0.4*(awidth)$);
  \coordinate[] (tilt)    at ($0.65*(aheight)+0.75*(awidth)$);
  \coordinate[] (hexapod) at ($0.7*(aheight)+0.5*(awidth)$);
  \coordinate[] (sample)  at ($0.9*(aheight)+0.55*(awidth)$);

  % Granite
  \node[labelc] at (granite) {1};
  % Translation stage
  \node[labelc] at (trans) {2};
  % Tilt Stage
  \node[labelc] at (tilt) {3};
  % Micro-Hexapod
  \node[labelc] at (hexapod) {4};
  % Sample
  \node[labelc] at (sample) {5};

  % Axis
  \begin{scope}[shift={($0.07*(aheight)+0.87*(awidth)$)}]
    \draw[->] (0, 0) -- ++(55:0.7) node[above] {$y$};
    \draw[->] (0, 0) -- ++(90:0.9) node[left] {$z$};
    \draw[->] (0, 0) -- ++(-20:0.7) node[above] {$x$};
  \end{scope}
\end{tikzpicture}
#+end_src

#+name: fig:id31_microstation_picture
#+caption: Picture of the ID31 Micro-Station with annotations
#+attr_latex: :width 0.49\linewidth
#+RESULTS:
[[file:figs/id31_microstation_picture.png]]

Alternative: =id31_microstation_cad_view.png= (CAD view)

- X-ray beam + detectors + sample stage (Figure [[fig:id31_beamline_schematic]])

#+begin_src latex :file id31_beamline_schematic.pdf
  \begin{tikzpicture}
    % Parameters
    \def\blockw{6.0cm}
    \def\blockh{1.2cm}

    \def\tiltdeg{3}
    \coordinate[] (rotationpoint) at (0, 4.5*\blockh);

    \begin{scope}[rotate around={\tiltdeg:(rotationpoint)}]
      % Tilt
      \path[] ([shift=(-120:4*\blockh)]rotationpoint) coordinate(beginarc) arc (-120:-110:4*\blockh) %
      -- ([shift=(-70:4*\blockh)]rotationpoint) arc (-70:-60:4*\blockh)%
      |- ++(-0.15*\blockw, 0.6*\blockh) coordinate (spindlene)%
      |- ($(beginarc) + (0.15*\blockw, 0.2*\blockh)$) coordinate (spindlesw) -- ++(0, 0.4*\blockh) coordinate(tiltte) -| cycle;

      % Spindle
      \coordinate[] (spindlese) at (spindlesw-|spindlene);
      \draw[fill=black!30] ($(spindlese)+(-0.1,0.1)+(-0.1*\blockw, 0)$) -| ($(spindlene)+(-0.1, 0)$) -| coordinate[pos=0.25](spindletop) ($(spindlesw)+(0.1,0.1)$) -| ++(0.1*\blockw, -\blockh) -| coordinate[pos=0.25](spindlebot) cycle;

      % \draw[dashed, color=black!60] ($(spindletop)+(0, 0.2)$) -- ($(spindlebot)+(0,-0.2)$);

      % Tilt
      \draw[fill=black!60] ([shift=(-120:4*\blockh)]rotationpoint) coordinate(beginarc) arc (-120:-110:4*\blockh) %
      -- ([shift=(-70:4*\blockh)]rotationpoint) arc (-70:-60:4*\blockh)%
      |- coordinate (tiltne) ++(-0.15*\blockw, 0.6*\blockh) coordinate (spindlene)%
      |- ($(beginarc) + (0.15*\blockw, 0.2*\blockh)$) coordinate (spindlesw) -- ++(0, 0.4*\blockh) -| cycle;

      % Micro-Hexapod
      \begin{scope}[shift={(spindletop)}]
        % Parameters definitions
        \def\baseh{0.22*\blockh} % Height of the base
        \def\naceh{0.18*\blockh} % Height of the nacelle
        \def\baser{0.22*\blockw} % Radius of the base
        \def\nacer{0.18*\blockw} % Radius of the nacelle

        \def\armr{0.2*\blockh} % Radius of the arms
        \def\basearmborder{0.2}
        \def\nacearmborder{0.2}

        \def\xnace{0} \def\ynace{\blockh-\naceh} \def\anace{0}
        \def\xbase{0} \def\ybase{0} \def\abase{0}

        % Hexapod1
        \begin{scope}[shift={(\xbase, \ybase)}, rotate=\abase]
          % Base
          \draw[fill=white] (-\baser, 0) coordinate[](uhexabot) rectangle (\baser, \baseh);

          \coordinate[] (armbasel) at (-\baser+\basearmborder+\armr, \baseh);
          \coordinate[] (armbasec) at (0, \baseh);
          \coordinate[] (armbaser) at (\baser-\basearmborder-\armr, \baseh);

          \begin{scope}[shift={(\xnace, \ynace)}, rotate=\anace]
            \draw[fill=white] (-\nacer, 0) rectangle (\nacer, \naceh);
            \coordinate[] (uhexatop) at (0, \naceh);
            \coordinate[] (armnacel) at (-\nacer+\nacearmborder+\armr, 0);
            \coordinate[] (armnacec) at (0, 0);
            \coordinate[] (armnacer) at (\nacer-\nacearmborder-\armr, 0);
          \end{scope}

          \draw[] (armbasec) -- (armnacer);
          \draw[] (armbasec) -- (armnacel);
          \draw[] (armbasel) -- coordinate(mhexaw) (armnacel);
          \draw[] (armbasel) -- (armnacec);
          \draw[] (armbaser) -- (armnacec);
          \draw[] (armbaser) -- coordinate(mhexae) (armnacer);
        \end{scope}
      \end{scope}

