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2021-08-27 19:04:48 +02:00 · 2021-07-28 09:43:36 +02:00 · 2021-07-26 21:46:38 +02:00 · 2021-07-26 20:38:52 +02:00 · 2021-07-22 23:52:44 +02:00 · 2021-07-22 11:34:05 +02:00
299 changed files with 496418 additions and 12508 deletions
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--- a/dehaeze21_mechatronics_approach_nass.bib
+++ b/dehaeze21_mechatronics_approach_nass.bib
@@ -0,0 +1,12 @@
@inproceedings{dehaeze21_mechat_approac_devel_nano_activ_stabil_system,
  author          = {Dehaeze, T. and Bonnefoy, J. and Collette, C.},
  title           = {Mechatronics Approach for the Development of a
                  Nano-Active-Stabilization-System},
  booktitle       = {MEDSI'20},
  year            = 2021,
  language        = {english},
  publisher       = {JACoW Publishing},
  series          = {Mechanical Engineering Design of Synchrotron Radiation
                  Equipment and Instrumentation},
  venue           = {Chicago, USA},
 }
--- a/index.html
+++ b/index.html
@@ -3,7 +3,7 @@
 "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
 <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
 <head>
-<!-- 2021-06-28 lun. 11:43 -->
+<!-- 2021-07-28 mer. 09:43 -->
 <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
 <title>Mechatronics Approach for the Development of a Nano-Active-Stabilization-System</title>
 <meta name="author" content="Thomas Dehaeze" />
@@ -17,7 +17,7 @@
 <a accesskey="h" href="../index.html"> UP </a>
 |
 <a accesskey="H" href="../index.html"> HOME </a>
-</div><div id="content">
+</div><div id="content" class="content">
 <h1 class="title">Mechatronics Approach for the Development of a Nano-Active-Stabilization-System
 <br />
 <span class="subtitle">Dehaeze Thomas, Bonnefoy Julien, Collette Christophe</span>
@@ -42,14 +42,42 @@ The presented development approach is foreseen to be applied more frequently to
 </p>
 </blockquote>
-<div id="outline-container-org3cd2d8c" class="outline-2">
+<div id="outline-container-org880994d" class="outline-2">
-<h2 id="org3cd2d8c">Conference Paper (<a href="paper/dehaeze21_mechatronics_approach_nass.pdf">pdf</a>)</h2>
+<h2 id="org880994d">Conference Paper (<a href="paper/dehaeze21_mechatronics_approach_nass.pdf">pdf</a>)</h2>
-<div class="outline-text-2" id="text-org3cd2d8c">
+<div class="outline-text-2" id="text-org880994d">
 </div>
 </div>
 <div id="outline-container-org95479e9" class="outline-2">
 <h2 id="org95479e9">Talk (<a href="talk/dehaeze21_mechatronics_approach_nass_talk.pdf">link</a>)</h2>
 <div class="outline-text-2" id="text-org95479e9">
 <iframe width="720"
 height="540"
 src="https://www.youtube.com/embed/kaplQJoqqDg"
 frameborder="0" allowfullscreen> </iframe>
 </div>
 </div>
 <div id="outline-container-orgb29f224" class="outline-2">
 <h2 id="orgb29f224">Cite this work</h2>
 <div class="outline-text-2" id="text-orgb29f224">
 <p>
-To cite this conference paper use the following bibtex code.
+To cite this conference paper use the following bibTeX code.
 </p>
 <div class="org-src-container">
-<pre class="src src-bibtex">
+<pre class="src src-bibtex"><span class="org-function-name">@inproceedings</span>{<span class="org-constant">dehaeze21_mechat_approac_devel_nano_activ_stabil_system</span>,
  <span class="org-variable-name">author</span>          = {Dehaeze, T. and Bonnefoy, J. and Collette, C.},
  <span class="org-variable-name">title</span>           = {Mechatronics Approach for the Development of a
                  Nano-Active-Stabilization-System},
  <span class="org-variable-name">booktitle</span>       = {MEDSI'20},
  <span class="org-variable-name">year</span>            = 2021,
  <span class="org-variable-name">language</span>        = {english},
  <span class="org-variable-name">publisher</span>       = {JACoW Publishing},
  <span class="org-variable-name">series</span>          = {Mechanical Engineering Design of Synchrotron Radiation
                  Equipment and Instrumentation},
  <span class="org-variable-name">venue</span>           = {Chicago, USA},
 }
 </pre>
 </div>
@@ -58,7 +86,7 @@ You can also use the formatted citation below.
 </p>
 <blockquote>
 <p>
-
+Dehaeze, T., Bonnefoy, J., &amp; Collette, C., Mechatronics approach for the development of a nano-active-stabilization-system, In MEDSI&rsquo;20 (2021), JACoW Publishing.
 </p>
 </blockquote>
 </div>
--- a/index.org
+++ b/index.org
@@ -34,17 +34,7 @@ The presented development approach is foreseen to be applied more frequently to
 :UNNUMBERED: t
 :END:
-To cite this conference paper use the following bibtex code.
+* Talk ([[file:talk/dehaeze21_mechatronics_approach_nass_talk.pdf][link]])
 #+begin_src bibtex
 #+end_src
 You can also use the formatted citation below.
 #+begin_quote
 #+end_quote
 * Talk ([[file:talk/dehaeze21_mechatronics_approach_nass_talk.pdf][link]])                                                       :noexport:
 :PROPERTIES:
 :UNNUMBERED: t
 :END:
@@ -52,7 +42,32 @@ You can also use the formatted citation below.
 #+begin_export html
    <iframe width="720"
     height="540"
-     src="https://www.youtube.com/embed/****"
+     src="https://www.youtube.com/embed/kaplQJoqqDg"
     frameborder="0" allowfullscreen> </iframe>
 #+end_export
 * Cite this work
 :PROPERTIES:
 :UNNUMBERED: t
 :END:
 To cite this conference paper use the following bibTeX code.
 #+begin_src bibtex
@inproceedings{dehaeze21_mechat_approac_devel_nano_activ_stabil_system,
  author          = {Dehaeze, T. and Bonnefoy, J. and Collette, C.},
  title           = {Mechatronics Approach for the Development of a
                  Nano-Active-Stabilization-System},
  booktitle       = {MEDSI'20},
  year            = 2021,
  language        = {english},
  publisher       = {JACoW Publishing},
  series          = {Mechanical Engineering Design of Synchrotron Radiation
                  Equipment and Instrumentation},
  venue           = {Chicago, USA},
 }
 #+end_src
 You can also use the formatted citation below.
 #+begin_quote
 Dehaeze, T., Bonnefoy, J., & Collette, C., Mechatronics approach for the development of a nano-active-stabilization-system, In MEDSI'20 (2021), JACoW Publishing.
 #+end_quote
--- a/paper/dehaeze21_mechatronics_approach_nass.org
+++ b/paper/dehaeze21_mechatronics_approach_nass.org
@@ -1,7 +1,7 @@
 #+TITLE: MECHATRONICS APPROACH FOR THE DEVELOPMENT OF A NANO-ACTIVE-STABILIZATION-SYSTEM
 :DRAWER:
 #+LATEX_CLASS: jacow
-#+LATEX_CLASS_OPTIONS: [a4paper, keeplastbox, biblatex, boxit]
+#+LATEX_CLASS_OPTIONS: [a4paper, keeplastbox, biblatex]
 #+OPTIONS: toc:nil
 #+STARTUP: overview
@@ -17,12 +17,15 @@
 #+AUTHOR: @@latex:\\@@
 #+AUTHOR: \textsuperscript{1}also at Precision Mechatronics Laboratory, University of Liege, Belgium
-#+LATEX_HEADER: \usepackage{pdfpages,multirow,ragged2e}
+#+latex_header: \usepackage{graphicx}
-#+LATEX_HEADER: \usepackage{graphicx,tabularx,booktabs}
+#+latex_header: \usepackage{tabularx}
-#+LATEX_HEADER: \usepackage{blindtext,bm}
+#+latex_header: \usepackage{booktabs}
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 #+LATEX_HEADER: \usepackage{siunitx}
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-#+LATEX_HEADER: \setcounter{footnote}{1}
+#+LATEX_HEADER_EXTRA: \setcounter{footnote}{1}
 #+LATEX_HEADER_EXTRA: \setlist[itemize]{noitemsep}
 #+LATEX_HEADER_EXTRA: \usepackage[colorlinks=true, allcolors=blue]{hyperref}
 #+LATEX_HEADER_EXTRA: \addbibresource{ref.bib}
 :END:
@@ -49,10 +52,8 @@
 (add-to-list 'org-export-filter-headline-functions
             'my-latex-filter-removeOrgAutoLabels)
 #+end_src
-In order to compile this document, just use the =latexmk= command.
+;; Function to compile to PDF
 #+begin_src emacs-lisp
 (defun my-compile-to-pdf ()
  (interactive)
  (org-latex-export-to-latex)
@@ -60,221 +61,222 @@ In order to compile this document, just use the =latexmk= command.
    (async-shell-command "latexmk")))
 #+end_src
 #+RESULTS:
 : #<window 72 on *Async Shell Command*>
 : #<window 64 on *Async Shell Command*>
 * ABSTRACT                                                           :ignore:
-#+BEGIN_abstract
+#+begin_abstract
 With the growing number of fourth generation light sources, there is an increased need of fast positioning end-stations with nanometric precision.
 Such systems are usually including dedicated control strategies, and many factors may limit their performances.
-In order to design such complex systems in a predictive way, a mechatronic design approach also known as "model based design", may be utilized.
+In order to design such complex systems in a predictive way, a mechatronics design approach also known as "model based design", may be utilized.
-In this paper, we present how this mechatronic design approach was used for the development of a nano-hexapod for the ESRF ID31 beamline.
+In this paper, we present how this mechatronics design approach was used for the development of a nano-hexapod for the ESRF ID31 beamline.
-The chosen design approach consists of using models of the mechatronic system (including sensors, actuators and control strategies) to predict its behavior.
+The chosen design approach consists of using models of the mechatronics system (including sensors, actuators and control strategies) to predict its behavior.
 Based on this behavior and closed-loop simulations, the elements that are limiting the performances can be identified and re-designed accordingly.
-This allows to make adequate choices concerning the design of the nano-hexapod and the overall mechatronic architecture early in the project and save precious time and resources.
+This allows to make adequate choices regarding the design of the nano-hexapod and the overall mechatronics architecture early in the project and therefore save precious time and resources.
 Several test benches were used to validate the models and to gain confidence on the predictability of the final system's performances.
 Measured nano-hexapod's dynamics was shown to be in very good agreement with the models.
 Further tests should be done in order to confirm that the performances of the system match the predicted one.
-The presented development approach is foreseen to be applied more frequently to future mechatronic system design at the ESRF.
+The presented development approach is foreseen to be applied more frequently to future mechatronics system design at the ESRF.
-#+END_abstract
+#+end_abstract
 * INTRODUCTION
-** Establish Significance                                            :ignore:
+With the new $4^\text{th}$ generation machines, there is an increasing need of fast and accurate positioning systems cite:dimper15_esrf_upgrad_progr_phase_ii.
 These systems are usually including feedback control loops and therefore their performances are not only depending on the quality of the mechanical design, but also on its correct integration with the actuators, sensors and control system.
 In order to optimize the performances of such system, it is essential to consider a design approach in which the structural design and the control design are integrated.
 This approach, also called the "mechatronics approach", was shown to be very effective for the design many complex systems cite:rankers98_machin,schmidt20_desig_high_perfor_mechat_third_revis_edition.
 Such design methodology was recently used for the development of several systems used by the synchrotron community cite:geraldes17_mechat_concep_new_high_dynam_dcm_sirius,holler18_omny_tomog_nano_cryo_stage,brendike19_esrf_doubl_cryst_monoc_protot.
-** Previous and/or current research and contributions                :ignore:
+The present paper presents how the "mechatronic approach" was used for the design of a Nano Active Stabilization System (NASS) for the ESRF ID31 beamline.
-
+* NASS - MECHATRONICS APPROACH
-** Locate a gap in the research / problem / question / prediction    :ignore:
+** The ID31 Micro-Station
-
+The ID31 micro-station is used to position samples along complex trajectories cite:dehaeze18_sampl_stabil_for_tomog_exper.
-Such mechatronic approach is widely used in the dutch industry cite:rankers98_machin and much less in the Synchrotron's world.
+It is composed of several stacked stages (represented in yellow in Fig.\nbsp{}ref:fig:nass_concept_schematic) which allows an high mobility.
-
+This however limits the position accuracy to tens of micrometers.
 ** The present work                                                  :ignore:
 In this paper, is presented how the mechatronic approach is used for the development of a nano active stabilization system.
 cite:dehaeze21_activ_dampin_rotat_platf_using
 cite:souleille18_concep_activ_mount_space_applic
 cite:brumund21_multib_simul_reduc_order_flexib_bodies_fea
 cite:dehaeze18_sampl_stabil_for_tomog_exper
 cite:schmidt20_desig_high_perfor_mechat_third_revis_edition
 * NASS - MECHATRONIC APPROACH
 ** The ID31 Micro Station
 The ID31 Micro Station is used to position samples along complex trajectories cite:dehaeze18_sampl_stabil_for_tomog_exper.
 It is composed of several stacked stages (represented in yellow in Fig.\nbsp{}ref:fig:nass_concept_schematic).
 This allows this station to have high mobility, however, this limits the position accuracy to tens of $\mu m$.
 ** The Nano Active Stabilization System
-The Nano Active Stabilization System (NASS) is a system whose goal is to improve the positioning accuracy of the ID31 Micro Station.
+The NASS is a system whose goal is to improve the positioning accuracy of the micro-station.
 It is represented in Fig.\nbsp{}ref:fig:nass_concept_schematic and consists of three main elements:
- a nano-hexapod located between the sample to be positioned and the micro-station.
+- A nano-hexapod located between the sample to be positioned and the micro-station
- a interferometric metrology system measuring the sample's position with respect to the focusing optics
+- An interferometric metrology system measuring the sample's position with respect to the focusing optics
- a control system (not represented), which base on the measured position, properly actuates the nano-hexapod in order to stabilize the sample's position
+- A control system (not represented), which based on the measured position, properly actuates the nano-hexapod in order to stabilize the sample's position.
 This system should be able to actively stabilize the sample position down to tens of nanometers while the micro-station is performing complex trajectories.
 #+name: fig:nass_concept_schematic
-#+attr_latex: :scale 1
+#+attr_latex: :scale 0.9
-#+caption: Nano Active Stabilization System - Schematic representation. 1) micro-station, 2) nano-hexapod, 3) sample, 4) metrology system
+#+caption: NASS - Schematic representation. 1) Micro-station, 2) Nano-hexapod, 3) Sample, 4) Metrology system.
 [[file:figs/nass_concept_schematic.pdf]]
-** Mechatronic Approach - Overview
+** Mechatronics Approach - Overview
-In order to design the NASS in a predictive way, a mechatronic approach, schematically represented in Fig.\nbsp{}ref:fig:nass_mechatronics_approach, is used.
+In order to design the NASS in a predictive way, a mechatronics approach, schematically represented in Fig.\nbsp{}ref:fig:nass_mechatronics_approach, was used.
 It consists of three main phases:
 1. Conceptual phase: Simple models of both the micro-station and the nano-hexapod are used to first evaluate the performances of several concepts.
   During this phase, the type of sensors to use and the approximate required dynamical characteristics of the nano-hexapod are determined.
 2. Detail design phase: Once the concept is validated, the models are used to list specifications both for the mechanics and the instrumentation.
   Each critical elements can then be properly designed.
   The models are updated as the design progresses.
 3. Experimental phase: Once the design is completed and the parts received, several test benches are used to verify the properties of the key elements.
   Then the hexapod can be mounted and fully tested with the instrumentation and the control system.
 #+name: fig:nass_mechatronics_approach
-#+attr_latex: :float multicolumn :width \linewidth
+#+attr_latex: :float multicolumn :width 0.9\linewidth
-#+caption: Overview of the mechatronic approach
+#+caption: Overview of the mechatronics approach used for the design of the NASS.
