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2021-07-28 09:43:36 +02:00 · 2021-07-26 21:46:38 +02:00 · 2021-07-26 20:38:52 +02:00
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 "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
 <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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-<!-- 2021-07-19 lun. 11:23 -->
+<!-- 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>
@ -42,15 +42,26 @@ The presented development approach is foreseen to be applied more frequently to
 </p>
 </blockquote>

-<div id="outline-container-org5135f26" class="outline-2">
-<h2 id="org5135f26">Conference Paper (<a href="paper/dehaeze21_mechatronics_approach_nass.pdf">pdf</a>)</h2>
-<div class="outline-text-2" id="text-org5135f26">
+<div id="outline-container-org880994d" class="outline-2">
+<h2 id="org880994d">Conference Paper (<a href="paper/dehaeze21_mechatronics_approach_nass.pdf">pdf</a>)</h2>
+<div class="outline-text-2" id="text-org880994d">
 </div>
 </div>

-<div id="outline-container-org18ea867" class="outline-2">
-<h2 id="org18ea867">Cite this work</h2>
-<div class="outline-text-2" id="text-org18ea867">
+<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.
 </p>
@ -75,7 +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 (pp. ) (2021), JACoW Publishing.
+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
@ -34,7 +34,7 @@ The presented development approach is foreseen to be applied more frequently to
 :UNNUMBERED: t
 :END:

-* Talk ([[file:talk/dehaeze21_mechatronics_approach_nass_talk.pdf][link]])                                                       :noexport:
+* Talk ([[file:talk/dehaeze21_mechatronics_approach_nass_talk.pdf][link]])
 :PROPERTIES:
 :UNNUMBERED: t
 :END:
@ -42,7 +42,7 @@ The presented development approach is foreseen to be applied more frequently to
 #+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

@ -69,5 +69,5 @@ To cite this conference paper use the following bibTeX code.

 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 (pp. ) (2021), JACoW Publishing.
+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
@ -76,16 +76,15 @@ Further tests should be done in order to confirm that the performances of the sy
 The presented development approach is foreseen to be applied more frequently to future mechatronics system design at the ESRF.
 #+end_abstract

-* TODO INTRODUCTION
+* 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 depending on the mechanical system alone, but also on its interaction with the actuators, sensors and control electronics.
+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 is called the "mechatronics approach" and was shown to be very effective for the design many complex systems cite:rankers98_machin,schmidt20_desig_high_perfor_mechat_third_revis_edition.
+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.

-In this paper, such approach is described for the design of a Nano Active Stabilization System (NASS).
+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
 ** The ID31 Micro-Station
@ -104,18 +103,18 @@ This system should be able to actively stabilize the sample position down to ten

 #+name: fig:nass_concept_schematic
 #+attr_latex: :scale 0.9
-#+caption: NASS - 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]]

 ** Mechatronics Approach - Overview
 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:

 #+name: fig:nass_mechatronics_approach
 #+attr_latex: :float multicolumn :width 0.9\linewidth
 #+caption: Overview of the mechatronics approach used for the design of the NASS.
 [[file:figs/nass_mechatronics_approach.pdf]]

-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.
@ -124,6 +123,7 @@ It consists of three main phases:
 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 mechatronics approach.
 Indeed, several models are used throughout the design with increasing level of complexity (Fig.\nbsp{}ref:fig:nass_models).
@ -133,19 +133,19 @@ Indeed, several models are used throughout the design with increasing level of c
  \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.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 mechatronics design process.}
@ -153,10 +153,10 @@ Indeed, several models are used throughout the design with increasing level of c
 \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) were used in order to easily study multiple 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.
 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 "plant" dynamics which is easy to control in a robust way.
+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.\nbsp{}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.
@ -181,8 +181,7 @@ Therefore, an alternative configuration with the encoders fixed to the plates wa

 * NANO-HEXAPOD DESIGN
 ** Nano-Hexapod Specifications
-The nano-hexapod is a fully parallel manipulator also called "Gough-Stewart platform".
-It is composed of few parts as shown in Fig.\nbsp{}ref:fig:nano_hexapod_elements: only two plates linked by 6 active struts.
+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.
 Each strut has one rotational joint at each end, and one actuator in between (Fig.\nbsp{}ref:fig:nano_heaxpod_strut_picture).

