phd-thesis/phd-thesis.org

Glossary and Acronyms - Tables

label	name	description
ka	\ensuremath{k_a}	Actuator Stiffness in
phi	\ensuremath{ɸ}	A woody bush

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
esrf	ESRF	European Synchrotron Radiation Facility

Title Page

Abstract

\gls{phi}

Résumé

Acknowledgments

Table of Contents

Introduction

Context of this thesis / Background and Motivation

• \gls{esrf} (Figure fig:esrf_picture)

• ID31 and Micro Station (Figure fig:id31_microstation_picture)

\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}

Alternative: id31_microstation_cad_view.png (CAD view)

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

  \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}

• Few words about science made on ID31 and why nano-meter accuracy is required
• Typical experiments (tomography, …), various samples (up to 50kg)
• Where to explain the goal of each stage? (e.g. micro-hexapod: static positioning, Ty and Rz: scans, …)
• Example of picture obtained (Figure fig:id31_tomography_result)

• Explain wanted positioning accuracy and why micro-station cannot have this accuracy (backlash, play, thermal expansion, …)
• Speak about the metrology concept, and why it is not included in this thesis

Challenge definition

Nass Concept. 1: micro-station, 2: nano-hexapod, 3: sample, 4: 5DoF metrology

• 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

Examples of Stewart Platforms

• 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 /tdehaeze/phd-thesis/src/commit/893fabe70bfca627ed0d928d03d9cb04c4a768c0/~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/bibliography.org
• 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.

% \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}

Goals:

• Design \gls{nass} such that it is easy to control (and maintain). Have good performances by design and not by complex control strategies.

Models:

• Uniaxial Model:

  • Effect of limited support compliance
  • Effect of change of payload

• Rotating Model

  • Gyroscopic effects
• Multi Body Model
• Finite Element Models

Conceptual Design Development

minitoc

Abstract

Uni-axial Model

Introduction

• 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{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}

3-DoF uniaxial mass-spring-damper model of the NASS

Micro Station Model

Nano Hexapod Model

Disturbance Identification

Open Loop Dynamic Noise Budgeting

• List all disturbances with their spectral densities
• Show how they have been measured
• Say that repeatable errors can be calibrated (show measurement of Hans-Peter?)

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

Position Feedback Controller

Effect of support compliance

• 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

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

Conclusion

Effect of rotation

Introduction

Papers:

• cite:dehaeze20_activ_dampin_rotat_platf_integ_force_feedb
• cite:dehaeze21_activ_dampin_rotat_platf_using

System Description and Analysis

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

  \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}

Mass spring damper model of an X-Y stage on top of a rotating stage

Integral Force Feedback

• Control diagram
• Root Locus: unstable with pure IFF

IFF with an High Pass Filter

IFF with a stiffness in parallel with the force sensor

Relative Damping Control

Comparison of Active Damping Techniques

Rotating Nano-Hexapod

Nano Active Stabilization System with rotation

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)

Micro Station - Modal Analysis

Introduction

Conclusion:

• complex dynamics: need multi-body model of the micro-station to represent the limited compliance…

Measurement Setup

Frequency Analysis

Modal Analysis

Micro Station - Multi Body Model

Introduction

Kinematics

/tdehaeze/phd-thesis/src/commit/893fabe70bfca627ed0d928d03d9cb04c4a768c0/~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/kinematics.org::+TITLE:%20Kinematics%20of%20the%20station

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

Modal Analysis and Dynamic Modeling

• 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

Disturbances and Positioning errors

Validation of the Model

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

Nano Hexapod - Multi Body Model

Introduction

• 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

Stewart Platform Architecture

Configurable Simscape Model: /tdehaeze/phd-thesis/src/commit/893fabe70bfca627ed0d928d03d9cb04c4a768c0/~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org

• Explain the different frames, etc…
• 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
• Here, just a basic 2DoF model of the APA is used

Dynamics of the Nano-Hexapod

• Effect of joints stiffnesses
• The APA model should maybe not be used here, same for the nice top and bottom plates. Here the detailed design is not yet performed

Control Architecture - Concept Validation

Introduction

Discussion of:

• Transformation matrices / control architecture (computation of the position error in the frame of the nano-hexapod)
• Control of parallel architectures
• Control in the frame of struts or cartesian?
• Effect of rotation on IFF? => APA
• HAC-LAC
• New noise budgeting?

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

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

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

Decoupling Strategies for parallel manipulators

study

• Jacobian matrices, CoK, CoM, …
• Discussion of cubic architecture
• SVD, Modal, …

Decentralized Integral Force Feedback (LAC)

• Root Locus
• Damping optimization

Decoupled Dynamics

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

Centralized Position Controller (HAC)

• Decoupled plant
• Controller design

Conceptual Design - Conclusion

Detailed Design

minitoc

Abstract

Nano-Hexapod Kinematics - Optimal Geometry?

• Maybe this can be just merged with the last section in this chapter?

Introduction

Optimal strut orientation

Cubic Architecture: a Special Case?

/tdehaeze/phd-thesis/src/commit/893fabe70bfca627ed0d928d03d9cb04c4a768c0/~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/cubic-configuration.org

Nano-Hexapod Dynamics - Including Flexible elements in the Multi-body model

• Should this be an appendix?

Introduction

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

Actuator Choice

Introduction

• From previous study: APA seems a nice choice
• First tests with the APA95ML: validation of a basic model (maybe already presented)
• Optimal stiffness?
• Talk about piezoelectric actuator? bandwidth? noise?
• Specifications: stiffness, stroke, … => choice of the APA
• FEM of the APA
• Validation with flexible APA in the simscape model

Model

Piezoelectric equations

• FEM
• Simscape model
• (2 DoF, FEM, …)

Limitation of the attainable damping due to the APA design

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

Design of Nano-Hexapod Flexible Joints

Introduction

• Perfect flexible joint
• Imperfection of the flexible joint: Model
• Study of the effect of limited stiffness in constrain directions and non-null stiffness in other directions
• Obtained Specification
• Design optimisation (FEM)
• Implementation of flexible elements in the Simscape model: close to simplified model

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
• Show different existing geometry for flexible joints used on hexapods
• Optimisation with Ansys
• Validation with Simscape model

Experimental identification

• Experimental validation, characterisation (study)
• Visual inspection
• Test bench
• Obtained results

Choice of Instrumentation

Introduction

• Discussion of the choice of other elements:

  • Encoder
  • DAC
  • ADC (reading of the force sensors)
  • real time controller
  • Voltage amplifiers
• Give some requirements + chosen elements + measurements / validation

DAC and ADC

• Force sensor

Voltage amplifier (link)

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

Encoder (link)

• Noise measurement

Obtained Design

• Explain again the different specifications in terms of space, payload, etc..
• CAD view of the nano-hexapod
• Chosen geometry, materials, ease of mounting, cabling, …
• Validation on Simscape with accurate model?

Detailed Design - Conclusion

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

Flexible Joints

Struts

SCHEDULED:

Nano-Hexapod

Rotating Nano-Hexapod

ID31 Micro Station

Experimental Validation - Conclusion

Conclusion and Future Work

Alternative Architecture

/tdehaeze/phd-thesis/src/commit/893fabe70bfca627ed0d928d03d9cb04c4a768c0/~/Cloud/work-projects/ID31-NASS/matlab/nass-simscape/org/alternative-micro-station-architecture.org

Appendix

Mathematical Tools for Mechatronics

Feedback Control

Dynamical Noise Budgeting

Power Spectral Density

Cumulative Amplitude Spectrum

Stewart Platform - Kinematics

Bibliography

List of Publications

Glossary

Footnotes

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

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