 [[file:figs/nass_mechatronics_approach.pdf]]
 1. /Conceptual phase/: Simple models of both the micro-station and the nano-hexapod are used to first evaluate the performances of several concepts.
   During this phase, the type of sensors to use and the approximate required dynamical characteristics of the nano-hexapod are determined.
 2. /Detail design phase/: Once the concept is validated, the models are used to list specifications both for the mechanics and the instrumentation.
   Each critical elements can then be properly designed.
   The models are updated as the design progresses.
 3. /Experimental phase/: Once the design is completed and the parts received, several test benches are used to verify the properties of the key elements.
   Then the hexapod can be mounted and fully tested with the instrumentation and the control system.
 ** Models
-As shown in Fig.\nbsp{}ref:fig:nass_mechatronics_approach, the models are at the core of the mechatronic approach.
+As shown in Fig.\nbsp{}ref:fig:nass_mechatronics_approach, the models are at the core of the mechatronics approach.
-Not only one, but several models are used throughout the design with increasing level of complexity (Fig.\nbsp{fig:nass_models}).
+Indeed, several models are used throughout the design with increasing level of complexity (Fig.\nbsp{}ref:fig:nass_models).
 #+begin_export latex
 \begin{figure*}[htbp]
  \begin{subfigure}[t]{0.25\linewidth}
    \centering
    \includegraphics[width=0.68\linewidth]{figs/mass_spring_damper_hac_lac.pdf}
-    \caption{\label{fig:mass_spring_damper_hac_lac} Mass Spring Damper Model}
+    \caption{\label{fig:mass_spring_damper_hac_lac} Mass Spring Damper Model.}
  \end{subfigure}
  \hfill
  \begin{subfigure}[t]{0.48\linewidth}
    \centering
-    \includegraphics[width=0.89\linewidth]{figs/nass_simscape_3d.png}
+    \includegraphics[width=0.89\linewidth]{figs/nass_simscape_3d.pdf}
-    \caption{\label{fig:nass_simscape_3d} Multi Body Model}
+    \caption{\label{fig:nass_simscape_3d} Multi Body Model.}
  \end{subfigure}
  \hfill
  \begin{subfigure}[t]{0.25\linewidth}
    \centering
    \includegraphics[width=0.93\linewidth]{figs/super_element_simscape_alt.pdf}
-    \caption{\label{fig:super_element_simscape} Finite Element Model}
+    \caption{\label{fig:super_element_simscape} Finite Element Model.}
  \end{subfigure}
  \hfill
-  \caption{\label{fig:nass_models}Schematic of several models used during all the mechatronic design process.}
+  \caption{\label{fig:nass_models}Schematic of several models used during all the mechatronics design process.}
  \centering
 \end{figure*}
 #+end_export
-At the beginning of the conceptual phase, simple "mass-spring-dampers" models (Fig.\nbsp{}ref:fig:mass_spring_damper_hac_lac) are used in order to evaluate the performances of different concepts.
+At the beginning of the conceptual phase, simple "mass-spring-damper" models (Fig.\nbsp{}ref:fig:mass_spring_damper_hac_lac) were used in order to easily study multiple concepts.
-Based on this model, it has been concluded that a nano-hexapod with low frequency "suspension" modes would help both for the reduction of the effects of several disturbances and for the decoupling between the nano-hexapod dynamics and the complex micro-station dynamics.
+Noise budgeting and closed-loop simulations were performed, and it was concluded that a nano-hexapod with low frequency "suspension" modes would help both for the reduction of the effects of disturbances and for the decoupling between the nano-hexapod dynamics and the complex micro-station dynamics.
-This will greatly help simplifying the control.
+I was found that by including a force sensor in series with the nano-hexapod's actuators, "Integral Force Feedback" (IFF) strategy could be used to actively damp the nano hexapod's resonances without impacting the high frequency disturbance rejection.
-# Say that HAC-LAC is tested with the model => should include force sensor
+The overall goal was to obtain a system dynamics which is easy to control in a robust way.
-Rapidly, a more sophisticated multi-body model (Fig.\nbsp{}ref:fig:nass_simscape_3d) has been used.
+Rapidly, a more sophisticated and more realistic multi-body model (Fig.\nbsp{}ref:fig:nass_simscape_3d) using Simscape cite:matlab20 was used.
-This model is based on the 3D representation of the micro-station as well as on extensive dynamical measurements.
+This model was based on the 3D representation of the micro-station as well as on extensive dynamical measurements.
-Time domain simulations can then be performed where each stage is moving with the associated positioning errors and disturbances.
+Time domain simulations were performed with every stage of the micro-station moving and the nano hexapod actively stabilizing the sample against the many disturbances.
-The multi-input multi-output control strategy can be developed and tested.
+The multi-body model permitted to study effects such as the coupling between the actuators and the sensors as well as the effect of the spindle's rotational speed on the nano-hexapod's dynamics cite:dehaeze21_activ_dampin_rotat_platf_using.
 The multi-input multi-output control strategy could be developed and tested.
-During the detail design phase, the nano-hexapod model is updated by importing the 3D parts exported from the CAD software.
+During the detail design phase, the nano-hexapod model was updated using 3D parts exported from the CAD software as the mechanical design progressed.
-The key elements of the nano-hexapod such as the flexible joints and the APA are optimized using a Finite Element Software.
+The key elements of the nano-hexapod such as the flexible joints and the APA were optimized using a Finite Element Analysis (FEA) Software.
-As the flexible modes of the system are what generally limit the controller bandwidth, they are important to model in order to understand which are problematic and which are to be maximized.
+As the flexible modes of the mechanics are what generally limit the controller bandwidth, they are important to model in order to understand which modes are problematic and should be addressed.
-In order to do so, a "super-element" can be exported and imported in Simscape (Fig.\nbsp{}ref:fig:super_element_simscape).
+To do so, a "super-element" can be exported using a FEA software and imported into the multi-body model (Fig.\nbsp{}ref:fig:super_element_simscape).
 Such process is described in cite:brumund21_multib_simul_reduc_order_flexib_bodies_fea.
 The multi-body model with included flexible elements can be used to very accurately estimate the dynamics of the system.
 However due to the large number of states included, it becomes unpractical to perform time domain simulations.
-# - [ ] Table that compares the three models in terms of:
+Finally, during the experimental phase, the models were refined using experimental system identification data.
-#   - time simulation
+At this phase of the development, models are still useful.
-#   - FRF
+They can help with the controller optimization, to understand the measurements, the associated performance limitations and to gain insight on which measures to take in order to overcome these limitations.
 #   - accuracy
 #   - easy to use
 Finally, during the experimental phase, the models are refined using experimental system identification.
 The models are still very useful to understand the measurements and the associated performance limitations.
 They are used to have a better insight on which measures to take in order to overcome the current limitations.
 For instance, it has been found that when fixing encoders to the struts (Fig.\nbsp{}ref:fig:nano_hexapod_elements), several flexible modes of the APA were appearing the dynamics which render the control using the encoders very complex.
 Therefore, an alternative configuration with the encoders fixed to the plates instead was used.
 For instance, it has been found that when fixing the encoders to the struts, as in Fig.\nbsp{}ref:fig:nano_hexapod_elements, several flexible modes of the APA were appearing in the dynamics which would render the control using the encoders very complex.
 Therefore, an alternative configuration with the encoders fixed to the plates was used instead.
 * NANO-HEXAPOD DESIGN
 ** Nano-Hexapod Specifications
-A CAD view of the nano-hexapod is shown in Fig.\nbsp{}ref:fig:nano_hexapod_elements.
+The nano-hexapod is a "Gough-Stewart platform", which is a fully parallel manipulator composed of few parts as shown in Fig.\nbsp{}ref:fig:nano_hexapod_elements: only two plates linked by 6 active struts.
-It is composed of 6 struts fixed in between two plates.
+Each strut has one rotational joint at each end, and one actuator in between (Fig.\nbsp{}ref:fig:nano_heaxpod_strut_picture).
 Each strut is composed of one flexible joints at each end, and one actuator (Fig.\nbsp{}ref:fig:picture_nano_hexapod_strut).
 ).
 And encoder can be fixed to the struts as shown, but can also be directly fixed to the plates (not represented here).
-Basic specifications:
+#+begin_export latex
- Limited height (95mm)
+\begin{figure*}[htbp]
- Stroke $\approx 100\,\mu m$
+  \begin{subfigure}[t]{0.80\linewidth}
- Load up to $50\,kg$
+    \centering
    \includegraphics[width=\linewidth]{figs/nano_hexapod_elements.pdf}
    \caption{\label{fig:nano_hexapod_elements} CAD view of the nano-hexapod with key elements.}
  \end{subfigure}
  \hfill
  \begin{subfigure}[t]{0.19\linewidth}
    \centering
    \includegraphics[width=0.95\linewidth]{figs/nano_heaxpod_strut_picture.pdf}
    \caption{\label{fig:nano_heaxpod_strut_picture} Mounted strut.}
  \end{subfigure}
  \caption{\label{fig:nano_hexapod}Nano-hexapod: A Stewart platform architecture.}
  \centering
 \end{figure*}
 #+end_export
-Based on the models used throughout the mechatronic approach, several specifications was obtained in order to maximize the performances of the system:
+The main benefits of this architecture are its compact design, good dynamical properties, high load capability over weight ratio, and to possibility to control the motion in 6 degrees of freedom.
- Axial stiffness of the struts $\approx 2\,\mu m/N$ such that the nano-hexapod dynamics is insensible to the rotation as well as decoupled from the micro-station dynamics
+The nano-hexapod should have a maximum height of $95\,mm$, support samples up to $50\,kg$, have a stroke of $\approx 100\,\mu m$ and be fully compliant to avoid any wear, backlash, play and to have predictable dynamics.
 - Small bending stiffness and high axial stiffness of the flexible joints
 - Precise positioning of the $b_i$ and $\hat{s}_i$
 - Flexible modes of the top-plate as high as possible
 - Integration of a force sensor for active damping purposes (more in the next section)
-** Parts' Optimization
+Based on the models used throughout the mechatronics approach, several specifications were added in order to maximize the performances of the system:
- APA / Flexible Joints / Plates
+- Actuator axial stiffness $\approx \SI{2}{N/\um}$ as it is a good trade-off between disturbance filtering, dynamic decoupling from the micro-station and insensibility to the spindle's rotational speed.
 - Flexible joint bending stiffness $< \SI{100}{Nm/rad}$ as high bending stiffness can limit IFF performances cite:preumont07_six_axis_singl_stage_activ.
 - Flexible joint axial stiffness $> \SI{100}{N/\um}$ to maximize the frequency of spurious resonances.
 - Precise positioning of the $b_i$ and $\hat{s}_i$ to accurately determine the hexapod's kinematics.
 - Flexible modes of the top-plate as high as possible as it can limit the achievable controller bandwidth.
 - Integration of a force sensor in series with each actuator for active damping purposes.
-The flexible joints and the top plates have been optimize using a Finite Element Model combine with the multi-body model of the nano-hexapod.
+** Parts Optimization
 During the detail design phase, several parts were optimized to fit the above specifications.
-The actuators are APA300ML from Cedrat Technologies.
+The flexible joint geometry was optimized using a finite element software while the top plate geometry was manually optimized to maximize the frequency of its flexible modes.
 Three stacks: two as actuator one as sensor
-#+name: fig:nano_hexapod_elements
+Amplified Piezoelectric Actuators (APA) were found to be the most suitable actuator for the nano-hexapod due to its compact size, large stroke and adequate stiffness.
-#+attr_latex: :float multicolumn :width \linewidth
+The chosen model was the APA300ML from Cedrat Technologies (Fig.\nbsp{}ref:fig:nano_heaxpod_strut_picture).
-#+caption: CAD view of the nano-hexapod with key elements
+It is composed of three piezoelectric stacks, a lever mechanism increasing the stroke up to $\approx \SI{300}{\um}$ and decreasing the axial stiffness down to $\approx \SI{1.8}{N/\um}$.
-[[file:figs/nano_hexapod_elements.pdf]]
+One of the three stacks can be used as a force sensor, at the price of loosing $1/3$ of the stroke.
 This has the benefits of providing good "collocation" between the sensor stack and the actuator stacks, meaning that the active damping controller will be robust cite:souleille18_concep_activ_mount_space_applic.
-** Mounted Nano-Hexapod
+** Nano-Hexapod Mounting
- Mounting benches
+Using the multi-body model of the nano-hexapod with the APA modeled as a flexible element, it was found that a misalignment between the APA and the two flexible joints was adding several resonances to the dynamics that were difficult to control.
 Therefore, a bench was developed to help the alignment the flexible joints and the APA during the mounting of the struts.
-#+name: fig:picture_nano_hexapod_strut
+A second mounting tool was used to fix the six struts to the two plates without inducing too much strain in the flexible joints.
-#+attr_latex: :width 0.9\linewidth
+The mounted nano-hexapod is shown in Fig.\nbsp{}ref:fig:nano_hexapod_picture.
 #+caption: Picture of a nano-hexapod's strut
 [[file:figs/picture_nano_hexapod_strut.pdf]]
 #+name: fig:nano_hexapod_picture
 #+attr_latex: :width 0.9\linewidth
-#+caption: Nano-Hexapod on top of the ID31 micro-station
+#+caption: Nano-hexapod on top of the micro-station.
-[[file:figs/nano_hexapod_picture.jpg]]
+[[file:figs/nano_hexapod_picture.pdf]]
 * TEST-BENCHES
 ** Flexible Joints and Instrumentation
-** APA/Struts Dynamics
+Before mounting the nano-hexapod and performing control tests, several test benches were used to characterize the individual elements of the system.
 Several test benches were used for all the critical elements of the nano-hexapod.
 For instant, the bending stiffness of the flexible joints are measured, and the model is refined.
 The measurement noise of the encoders are also measured, and the input/output relationship and the output voltage noise of the voltage amplifiers are measured.
-Perhaps the most important test bench was the one used to identify the dynamics of the amplified piezoelectric actuator (shown in Fig.\nbsp{}ref:fig:test_bench_apa_schematic).
+The bending stiffness of the flexible joints was measured by applying a controlled force to one end of the joint while measuring its deflection at the same time.
-It consist of a $5\,\text{kg}$ granite vertical guided with an air bearing and fixed on top of the APA.
+This helped exclude the ones that were not compliant with the requirement and pair the remaining ones.
 An excitation signal (low pass filtered white noise) is generated and applied to two of the piezoelectric stacks.
 Both the voltage generated by the third piezoelectric stack and the displacement measured by the encoder are recorded.
 The two obtained FRF can then be compared with the model and the piezoelectric constant are identified.
 These constants are used to do the conversion from the mechanical domain (force, strain) easily accessible on the model to the electrical domain (voltages, charges) easily measured.
 After identification of these constant, the match between the measured FRF and the model dynamics is quite good (Fig.\nbsp{}ref:fig:apa_test_bench_results)
-The same bench was also used with the struts in order to study the effects of the flexible joints.
+The transfer function from the input to the output voltage of the voltage amplifier[fn:1] as well as its output noise were measured.
 Similarly, the measurement noise of the encoders[fn:2] was also measured.
 These simple measurements on individual elements were useful to refine their models, to found any problem as early as possible, and to help analyzing the results obtained when the the nano-hexapod is mounted and all the elements combined.
 ** APA and Struts Dynamics
 A test bench schematically shown in Fig.\nbsp{}ref:fig:test_bench_apa_schematic was used to identify the dynamics of the APA.
 It consist of a $5\,\text{kg}$ granite fixed on top of the APA and vertical guided with an air bearing.
 An excitation signal (low pass filtered white noise) was generated and applied to two of the piezoelectric stacks.
 Both the voltage generated by the third piezoelectric stack and the displacement measured by the encoder were recorded.
 The two obtained frequency response functions (FRF) are compared with the model in Fig.\nbsp{}ref:fig:apa_test_bench_results.
 The piezoelectric constants describing the conversion from the mechanical domain (force, strain), easily accessible on the model, to the electrical domain (voltages, charges) easily measured can be estimated.