      % Sample
      \begin{scope}[shift={(uhexatop)}]
        \draw[fill=white] (-0.1*\blockw, 0) coordinate[](samplebot) rectangle coordinate[pos=0.5](samplecenter) node[pos=0.5, above]{Sample} (0.1*\blockw, \blockh) coordinate[](samplene);
        \coordinate[](samplenw) at (-0.1*\blockw, \blockh);
      \end{scope}
    \end{scope}

    \begin{scope}[shift={(0, -0.3*\blockh)}]
      % Translation Stage - fixed part
      \draw[fill=black!40] (-0.5*\blockw, 0) coordinate[](tyb) rectangle (0.5*\blockw, 0.15*\blockh);
      \coordinate[] (measposbot) at (0.5*\blockw, 0);

      % Translation Stage - mobile part
      \draw[fill=black!10, fill opacity=0.5] (-0.5*\blockw, 0.2*\blockh) -- (-0.5*\blockw, 1.5*\blockh) coordinate[](tyt) -- (0.5*\blockw, 1.5*\blockh) -- (0.5*\blockw, 0.2*\blockh) -- (0.35*\blockw, 0.2*\blockh) -- (0.35*\blockw, 0.8*\blockh) -- (-0.35*\blockw, 0.8*\blockh) -- (-0.35*\blockw, 0.2*\blockh) -- cycle;

      % Translation Guidance
      \draw[dashed, color=black!60] ($(-0.5*\blockw, 0)+( 0.075*\blockw,0.5*\blockh)$) circle (0.2*\blockh);
      \draw[dashed, color=black!60] ($( 0.5*\blockw, 0)+(-0.075*\blockw,0.5*\blockh)$) circle (0.2*\blockh);

      % Tilt Guidance
      \draw[dashed, color=black!60] ([shift=(-107:4.1*\blockh)]rotationpoint) arc (-107:-120:4.1*\blockh);
      \draw[dashed, color=black!60] ([shift=( -73:4.1*\blockh)]rotationpoint) arc (-73:-60:4.1*\blockh);
    \end{scope}

    % % Vertical line
    % \draw[dashed, color=black] (samplecenter) -- ++(0, -4*\blockh);
    % \begin{scope}[rotate around={\tiltdeg:(samplecenter)}]
    %   \draw[dashed, color=black] (samplecenter) -- ++(0, -4*\blockh);
    %   \node[] at ($(samplecenter)+(0, -2.3*\blockh)$) {\AxisRotator[rotate=-90]};
    %   \node[right, shift={(0.3,0)}] at ($(samplecenter)+(0, -2.3*\blockh)$) {$\theta_z$};
    % \end{scope}
    % \draw[->] ([shift=(-90:3.6*\blockh)]samplecenter) arc (-90:-87:3.6*\blockh) node[right]{$\theta_y$};

    % Laser
    \begin{scope}[shift={(samplecenter)}]
      \draw[color=red, -<-=0.3] (samplecenter) node[circle, fill=red, inner sep=0pt, minimum size=3pt]{} -- node[pos=0.3, above, color=black]{X-ray} ($(samplecenter)+(1.2*\blockw,0)$);
    \end{scope}

    % Axis
    \begin{scope}[shift={(-0.35*\blockw, 3*\blockh)}]
      \def\axissize{0.8cm}
      \draw[->] (0, 0) -- ++(0, \axissize) node[right]{$z$};
      \draw[->] (0, 0) -- ++(-\axissize, 0) node[above]{$x$};
      \draw[fill, color=black] (0, 0) circle (0.05*\axissize);
      \node[draw, circle, inner sep=0pt, minimum size=0.4*\axissize, label=right:$y$] (yaxis) at (0, 0){};
      % \node[draw, circle, inner sep=0pt, cross, minimum size=0.4*\axissize, label=left:$y$] (yaxis) at (0, 0){};
    \end{scope}

    \node[fit={($(-0.6*\blockw, -0.5*\blockh)$) ($(0.6*\blockw, 4*\blockh)$)}, inner sep=0pt, draw, dashed, color=gray, label={Positioning Station}] (possystem) {};

    \draw[fill=black!30] ($(tyb)+(-5, -1)$) coordinate[](granitesw) rectangle node[pos=0.5]{Granite Frame} ($(measposbot)+(5, 0)$) coordinate[](granitene);

    % Focusing Optics
    \draw[fill=black!20] ($(granitene)+(-1.5, 3)$) rectangle ++(-1, 2);
    \draw[spring] ($(granitene)+(-2, 0)$) -- ++(0, 3);

    \node[fit={($(granitene)+(-2.8, -0.2)$) ($(granitene)+(-1.2, 5.2)$)}, inner sep=0pt, draw, dashed, color=gray, label={Focusing Optics}] () {};

    % Measurement Optics
    \draw[fill=black!20] ($(granitesw)+(1.5, 4)$) rectangle ++(1, 2);
    \draw[spring] ($(granitesw)+(2, 1)$) -- ++(0, 3);

    \node[fit={($(granitesw)+(2.8, 0.8)$) ($(granitesw)+(1.2, 6.2)$)}, inner sep=0pt, draw, dashed, color=gray, label={Imagery System}] () {};
  \end{tikzpicture}
#+end_src

#+name: fig:id31_beamline_schematic
#+caption: ID31 Beamline Schematic. With light source, nano-focusing optics, sample stage and detector.
#+attr_latex: :width \linewidth
#+RESULTS:
[[file:figs/id31_beamline_schematic.png]]

- Few words about science made on ID31 and why nano-meter accuracy is required
- Typical experiments (tomography, ...), various samples (up to 50kg)
- Example of picture obtained (Figure [[fig:id31_tomography_result]])

#+name: fig:id31_tomography_result
#+caption: Image obtained on the ID31 beamline
#+attr_latex: :width 0.49\linewidth
[[file:example-image-c.png]]

- Explain wanted positioning accuracy and why micro-station cannot have this accuracy (backlash, play, thermal expansion, ...)