 #+begin_export latex
@ -190,13 +189,13 @@ Each strut has one rotational joint at each end, and one actuator in between (Fi
  \begin{subfigure}[t]{0.80\linewidth}
    \centering
    \includegraphics[width=\linewidth]{figs/nano_hexapod_elements.pdf}
-    \caption{\label{fig:nano_hexapod_elements} CAD view of the nano-hexapod with key elements}
+    \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}
+    \caption{\label{fig:nano_heaxpod_strut_picture} Mounted strut.}
  \end{subfigure}
  \caption{\label{fig:nano_hexapod}Nano-hexapod: A Stewart platform architecture.}
  \centering
@ -207,26 +206,26 @@ The main benefits of this architecture are its compact design, good dynamical pr
 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:
- Actuator axial stiffness $\approx \SI{2}{N/\um}$ as it is a good trade-off between disturbance filtering and dynamic decoupling from the micro-station.
+- 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 maximum the frequency of spurious resonances.
+- 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 controller bandwidth.
+- 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.

 ** 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 its flexible modes.
+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 (shown in Fig.\nbsp{}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 $\approx \SI{1.8}{\um}$.
+The chosen model was the APA300ML from Cedrat Technologies (Fig.\nbsp{}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 easily be made robust cite:souleille18_concep_activ_mount_space_applic.
+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.

 ** 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 plant that were difficult to control.
+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.
@ -239,10 +238,10 @@ The mounted nano-hexapod is shown in Fig.\nbsp{}ref:fig:nano_hexapod_picture.

 * TEST-BENCHES
 ** Flexible Joints and Instrumentation
-Before mounting the nano-hexapod and going control tests, several test benches were used to characterize the individual elements of the system.
+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 few of them that were not compliant with the requirement and pair the remaining ones.
+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[fn:1] as well as its output noise were measured.
 Similarly, the measurement noise of the encoders[fn:2] was also measured.
@ -250,7 +249,7 @@ 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
-An other test bench schematically shown in Fig.\nbsp{}ref:fig:test_bench_apa_schematic was used to identify the dynamics of the APA.
+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.
@ -263,7 +262,7 @@ The same bench was also used with the struts in order to study the added effects

 #+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
@ -271,13 +270,13 @@ The same bench was also used with the struts in order to study the added effects
  \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 $d_e/V_a$}
+    \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]{figs/apa_test_bench_results_Vs.pdf}
-    \caption{\label{fig:apa_test_bench_results_Vs} Force sensor $V_s/V_a$}
+    \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
@ -285,34 +284,34 @@ The same bench was also used with the struts in order to study the added effects
 #+end_export

 ** Nano-Hexapod
-After the nano-hexapod was mounted, its dynamics was identified by individually exciting each of the actuators and simultaneously recording the six force sensors and six encoders signals.
+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.

 In Fig.\nbsp{}ref:fig:nano_hexapod_identification_comp_simscape_de one can observe the following modes:
 - From $\SI{100}{Hz}$ to $\SI{200}{Hz}$: six suspension modes.
 - At $\SI{230}{Hz}$ and $\SI{340}{Hz}$: flexible modes of the APA, also modeled thanks to the flexible model of the APA.
- At $\SI{700}{Hz}$: flexible modes of the top plate. The model is not matching the FRF because a rigid body was used.
+- 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 (Fig.\nbsp{}ref:fig:nano_hexapod_identification_comp_simscape_Vs) as expected.
+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 critically 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 to another strut) is very well modeled (Fig.\nbsp{}ref:fig:nano_hexapod_identification_damp_comp_simscape_off_diag).
+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).