 With these constants, the match between the measured FRF and the model dynamics is very good (Fig.\nbsp{}ref:fig:apa_test_bench_results).
 The same bench was also used with the struts in order to study the added effects of the flexible joints.
 #+name: fig:test_bench_apa_schematic
 #+attr_latex: :scale 1
-#+caption: Schematic of the bench used to identify the APA dynamics
+#+caption: Schematic of the bench used to identify the APA dynamics.
 [[file:figs/test_bench_apa_schematic.pdf]]
 #+begin_export latex
 \begin{figure}[htbp]
-  \begin{subfigure}[t]{0.48\linewidth}
+  \begin{subfigure}[t]{0.49\linewidth}
    \centering
    \includegraphics[width=0.95\linewidth]{figs/apa_test_bench_results_de.pdf}
-    \caption{\label{fig:apa_test_bench_results_de} Encoder}
+    \caption{\label{fig:apa_test_bench_results_de} Encoder $d_e/V_a$.}
  \end{subfigure}
  \hfill
-  \begin{subfigure}[t]{0.48\linewidth}
+  \begin{subfigure}[t]{0.49\linewidth}
    \centering
    \includegraphics[width=0.95\linewidth]{figs/apa_test_bench_results_Vs.pdf}
-    \caption{\label{fig:apa_test_bench_results_Vs} Force Sensor}
+    \caption{\label{fig:apa_test_bench_results_Vs} Force sensor $V_s/V_a$.}
  \end{subfigure}
  \caption{\label{fig:apa_test_bench_results}Measured Frequency Response functions compared with the Simscape model. From the actuator stacks voltage to the encoder (\subref{fig:apa_test_bench_results_de}) and to the force sensor stack (\subref{fig:apa_test_bench_results_Vs}).}
  \centering
@@ -282,29 +284,75 @@ The same bench was also used with the struts in order to study the effects of th
 #+end_export
 ** Nano-Hexapod
 After the nano-hexapod has been mounted, its dynamics was identified by individually exciting each of the actuators and simultaneously recording the six force sensors and six encoders signals.
 Two $6$ by $6$ FRF matrices were computed.
 Their diagonal elements are shown in Fig.\nbsp{}ref:fig:nano_hexapod_identification_comp_simscape and compared with the model.
-#+name: fig:nass_hac_lac_schematic_test
+In Fig.\nbsp{}ref:fig:nano_hexapod_identification_comp_simscape_de one can observe the following modes:
-#+attr_latex: :width \linewidth
+- From $\SI{100}{Hz}$ to $\SI{200}{Hz}$: six suspension modes.
-#+caption: HAC-LAC Strategy - Block Diagram. The signals are: $\bm{r}$ the wanted sample's position, $\bm{X}$ the measured sample's position, $\bm{\epsilon}_{\mathcal{X}}$ the sample's position error, $\bm{\epsilon}_{\mathcal{L}}$ the sample position error expressed in the "frame" of the nano-hexapod struts, $\bm{u}$ the generated DAC voltages applied to the voltage amplifiers and then to the piezoelectric actuator stacks, $\bm{u}^\prime$ the new inputs corresponding to the damped plant, $\bm{\tau}$ the measured sensor stack voltages. $\bm{T}$ is . $\bm{K}_{\tiny IFF}$ is the Low Authority Controller used for active damping. $\bm{K}_{L}$ is the High Authority Controller.
+- At $\SI{230}{Hz}$ and $\SI{340}{Hz}$: flexible modes of the APA, also modeled thanks to the flexible model of the APA.
-[[file:figs/nass_hac_lac_block_diagram_without_elec.pdf]]
+- At $\SI{700}{Hz}$: flexible modes of the top plate. The model is not matching the FRF because a rigid body model was used for the top plate.
 The transfer functions from the actuators to their "collocated" force sensors have alternating poles and zeros as expected (Fig.\nbsp{}ref:fig:nano_hexapod_identification_comp_simscape_Vs).
 IFF was then applied individually on each pair of actuator/force sensor in order to actively damp the suspension modes.
 The optimal gain of the IFF controller was determined using the model.
 After applying the active damping technique, the $6$ by $6$ FRF matrix from the actuator to the encoders was identified again and shown in Fig.\nbsp{}ref:fig:nano_hexapod_identification_damp_comp_simscape.
 It is shown that all the suspension modes are well damped, and that the model is able to predict the closed-loop behavior of the system.
 Even the off-diagonal elements (effect of one actuator on the encoder fixed in parallel to another strut) is very well modeled (Fig.\nbsp{}ref:fig:nano_hexapod_identification_damp_comp_simscape_off_diag).
-#+name: fig:nano_hexapod_identification_comp_simscape
+#+begin_export latex
-#+attr_latex: :width \linewidth
+\begin{figure}[htbp]
-#+caption: Measured FRF and Simscape dynamics.
+  \begin{subfigure}[t]{0.49\linewidth}
-[[file:figs/nano_hexapod_identification_comp_simscape.pdf]]
+    \centering
    \includegraphics[width=0.95\linewidth]{figs/nano_hexapod_identification_comp_simscape_de.pdf}
    \caption{\label{fig:nano_hexapod_identification_comp_simscape_de} Encoder $d_{e_i}/u_i$.}
  \end{subfigure}
  \hfill
  \begin{subfigure}[t]{0.49\linewidth}
    \centering
    \includegraphics[width=0.95\linewidth]{figs/nano_hexapod_identification_comp_simscape_Vs.pdf}
    \caption{\label{fig:nano_hexapod_identification_comp_simscape_Vs} Force sensor $V_{s_i}/u_i$.}
  \end{subfigure}
  \caption{\label{fig:nano_hexapod_identification_comp_simscape}Comparison of the measured Frequency Response functions (FRF) with the Simscape model. From the excitation voltage to the associated encoder (\subref{fig:apa_test_bench_results_de}) and to the associated force sensor stack (\subref{fig:apa_test_bench_results_Vs}).}
  \centering
 \end{figure}
 #+end_export
-
+#+begin_export latex
-#+name: fig:nano_hexapod_identification_damp_comp_simscape
+\begin{figure}[htbp]
-#+attr_latex: :width \linewidth
+  \begin{subfigure}[t]{0.49\linewidth}
-#+caption: Undamped and Damped plant using IFF (measured FRF and Simscape model).
+    \centering
-[[file:figs/nano_hexapod_identification_damp_comp_simscape.pdf]]
+    \includegraphics[width=0.98\linewidth]{figs/nano_hexapod_identification_damp_comp_simscape_diag.pdf}
    \caption{\label{fig:nano_hexapod_identification_damp_comp_simscape_diag} Diagonal term.}
  \end{subfigure}
  \hfill
  \begin{subfigure}[t]{0.49\linewidth}
    \centering
    \includegraphics[width=0.98\linewidth]{figs/nano_hexapod_identification_damp_comp_simscape_off_diag.pdf}
    \caption{\label{fig:nano_hexapod_identification_damp_comp_simscape_off_diag} Off-Diagonal term.}
  \end{subfigure}
  \caption{\label{fig:nano_hexapod_identification_damp_comp_simscape}Transfer functions from actuator to encoder with (input $u$) and without (input $u^\prime$) IFF applied.}
  \centering
 \end{figure}
 #+end_export
 * CONCLUSION
 The mechatronics approach used for the development of a nano active stabilization system was presented.
 The extensive use of models allowed to design the system in a predictive way and to make reasonable design decisions early in the project.
 Measurements made on the nano-hexapod were found to match very well with the models indicating that the final performances should match the predicted one.
 The current performance limitation is coming from the flexible modes of the top platform, so future work will focus on overcoming this limitation.
 This design methodology can be easily transposed to other complex mechatronics systems and are foreseen to be applied for future mechatronics systems at the ESRF.
 * ACKNOWLEDGMENTS
 This research was made possible by a grant from the FRIA.
-We thank the following people for their support, without whose help this work would never have been possible: V. Honkimaki, L. Ducotte and M. Lessourd and the whole team of the Precision Mechatronic Laboratory.
+The authors wish to thank L. Ducotte, V. Honkim\auml{}ki, D. Coulon, P. Brumund, M. Lesourd, P. Got, JM. Clement, K. Amraoui and Y. Benyakhlef for their help throughout the project.
-* REFERENCES                                                         :ignore:
+* REFERENCES                                                          :ignore:
 \printbibliography{}
 * Footnotes                                                           :ignore:
 [fn:1]PD200 from PiezoDrive
 [fn:2]Vionic from Renishaw
--- a/paper/dehaeze21_mechatronics_approach_nass.pdf
+++ b/paper/dehaeze21_mechatronics_approach_nass.pdf
--- a/paper/dehaeze21_mechatronics_approach_nass.tex
+++ b/paper/dehaeze21_mechatronics_approach_nass.tex
@@ -1,17 +1,20 @@
-% Created 2021-07-14 mer. 12:41
+% Created 2021-07-26 lun. 21:40
 % Intended LaTeX compiler: pdflatex
-\documentclass[a4paper, keeplastbox, biblatex, boxit]{jacow}
+\documentclass[a4paper, keeplastbox, biblatex]{jacow}
-\usepackage{pdfpages,multirow,ragged2e}
+\usepackage{graphicx}
-\usepackage{graphicx,tabularx,booktabs}
+\usepackage{tabularx}
-\usepackage{blindtext,bm}
+\usepackage{booktabs}
 \usepackage{bm}
 \usepackage{subcaption}
 \usepackage{siunitx}
 \usepackage[USenglish, english]{babel}
 \setcounter{footnote}{1}
 \setlist[itemize]{noitemsep}
 \usepackage[colorlinks=true, allcolors=blue]{hyperref}
 \addbibresource{ref.bib}
 \author{T. Dehaeze\textsuperscript{1,}\thanks{thomas.dehaeze@esrf.fr}, J. Bonnefoy, ESRF, Grenoble, France \\ C. Collette\textsuperscript{1}, Université Libre de Bruxelles, BEAMS department, Brussels, Belgium \\ \textsuperscript{1}also at Precision Mechatronics Laboratory, University of Liege, Belgium}
-\date{2021-07-14}
+\date{2021-07-26}
 \title{MECHATRONICS APPROACH FOR THE DEVELOPMENT OF A NANO-ACTIVE-STABILIZATION-SYSTEM}
 \begin{document}
@@ -20,242 +23,291 @@
 \begin{abstract}
 With the growing number of fourth generation light sources, there is an increased need of fast positioning end-stations with nanometric precision.
 Such systems are usually including dedicated control strategies, and many factors may limit their performances.
-In order to design such complex systems in a predictive way, a mechatronic design approach also known as ``model based design'', may be utilized.
+In order to design such complex systems in a predictive way, a mechatronics design approach also known as ``model based design'', may be utilized.
-In this paper, we present how this mechatronic design approach was used for the development of a nano-hexapod for the ESRF ID31 beamline.
+In this paper, we present how this mechatronics design approach was used for the development of a nano-hexapod for the ESRF ID31 beamline.
-The chosen design approach consists of using models of the mechatronic system (including sensors, actuators and control strategies) to predict its behavior.
+The chosen design approach consists of using models of the mechatronics system (including sensors, actuators and control strategies) to predict its behavior.
 Based on this behavior and closed-loop simulations, the elements that are limiting the performances can be identified and re-designed accordingly.
-This allows to make adequate choices concerning the design of the nano-hexapod and the overall mechatronic architecture early in the project and save precious time and resources.
+This allows to make adequate choices regarding the design of the nano-hexapod and the overall mechatronics architecture early in the project and therefore save precious time and resources.
 Several test benches were used to validate the models and to gain confidence on the predictability of the final system's performances.
 Measured nano-hexapod's dynamics was shown to be in very good agreement with the models.
 Further tests should be done in order to confirm that the performances of the system match the predicted one.
-The presented development approach is foreseen to be applied more frequently to future mechatronic system design at the ESRF.
+The presented development approach is foreseen to be applied more frequently to future mechatronics system design at the ESRF.
 \end{abstract}
 \section{INTRODUCTION}
-Such mechatronic approach is widely used in the dutch industry \cite{rankers98_machin} and much less in the Synchrotron's world.
+With the new \(4^\text{th}\) generation machines, there is an increasing need of fast and accurate positioning systems \cite{dimper15_esrf_upgrad_progr_phase_ii}.
-In this paper, is presented how the mechatronic approach is used for the development of a nano active stabilization system.
+These systems are usually including feedback control loops and therefore their performances are not only depending on the quality of the mechanical design, but also on its correct integration with the actuators, sensors and control system.
-\cite{dehaeze21_activ_dampin_rotat_platf_using}
+In order to optimize the performances of such system, it is essential to consider a design approach in which the structural design and the control design are integrated.
-\cite{souleille18_concep_activ_mount_space_applic}
+This approach, also called the ``mechatronics approach'', was shown to be very effective for the design many complex systems \cite{rankers98_machin,schmidt20_desig_high_perfor_mechat_third_revis_edition}.
-\cite{brumund21_multib_simul_reduc_order_flexib_bodies_fea}
+Such design methodology was recently used for the development of several systems used by the synchrotron community \cite{geraldes17_mechat_concep_new_high_dynam_dcm_sirius,holler18_omny_tomog_nano_cryo_stage,brendike19_esrf_doubl_cryst_monoc_protot}.
 \cite{dehaeze18_sampl_stabil_for_tomog_exper}
 \cite{schmidt20_desig_high_perfor_mechat_third_revis_edition}
-\section{NASS - MECHATRONIC APPROACH}
+The present paper presents how the ``mechatronic approach'' was used for the design of a Nano Active Stabilization System (NASS) for the ESRF ID31 beamline.
-\subsection{The ID31 Micro Station}
+
-The ID31 Micro Station is used to position samples along complex trajectories \cite{dehaeze18_sampl_stabil_for_tomog_exper}.
+\section{NASS - MECHATRONICS APPROACH}
-It is composed of several stacked stages (represented in yellow in Fig.~\ref{fig:nass_concept_schematic}).
+\subsection{The ID31 Micro-Station}
-This allows this station to have high mobility, however, this limits the position accuracy to tens of \(\mu m\).
+The ID31 micro-station is used to position samples along complex trajectories \cite{dehaeze18_sampl_stabil_for_tomog_exper}.
 It is composed of several stacked stages (represented in yellow in Fig.~\ref{fig:nass_concept_schematic}) which allows an high mobility.
 This however limits the position accuracy to tens of micrometers.
 \subsection{The Nano Active Stabilization System}
-The Nano Active Stabilization System (NASS) is a system whose goal is to improve the positioning accuracy of the ID31 Micro Station.
+The NASS is a system whose goal is to improve the positioning accuracy of the micro-station.
 It is represented in Fig.~\ref{fig:nass_concept_schematic} and consists of three main elements:
 \begin{itemize}
-\item a nano-hexapod located between the sample to be positioned and the micro-station.
+\item A nano-hexapod located between the sample to be positioned and the micro-station
-\item a interferometric metrology system measuring the sample's position with respect to the focusing optics
+\item An interferometric metrology system measuring the sample's position with respect to the focusing optics
-\item a control system (not represented), which base on the measured position, properly actuates the nano-hexapod in order to stabilize the sample's position
+\item A control system (not represented), which based on the measured position, properly actuates the nano-hexapod in order to stabilize the sample's position.
 \end{itemize}
 This system should be able to actively stabilize the sample position down to tens of nanometers while the micro-station is performing complex trajectories.
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1,scale=1]{figs/nass_concept_schematic.pdf}
+\includegraphics[scale=1,scale=0.9]{figs/nass_concept_schematic.pdf}
-\caption{\label{fig:nass_concept_schematic}Nano Active Stabilization System - Schematic representation. 1) micro-station, 2) nano-hexapod, 3) sample, 4) metrology system}
+\caption{\label{fig:nass_concept_schematic}NASS - Schematic representation. 1) Micro-station, 2) Nano-hexapod, 3) Sample, 4) Metrology system.}
 \end{figure}
-\subsection{Mechatronic Approach - Overview}
+\subsection{Mechatronics Approach - Overview}
-In order to design the NASS in a predictive way, a mechatronic approach, schematically represented in Fig.~\ref{fig:nass_mechatronics_approach}, is used.