** Challenge definition

#+name: fig:nass_concept_schematic
#+caption: Nass Concept. 1: micro-station, 2: nano-hexapod, 3: sample, 4: 5DoF metrology
[[file:figs/nass_concept_schematic.png]]

- 6DoF vibration control platform on top of a complex positioning platform
- *Goal*: Improve accuracy of 6DoF long stroke position platform
- *Approach*: Mechatronic approach / model based / predictive
- *Control*: Robust control approach / various payloads.
  First hexapod with control bandwidth higher than the suspension modes that accepts various payloads?
- Rotation aspect
- Compactness? (more related to mechanical design)

** Literature Review

#+name: fig:stewart_platform_examples
#+caption: Examples of Stewart Platforms
#+begin_figure
#+name: fig:stewart_platform_a
#+attr_latex: :caption \subcaption{Stewart platform based on voice coil actuators}
#+attr_latex: :options {0.49\textwidth}
#+begin_subfigure
#+attr_latex: :width 0.8\linewidth
[[file:example-image-a.png]]
#+end_subfigure
#+name: fig:stewart_platform_a
#+attr_latex: :options {0.49\textwidth}
#+attr_latex: :caption \subcaption{Stewart platform based on piezoelectric actuators}
#+begin_subfigure
#+attr_latex: :width 0.8\linewidth
[[file:example-image-b.png]]
#+end_subfigure
#+end_figure

- Hexapods
  cite:li01_simul_fault_vibrat_isolat_point
  cite:bishop02_devel_precis_point_contr_vibrat
  cite:hanieh03_activ_stewar
  cite:afzali-far16_vibrat_dynam_isotr_hexap_analy_studies
  cite:naves20_desig
- Positioning stations
- Mechatronic approach?
  cite:rankers98_machin
  cite:monkhorst04_dynam_error_budget
  cite:jabben07_mechat

** Outline of thesis / Thesis Summary / Thesis Contributions

*Mechatronic Design Approach* / *Model Based Design*:
- [[cite:&monkhorst04_dynam_error_budget]] high costs of the design process: the designed system must be *first time right*.
  When the system is finally build, its performance level should satisfy the specifications.
  No significant changes are allowed in the post design phase.
  Because of this, the designer wants to be able to predict the performance of the system a-priori and gain insight in the performance limiting factors of the system.

#+begin_src latex :file nass_mechatronics_approach.pdf
% \graphicspath{ {/home/thomas/Cloud/thesis/papers/dehaeze21_mechatronics_approach_nass/tikz/figs-tikz} }

\begin{tikzpicture}
  % Styles
  \tikzset{myblock/.style= {draw, thin, color=white!70!black, fill=white, text width=3cm, align=center, minimum height=1.4cm}};
  \tikzset{mylabel/.style= {anchor=north, below, font=\bfseries\small, color=black, text width=3cm, align=center}};
  \tikzset{mymodel/.style= {anchor=south, above, font=\small, color=black, text width=3cm, align=center}};
  \tikzset{mystep/.style=  {->, ultra thick}};

  % Blocks
  \node[draw, fill=lightblue, align=center, label={[mylabel, text width=8.0cm] Dynamical Models}, minimum height = 4.5cm, text width = 8.0cm] (model) at (0, 0) {};

  \node[myblock, fill=lightgreen, label={[mylabel] Disturbances},  left = 3 of model.west]                          (dist) {};
  \node[myblock, fill=lightgreen, label={[mylabel] $\mu$ Station}, below = 2pt of dist] (mustation) {};
  \node[myblock, fill=lightgreen, label={[mylabel] $\nu$ Hexapod}, above = 2pt of dist] (nanohexapod) {};

  \node[myblock, fill=lightyellow, label={[mylabel] Mech. Design},    above = 1 of model.north] (mechanical) {};
  \node[myblock, fill=lightyellow, label={[mylabel] Instrumentation}, left  = 2pt of mechanical]  (instrumentation) {};
  \node[myblock, fill=lightyellow, label={[mylabel] FEM},             right = 2pt of mechanical]  (fem) {};

  \node[myblock, fill=lightred, label={[mylabel] Test Benches},   right = 3 of model.east]                          (testbenches) {};
  \node[myblock, fill=lightred, label={[mylabel] Assembly},       above = 2pt of testbenches] (mounting) {};
  \node[myblock, fill=lightred, label={[mylabel] Implementation}, below = 2pt of testbenches] (implementation) {};

  % Text
  \node[anchor=south, above, text width=8cm, align=left] at (model.south) {Extensive use of models for:\begin{itemize}[noitemsep,topsep=5pt]\item Extraction of transfer functions \\ \item Choice of appropriate control architecture \\ \item Tuning of control laws \\ \item Closed loop simulations \\ \item Noise budgets / Evaluation of performances \\ \item Sensibility to parameters / disturbances\end{itemize}\centerline{Models are at the core the mecatronic approach!}};

  \node[mymodel] at (mustation.south)       {Multiple stages     \\ Complex dynamics};
  \node[mymodel] at (dist.south)            {Ground motion       \\ Position errors};
  \node[mymodel] at (nanohexapod.south)     {Different concepts  \\ Sensors, Actuators};