 #+begin_export latex
 \begin{figure}[htbp]
  \begin{subfigure}[t]{0.49\linewidth}
    \centering
    \includegraphics[width=0.95\linewidth]{figs/nano_hexapod_identification_comp_simscape_de.pdf}
-    \caption{\label{fig:nano_hexapod_identification_comp_simscape_de} Encoder $d\mathcal{L}_i/u_i$}
+    \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 $V_{si}/u_i$}
+    \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
@ -324,22 +323,22 @@ Even the off-diagonal elements (effect of one actuator on the encoder fixed to a
  \begin{subfigure}[t]{0.49\linewidth}
    \centering
    \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}
+    \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}
+    \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 and without the active damping technique applied.}
+  \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.
-Such approach allowed to design the system in a predictive and optimal way.
+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.
@ -348,7 +347,7 @@ This design methodology can be easily transposed to other complex mechatronics s

 * ACKNOWLEDGMENTS
 This research was made possible by a grant from the FRIA.
-The authors wish to thank L. Ducotte, D. Coulon, P. Brumund, M. Lesourd and Y. Benyakhlef for their help throughout the project.
+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:
 \printbibliography{}
--- 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
@ -1,6 +1,6 @@
-% Created 2021-07-16 ven. 00:05
+% Created 2021-07-26 lun. 21:40
 % Intended LaTeX compiler: pdflatex
-\documentclass[a4paper, keeplastbox, biblatex, boxit]{jacow}
+\documentclass[a4paper, keeplastbox, biblatex]{jacow}

 \usepackage{graphicx}
 \usepackage{tabularx}
@ -14,7 +14,7 @@
 \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{2021-07-16}
+\date{2021-07-26}
 \title{MECHATRONICS APPROACH FOR THE DEVELOPMENT OF A NANO-ACTIVE-STABILIZATION-SYSTEM}
 \begin{document}

@ -36,14 +36,13 @@ The presented development approach is foreseen to be applied more frequently to

 \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 depending on the mechanical system alone, but also on its interaction with the actuators, sensors and control electronics.
+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 is called the ``mechatronics approach'' and was shown to be very effective for the design many complex systems \cite{rankers98_machin,schmidt20_desig_high_perfor_mechat_third_revis_edition}.
+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}.

-In this paper, such approach is described for the design of a Nano Active Stabilization System (NASS).
+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}
@ -65,11 +64,12 @@ This system should be able to actively stabilize the sample position down to ten
 \begin{figure}[htbp]
 \centering
 \includegraphics[scale=1,scale=0.9]{figs/nass_concept_schematic.pdf}
-\caption{\label{fig:nass_concept_schematic}NASS - 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{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
@ -77,7 +77,6 @@ In order to design the NASS in a predictive way, a mechatronics approach, schema
 \caption{\label{fig:nass_mechatronics_approach}Overview of the mechatronics approach used for the design of the NASS.}
 \end{figure*}

-It consists of three main phases:
 \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.
@ -88,6 +87,7 @@ The models are updated as the design progresses.
 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}).
@ -96,29 +96,29 @@ Indeed, several models are used throughout the design with increasing level of c
  \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.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 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}) were used in order to easily study multiple 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.
 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 ``plant'' dynamics which is easy to control in a robust way.
+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.
@ -143,21 +143,20 @@ Therefore, an alternative configuration with the encoders fixed to the plates wa

 \section{NANO-HEXAPOD DESIGN}
 \subsection{Nano-Hexapod Specifications}
-The nano-hexapod is a fully parallel manipulator also called ``Gough-Stewart platform''.
-It is composed of few parts as shown in Fig.~\ref{fig:nano_hexapod_elements}: only two plates linked by 6 active struts.
+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]{figs/nano_hexapod_elements.pdf}
-    \caption{\label{fig:nano_hexapod_elements} CAD view of the nano-hexapod with key elements}
+    \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}
+    \caption{\label{fig:nano_heaxpod_strut_picture} Mounted strut.}
  \end{subfigure}
  \caption{\label{fig:nano_hexapod}Nano-hexapod: A Stewart platform architecture.}
  \centering
@ -168,27 +167,27 @@ The nano-hexapod should have a maximum height of \(95\,mm\), support samples up

 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 and dynamic decoupling from the micro-station.
+\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 maximum the frequency of spurious resonances.
+\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 controller bandwidth.
+\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 its flexible modes.
+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 (shown in 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 \(\approx \SI{1.8}{\um}\).
+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 easily be made robust \cite{souleille18_concep_activ_mount_space_applic}.
+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 plant that were difficult to control.
+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.
@ -202,10 +201,10 @@ The mounted nano-hexapod is shown in Fig.~\ref{fig:nano_hexapod_picture}.