+In order to design the NASS in a predictive way, a mechatronics approach, schematically represented in Fig.~\ref{fig:nass_mechatronics_approach}, was used.
 It consists of three main phases:
 \begin{enumerate}
 \item Conceptual phase: Simple models of both the micro-station and the nano-hexapod are used to first evaluate the performances of several concepts.
 During this phase, the type of sensors to use and the approximate required dynamical characteristics of the nano-hexapod are determined.
 \item Detail design phase: Once the concept is validated, the models are used to list specifications both for the mechanics and the instrumentation.
 Each critical elements can then be properly designed.
 The models are updated as the design progresses.
 \item Experimental phase: Once the design is completed and the parts received, several test benches are used to verify the properties of the key elements.
 Then the hexapod can be mounted and fully tested with the instrumentation and the control system.
 \end{enumerate}
 \begin{figure*}
 \centering
-\includegraphics[scale=1,width=\linewidth]{figs/nass_mechatronics_approach.pdf}
+\includegraphics[scale=1,width=0.9\linewidth]{figs/nass_mechatronics_approach.pdf}
-\caption{\label{fig:nass_mechatronics_approach}Overview of the mechatronic approach}
+\caption{\label{fig:nass_mechatronics_approach}Overview of the mechatronics approach used for the design of the NASS.}
 \end{figure*}
 \begin{enumerate}
 \item \emph{Conceptual phase}: Simple models of both the micro-station and the nano-hexapod are used to first evaluate the performances of several concepts.
 During this phase, the type of sensors to use and the approximate required dynamical characteristics of the nano-hexapod are determined.
 \item \emph{Detail design phase}: Once the concept is validated, the models are used to list specifications both for the mechanics and the instrumentation.
 Each critical elements can then be properly designed.
 The models are updated as the design progresses.
 \item \emph{Experimental phase}: Once the design is completed and the parts received, several test benches are used to verify the properties of the key elements.
 Then the hexapod can be mounted and fully tested with the instrumentation and the control system.
 \end{enumerate}
 \subsection{Models}
-As shown in Fig.~\ref{fig:nass_mechatronics_approach}, the models are at the core of the mechatronic approach.
+As shown in Fig.~\ref{fig:nass_mechatronics_approach}, the models are at the core of the mechatronics approach.
-Not only one, but several models are used throughout the design with increasing level of complexity (Fig.~\{fig:nass\_models\}).
+Indeed, several models are used throughout the design with increasing level of complexity (Fig.~\ref{fig:nass_models}).
 \begin{figure*}[htbp]
  \begin{subfigure}[t]{0.25\linewidth}
    \centering
    \includegraphics[width=0.68\linewidth]{figs/mass_spring_damper_hac_lac.pdf}
-    \caption{\label{fig:mass_spring_damper_hac_lac} Mass Spring Damper Model}
+    \caption{\label{fig:mass_spring_damper_hac_lac} Mass Spring Damper Model.}
  \end{subfigure}
  \hfill
  \begin{subfigure}[t]{0.48\linewidth}
    \centering
-    \includegraphics[width=0.89\linewidth]{figs/nass_simscape_3d.png}
+    \includegraphics[width=0.89\linewidth]{figs/nass_simscape_3d.pdf}
-    \caption{\label{fig:nass_simscape_3d} Multi Body Model}
+    \caption{\label{fig:nass_simscape_3d} Multi Body Model.}
  \end{subfigure}
  \hfill
  \begin{subfigure}[t]{0.25\linewidth}
    \centering
    \includegraphics[width=0.93\linewidth]{figs/super_element_simscape_alt.pdf}
-    \caption{\label{fig:super_element_simscape} Finite Element Model}
+    \caption{\label{fig:super_element_simscape} Finite Element Model.}
  \end{subfigure}
  \hfill
-  \caption{\label{fig:nass_models}Schematic of several models used during all the mechatronic design process.}
+  \caption{\label{fig:nass_models}Schematic of several models used during all the mechatronics design process.}
  \centering
 \end{figure*}
-At the beginning of the conceptual phase, simple ``mass-spring-dampers'' models (Fig.~\ref{fig:mass_spring_damper_hac_lac}) are used in order to evaluate the performances of different concepts.
+At the beginning of the conceptual phase, simple ``mass-spring-damper'' models (Fig.~\ref{fig:mass_spring_damper_hac_lac}) were used in order to easily study multiple concepts.
-Based on this model, it has been concluded that a nano-hexapod with low frequency ``suspension'' modes would help both for the reduction of the effects of several disturbances and for the decoupling between the nano-hexapod dynamics and the complex micro-station dynamics.
+Noise budgeting and closed-loop simulations were performed, and it was concluded that a nano-hexapod with low frequency ``suspension'' modes would help both for the reduction of the effects of disturbances and for the decoupling between the nano-hexapod dynamics and the complex micro-station dynamics.
-This will greatly help simplifying the control.
+I was found that by including a force sensor in series with the nano-hexapod's actuators, ``Integral Force Feedback'' (IFF) strategy could be used to actively damp the nano hexapod's resonances without impacting the high frequency disturbance rejection.
 The overall goal was to obtain a system dynamics which is easy to control in a robust way.
-Rapidly, a more sophisticated multi-body model (Fig.~\ref{fig:nass_simscape_3d}) has been used.
+Rapidly, a more sophisticated and more realistic multi-body model (Fig.~\ref{fig:nass_simscape_3d}) using Simscape \cite{matlab20} was used.
-This model is based on the 3D representation of the micro-station as well as on extensive dynamical measurements.
+This model was based on the 3D representation of the micro-station as well as on extensive dynamical measurements.
-Time domain simulations can then be performed where each stage is moving with the associated positioning errors and disturbances.
+Time domain simulations were performed with every stage of the micro-station moving and the nano hexapod actively stabilizing the sample against the many disturbances.
-The multi-input multi-output control strategy can be developed and tested.
+The multi-body model permitted to study effects such as the coupling between the actuators and the sensors as well as the effect of the spindle's rotational speed on the nano-hexapod's dynamics \cite{dehaeze21_activ_dampin_rotat_platf_using}.
 The multi-input multi-output control strategy could be developed and tested.
-During the detail design phase, the nano-hexapod model is updated by importing the 3D parts exported from the CAD software.
+During the detail design phase, the nano-hexapod model was updated using 3D parts exported from the CAD software as the mechanical design progressed.
-The key elements of the nano-hexapod such as the flexible joints and the APA are optimized using a Finite Element Software.
+The key elements of the nano-hexapod such as the flexible joints and the APA were optimized using a Finite Element Analysis (FEA) Software.
-As the flexible modes of the system are what generally limit the controller bandwidth, they are important to model in order to understand which are problematic and which are to be maximized.
+As the flexible modes of the mechanics are what generally limit the controller bandwidth, they are important to model in order to understand which modes are problematic and should be addressed.
-In order to do so, a ``super-element'' can be exported and imported in Simscape (Fig.~\ref{fig:super_element_simscape}).
+To do so, a ``super-element'' can be exported using a FEA software and imported into the multi-body model (Fig.~\ref{fig:super_element_simscape}).
 Such process is described in \cite{brumund21_multib_simul_reduc_order_flexib_bodies_fea}.
 The multi-body model with included flexible elements can be used to very accurately estimate the dynamics of the system.
 However due to the large number of states included, it becomes unpractical to perform time domain simulations.
-Finally, during the experimental phase, the models are refined using experimental system identification.
+Finally, during the experimental phase, the models were refined using experimental system identification data.
-The models are still very useful to understand the measurements and the associated performance limitations.
+At this phase of the development, models are still useful.
-They are used to have a better insight on which measures to take in order to overcome the current limitations.
+They can help with the controller optimization, to understand the measurements, the associated performance limitations and to gain insight on which measures to take in order to overcome these limitations.
 For instance, it has been found that when fixing encoders to the struts (Fig.~\ref{fig:nano_hexapod_elements}), several flexible modes of the APA were appearing the dynamics which render the control using the encoders very complex.
 Therefore, an alternative configuration with the encoders fixed to the plates instead was used.
 For instance, it has been found that when fixing the encoders to the struts, as in Fig.~\ref{fig:nano_hexapod_elements}, several flexible modes of the APA were appearing in the dynamics which would render the control using the encoders very complex.
 Therefore, an alternative configuration with the encoders fixed to the plates was used instead.
 \section{NANO-HEXAPOD DESIGN}
 \subsection{Nano-Hexapod Specifications}
-A CAD view of the nano-hexapod is shown in Fig.~\ref{fig:nano_hexapod_elements}.
+The nano-hexapod is a ``Gough-Stewart platform'', which is a fully parallel manipulator composed of few parts as shown in Fig.~\ref{fig:nano_hexapod_elements}: only two plates linked by 6 active struts.
-It is composed of 6 struts fixed in between two plates.
+Each strut has one rotational joint at each end, and one actuator in between (Fig.~\ref{fig:nano_heaxpod_strut_picture}).
 Each strut is composed of one flexible joints at each end, and one actuator (Fig.~\ref{fig:picture_nano_hexapod_strut}).
 ).
 And encoder can be fixed to the struts as shown, but can also be directly fixed to the plates (not represented here).
-Basic specifications:
+\begin{figure*}[htbp]
-\begin{itemize}
+  \begin{subfigure}[t]{0.80\linewidth}
-\item Limited height (95mm)
+    \centering
-\item Stroke \(\approx 100\,\mu m\)
+    \includegraphics[width=\linewidth]{figs/nano_hexapod_elements.pdf}
-\item Load up to \(50\,kg\)
+    \caption{\label{fig:nano_hexapod_elements} CAD view of the nano-hexapod with key elements.}
-\end{itemize}
+  \end{subfigure}
-
+  \hfill
-Based on the models used throughout the mechatronic approach, several specifications was obtained in order to maximize the performances of the system:
+  \begin{subfigure}[t]{0.19\linewidth}
-\begin{itemize}
+    \centering
-\item Axial stiffness of the struts \(\approx 2\,\mu m/N\) such that the nano-hexapod dynamics is insensible to the rotation as well as decoupled from the micro-station dynamics
+    \includegraphics[width=0.95\linewidth]{figs/nano_heaxpod_strut_picture.pdf}
-\item Small bending stiffness and high axial stiffness of the flexible joints
+    \caption{\label{fig:nano_heaxpod_strut_picture} Mounted strut.}
-\item Precise positioning of the \(b_i\) and \(\hat{s}_i\)
+  \end{subfigure}
-\item Flexible modes of the top-plate as high as possible
+  \caption{\label{fig:nano_hexapod}Nano-hexapod: A Stewart platform architecture.}
-\item Integration of a force sensor for active damping purposes (more in the next section)
+  \centering
 \end{itemize}
 \subsection{Parts' Optimization}
 \begin{itemize}
 \item APA / Flexible Joints / Plates
 \end{itemize}
 The flexible joints and the top plates have been optimize using a Finite Element Model combine with the multi-body model of the nano-hexapod.
 The actuators are APA300ML from Cedrat Technologies.
 Three stacks: two as actuator one as sensor
 \begin{figure*}
 \centering
 \includegraphics[scale=1,width=\linewidth]{figs/nano_hexapod_elements.pdf}
 \caption{\label{fig:nano_hexapod_elements}CAD view of the nano-hexapod with key elements}
 \end{figure*}
-\subsection{Mounted Nano-Hexapod}
+The main benefits of this architecture are its compact design, good dynamical properties, high load capability over weight ratio, and to possibility to control the motion in 6 degrees of freedom.
 The nano-hexapod should have a maximum height of \(95\,mm\), support samples up to \(50\,kg\), have a stroke of \(\approx 100\,\mu m\) and be fully compliant to avoid any wear, backlash, play and to have predictable dynamics.
 Based on the models used throughout the mechatronics approach, several specifications were added in order to maximize the performances of the system:
 \begin{itemize}
-\item Mounting benches
+\item Actuator axial stiffness \(\approx \SI{2}{N/\um}\) as it is a good trade-off between disturbance filtering, dynamic decoupling from the micro-station and insensibility to the spindle's rotational speed.
 \item Flexible joint bending stiffness \(< \SI{100}{Nm/rad}\) as high bending stiffness can limit IFF performances \cite{preumont07_six_axis_singl_stage_activ}.
 \item Flexible joint axial stiffness \(> \SI{100}{N/\um}\) to maximize the frequency of spurious resonances.
 \item Precise positioning of the \(b_i\) and \(\hat{s}_i\) to accurately determine the hexapod's kinematics.
 \item Flexible modes of the top-plate as high as possible as it can limit the achievable controller bandwidth.
 \item Integration of a force sensor in series with each actuator for active damping purposes.
 \end{itemize}
-\begin{figure}[htbp]
+\subsection{Parts Optimization}
-\centering
+During the detail design phase, several parts were optimized to fit the above specifications.
-\includegraphics[scale=1,width=0.9\linewidth]{figs/picture_nano_hexapod_strut.pdf}
+
-\caption{\label{fig:picture_nano_hexapod_strut}Picture of a nano-hexapod's strut}
+The flexible joint geometry was optimized using a finite element software while the top plate geometry was manually optimized to maximize the frequency of its flexible modes.
-\end{figure}
+
 Amplified Piezoelectric Actuators (APA) were found to be the most suitable actuator for the nano-hexapod due to its compact size, large stroke and adequate stiffness.
 The chosen model was the APA300ML from Cedrat Technologies (Fig.~\ref{fig:nano_heaxpod_strut_picture}).
 It is composed of three piezoelectric stacks, a lever mechanism increasing the stroke up to \(\approx \SI{300}{\um}\) and decreasing the axial stiffness down to \(\approx \SI{1.8}{N/\um}\).
 One of the three stacks can be used as a force sensor, at the price of loosing \(1/3\) of the stroke.
 This has the benefits of providing good ``collocation'' between the sensor stack and the actuator stacks, meaning that the active damping controller will be robust \cite{souleille18_concep_activ_mount_space_applic}.
 \subsection{Nano-Hexapod Mounting}
 Using the multi-body model of the nano-hexapod with the APA modeled as a flexible element, it was found that a misalignment between the APA and the two flexible joints was adding several resonances to the dynamics that were difficult to control.
 Therefore, a bench was developed to help the alignment the flexible joints and the APA during the mounting of the struts.
 A second mounting tool was used to fix the six struts to the two plates without inducing too much strain in the flexible joints.
 The mounted nano-hexapod is shown in Fig.~\ref{fig:nano_hexapod_picture}.
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1,width=0.9\linewidth]{figs/nano_hexapod_picture.jpg}
+\includegraphics[scale=1,width=0.9\linewidth]{figs/nano_hexapod_picture.pdf}
-\caption{\label{fig:nano_hexapod_picture}Nano-Hexapod on top of the ID31 micro-station}
+\caption{\label{fig:nano_hexapod_picture}Nano-hexapod on top of the micro-station.}
 \end{figure}
 \section{TEST-BENCHES}
 \subsection{Flexible Joints and Instrumentation}
-\subsection{APA/Struts Dynamics}
+Before mounting the nano-hexapod and performing control tests, several test benches were used to characterize the individual elements of the system.
 Several test benches were used for all the critical elements of the nano-hexapod.
 For instant, the bending stiffness of the flexible joints are measured, and the model is refined.
 The measurement noise of the encoders are also measured, and the input/output relationship and the output voltage noise of the voltage amplifiers are measured.
-Perhaps the most important test bench was the one used to identify the dynamics of the amplified piezoelectric actuator (shown in Fig.~\ref{fig:test_bench_apa_schematic}).
+The bending stiffness of the flexible joints was measured by applying a controlled force to one end of the joint while measuring its deflection at the same time.
-It consist of a \(5\,\text{kg}\) granite vertical guided with an air bearing and fixed on top of the APA.
+This helped exclude the ones that were not compliant with the requirement and pair the remaining ones.