  \node[mymodel] at (instrumentation.south) {Sensors, Actuators  \\ Electronics};
  \node[mymodel] at (mechanical.south)      {Proper integration  \\ Ease of assembly};
  \node[mymodel] at (fem.south)             {Optimize key parts: \\ Joints, Plates, APA};

  \node[mymodel] at (mounting.south)        {Struts              \\ Nano-Hexapod};
  \node[mymodel] at (testbenches.south)     {Instrumentation     \\ APA, Struts};
  \node[mymodel] at (implementation.south)  {Control tests       \\ $\mu$ Station};

  % Links
  \draw[->] (dist.east)      -- node[above, midway]{{\small Measurements}} node[below,midway]{{\small Spectral Analysis}} (dist.east-|model.west);
  \draw[->] (mustation.east) -- node[above, midway]{{\small Measurements}} node[below, midway]{{\small CAD Model}} (mustation.east-|model.west);

  \draw[->] ($(nanohexapod.east-|model.west)-(0, 0.15)$) -- node[below, midway]{{\small Optimization}} ($(nanohexapod.east)-(0, 0.15)$);
  \draw[<-] ($(nanohexapod.east-|model.west)+(0, 0.15)$) -- node[above, midway]{{\small Model}} ($(nanohexapod.east)+(0, 0.15)$);

  \draw[->] ($(fem.south|-model.north)+(0.15, 0)$) -- node[right, midway]{{\small Specif.}} ($(fem.south)+(0.15,0)$);
  \draw[<-] ($(fem.south|-model.north)-(0.15, 0)$) -- node[left, midway,align=right]{{\small Super}\\{\small Element}}  ($(fem.south)-(0.15,0)$);

  \draw[->] ($(mechanical.south|-model.north)+(0.15, 0)$) -- node[right, midway]{{\small Specif.}} ($(mechanical.south)+(0.15,0)$);
  \draw[<-] ($(mechanical.south|-model.north)-(0.15, 0)$) -- node[left, midway,align=right]{{\small CAD}\\{\small model}}        ($(mechanical.south)-(0.15,0)$);

  \draw[->] ($(instrumentation.south|-model.north)+(0.15, 0)$) -- node[right, midway]{{\small Specif.}} ($(instrumentation.south)+(0.15,0)$);
  \draw[<-] ($(instrumentation.south|-model.north)-(0.15, 0)$) -- node[left, midway]{{\small Model}}         ($(instrumentation.south)-(0.15,0)$);

  \draw[->] ($(mounting.west-|model.east)+(0, 0.15)$) -- node[above, midway]{{\small Requirements}} ($(mounting.west)+(0, 0.15)$);
  \draw[<-] ($(mounting.west-|model.east)-(0, 0.15)$) -- node[below, midway]{{\small Model refinement}}   ($(mounting.west)-(0, 0.15)$);

  \draw[->] ($(testbenches.west-|model.east)+(0, 0.15)$) -- node[above, midway]{{\small Control Laws}} ($(testbenches.west)+(0, 0.15)$);
  \draw[<-] ($(testbenches.west-|model.east)-(0, 0.15)$) -- node[below, midway]{{\small Model refinement}}   ($(testbenches.west)-(0, 0.15)$);

  \draw[->] ($(implementation.west-|model.east)+(0, 0.15)$) -- node[above, midway]{{\small Control Laws}} ($(implementation.west)+(0, 0.15)$);
  \draw[<-] ($(implementation.west-|model.east)-(0, 0.15)$) -- node[below, midway]{{\small Model refinement}}   ($(implementation.west)-(0, 0.15)$);

  % Main steps
  \node[font=\bfseries, rotate=90, anchor=south, above] (conceptual_phase_node) at (dist.west) {1 - Conceptual Phase};
  \node[font=\bfseries, above] (detailed_phase_node) at (mechanical.north) {2 - Detail Design Phase};
  \node[font=\bfseries, rotate=-90, anchor=south, above] (implementation_phase_node) at (testbenches.east) {3 - Experimental Phase};
    \begin{scope}[on background layer]
      \node[fit={(conceptual_phase_node.north|-nanohexapod.north) (mustation.south east)}, fill=lightgreen!50!white, draw, inner sep=2pt] (conceptual_phase) {};
      \node[fit={(detailed_phase_node.north-|instrumentation.west) (fem.south east)}, fill=lightyellow!50!white, draw, inner sep=2pt] (detailed_phase) {};
      \node[fit={(implementation_phase_node.north|-mounting.north) (implementation.south west)}, fill=lightred!50!white, draw, inner sep=2pt] (implementation_phase) {};
      % \node[above left] at (dob.south east) {DOB};
    \end{scope}

  % Between main steps
  \draw[mystep, postaction={decorate,decoration={raise=1ex,text along path,text align=center,text={Concept Validation}}}] (conceptual_phase.north) to[out=90, in=180] (detailed_phase.west);
  \draw[mystep, postaction={decorate,decoration={raise=1ex,text along path,text align=center,text={Procurement}}}] (detailed_phase.east) to[out=0, in=90] (implementation_phase.north);

  % % Inside Model
  % \node[inner sep=1pt, outer sep=6pt, anchor=north west, draw, fill=white, thin] (multibodymodel) at ($(model.north west) - (0, 0.5)$)
  %   {\includegraphics[width=5.6cm]{simscape_nano_hexapod.png}};

  % \node[inner sep=1pt, outer sep=6pt, anchor=south west, draw, fill=white, thin] (simscape) at (model.south west)
  %   {\includegraphics[width=5.6cm]{simscape_picture.jpg}};

  % % Feedback Model
  % \node[inner sep=3pt, outer sep=6pt, anchor=north east, draw, fill=white, thin] (simscape_sim) at ($(model.north east) - (0, 0.5)$)
  %   {\includegraphics[width=3.6cm]{simscape_simulations.pdf}};