 An excitation signal (low pass filtered white noise) is generated and applied to two of the piezoelectric stacks.
 Both the voltage generated by the third piezoelectric stack and the displacement measured by the encoder are recorded.
 The two obtained FRF can then be compared with the model and the piezoelectric constant are identified.
 These constants are used to do the conversion from the mechanical domain (force, strain) easily accessible on the model to the electrical domain (voltages, charges) easily measured.
 After identification of these constant, the match between the measured FRF and the model dynamics is quite good (Fig.~\ref{fig:apa_test_bench_results})
-The same bench was also used with the struts in order to study the effects of the flexible joints.
+The transfer function from the input to the output voltage of the voltage amplifier\footnote{PD200 from PiezoDrive} as well as its output noise were measured.
 Similarly, the measurement noise of the encoders\footnote{Vionic from Renishaw} was also measured.
 These simple measurements on individual elements were useful to refine their models, to found any problem as early as possible, and to help analyzing the results obtained when the the nano-hexapod is mounted and all the elements combined.
 \subsection{APA and Struts Dynamics}
 A test bench schematically shown in Fig.~\ref{fig:test_bench_apa_schematic} was used to identify the dynamics of the APA.
 It consist of a \(5\,\text{kg}\) granite fixed on top of the APA and vertical guided with an air bearing.
 An excitation signal (low pass filtered white noise) was generated and applied to two of the piezoelectric stacks.
 Both the voltage generated by the third piezoelectric stack and the displacement measured by the encoder were recorded.
 The two obtained frequency response functions (FRF) are compared with the model in Fig.~\ref{fig:apa_test_bench_results}.
 The piezoelectric constants describing the conversion from the mechanical domain (force, strain), easily accessible on the model, to the electrical domain (voltages, charges) easily measured can be estimated.
 With these constants, the match between the measured FRF and the model dynamics is very good (Fig.~\ref{fig:apa_test_bench_results}).
 The same bench was also used with the struts in order to study the added effects of the flexible joints.
 \begin{figure}[htbp]
 \centering
 \includegraphics[scale=1,scale=1]{figs/test_bench_apa_schematic.pdf}
-\caption{\label{fig:test_bench_apa_schematic}Schematic of the bench used to identify the APA dynamics}
+\caption{\label{fig:test_bench_apa_schematic}Schematic of the bench used to identify the APA dynamics.}
 \end{figure}
 \begin{figure}[htbp]
-  \begin{subfigure}[t]{0.48\linewidth}
+  \begin{subfigure}[t]{0.49\linewidth}
    \centering
    \includegraphics[width=0.95\linewidth]{figs/apa_test_bench_results_de.pdf}
-    \caption{\label{fig:apa_test_bench_results_de} Encoder}
+    \caption{\label{fig:apa_test_bench_results_de} Encoder $d_e/V_a$.}
  \end{subfigure}
  \hfill
-  \begin{subfigure}[t]{0.48\linewidth}
+  \begin{subfigure}[t]{0.49\linewidth}
    \centering
    \includegraphics[width=0.95\linewidth]{figs/apa_test_bench_results_Vs.pdf}
-    \caption{\label{fig:apa_test_bench_results_Vs} Force Sensor}
+    \caption{\label{fig:apa_test_bench_results_Vs} Force sensor $V_s/V_a$.}
  \end{subfigure}
  \caption{\label{fig:apa_test_bench_results}Measured Frequency Response functions compared with the Simscape model. From the actuator stacks voltage to the encoder (\subref{fig:apa_test_bench_results_de}) and to the force sensor stack (\subref{fig:apa_test_bench_results_Vs}).}
  \centering
 \end{figure}
 \subsection{Nano-Hexapod}
 After the nano-hexapod has been mounted, its dynamics was identified by individually exciting each of the actuators and simultaneously recording the six force sensors and six encoders signals.
 Two \(6\) by \(6\) FRF matrices were computed.
 Their diagonal elements are shown in Fig.~\ref{fig:nano_hexapod_identification_comp_simscape} and compared with the model.
 In Fig.~\ref{fig:nano_hexapod_identification_comp_simscape_de} one can observe the following modes:
 \begin{itemize}
 \item From \(\SI{100}{Hz}\) to \(\SI{200}{Hz}\): six suspension modes.
 \item At \(\SI{230}{Hz}\) and \(\SI{340}{Hz}\): flexible modes of the APA, also modeled thanks to the flexible model of the APA.
 \item At \(\SI{700}{Hz}\): flexible modes of the top plate. The model is not matching the FRF because a rigid body model was used for the top plate.
 \end{itemize}
 The transfer functions from the actuators to their ``collocated'' force sensors have alternating poles and zeros as expected (Fig.~\ref{fig:nano_hexapod_identification_comp_simscape_Vs}).
 IFF was then applied individually on each pair of actuator/force sensor in order to actively damp the suspension modes.
 The optimal gain of the IFF controller was determined using the model.
 After applying the active damping technique, the \(6\) by \(6\) FRF matrix from the actuator to the encoders was identified again and shown in Fig.~\ref{fig:nano_hexapod_identification_damp_comp_simscape}.
 It is shown that all the suspension modes are well damped, and that the model is able to predict the closed-loop behavior of the system.
 Even the off-diagonal elements (effect of one actuator on the encoder fixed in parallel to another strut) is very well modeled (Fig.~\ref{fig:nano_hexapod_identification_damp_comp_simscape_off_diag}).
 \begin{figure}[htbp]
-\centering
+  \begin{subfigure}[t]{0.49\linewidth}
-\includegraphics[scale=1,width=\linewidth]{figs/nass_hac_lac_block_diagram_without_elec.pdf}
+    \centering
-\caption{\label{fig:nass_hac_lac_schematic_test}HAC-LAC Strategy - Block Diagram. The signals are: \(\bm{r}\) the wanted sample's position, \(\bm{X}\) the measured sample's position, \(\bm{\epsilon}_{\mathcal{X}}\) the sample's position error, \(\bm{\epsilon}_{\mathcal{L}}\) the sample position error expressed in the ``frame'' of the nano-hexapod struts, \(\bm{u}\) the generated DAC voltages applied to the voltage amplifiers and then to the piezoelectric actuator stacks, \(\bm{u}^\prime\) the new inputs corresponding to the damped plant, \(\bm{\tau}\) the measured sensor stack voltages. \(\bm{T}\) is . \(\bm{K}_{\tiny IFF}\) is the Low Authority Controller used for active damping. \(\bm{K}_{L}\) is the High Authority Controller.}
+    \includegraphics[width=0.95\linewidth]{figs/nano_hexapod_identification_comp_simscape_de.pdf}
    \caption{\label{fig:nano_hexapod_identification_comp_simscape_de} Encoder $d_{e_i}/u_i$.}
  \end{subfigure}
  \hfill
  \begin{subfigure}[t]{0.49\linewidth}
    \centering
    \includegraphics[width=0.95\linewidth]{figs/nano_hexapod_identification_comp_simscape_Vs.pdf}
    \caption{\label{fig:nano_hexapod_identification_comp_simscape_Vs} Force sensor $V_{s_i}/u_i$.}
  \end{subfigure}
  \caption{\label{fig:nano_hexapod_identification_comp_simscape}Comparison of the measured Frequency Response functions (FRF) with the Simscape model. From the excitation voltage to the associated encoder (\subref{fig:apa_test_bench_results_de}) and to the associated force sensor stack (\subref{fig:apa_test_bench_results_Vs}).}
  \centering
 \end{figure}
 \begin{figure}[htbp]
-\centering
+  \begin{subfigure}[t]{0.49\linewidth}
-\includegraphics[scale=1,width=\linewidth]{figs/nano_hexapod_identification_comp_simscape.pdf}
+    \centering
-\caption{\label{fig:nano_hexapod_identification_comp_simscape}Measured FRF and Simscape dynamics.}
+    \includegraphics[width=0.98\linewidth]{figs/nano_hexapod_identification_damp_comp_simscape_diag.pdf}
-\end{figure}
+    \caption{\label{fig:nano_hexapod_identification_damp_comp_simscape_diag} Diagonal term.}
-
+  \end{subfigure}
-
+  \hfill
-\begin{figure}[htbp]
+  \begin{subfigure}[t]{0.49\linewidth}
-\centering
+    \centering
-\includegraphics[scale=1,width=\linewidth]{figs/nano_hexapod_identification_damp_comp_simscape.pdf}
+    \includegraphics[width=0.98\linewidth]{figs/nano_hexapod_identification_damp_comp_simscape_off_diag.pdf}
-\caption{\label{fig:nano_hexapod_identification_damp_comp_simscape}Undamped and Damped plant using IFF (measured FRF and Simscape model).}
+    \caption{\label{fig:nano_hexapod_identification_damp_comp_simscape_off_diag} Off-Diagonal term.}
  \end{subfigure}
  \caption{\label{fig:nano_hexapod_identification_damp_comp_simscape}Transfer functions from actuator to encoder with (input $u$) and without (input $u^\prime$) IFF applied.}
  \centering
 \end{figure}
 \section{CONCLUSION}
 The mechatronics approach used for the development of a nano active stabilization system was presented.
 The extensive use of models allowed to design the system in a predictive way and to make reasonable design decisions early in the project.
 Measurements made on the nano-hexapod were found to match very well with the models indicating that the final performances should match the predicted one.
 The current performance limitation is coming from the flexible modes of the top platform, so future work will focus on overcoming this limitation.
 This design methodology can be easily transposed to other complex mechatronics systems and are foreseen to be applied for future mechatronics systems at the ESRF.
 \section{ACKNOWLEDGMENTS}
 This research was made possible by a grant from the FRIA.
-We thank the following people for their support, without whose help this work would never have been possible: V. Honkimaki, L. Ducotte and M. Lessourd and the whole team of the Precision Mechatronic Laboratory.
+The authors wish to thank L. Ducotte, V. Honkim\"{a}ki, D. Coulon, P. Brumund, M. Lesourd, P. Got, JM. Clement, K. Amraoui and Y. Benyakhlef for their help throughout the project.
 \printbibliography{}
 \end{document}
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+++ b/paper/figs/super_element_simscape_alt.svg
--- a/paper/ref.bib
+++ b/paper/ref.bib
@@ -5,18 +5,8 @@
                  Of Large Plant Uncertainty},
  booktitle       = {MEDSI'18},
  year            = 2018,
  number          = 10,
  pages           = {153--157},
  doi             = {10.18429/JACoW-MEDSI2018-WEOAMA02},
  url             = {https://doi.org/10.18429/JACoW-MEDSI2018-WEOAMA02},
  address         = {Geneva, Switzerland},
  isbn            = {978-3-95450-207-3},
  language        = {english},
  month           = 12,
  publisher       = {JACoW Publishing},
  series          = {Mechanical Engineering Design of Synchrotron Radiation
                  Equipment and Instrumentation},
  venue           = {Paris, France},
 }
@inproceedings{brumund21_multib_simul_reduc_order_flexib_bodies_fea,
@@ -25,11 +15,7 @@
                  obtained by FEA},
  booktitle       = {MEDSI'20},
  year            = 2021,
-  language        = {english},
+  month           = 07,
  publisher       = {JACoW Publishing},
  series          = {Mechanical Engineering Design of Synchrotron Radiation
                  Equipment and Instrumentation},
  venue           = {Chicago, USA},
 }
@article{souleille18_concep_activ_mount_space_applic,
@@ -38,9 +24,6 @@
                  Gon{\c{c}}alo and Collette, Christophe},
  title           = {A Concept of Active Mount for Space Applications},
  journal         = {CEAS Space Journal},
  volume          = 10,
  number          = 2,
  pages           = {157--165},
  year            = 2018,
 }
@@ -51,8 +34,7 @@
  journal         = {Engineering Research Express},
  year            = 2021,
  doi             = {10.1088/2631-8695/abe803},
-  url             = {https://doi.org/10.1088/2631-8695/abe803},
+  month           = 2,
  month           = {2},
 }
@phdthesis{rankers98_machin,
@@ -65,8 +47,73 @@
@book{schmidt20_desig_high_perfor_mechat_third_revis_edition,
  author          = {Schmidt, R Munnig and Schitter, Georg and Rankers, Adrian},
-  title           = {The Design of High Performance Mechatronics - Third Revised
+  title           = {The Design of High Performance Mechatronics},
                  Edition},
  year            = 2020,
  publisher       = {Ios Press},
 }
@inproceedings{geraldes17_mechat_concep_new_high_dynam_dcm_sirius,
  author          = {R.R. Geraldes and R.M. Caliari and G.B.Z.L. Moreno and
                  M.J.C. Ronde and T.A.M. Ruijl and R.M. Schneider},
  title           = {{Mechatronics Concepts for the New High-Dynamics DCM for
                  Sirius}},
  booktitle       = {MEDSI'16},
  year            = 2017,
  doi             = {10.18429/JACoW-MEDSI2016-MOPE19},
  month           = 6,
  publisher       = {JACoW Publishing, Geneva, Switzerland},
 }
@inproceedings{brendike19_esrf_doubl_cryst_monoc_protot,
  author          = {Brendike, Maxim and Berruyer, G and Gonzalez, H and
                  Ducott{\'e}, Ludovic and Guilloud, C and Perez, M and Baker,
                  R},
  title           = {ESRF-Double Crystal Monochromator Prototype--Control
                  Concept},
  booktitle       = {17th International Conference on Accelerator and Large
                  Experimental Physics Control Systems},
  year            = 2019,
 }
@article{holler18_omny_tomog_nano_cryo_stage,
  author          = {M. Holler and J. Raabe and A. Diaz and M. Guizar-Sicairos
                  and R. Wepf and M. Odstrcil and F. R. Shaik and V. Panneels
                  and A. Menzel and B. Sarafimov and S. Maag and X. Wang and V.
                  Thominet and H. Walther and T. Lachat and M. Vitins and O.
                  Bunk},
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                  A. Abu Hanieh},
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  year            = 2007,
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 }
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@inproceedings{dehaeze18_sampl_stabil_for_tomog_exper,
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  title           = {Sample Stabilization For Tomography Experiments In Presence
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  month           = 12,
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@inproceedings{brumund21_multib_simul_reduc_order_flexib_bodies_fea,
  author          = {Philipp Brumund and Thomas Dehaeze},
  title           = {Multibody Simulations with Reduced Order Flexible Bodies
                  obtained by FEA},
  booktitle       = {MEDSI'20},
  year            = 2021,
  month           = 07,
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@article{souleille18_concep_activ_mount_space_applic,
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                  Hellegouarch, Sylvain and Rondineau, Alan and Rodrigues,
                  Gon{\c{c}}alo and Collette, Christophe},
  title           = {A Concept of Active Mount for Space Applications},
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  year            = 2018,
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@article{dehaeze21_activ_dampin_rotat_platf_using,
  author          = {Thomas Dehaeze and Christophe Collette},
  title           = {Active Damping of Rotating Platforms Using Integral Force
                  Feedback},
  journal         = {Engineering Research Express},
  year            = 2021,
  doi             = {10.1088/2631-8695/abe803},
  month           = 2,
 }
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  school          = {University of Twente},
  title           = {Machine dynamics in mechatronic systems: An engineering
                  approach.},
  year            = 1998,
 }
@book{schmidt20_desig_high_perfor_mechat_third_revis_edition,
  author          = {Schmidt, R Munnig and Schitter, Georg and Rankers, Adrian},
  title           = {The Design of High Performance Mechatronics},
  year            = 2020,
  publisher       = {Ios Press},
 }
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  author          = {R.R. Geraldes and R.M. Caliari and G.B.Z.L. Moreno and
                  M.J.C. Ronde and T.A.M. Ruijl and R.M. Schneider},
  title           = {{Mechatronics Concepts for the New High-Dynamics DCM for
                  Sirius}},
  booktitle       = {MEDSI'16},
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  doi             = {10.18429/JACoW-MEDSI2016-MOPE19},
  month           = 6,
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 }
@inproceedings{brendike19_esrf_doubl_cryst_monoc_protot,
  author          = {Brendike, Maxim and Berruyer, G and Gonzalez, H and
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                  R},
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                  Bunk},
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@misc{dimper15_esrf_upgrad_progr_phase_ii,
  author          = {R. Dimper and H. Reichert and P. Raimondi and L. Ortiz and
                  F. Sette and J. Susini},
  note            = {The orange book},
  title           = {{ESRF} Upgrade Programme Phase {II} (2015-2022) - Technical
                  Design Study},
  year            = 2015,
 }
@book{matlab20,
  author          = {MATLAB},
  title           = {version 9.9.0 (R2020b)},
  year            = 2020,
  publisher       = {The MathWorks Inc.},
  address         = {Natick, Massachusetts},
 }
@article{preumont07_six_axis_singl_stage_activ,
  author          = {A. Preumont and M. Horodinca and I. Romanescu and B. de
                  Marneffe and M. Avraam and A. Deraemaeker and F. Bossens and
                  A. Abu Hanieh},
  title           = {A Six-Axis Single-Stage Active Vibration Isolator Based on
                  Stewart Platform},
  journal         = {Journal of Sound and Vibration},
  volume          = 300,
  number          = {3-5},
  pages           = {644-661},
  year            = 2007,
  doi             = {10.1016/j.jsv.2006.07.050},
 }
--- a/paper/submission/TUIO02.pdf
+++ b/paper/submission/TUIO02.pdf
--- a/paper/submission/TUIO02.tex
+++ b/paper/submission/TUIO02.tex
@@ -0,0 +1,313 @@
 % Created 2021-07-26 lun. 20:38
 % Intended LaTeX compiler: pdflatex
 \documentclass[a4paper, keeplastbox, biblatex]{jacow}
 \usepackage{graphicx}
 \usepackage{tabularx}
 \usepackage{booktabs}
 \usepackage{bm}
 \usepackage{subcaption}
 \usepackage{siunitx}
 \usepackage[USenglish, english]{babel}
 \setcounter{footnote}{1}
 \setlist[itemize]{noitemsep}
 \usepackage[colorlinks=true, allcolors=blue]{hyperref}
 \addbibresource{TUIO02.bib}
 \author{T. Dehaeze\textsuperscript{1,}\thanks{thomas.dehaeze@esrf.fr}, J. Bonnefoy, ESRF, Grenoble, France \\ C. Collette\textsuperscript{1}, Université Libre de Bruxelles, BEAMS department, Brussels, Belgium \\ \textsuperscript{1}also at Precision Mechatronics Laboratory, University of Liege, Belgium}
 \date{2021-07-26}
 \title{MECHATRONICS APPROACH FOR THE DEVELOPMENT OF A NANO-ACTIVE-STABILIZATION-SYSTEM}
 \begin{document}
 \maketitle
 \begin{abstract}
 With the growing number of fourth generation light sources, there is an increased need of fast positioning end-stations with nanometric precision.
 Such systems are usually including dedicated control strategies, and many factors may limit their performances.
 In order to design such complex systems in a predictive way, a mechatronics design approach also known as ``model based design'', may be utilized.
 In this paper, we present how this mechatronics design approach was used for the development of a nano-hexapod for the ESRF ID31 beamline.
 The chosen design approach consists of using models of the mechatronics system (including sensors, actuators and control strategies) to predict its behavior.
 Based on this behavior and closed-loop simulations, the elements that are limiting the performances can be identified and re-designed accordingly.
 This allows to make adequate choices regarding the design of the nano-hexapod and the overall mechatronics architecture early in the project and therefore save precious time and resources.
 Several test benches were used to validate the models and to gain confidence on the predictability of the final system's performances.
 Measured nano-hexapod's dynamics was shown to be in very good agreement with the models.
 Further tests should be done in order to confirm that the performances of the system match the predicted one.
 The presented development approach is foreseen to be applied more frequently to future mechatronics system design at the ESRF.
 \end{abstract}
 \section{INTRODUCTION}
 With the new \(4^\text{th}\) generation machines, there is an increasing need of fast and accurate positioning systems \cite{dimper15_esrf_upgrad_progr_phase_ii}.
 These systems are usually including feedback control loops and therefore their performances are not only depending on the quality of the mechanical design, but also on its correct integration with the actuators, sensors and control system.
 In order to optimize the performances of such system, it is essential to consider a design approach in which the structural design and the control design are integrated.
 This approach, also called the ``mechatronics approach'', was shown to be very effective for the design many complex systems \cite{rankers98_machin,schmidt20_desig_high_perfor_mechat_third_revis_edition}.
 Such design methodology was recently used for the development of several systems used by the synchrotron community \cite{geraldes17_mechat_concep_new_high_dynam_dcm_sirius,holler18_omny_tomog_nano_cryo_stage,brendike19_esrf_doubl_cryst_monoc_protot}.
 The present paper presents how the ``mechatronic approach'' was used for the design of a Nano Active Stabilization System (NASS) for the ESRF ID31 beamline.
 \section{NASS - MECHATRONICS APPROACH}
 \subsection{The ID31 Micro-Station}
 The ID31 micro-station is used to position samples along complex trajectories \cite{dehaeze18_sampl_stabil_for_tomog_exper}.
 It is composed of several stacked stages (represented in yellow in Fig.~\ref{fig:nass_concept_schematic}) which allows an high mobility.
 This however limits the position accuracy to tens of micrometers.
 \subsection{The Nano Active Stabilization System}
 The NASS is a system whose goal is to improve the positioning accuracy of the micro-station.
 It is represented in Fig.~\ref{fig:nass_concept_schematic} and consists of three main elements:
 \begin{itemize}
 \item A nano-hexapod located between the sample to be positioned and the micro-station
 \item An interferometric metrology system measuring the sample's position with respect to the focusing optics
 \item A control system (not represented), which based on the measured position, properly actuates the nano-hexapod in order to stabilize the sample's position.
 \end{itemize}
 This system should be able to actively stabilize the sample position down to tens of nanometers while the micro-station is performing complex trajectories.
 \begin{figure}[htbp]
 \centering
 \includegraphics[scale=1,scale=0.9]{TUIO02_f1.pdf}
 \caption{\label{fig:nass_concept_schematic}NASS - Schematic representation. 1) Micro-station, 2) Nano-hexapod, 3) Sample, 4) Metrology system.}
 \end{figure}
 \subsection{Mechatronics Approach - Overview}
 In order to design the NASS in a predictive way, a mechatronics approach, schematically represented in Fig.~\ref{fig:nass_mechatronics_approach}, was used.
 It consists of three main phases:
 \begin{figure*}
 \centering
 \includegraphics[scale=1,width=0.9\linewidth]{TUIO02_f2.pdf}
 \caption{\label{fig:nass_mechatronics_approach}Overview of the mechatronics approach used for the design of the NASS.}
 \end{figure*}
 \begin{enumerate}
 \item \emph{Conceptual phase}: Simple models of both the micro-station and the nano-hexapod are used to first evaluate the performances of several concepts.
 During this phase, the type of sensors to use and the approximate required dynamical characteristics of the nano-hexapod are determined.
 \item \emph{Detail design phase}: Once the concept is validated, the models are used to list specifications both for the mechanics and the instrumentation.
 Each critical elements can then be properly designed.
 The models are updated as the design progresses.
 \item \emph{Experimental phase}: Once the design is completed and the parts received, several test benches are used to verify the properties of the key elements.
 Then the hexapod can be mounted and fully tested with the instrumentation and the control system.
 \end{enumerate}
 \subsection{Models}
 As shown in Fig.~\ref{fig:nass_mechatronics_approach}, the models are at the core of the mechatronics approach.
 Indeed, several models are used throughout the design with increasing level of complexity (Fig.~\ref{fig:nass_models}).
 \begin{figure*}[htbp]
  \begin{subfigure}[t]{0.25\linewidth}
    \centering
    \includegraphics[width=0.68\linewidth]{TUIO02_f3a.pdf}
    \caption{\label{fig:mass_spring_damper_hac_lac} Mass Spring Damper Model.}
  \end{subfigure}
  \hfill
  \begin{subfigure}[t]{0.48\linewidth}
    \centering
    \includegraphics[width=0.89\linewidth]{TUIO02_f3b.pdf}
    \caption{\label{fig:nass_simscape_3d} Multi Body Model.}
  \end{subfigure}
  \hfill
  \begin{subfigure}[t]{0.25\linewidth}
    \centering
    \includegraphics[width=0.93\linewidth]{TUIO02_f3c.pdf}
    \caption{\label{fig:super_element_simscape} Finite Element Model.}
  \end{subfigure}
  \hfill
  \caption{\label{fig:nass_models}Schematic of several models used during all the mechatronics design process.}
  \centering
 \end{figure*}
 At the beginning of the conceptual phase, simple ``mass-spring-damper'' models (Fig.~\ref{fig:mass_spring_damper_hac_lac}) were used in order to easily study multiple concepts.
 Noise budgeting and closed-loop simulations were performed, and it was concluded that a nano-hexapod with low frequency ``suspension'' modes would help both for the reduction of the effects of disturbances and for the decoupling between the nano-hexapod dynamics and the complex micro-station dynamics.
 I was found that by including a force sensor in series with the nano-hexapod's actuators, ``Integral Force Feedback'' (IFF) strategy could be used to actively damp the nano hexapod's resonances without impacting the high frequency disturbance rejection.
 The overall goal was to obtain a system dynamics which is easy to control in a robust way.
 Rapidly, a more sophisticated and more realistic multi-body model (Fig.~\ref{fig:nass_simscape_3d}) using Simscape \cite{matlab20} was used.
 This model was based on the 3D representation of the micro-station as well as on extensive dynamical measurements.
 Time domain simulations were performed with every stage of the micro-station moving and the nano hexapod actively stabilizing the sample against the many disturbances.
 The multi-body model permitted to study effects such as the coupling between the actuators and the sensors as well as the effect of the spindle's rotational speed on the nano-hexapod's dynamics \cite{dehaeze21_activ_dampin_rotat_platf_using}.
 The multi-input multi-output control strategy could be developed and tested.
 During the detail design phase, the nano-hexapod model was updated using 3D parts exported from the CAD software as the mechanical design progressed.
 The key elements of the nano-hexapod such as the flexible joints and the APA were optimized using a Finite Element Analysis (FEA) Software.
 As the flexible modes of the mechanics are what generally limit the controller bandwidth, they are important to model in order to understand which modes are problematic and should be addressed.
 To do so, a ``super-element'' can be exported using a FEA software and imported into the multi-body model (Fig.~\ref{fig:super_element_simscape}).
 Such process is described in \cite{brumund21_multib_simul_reduc_order_flexib_bodies_fea}.
 The multi-body model with included flexible elements can be used to very accurately estimate the dynamics of the system.
 However due to the large number of states included, it becomes unpractical to perform time domain simulations.
 Finally, during the experimental phase, the models were refined using experimental system identification data.
 At this phase of the development, models are still useful.
 They can help with the controller optimization, to understand the measurements, the associated performance limitations and to gain insight on which measures to take in order to overcome these limitations.
 For instance, it has been found that when fixing the encoders to the struts, as in Fig.~\ref{fig:nano_hexapod_elements}, several flexible modes of the APA were appearing in the dynamics which would render the control using the encoders very complex.
 Therefore, an alternative configuration with the encoders fixed to the plates was used instead.
 \section{NANO-HEXAPOD DESIGN}
 \subsection{Nano-Hexapod Specifications}
 The nano-hexapod is a ``Gough-Stewart platform'', which is a fully parallel manipulator composed of few parts as shown in Fig.~\ref{fig:nano_hexapod_elements}: only two plates linked by 6 active struts.
 Each strut has one rotational joint at each end, and one actuator in between (Fig.~\ref{fig:nano_heaxpod_strut_picture}).
 \begin{figure*}[htbp]
  \begin{subfigure}[t]{0.80\linewidth}
    \centering
    \includegraphics[width=\linewidth]{TUIO02_f4a.pdf}
    \caption{\label{fig:nano_hexapod_elements} CAD view of the nano-hexapod with key elements.}
  \end{subfigure}
  \hfill
  \begin{subfigure}[t]{0.19\linewidth}
    \centering
    \includegraphics[width=0.95\linewidth]{TUIO02_f4b.pdf}
    \caption{\label{fig:nano_heaxpod_strut_picture} Mounted strut.}
  \end{subfigure}
  \caption{\label{fig:nano_hexapod}Nano-hexapod: A Stewart platform architecture.}
  \centering
 \end{figure*}
 The main benefits of this architecture are its compact design, good dynamical properties, high load capability over weight ratio, and to possibility to control the motion in 6 degrees of freedom.
 The nano-hexapod should have a maximum height of \(95\,mm\), support samples up to \(50\,kg\), have a stroke of \(\approx 100\,\mu m\) and be fully compliant to avoid any wear, backlash, play and to have predictable dynamics.
 Based on the models used throughout the mechatronics approach, several specifications were added in order to maximize the performances of the system:
 \begin{itemize}
 \item Actuator axial stiffness \(\approx \SI{2}{N/\um}\) as it is a good trade-off between disturbance filtering, dynamic decoupling from the micro-station and insensibility to the spindle's rotational speed.
 \item Flexible joint bending stiffness \(< \SI{100}{Nm/rad}\) as high bending stiffness can limit IFF performances \cite{preumont07_six_axis_singl_stage_activ}.
 \item Flexible joint axial stiffness \(> \SI{100}{N/\um}\) to maximize the frequency of spurious resonances.
 \item Precise positioning of the \(b_i\) and \(\hat{s}_i\) to accurately determine the hexapod's kinematics.
 \item Flexible modes of the top-plate as high as possible as it can limit the achievable controller bandwidth.
 \item Integration of a force sensor in series with each actuator for active damping purposes.
 \end{itemize}
 \subsection{Parts Optimization}
 During the detail design phase, several parts were optimized to fit the above specifications.
 The flexible joint geometry was optimized using a finite element software while the top plate geometry was manually optimized to maximize the frequency of its flexible modes.
 Amplified Piezoelectric Actuators (APA) were found to be the most suitable actuator for the nano-hexapod due to its compact size, large stroke and adequate stiffness.
 The chosen model was the APA300ML from Cedrat Technologies (Fig.~\ref{fig:nano_heaxpod_strut_picture}).
 It is composed of three piezoelectric stacks, a lever mechanism increasing the stroke up to \(\approx \SI{300}{\um}\) and decreasing the axial stiffness down to \(\approx \SI{1.8}{N/\um}\).
 One of the three stacks can be used as a force sensor, at the price of loosing \(1/3\) of the stroke.
 This has the benefits of providing good ``collocation'' between the sensor stack and the actuator stacks, meaning that the active damping controller will be robust \cite{souleille18_concep_activ_mount_space_applic}.
 \subsection{Nano-Hexapod Mounting}
 Using the multi-body model of the nano-hexapod with the APA modeled as a flexible element, it was found that a misalignment between the APA and the two flexible joints was adding several resonances to the dynamics that were difficult to control.
 Therefore, a bench was developed to help the alignment the flexible joints and the APA during the mounting of the struts.
 A second mounting tool was used to fix the six struts to the two plates without inducing too much strain in the flexible joints.
 The mounted nano-hexapod is shown in Fig.~\ref{fig:nano_hexapod_picture}.
 \begin{figure}[htbp]
 \centering
 \includegraphics[scale=1,width=0.9\linewidth]{TUIO02_f5.pdf}
 \caption{\label{fig:nano_hexapod_picture}Nano-hexapod on top of the micro-station.}
 \end{figure}
 \section{TEST-BENCHES}
 \subsection{Flexible Joints and Instrumentation}
 Before mounting the nano-hexapod and performing control tests, several test benches were used to characterize the individual elements of the system.
 The bending stiffness of the flexible joints was measured by applying a controlled force to one end of the joint while measuring its deflection at the same time.
 This helped exclude the ones that were not compliant with the requirement and pair the remaining ones.
 The transfer function from the input to the output voltage of the voltage amplifier\footnote{PD200 from PiezoDrive} as well as its output noise were measured.