  % % FeedBack
  % \node[inner sep=3pt, outer sep=6pt, anchor=south east, draw, fill=white, thin] (feedback) at (model.south east)
  %   {\includegraphics[width=3.6cm]{classical_feedback_small.pdf}};
\end{tikzpicture}
#+end_src

#+name: fig:nass_mechatronics_approach
#+caption: Overview of the mechatronic approach used for the Nano-Active-Stabilization-System
#+attr_latex: :width \linewidth
#+RESULTS:
[[file:figs/nass_mechatronics_approach.png]]


* Conceptual Design Development
\minitoc
**** Abstract

Schematic that summarizes this phase.
Uniaxial => Rotation => Multi body => Simulations

** Constrains on the system

- Size
- Payload
- Connections to samples
- ... should justify the nano-hexapod design
  - choice of parallel architecture

- [ ] Picture/schematic of the micro-station with indicated location of Nano-Hexapod

** Uni-axial Model
*** Introduction                                                    :ignore:

- Explain what we want to capture with this model
- Schematic of the uniaxial model (with X-ray)
- Identification of disturbances (ground motion, stage vibrations)
- Optimal nano-hexapod stiffness/actuator: Voice coil VS Piezo (conclusion?)
- Control architecture (IFF, DVF, ...)?
- Conclusion

#+begin_src latex :file mass_spring_damper_nass.pdf
\begin{tikzpicture}
  % ====================
  % Parameters
  % ====================
  \def\bracs{0.05} % Brace spacing vertically
  \def\brach{-12pt} % Brace shift horizontaly
  % ====================

  % ====================
  % Ground
  % ====================
  \draw (-0.9, 0) -- (0.9, 0);
  \draw[dashed] (0.9, 0) -- ++(0.5, 0);
  \draw[->] (1.3, 0) -- ++(0, 0.4) node[right]{$w$};
  % ====================

  % ====================
  % Granite
  \begin{scope}[shift={(0, 0)}]
    \draw[fill=white] (-0.9, 1.2) rectangle (0.9, 2.0) node[pos=0.5]{$\scriptstyle\text{granite}$};
    \draw[spring] (-0.7, 0)   -- ++(0, 1.2);
    \draw[damper] ( 0,   0)   -- ++(0, 1.2);

    \draw[dashed] ( 0.9, 2.0) -- ++(2.0, 0) coordinate(xg);

    % \draw[decorate, decoration={brace, amplitude=8pt}, xshift=\brach] %
    % (-0.9, \bracs) -- ++(0, 2.0) node[midway,rotate=90,anchor=south,yshift=10pt]{Granite};
  \end{scope}
  % ====================

  % ====================
  % Stages
  \begin{scope}[shift={(0, 2.0)}]
    \draw[fill=white] (-0.9, 1.2) rectangle (0.9, 2.0) node[pos=0.5]{$\scriptstyle\mu\text{-station}$};

    \coordinate (mustation) at (0.9, 1.6);

    \draw[spring]   (-0.7, 0) -- ++(0, 1.2);
    \draw[damper]   ( 0,   0) -- ++(0, 1.2);
    \draw[actuator] ( 0.7, 0) -- ++(0, 1.2) node[midway, right=0.1](ft){$f_t$};

    % \draw[decorate, decoration={brace, amplitude=8pt}, xshift=\brach] %
    % (-0.9, \bracs) -- ++(0, 2.0) node[midway,rotate=90,anchor=south,yshift=10pt]{$\mu\text{-station}$};
  \end{scope}
  % ====================


  % ====================
  % NASS
  \begin{scope}[shift={(0, 4.0)}]
    \draw[fill=white] (-0.9, 1.2) rectangle (0.9, 2.0) node[pos=0.5]{$\scriptstyle\nu\text{-hexapod}$};
    \draw[dashed] (0.9, 2.0) -- ++(2.0, 0) coordinate(xnpos);

    \draw[spring]   (-0.7, 0) -- ++(0, 1.2) node[midway, left=0.1]{};
    \draw[damper]   ( 0,   0) -- ++(0, 1.2) node[midway, left=0.2]{};
    \draw[actuator] ( 0.7, 0) -- ++(0, 1.2) coordinate[midway, right=0.1](f);

    % \draw[decorate, decoration={brace, amplitude=8pt}, xshift=\brach] %
    % (-0.9, \bracs) -- ++(0, 2.2) node[midway,rotate=90,anchor=south,yshift=10pt]{$\nu\text{-hexapod}$};
  \end{scope}
  % ====================

  % ====================
  % Measured Displacement
  \draw[<->, dashed] ($(xg)+(-0.1, 0)$) node[above left](d){$d$} -- ($(xnpos)+(-0.1, 0)$);
  % ====================

  % ====================
  % IFF Control
  % \node[block={2em}{1.5em}, right=0.6 of fsensn] (iff) {$K_{\scriptscriptstyle IFF}$};
  % \node[addb] (ctrladd) at (f-|iff) {};
  \node[block={2em}{1.5em}, right=0.6 of mustation] (ctrl) {$K$};

  % \draw[->] (fsensn.east)  -- node[midway, above]{$\tau_m$} (iff.west);
  % \draw[->] (iff.south)    -- (ctrladd.north);
  % \draw[->] (ctrladd.west) -- (f.east) node[above right]{$u$};
  \draw[->] (d.west)       -| (ctrl.south);
  \draw[->] (ctrl.north)   |- (f) node[above right]{$u$};
  % ====================
\end{tikzpicture}
#+end_src