 Similarly, the measurement noise of the encoders\footnote{Vionic from Renishaw} was also measured.
 These simple measurements on individual elements were useful to refine their models, to found any problem as early as possible, and to help analyzing the results obtained when the the nano-hexapod is mounted and all the elements combined.
 \subsection{APA and Struts Dynamics}
 A test bench schematically shown in Fig.~\ref{fig:test_bench_apa_schematic} was used to identify the dynamics of the APA.
 It consist of a \(5\,\text{kg}\) granite fixed on top of the APA and vertical guided with an air bearing.
 An excitation signal (low pass filtered white noise) was generated and applied to two of the piezoelectric stacks.
 Both the voltage generated by the third piezoelectric stack and the displacement measured by the encoder were recorded.
 The two obtained frequency response functions (FRF) are compared with the model in Fig.~\ref{fig:apa_test_bench_results}.
 The piezoelectric constants describing the conversion from the mechanical domain (force, strain), easily accessible on the model, to the electrical domain (voltages, charges) easily measured can be estimated.
 With these constants, the match between the measured FRF and the model dynamics is very good (Fig.~\ref{fig:apa_test_bench_results}).
 The same bench was also used with the struts in order to study the added effects of the flexible joints.
 \begin{figure}[htbp]
 \centering
 \includegraphics[scale=1,scale=1]{TUIO02_f6.pdf}
 \caption{\label{fig:test_bench_apa_schematic}Schematic of the bench used to identify the APA dynamics.}
 \end{figure}
 \begin{figure}[htbp]
  \begin{subfigure}[t]{0.49\linewidth}
    \centering
    \includegraphics[width=0.95\linewidth]{TUIO02_f7a.pdf}
    \caption{\label{fig:apa_test_bench_results_de} Encoder $d_e/V_a$.}
  \end{subfigure}
  \hfill
  \begin{subfigure}[t]{0.49\linewidth}
    \centering
    \includegraphics[width=0.95\linewidth]{TUIO02_f7b.pdf}
    \caption{\label{fig:apa_test_bench_results_Vs} Force sensor $V_s/V_a$.}
  \end{subfigure}
  \caption{\label{fig:apa_test_bench_results}Measured Frequency Response functions compared with the Simscape model. From the actuator stacks voltage to the encoder (\subref{fig:apa_test_bench_results_de}) and to the force sensor stack (\subref{fig:apa_test_bench_results_Vs}).}
  \centering
 \end{figure}
 \subsection{Nano-Hexapod}
 After the nano-hexapod has been mounted, its dynamics was identified by individually exciting each of the actuators and simultaneously recording the six force sensors and six encoders signals.
 Two \(6\) by \(6\) FRF matrices were computed.
 Their diagonal elements are shown in Fig.~\ref{fig:nano_hexapod_identification_comp_simscape} and compared with the model.
 In Fig.~\ref{fig:nano_hexapod_identification_comp_simscape_de} one can observe the following modes:
 \begin{itemize}
 \item From \(\SI{100}{Hz}\) to \(\SI{200}{Hz}\): six suspension modes.
 \item At \(\SI{230}{Hz}\) and \(\SI{340}{Hz}\): flexible modes of the APA, also modeled thanks to the flexible model of the APA.
 \item At \(\SI{700}{Hz}\): flexible modes of the top plate. The model is not matching the FRF because a rigid body model was used for the top plate.
 \end{itemize}
 The transfer functions from the actuators to their ``collocated'' force sensors have alternating poles and zeros as expected (Fig.~\ref{fig:nano_hexapod_identification_comp_simscape_Vs}).
 IFF was then applied individually on each pair of actuator/force sensor in order to actively damp the suspension modes.
 The optimal gain of the IFF controller was determined using the model.
 After applying the active damping technique, the \(6\) by \(6\) FRF matrix from the actuator to the encoders was identified again and shown in Fig.~\ref{fig:nano_hexapod_identification_damp_comp_simscape}.
 It is shown that all the suspension modes are well damped, and that the model is able to predict the closed-loop behavior of the system.
 Even the off-diagonal elements (effect of one actuator on the encoder fixed in parallel to another strut) is very well modeled (Fig.~\ref{fig:nano_hexapod_identification_damp_comp_simscape_off_diag}).
 \begin{figure}[htbp]
  \begin{subfigure}[t]{0.49\linewidth}
    \centering
    \includegraphics[width=0.95\linewidth]{TUIO02_f8a.pdf}
    \caption{\label{fig:nano_hexapod_identification_comp_simscape_de} Encoder $d_{e_i}/u_i$.}
  \end{subfigure}
  \hfill
  \begin{subfigure}[t]{0.49\linewidth}
    \centering
    \includegraphics[width=0.95\linewidth]{TUIO02_f8b.pdf}
    \caption{\label{fig:nano_hexapod_identification_comp_simscape_Vs} Force sensor $V_{s_i}/u_i$.}
  \end{subfigure}
  \caption{\label{fig:nano_hexapod_identification_comp_simscape}Comparison of the measured Frequency Response functions (FRF) with the Simscape model. From the excitation voltage to the associated encoder (\subref{fig:apa_test_bench_results_de}) and to the associated force sensor stack (\subref{fig:apa_test_bench_results_Vs}).}
  \centering
 \end{figure}
 \begin{figure}[htbp]
  \begin{subfigure}[t]{0.49\linewidth}
    \centering
    \includegraphics[width=0.98\linewidth]{TUIO02_f9a.pdf}
    \caption{\label{fig:nano_hexapod_identification_damp_comp_simscape_diag} Diagonal term.}
  \end{subfigure}
  \hfill
  \begin{subfigure}[t]{0.49\linewidth}
    \centering
    \includegraphics[width=0.98\linewidth]{TUIO02_f9b.pdf}
    \caption{\label{fig:nano_hexapod_identification_damp_comp_simscape_off_diag} Off-Diagonal term.}
  \end{subfigure}
  \caption{\label{fig:nano_hexapod_identification_damp_comp_simscape}Transfer functions from actuator to encoder with (input $u$) and without (input $u^\prime$) IFF applied.}
  \centering
 \end{figure}
 \section{CONCLUSION}
 The mechatronics approach used for the development of a nano active stabilization system was presented.
 The extensive use of models allowed to design the system in a predictive way and to make reasonable design decisions early in the project.
 Measurements made on the nano-hexapod were found to match very well with the models indicating that the final performances should match the predicted one.
 The current performance limitation is coming from the flexible modes of the top platform, so future work will focus on overcoming this limitation.
 This design methodology can be easily transposed to other complex mechatronics systems and are foreseen to be applied for future mechatronics systems at the ESRF.
 \section{ACKNOWLEDGMENTS}
 This research was made possible by a grant from the FRIA.
 The authors wish to thank L. Ducotte, V. Honkim\"{a}ki, D. Coulon, P. Brumund, M. Lesourd, P. Got, JM. Clement, K. Amraoui and Y. Benyakhlef for their help throughout the project.
 \printbibliography{}
 \end{document}
--- a/paper/submission/TUIO02_f1.pdf
+++ b/paper/submission/TUIO02_f1.pdf
--- a/paper/submission/TUIO02_f2.pdf
+++ b/paper/submission/TUIO02_f2.pdf
--- a/paper/submission/TUIO02_f3a.pdf
+++ b/paper/submission/TUIO02_f3a.pdf
--- a/paper/submission/TUIO02_f3b.pdf
+++ b/paper/submission/TUIO02_f3b.pdf
--- a/paper/submission/TUIO02_f3c.pdf
+++ b/paper/submission/TUIO02_f3c.pdf
--- a/paper/submission/TUIO02_f4a.pdf
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--- a/paper/submission/TUIO02_f4b.pdf
+++ b/paper/submission/TUIO02_f4b.pdf
--- a/paper/submission/TUIO02_f5.pdf
+++ b/paper/submission/TUIO02_f5.pdf
--- a/paper/submission/TUIO02_f6.pdf
+++ b/paper/submission/TUIO02_f6.pdf
--- a/paper/submission/TUIO02_f7a.pdf
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--- a/paper/submission/TUIO02_f7b.pdf
+++ b/paper/submission/TUIO02_f7b.pdf
--- a/paper/submission/TUIO02_f8a.pdf
+++ b/paper/submission/TUIO02_f8a.pdf
--- a/paper/submission/TUIO02_f8b.pdf
+++ b/paper/submission/TUIO02_f8b.pdf
--- a/paper/submission/TUIO02_f9a.pdf
+++ b/paper/submission/TUIO02_f9a.pdf
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+++ b/paper/submission/TUIO02_f9b.pdf
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+++ b/paper/submission/jacow.cls
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--- a/talk/animations/1_micro_station_60rpm.mp4
+++ b/talk/animations/1_micro_station_60rpm.mp4
--- a/talk/animations/2_micro_station_mode_shapes.mp4
+++ b/talk/animations/2_micro_station_mode_shapes.mp4
--- a/talk/animations/3_close_loop_zoom.mp4
+++ b/talk/animations/3_close_loop_zoom.mp4
--- a/talk/animations/3_open_close_loop.mp4
+++ b/talk/animations/3_open_close_loop.mp4
--- a/talk/animations/3_tomography_exp_nass.mp4
+++ b/talk/animations/3_tomography_exp_nass.mp4
--- a/talk/animations/4_strut_mounting.mp4
+++ b/talk/animations/4_strut_mounting.mp4
--- a/talk/animations/5_strut_modes.mp4
+++ b/talk/animations/5_strut_modes.mp4
--- a/talk/animations/6_hexapod_mounting.mp4
+++ b/talk/animations/6_hexapod_mounting.mp4
--- a/talk/dehaeze21_mechatronics_approach_nass_talk.org
+++ b/talk/dehaeze21_mechatronics_approach_nass_talk.org
--- a/talk/dehaeze21_mechatronics_approach_nass_talk.pdf
+++ b/talk/dehaeze21_mechatronics_approach_nass_talk.pdf
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+++ b/talk/dehaeze21_mechatronics_approach_nass_talk.tex
@@ -0,0 +1,705 @@
 % Created 2021-07-27 mar. 08:42
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 \author[shortname]{Thomas Dehaeze \inst{1,2}, Julien Bonnefoy \inst{1} and Christophe Collette \inst{2,3}}
 \institute[shortinst]{\inst{1} European Synchrotron Radiation Facility, Grenoble, France \and %
 \inst{2} Precision Mechatronics Laboratory, University of Liege, Belgium \and %
 \inst{3} BEAMS Department, Free University of Brussels, Belgium}
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 \date{}
 \title{Mechatronics Approach for the Development of a Nano-Active-Stabilization-System}
 \subtitle{MEDSI2020, July 26-29, 2021}
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 pdfauthor={},
 pdftitle={Mechatronics Approach for the Development of a Nano-Active-Stabilization-System},
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 \begin{document}
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 \section*{Introduction}
 \label{sec:orgdabb222}
 \begin{frame}[label={sec:org75433ab}]{The ID31 Micro Station}
 \begin{center}
 \includegraphics[scale=1,width=0.95\linewidth]{figs/micro_hexapod_render.pdf}
 \end{center}
 \begin{tikzpicture}[remember picture,overlay]
    \node[anchor=north east] at (current page.north east){%
    \includegraphics[width=2em]{figs/icon_animation.pdf}};
 \end{tikzpicture}
 \end{frame}
 \begin{frame}[label={sec:orga898a71}]{Introduction - The Nano Active Stabilization System (NASS)}
 \textbf{Objective}: Improve the position accuracy from \(\approx 10\,\mu m\) down to \(\approx 10\,nm\) \newline
 \textbf{Design approach}: ``Model based design'' / ``Predictive Design''
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/nass-concept.red.pdf}
 \end{center}
 \end{frame}
 \begin{frame}[label={sec:org9574917}]{Overview of the Mechatronic Approach - Model Based Design}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/nass_mechatronics_approach.png}
 \end{center}
 \end{frame}
 \section{Conceptual Phase}
 \label{sec:org62eb09b}
 \begin{frame}[label={sec:orgd53fdb4}]{Outline - Conceptual Phase}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/nass_mechatronics_approach_conceptual_phase.pdf}
 \end{center}
 \end{frame}
 \begin{frame}[label={sec:orgf99643e}]{Feedback Control - The Control Loop}
 \vspace{-1em}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/classical_feedback_schematic.png}
 \end{center}
 \vspace{-1em}
 \begin{columns}
 \begin{column}{0.4\columnwidth}
 \begin{tcolorbox}[title=Why Feedback?]
 \begin{itemize}
 \item Model uncertainties
 \item Unknown disturbances
 \end{itemize}
 \end{tcolorbox}
 \end{column}
 \begin{column}{0.6\columnwidth}
 \begin{tcolorbox}[title=Every elements can limit the performances]
 \begin{itemize}
 \item Drivers, Actuators, Sensors
 \item Mechanical System
 \item Controller
 \end{itemize}
 \end{tcolorbox}
 \end{column}
 \end{columns}
 \end{frame}
 \begin{frame}[label={sec:orge603014}]{Noise Budgeting and Required Control Bandwidth}
 \vspace{-1em}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/identification_control_noise_budget.red.pdf}
 \end{center}
 \end{frame}
 \begin{frame}[label={sec:org1a8d575}]{Limitation of the Controller Bandwidth?}
 \begin{columns}
 \begin{column}{0.6\columnwidth}
 \vspace{-2em}
 \only<1>{
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/control_bandwidth_1_classical.pdf}
 \end{center}
 }\only<2>{
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/control_bandwidth_2_above_res.pdf}
 \end{center}
 }
 \end{column}
 \begin{column}{0.4\columnwidth}
 \vspace{-2em}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/test_bench_apa_simple.pdf}
 \end{center}
 \only<1>{
 \begin{tcolorbox}[title=Typical Approach, fontupper=\small]
 ``As stiff as possible'' \newline
 Simple controller (e.g. PID)
 \end{tcolorbox}
 }\only<2>{
 \begin{tcolorbox}[title=Alternative Approach, fontupper=\small]
 Limited by complex dynamics\newline
 Model based controller
 \end{tcolorbox}
 }
 \end{column}
 \end{columns}
 \end{frame}
 \begin{frame}[label={sec:org239155a}]{Soft or Stiff \(\nu\text{-hexapod}\) ? Interaction with the \(\mu\text{-station}\)}
 \vspace{-3em}
 \begin{columns}
 \begin{column}{0.3\columnwidth}
 \onslide<1->{
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/nass_example_uncertainty_support_only_hexapod.pdf}
 \end{center}
 }\onslide<2->{
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/nass_example_uncertainty_support.pdf}
 \end{center}
 }
 \end{column}
 \begin{column}{0.7\columnwidth}
 \onslide<1->{
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/nass_example_alone_b.pdf}
 \end{center}
 \vspace{-2em}
 }\onslide<2->{
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/nass_example_support_uncertainty_d_L_b.pdf}
 \end{center}
 }
 \end{column}
 \end{columns}
 \end{frame}
 \begin{frame}[label={sec:orgeb9ee99}]{Complexity of the Micro-Station Dynamics (Model Analysis)}
 \vspace{-1em}
 \begin{center}
 \includegraphics[scale=1,width=0.95\linewidth]{figs/modes_annotated.png}
 \end{center}
 \begin{tikzpicture}[remember picture,overlay]
    \node[anchor=north east] at (current page.north east){%
    \includegraphics[width=2em]{figs/icon_animation.pdf}};
 \end{tikzpicture}
 \end{frame}
 \begin{frame}[label={sec:orgb8ddd28}]{Control Strategy: HAC-LAC}
 \vspace{-0.5em}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/nass_schematic_test.pdf}
 \end{center}
 \vspace{-2.0em}
 \begin{columns}
 \begin{column}{0.5\columnwidth}
 \begin{tcolorbox}[title=Low Authority Control]
 \begin{itemize}
 \item Collocated sensors/actuators
 \item Guaranteed Stability, simple \(K\)
 \item Adds damping
 \item \(\searrow\) vibration near resonances
 \end{itemize}
 \end{tcolorbox}
 \end{column}
 \begin{column}{0.5\columnwidth}
 \begin{tcolorbox}[title=High Authority Control]
 \begin{itemize}
 \item Position sensors
 \item Complex dynamics
 \item Use transformation matrices
 \item \(\searrow\) vibration in the bandwidth
 \end{itemize}
 \end{tcolorbox}
 \end{column}
 \end{columns}
 \end{frame}
 \begin{frame}[label={sec:org0579a05}]{Multi-Body Models - Simulations}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/simscape_simulation.jpg}
 \end{center}
 \begin{tikzpicture}[remember picture, overlay]
  \node[align=left, anchor=south east, text width=5.5cm,shift={(-1em, 1em)}] at (current page.south east){%
  \begin{tcolorbox}
  \begin{center}
    Validation of the concept
  \end{center}
  \end{tcolorbox}};
 \end{tikzpicture}
 \begin{tikzpicture}[remember picture,overlay]
    \node[anchor=north east] at (current page.north east){%
    \includegraphics[width=2em]{figs/icon_animation.pdf}};
 \end{tikzpicture}
 \end{frame}
 \section{Detail Design Phase}
 \label{sec:orga9ae877}
 \begin{frame}[label={sec:org1b0984d}]{Outline - Detail Design Phase}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/nass_mechatronics_approach_detailed_phase.pdf}
 \end{center}
 \end{frame}
 \begin{frame}[label={sec:org1f20e49}]{Nano-Hexapod Overview - Key elements}
 \vspace{-1.5em}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/nano_hexapod_elements.red.pdf}
 \end{center}
 \begin{tcolorbox}[title=General Specifications, sidebyside]
 \begin{itemize}
 \item Flexible modes as high as possible
 \item Only flexible elements (no backlash, play, etc.)
 \end{itemize}
 \tcblower
 \begin{itemize}
 \item Integrated Force Sensor and Displacement Sensor
 \item Predictable dynamics
 \end{itemize}
 \end{tcolorbox}
 \end{frame}
 \begin{frame}[label={sec:orge2a3011}]{Choice of Actuator and Flexible Joint Design}
 \vspace{-2em}
 \begin{columns}
 \begin{column}{0.5\columnwidth}
 \scriptsize
 \begin{center}
 \begin{tabularx}{0.8\linewidth}{ccc}
 \toprule
 \textbf{Characteristic} & \textbf{Specs} & \textbf{Doc.}\\
 \midrule
 Axial Stiff. & \SI{\approx 2}{\newton/\micro\meter} & \SI{1.8}{\newton/\micro\meter}\\
 Sufficient Stroke & \SI{> 100}{\micro\meter} & \SI{368}{\micro\meter}\\
 Height & \SI{< 50}{\milli\meter} & \SI{30}{\milli\meter}\\
 High Resolution & \SI{< 5}{\nano\meter} & \SI{3}{\nano\meter}\\
 \bottomrule
 \end{tabularx}
 \end{center}
 \normalsize
 \vspace{-1em}
 \begin{figure}[htbp]
 \centering
 \includegraphics[scale=1,width=0.9\linewidth]{figs/apa300ml_picture.jpg}
 \caption{Picture of the APA300ML}
 \end{figure}
 \end{column}
 \begin{column}{0.5\columnwidth}
 \scriptsize
 \begin{center}
 \begin{tabularx}{0.9\linewidth}{cccc}
 \toprule
 \textbf{Characteristic} & \textbf{Specs} & \textbf{FEM}\\
 \midrule
 Axial Stiff. & \SI{> 100}{\newton/\micro\meter} & 94\\
 Bending Stiff. & \SI{< 100}{\newton\meter/\radian} & 5\\
 Torsion Stiff. & \SI{< 500}{\newton\meter/\radian} & 260\\
 Bending Stroke & \SI{> 1}{\milli\radian} & 20\\
 \bottomrule
 \end{tabularx}
 \end{center}
 \normalsize
 \vspace{-1em}
 \begin{figure}[htbp]
 \centering
 \includegraphics[scale=1,width=0.9\linewidth]{figs/flexible_joint_picture.jpg}
 \caption{Picture of the joint}
 \end{figure}
 \end{column}
 \end{columns}
 \end{frame}
 \begin{frame}[label={sec:orgc5a1632}]{Instrumentation}
 \vspace{-1em}
 \begin{columns}
 \begin{column}{0.33\columnwidth}
 \begin{figure}[htbp]
 \centering
 \includegraphics[scale=1,height=2.2cm]{figs/amplifier_PD200.jpg}
 \caption{PiezoDrive - PD200 Amplifier}
 \end{figure}
 \vspace{-1em}
 \tiny
 \begin{center}
 \begin{tabularx}{0.75\linewidth}{lc}
 \toprule
 \textbf{Characteristics} & \textbf{Manual}\\
 \midrule
 Gain & \num{20}\\
 Noise & \SI{0.7}{\milli\volt\rms}\\
 Small Signal BW & \SI{7.4}{\kilo\hertz}\\
 Large Signal BW & \SI{300}{\hertz}\\
 \bottomrule
 \end{tabularx}
 \end{center}
 \normalsize
 \end{column}
 \begin{column}{0.33\columnwidth}
 \begin{figure}[htbp]
 \centering
 \includegraphics[scale=1,height=2.2cm]{figs/encoder_vionic.jpg}
 \caption{Renishaw - Vionic Encoder}
 \end{figure}
 \vspace{-1em}
 \tiny
 \begin{center}
 \begin{tabularx}{0.85\linewidth}{lc}
 \toprule
 \textbf{Characteristics} & \textbf{Manual}\\
 \midrule
 Range & Ruler length\\
 Resolution & \SI{2.5}{\nano\meter}\\
 Sub-Divisional Error & \SI{<\pm 15}{\nano\meter}\\
 Bandwidth & \SI{>5}{kHz}\\
 \bottomrule
 \end{tabularx}
 \end{center}
 \normalsize
 \end{column}
 \begin{column}{0.33\columnwidth}
 \begin{figure}[htbp]
 \centering
 \includegraphics[scale=1,height=2.2cm]{figs/Speedgoat-Performance-Real-Time-Target-Machine.jpg}
 \caption{Speedgoat - Target Machine}
 \end{figure}
 \vspace{-1em}
 \tiny
 \begin{center}
 \begin{tabularx}{0.8\linewidth}{lc}
 \toprule
 \textbf{Characteristics} & \textbf{Manual}\\
 \midrule
 ADC (x16) & 16bit, \SI{\pm 10}{V}\\
 DAC (x8) & 16bit, \SI{\pm 10}{V}\\
 Digital I/O (x30) & \SI{<\pm 15}{\nano\meter}\\
 Sampling Freq. & \SI{>10}{kHz}\\
 \bottomrule
 \end{tabularx}
 \end{center}
 \normalsize
 \end{column}
 \end{columns}
 \vspace{1em}
 \begin{tcolorbox}
 \begin{center}
 All elements could be chosen/design based on the models
 \end{center}
 \end{tcolorbox}
 \end{frame}
 \section{Experimental Phase}
 \label{sec:org000fc13}
 \begin{frame}[label={sec:org5a3d17b}]{Outline - Experimental Phase}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/nass_mechatronics_approach_experimental_phase.red.pdf}
 \end{center}
 \end{frame}
 \begin{frame}[label={sec:orge94eaf3}]{Flexible Joints - Measurements}
 \vspace{-2em}
 \begin{columns}
 \begin{column}{0.45\columnwidth}
 \begin{center}
 \includegraphics[scale=1,width=0.95\linewidth]{figs/received_flexible_joints.jpg}
 \end{center}
 \begin{center}
 \includegraphics[scale=1,width=0.95\linewidth]{figs/flexible_joint_bench.pdf}
 \end{center}
 \end{column}
 \begin{column}{0.55\columnwidth}
 \begin{center}
 \includegraphics[scale=1,width=0.9\linewidth]{figs/flex_joint_meas_example_F_d_lin_fit.pdf}
 \end{center}
 \begin{tcolorbox}[title=Other Measurement Benches]
 \begin{itemize}
 \item Amplifier Output Noise and Bandwidth
 \item Encoder Measurement Noise
 \item DAC Output Noise
 \end{itemize}
 \end{tcolorbox}
 \end{column}
 \end{columns}
 \end{frame}
 \begin{frame}[label={sec:org518f2db}]{Amplified Piezoelectric Actuator - Test Bench}
 \vspace{-1em}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/test_bench_apa300ml.red.pdf}
 \end{center}
 \begin{tikzpicture}[remember picture, overlay]
  \node[align=left, anchor=north east, text width=4.5cm] at (current page.north east){%
  \begin{tcolorbox}[title=Goals]
  \begin{itemize}
    \item Identify Dynamics
    \item Tune APA Model
    \item Test IFF
  \end{itemize}
  \end{tcolorbox}};
 \end{tikzpicture}
 \end{frame}
 \begin{frame}[label={sec:org749c413}]{Amplified Piezoelectric Actuator - Measured FRF and Extracted Model}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/apa_comp_model_frf.pdf}
 \end{center}
 \end{frame}
 \begin{frame}[label={sec:org1d672c7}]{Amplified Piezoelectric Actuator - Integral Force Feedback}
 \vspace{-3em}
 \begin{columns}
 \begin{column}{0.62\columnwidth}
 \vspace{1em}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/test_bench_apa300ml_iff.pdf}
 \end{center}
 \[ K_{\text{IFF}}(s) = \frac{g}{s} \]
 \end{column}
 \begin{column}{0.38\columnwidth}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/iff_results_apa95ml.pdf}
 \end{center}
 \end{column}
 \end{columns}
 \end{frame}
 \begin{frame}[label={sec:org7b5008c}]{Strut - Mounting Tool}
 \vspace{-2.5em}
 \begin{columns}
 \begin{column}{0.63\columnwidth}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/image_mounting_strut_bench.JPG}
 \end{center}
 \end{column}
 \begin{column}{0.37\columnwidth}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/mounted_strut_picture.jpg}
 \end{center}
 \begin{tikzpicture}[remember picture,overlay]
    \node[anchor=north east] at (current page.north east){%
    \includegraphics[width=2em]{figs/icon_animation.pdf}};
 \end{tikzpicture}
 \end{column}
 \end{columns}
 \end{frame}
 \begin{frame}[label={sec:orgc1ecd2e}]{Strut - Dynamical Measurements}
 \vspace{-1em}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/test_bench_strut.red.pdf}
 \end{center}
 \begin{tikzpicture}[remember picture, overlay]
  \node[align=left, anchor=north east, text width=5cm] at (current page.north east){%
  \begin{tcolorbox}[title=Goals]
  \begin{itemize}
    \item Identify Dynamics
    \item Tune Model
    \item Flexible joints effects
    \item Encoder effect
  \end{itemize}
  \end{tcolorbox}};
 \end{tikzpicture}
 \end{frame}
 \begin{frame}[label={sec:org8ce2d42}]{Strut - Encoders Output and Spurious Modes}
 \vspace{-3em}
 \begin{columns}
 \begin{column}{0.43\columnwidth}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/frf_struts_enc_int.pdf}
 \end{center}
 \end{column}
 \begin{column}{0.57\columnwidth}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/meas_spur_res_struts_2_encoder.jpg}
 \end{center}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/mode_shapes_annotated.pdf}
 \end{center}
 \begin{tikzpicture}[remember picture,overlay]
    \node[anchor=north east] at (current page.north east){%
    \includegraphics[width=2em]{figs/icon_animation.pdf}};
 \end{tikzpicture}
 \end{column}
 \end{columns}
 \end{frame}
 \begin{frame}[label={sec:orgb6be716}]{Nano-Hexapod Mounting Tool}
 \begin{center}
 \includegraphics[scale=1,width=0.9\linewidth]{figs/nano_hexapod_mounting.JPG}
 \end{center}
 \begin{tikzpicture}[remember picture,overlay]
    \node[anchor=north east] at (current page.north east){%
    \includegraphics[width=2em]{figs/icon_animation.pdf}};
 \end{tikzpicture}
 \end{frame}
 \begin{frame}[label={sec:org281520e}]{Mounted Nano-Hexapod}
 \vspace{-1em}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/mounted_nano_hexapod_picture.jpg}
 \end{center}
 \end{frame}
 \begin{frame}[label={sec:org351990a}]{Nano-Hexapod - Identified Dynamics (Diagonal elements)}
 \vspace{-1em}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/nano_hexapod_enc_iff_bode_plot.pdf}
 \end{center}
 \end{frame}
 \begin{frame}[label={sec:org18b6334}]{Nano-Hexapod - Damped Dynamics}
 \vspace{-1em}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/nano_hexapod_damped_bode_plot.pdf}
 \end{center}
 \end{frame}
 \begin{frame}[label={sec:org79d4d53}]{The Nano-Hexapod on top of the Micro-Station}
 \vspace{-0.5em}
 \only<1>{
 \begin{center}
 \includegraphics[scale=1,width=0.85\linewidth]{figs/nano_hexapod_id31.jpg}
 \end{center}
 }\only<2>{
 \begin{center}
 \includegraphics[scale=1,width=0.85\linewidth]{figs/nano_hexapod_id31_zoom.jpg}
 \end{center}
 }
 \end{frame}
 \section{Conclusion}
 \label{sec:org5c1e008}
 \begin{frame}[label={sec:orgd50b8eb}]{Conclusion}
 \begin{columns}
 \begin{column}{0.4\columnwidth}
 \textbf{Mechatronics Approach}:
 \begin{itemize}
 \item Use of several models
 \item Predictive design
 \item Beneficial in terms of: cost, delays, performances
 \end{itemize}
 \vspace{0.5em}
 \textbf{Future Work}:
 \begin{itemize}
 \item Optimal/Robust control
 \item Control Test Bench
 \item Implementation on ID31
 \end{itemize}
 \end{column}
 \begin{column}{0.6\columnwidth}
 \vspace{-3em}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/nass_ref_tracking_results.pdf}
 \end{center}
 \end{column}
 \end{columns}
 \begin{tcolorbox}[title=Many thanks to, sidebyside]
 Philipp Brumund, Ludovic Ducotte\newline
 Jose-Maria Clement, Marc Lesourd
 \tcblower
 Youness Benyakhlef, Pierrick Got\newline
 Damien Coulon and the whole team
 \end{tcolorbox}
 \end{frame}
 \end{document}
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Author	SHA1	Message	Date
Thomas Dehaeze	5399416bb3	Add bib file	2021-08-27 19:04:48 +02:00
Thomas Dehaeze	8e1247893b	Update main page	2021-07-28 09:43:36 +02:00
Thomas Dehaeze	6eeb130290	Add submission files	2021-07-26 21:46:38 +02:00
Thomas Dehaeze	325a27b323	Submitted paper	2021-07-26 20:38:52 +02:00
Thomas Dehaeze	831dc79c3e	Talk ready to be recorded	2021-07-22 23:52:44 +02:00
Thomas Dehaeze	b9642201dc	Rework figures	2021-07-22 11:34:05 +02:00
Thomas Dehaeze	656e85fa3d	Update talk	2021-07-22 10:17:20 +02:00
Thomas Dehaeze	0d1a43eecf	Update talk files	2021-07-22 09:09:03 +02:00
Thomas Dehaeze	aa74cc8471	Work on the talk	2021-07-22 09:00:04 +02:00
Thomas Dehaeze	2425ceff3f	Add talk files	2021-07-20 14:24:17 +02:00
Thomas Dehaeze	ed1cf9f44a	Update main page	2021-07-19 11:23:14 +02:00
Thomas Dehaeze	fb5f82586b	Re-read one time	2021-07-16 00:05:49 +02:00
Thomas Dehaeze	07ecb9c34a	Update figures to gain some space	2021-07-15 21:33:15 +02:00
Thomas Dehaeze	2dae264074	Finished all sections	2021-07-15 17:26:54 +02:00
Thomas Dehaeze	f41c916c47	Figure update + re-read all the paper	2021-07-15 15:36:45 +02:00
Thomas Dehaeze	b7647b762f	Work on test bench section + rework figures	2021-07-14 18:48:44 +02:00