#+name: fig:mass_spring_damper_nass
#+caption: 3-DoF uniaxial mass-spring-damper model of the NASS
#+RESULTS:
[[file:figs/mass_spring_damper_nass.png]]

*** Noise Budgeting

#+name: fig:measurement_microstation_vibration_picture
#+caption: Setup used to measure the micro-station vibrations during operation
#+attr_latex: :width 0.4\linewidth
[[file:measurement_microstation_vibration_picture.jpg]]

#+name: fig:asd_ground_motion_ustation_dist
#+caption: Amplitude Spectral density of the measured disturbance sources
#+attr_latex: :width 0.49\linewidth
[[file:example-image-b.png]]

*** Effect of support compliance
[[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/uncertainty_support.org::+TITLE: Effect of Uncertainty on the support's dynamics on the isolation platform dynamics][study]]

- *goal*: make the nano-hexapod independent of the support compliance
- Simple 2DoF model
- Generalized to any support compliance
- *conclusion*: frequency of nano-hexapod resonances should be lower than first suspension mode of the support

*** Effect of payload dynamics
[[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/uncertainty_payload.org::+TITLE: Effect of Uncertainty on the payload's dynamics on the isolation platform dynamics][study]]

- *goal*: be robust to a change of payload
- Simple 2DoF model
- Generalized to any payload dynamics

*** Active Damping

Conclusion: IFF is better for this application

**** Integral Force Feedback

- Mass spring damper model
- Root Locus
- Sensitivity to disturbances

**** Direct Velocity Feedback

- Mass spring damper model
- Root Locus
- Sensitivity to disturbances


** Effect of rotation
*** Introduction                                                    :ignore:

[[cite:&dehaeze20_activ_dampin_rotat_platf_integ_force_feedb;&dehaeze21_activ_dampin_rotat_platf_using]]

*** X-Y rotating platform model

- x-y-Rz model
- explain why this is representing the NASS
- Equation of motion
- Centrifugal forces, Coriolis

#+begin_src latex :file 2dof_rotating_system.pdf
  \begin{tikzpicture}
    % Angle
    \def\thetau{25}

    % Rotational Stage
    \draw[fill=black!60!white] (0, 0) circle (4.3);
    \draw[fill=black!40!white] (0, 0) circle (3.8);

    % Label
    \node[anchor=north west, rotate=\thetau] at (-2.5, 2.5) {\small Rotating Stage};

    % Rotating Scope
    \begin{scope}[rotate=\thetau]
      % Rotating Frame
      \draw[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6);
      % Label
      \node[anchor=north west, rotate=\thetau] at (-2.6, 2.6) {\small Suspended Platform};

      % Mass
      \draw[fill=white] (-1, -1) rectangle (1, 1);
      % Label
      \node[anchor=south west, rotate=\thetau] at (-1, -1) {\small Payload};

      % Attached Points
      \node[] at (-1, 0){$\bullet$};
      \draw[] (-1, 0) -- ++(-0.2, 0) coordinate(cu);
      \draw[] ($(cu) + (0, -0.8)$) coordinate(actu) -- ($(cu) + (0, 0.8)$) coordinate(ku);
      \node[] at (0, -1){$\bullet$};
      \draw[] (0, -1) -- ++(0, -0.2) coordinate(cv);
      \draw[] ($(cv) + (-0.8, 0)$)coordinate(kv) -- ($(cv) + (0.8, 0)$) coordinate(actv);

      % Spring and Actuator for U
      \draw[actuator={0.6}{0.2}] (actu) -- node[above=0.1, rotate=\thetau]{$F_u$} (actu-|-2.6,0);
      \draw[spring=0.2] (ku) -- node[above=0.1, rotate=\thetau]{$k$} (ku-|-2.6,0);
      \draw[damper={8}{8}] (cu) -- node[above left=0.2 and -0.1, rotate=\thetau]{$c$} (cu-|-2.6,0);

      \draw[actuator={0.6}{0.2}] (actv) -- node[left, rotate=\thetau]{$F_v$} (actv|-0,-2.6);
      \draw[spring=0.2] (kv) -- node[left, rotate=\thetau]{$k$} (kv|-0,-2.6);
      \draw[damper={8}{8}] (cv) -- node[left=0.1, rotate=\thetau]{$c$} (cv|-0,-2.6);
    \end{scope}

    % Inertial Frame
    \draw[->] (-4, -4) -- ++(2, 0) node[below]{$\vec{i}_x$};
    \draw[->] (-4, -4) -- ++(0, 2) node[left]{$\vec{i}_y$};
    \draw[fill, color=black] (-4, -4) circle (0.06);
    \node[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:$\vec{i}_z$] at (-4, -4){};

    \draw[->] (0, 0) node[above left, rotate=\thetau]{$\vec{i}_w$} -- ++(\thetau:2) node[above, rotate=\thetau]{$\vec{i}_u$};
    \draw[->] (0, 0) -- ++(\thetau+90:2) node[left, rotate=\thetau]{$\vec{i}_v$};
    \draw[fill, color=black] (0,0) circle (0.06);
    \node[draw, circle, inner sep=0pt, minimum size=0.3cm] at (0, 0){};
    \draw[dashed] (0, 0) -- ++(2, 0);
    \draw[] (1.5, 0) arc (0:\thetau:1.5) node[midway, right]{$\theta$};

    \draw[->] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$};
  \end{tikzpicture}
#+end_src

#+name: fig:2dof_rotating_system
#+caption: Mass spring damper model of an X-Y stage on top of a rotating stage
#+RESULTS:
[[file:figs/2dof_rotating_system.png]]

*** Effect of rotational velocity on the system dynamics

- Campbell diagram

*** Decentralized Integral Force Feedback

- Control diagram
- Root Locus: unstable with pure IFF

*** Two proposed modification of IFF

- Comparison of parallel stiffness and change of controller
- Transmissibility

*** Conclusion

- problem with voice coil actuator
- Two solutions: add parallel stiffness, or change controller
- Conclusion: minimum stiffness is required
- APA is a nice architecture for parallel stiffness + integrated force sensor (have to speak about IFF before that)

** Multi Body Model - Nano Hexapod
*** Introduction                                                    :ignore:

- What we want to capture with this model
- Explain what is a multi body model (rigid body, springs, etc...)
- Key elements (plates, joints, struts): for now simplistic model (rigid body elements, perfect joints, ...), but in next section, FEM will be used
- Matlab/Simulink developed toolbox for the study of Stewart platforms

*** Stewart Platform Architecture

#+name: fig:stewart_platform_architecture
#+caption: Stewart Platform Architecture
#+begin_figure
#+name: fig:stewart_architecture_example
#+attr_latex: :caption \subcaption{Initial position}
#+attr_latex: :options {0.49\textwidth}
#+begin_subfigure
#+attr_latex: :width 0.8\linewidth
[[file:stewart_architecture_example.png]]
#+end_subfigure
#+name: fig:stewart_architecture_example_pose
#+attr_latex: :options {0.49\textwidth}
#+attr_latex: :caption \subcaption{After some motion}
#+begin_subfigure
#+attr_latex: :width 0.8\linewidth
[[file:stewart_architecture_example_pose.png]]
#+end_subfigure
#+end_figure


- Little review
- explain key elements:
  - two plates
  - joints
  - actuators
- explain advantages compared to serial architecture

*** Kinematics

- Well define elements, frames, ...
- Derivation of jacobian matrices: for forces and for displacement
- Explain this is true for small displacements (show how small)

*** Model of an Amplified Piezoelectric Actuator

- APA test bench
- Piezoelectric effects
- mass spring damper representation (2dof)
- Compare the model and the experiment

*** Dynamics

- Effect of joints stiffnesses

#+name: fig:simscape_nano_hexapod
#+caption: 3D view of the multi-body model of the Nano-Hexapod (simplified)
#+attr_latex: :width \linewidth
[[file:figs/simscape_nano_hexapod.png]]

** Multi Body Model - Micro Station
*** Introduction                                                    :ignore:

#+name: fig:simscape_first_model_screenshot
#+caption: 3D view of the multi-body model of the micro-station
#+attr_latex: :width 0.7\linewidth
[[file:figs/simscape_first_model_screenshot.jpg]]

*** Kinematics

- Small overview of each stage and associated stiffnesses / inertia
- schematic that shows to considered DoF
- import from CAD

*** Modal Analysis
[[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-measurements/modal-analysis/index.org][study]]

- Picture of the experimental setup
- Location of accelerometers
- Show obtained modes
- Validation of rigid body assumption
- Explain how this helps tuning the multi-body model

*** Validation of the Model

- Most important metric: support compliance
- Compare model and measurement

** Control Architecture
*** Introduction                                                    :ignore:

Discussion of:
- Transformation matrices / control architecture
- Control in the frame of struts or cartesian?
- Effect of rotation on IFF? => APA
- HAC-LAC

*** High Authority Control - Low Authority Control (HAC-LAC)

- general idea
- case for parallel manipulator: decentralized LAC + centralized HAC

*** Decoupling Strategies for parallel manipulators
[[file:~/Cloud/research/matlab/decoupling-strategies/svd-control.org::+TITLE: Diagonal control using the SVD and the Jacobian Matrix][study]]

- Jacobian matrices, CoK, CoM, ...
- Discussion of cubic architecture
- SVD, Modal, ...

*** Decentralized Integral Force Feedback (LAC)

- Root Locus
- Damping optimization

*** Control Kinematics

- Explain how the position error can be expressed in the frame of the nano-hexapod
- block diagram
- Explain how to go from external metrology to the frame of the nano-hexapod

*** Decoupled Dynamics

- Centralized HAC
- Control in the frame of the struts
- Effect of IFF

*** Centralized Position Controller (HAC)

- Decoupled plant
- Controller design

** Simulations - Concept Validation
*** Introduction                                                    :ignore:

- Tomography experiment
- Open VS Closed loop results
- *Conclusion*: concept validation
  nano hexapod architecture with APA
  decentralized IFF + centralized HAC

#+name: fig:simscape_nass_final
#+caption: 3D view of the multi-body model including the micro-station, the nano-hexapod and the associated metrology
#+attr_latex: :width \linewidth
[[file:figs/simscape_nass_final.png]]

** Conclusion


* Detailed Design
\minitoc
**** Abstract

CAD view of the nano-hexapod with key components:
- plates
- flexible joints
- APA
- required instrumentation (ADC, DAC, Speedgoat, Amplifiers, Force Sensor instrumentation, ...)

** Optimal Nano-Hexapod geometry
*** Introduction                                                    :ignore:
- [ ] Geometry?
  - [ ] Cubic architecture?
  - [ ] Kinematics
  - [ ] Trade-off for the strut orientation
- [ ] Sensors required

*** Optimal strut orientation

*** Cubic Architecture: a Special Case?

** Including Flexible elements in the Multi-body model
*** Introduction                                                    :ignore:
Reduced order flexible bodies [[cite:brumund21_multib_simul_reduc_order_flexib_bodies_fea]]
- Used with APA, Flexible joints, Plates

*** Reduced order flexible bodies

- Quick explanation of the theory
- Implementation with Ansys (or Comsol) and Simscape

*** Numerical Validation

- Numerical Validation Ansys VS Simscape (APA)
- Figure with 0 and 1kg mass

*** Experimental Validation

- Test bench
- Obtained transfer functions and comparison with Simscape model with reduced order flexible body

** Amplified Piezoelectric Actuator
*** Introduction                                                    :ignore:
[[file:~/Cloud/work-projects/ID31-NASS/matlab/test-bench-apa/index.org::+TITLE: Test Bench - Amplified Piezoelectric Actuator][study 1]], [[file:~/Cloud/work-projects/ID31-NASS/matlab/test-bench-apa300ml/test-bench-apa300ml.org::+TITLE: Nano-Hexapod Struts - Test Bench][study 2]]

#+name: fig:apa_schmeatic
#+caption: Schematical representation of an Amplified Piezoelectric Actuator
#+attr_latex: :width 0.49\linewidth
[[file:example-image-a.png]]

- First tests with the APA95ML

*** Model

Piezoelectric equations

#+name: fig:apa_schmeatic_2dof
#+caption: Schematical representation of a 2DoF model of an Amplified Piezoelectric Actuator
#+attr_latex: :width 0.49\linewidth
[[file:example-image-a.png]]

#+name: fig:apa_schmeatic_fem
#+caption: Schematical representation of a FEM of an Amplified Piezoelectric Actuator
#+attr_latex: :width 0.49\linewidth
[[file:example-image-b.png]]

- FEM
- Simscape model
- (2 DoF, FEM, ...)

#+name: fig:root_locus_iff_rot_stiffness
#+caption: Limitation of the attainable damping due to the APA design
[[file:figs/root_locus_iff_rot_stiffness.png]]

*** Experimental System Identification

- Experimental validation (granite test bench)
- Electrical parameters
- Required instrumentation to read force sensor?
- Add resistor to include high pass filtering: no risk of saturating the ADC
- Estimation of piezoelectric parameters

*** Validation with Simscape model

- Tuned Simscape model
- IFF results: OK

** Flexible Joints
*** Introduction                                                    :ignore:

*** Effect of flexible joint characteristics on obtained dynamics

- Based on Simscape model
- Effect of axial stiffness, bending stiffness, ...
- Obtained specifications (trade-off)


*** Flexible joint geometry optimization

- Chosen geometry
- Optimisation with Ansys
- Validation with Simscape model

*** Experimental identification

- Experimental validation, characterisation ([[file:~/Cloud/work-projects/ID31-NASS/matlab/test-bench-flexible-joints-adv/bending.org::+TITLE: Flexible Joint - Measurement of the Bending Stiffness][study]])
- Visual inspection
- Test bench
- Obtained results

** Instrumentation
*** Introduction                                                    :ignore:

*** DAC


*** ADC

Force sensor

*** Voltage amplifier ([[https://research.tdehaeze.xyz/test-bench-pd200/][link]])

- Test Bench: capacitive load, ADC, DAC, Instrumentation amplifier
- Noise measurement
- Transfer function measurement

*** Encoder ([[https://research.tdehaeze.xyz/test-bench-vionic/][link]])
- Noise measurement

** Obtained Design

- CAD view of the nano-hexapod
- Chosen geometry, materials, ease of mounting, cabling, ...

* Experimental Validation
\minitoc
**** Abstract

Schematic representation of the experimental validation process.
- APA
- Strut
- Nano-hexapod on suspended table
- Nano-hexapod with Spindle

** Amplified Piezoelectric Actuator ([[https://research.tdehaeze.xyz/test-bench-apa300ml/][link]])

APA alone:
- *Goal*: Tune model of APA
- [ ] FRF and fit with FEM model
- [ ] Show all six FRF and how close they are
- [ ] IFF

** Struts

Strut (APA + joints):
- [ ] FRF, tune model
- [ ] Issue with encoder (comparison with axial motion)
- [ ] IFF

** Nano-Hexapod

Mounting

Test bench on top of soft table:
- *Goal*: Tune model of nano-hexapod, validation of dynamics
- modal analysis soft table (first mode at xxx Hz => rigid body in Simscape)
- FRF + comp model (multiple masses)
- IFF and robustness to change of mass

** Rotating Nano-Hexapod

- *Goal*: validation of control strategy with rotation
- Interferometers to have more stroke

#+name: fig:rot_nano_hexapod_bench_schematic
#+caption: Schematic of the rotating nano-hexapod test bench
#+attr_latex: :width 0.49\linewidth
[[file:example-image-a.png]]

** ID31 Micro Station

- *Goal*: full validation without the full metrology

* Conclusion and Future Work

* Appendix                                                            :ignore:
#+latex: \appendix

* Stewart Platform - Kinematics
* Comments on something
* Bibliography                                                        :ignore:
#+latex: \printbibliography[heading=bibintoc,title={Bibliography}]

* List of Publications
:PROPERTIES:
:UNNUMBERED: notoc
:END:

#+begin_export latex
\begin{refsection}[ref.bib]
  % List all papers even if not cited
  \nocite{*}
  % Sort by year
  \newrefcontext[sorting=ynt]
  % Articles
  \printbibliography[keyword={publication},heading={subbibliography},title={Articles},env=mypubs,type={article}]
  % Proceedings
  \printbibliography[keyword={publication},heading={subbibliography},title={In Proceedings},env=mypubs,type={inproceedings}]
\end{refsection}
#+end_export

* Glossary                                                            :ignore:
#+latex: \printglossary[type=\acronymtype]
#+latex: \printglossary

* Footnotes

[fn:1]this is a footnote with citation [[cite:&dehaeze21_mechat_approac_devel_nano_activ_stabil_system]].