 \section{TEST-BENCHES}
 \subsection{Flexible Joints and Instrumentation}
-Before mounting the nano-hexapod and going control tests, several test benches were used to characterize the individual elements of the system.
+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 few of them that were not compliant with the requirement and pair the remaining ones.
+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.
@ -213,7 +212,7 @@ Similarly, the measurement noise of the encoders\footnote{Vionic from Renishaw}
 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}
-An other test bench schematically shown in Fig.~\ref{fig:test_bench_apa_schematic} was used to identify the dynamics of the APA.
+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.
@ -227,27 +226,27 @@ The same bench was also used with the struts in order to study the added effects
 \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]{0.49\linewidth}
    \centering
    \includegraphics[width=0.95\linewidth]{figs/apa_test_bench_results_de.pdf}
-    \caption{\label{fig:apa_test_bench_results_de} Encoder $d_e/V_a$}
+    \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]{figs/apa_test_bench_results_Vs.pdf}
-    \caption{\label{fig:apa_test_bench_results_Vs} Force sensor $V_s/V_a$}
+    \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 was mounted, its dynamics was identified by individually exciting each of the actuators and simultaneously recording the six force sensors and six encoders signals.
+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.

@ -255,27 +254,27 @@ In Fig.~\ref{fig:nano_hexapod_identification_comp_simscape_de} one can observe t
 \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 was used.
+\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 (Fig.~\ref{fig:nano_hexapod_identification_comp_simscape_Vs}) as expected.
+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 critically 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 to another strut) is very well modeled (Fig.~\ref{fig:nano_hexapod_identification_damp_comp_simscape_off_diag}).
+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]{figs/nano_hexapod_identification_comp_simscape_de.pdf}
-    \caption{\label{fig:nano_hexapod_identification_comp_simscape_de} Encoder $d\mathcal{L}_i/u_i$}
+    \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 $V_{si}/u_i$}
+    \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
@ -285,21 +284,21 @@ Even the off-diagonal elements (effect of one actuator on the encoder fixed to a
  \begin{subfigure}[t]{0.49\linewidth}
    \centering
    \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}
+    \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}
+    \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 and without the active damping technique applied.}
+  \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.
-Such approach allowed to design the system in a predictive and optimal way.
+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.
@ -308,7 +307,7 @@ This design methodology can be easily transposed to other complex mechatronics s

 \section{ACKNOWLEDGMENTS}
 This research was made possible by a grant from the FRIA.
-The authors wish to thank L. Ducotte, D. Coulon, P. Brumund, M. Lesourd and Y. Benyakhlef for their help throughout the project.
+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/figs/mass_spring_damper_hac_lac.pdf
+++ b/paper/figs/mass_spring_damper_hac_lac.pdf
--- a/paper/figs/mass_spring_damper_hac_lac.png
+++ b/paper/figs/mass_spring_damper_hac_lac.png
--- a/paper/figs/mass_spring_damper_hac_lac.svg
+++ b/paper/figs/mass_spring_damper_hac_lac.svg
--- a/paper/figs/mass_spring_damper_nass.pdf
+++ b/paper/figs/mass_spring_damper_nass.pdf
--- a/paper/figs/mass_spring_damper_nass.png
+++ b/paper/figs/mass_spring_damper_nass.png
--- a/paper/figs/mass_spring_damper_nass.svg
+++ b/paper/figs/mass_spring_damper_nass.svg
--- a/paper/figs/nano_hexapod_identification_damp_comp_simscape_both.pdf
+++ b/paper/figs/nano_hexapod_identification_damp_comp_simscape_both.pdf
--- a/paper/figs/nano_hexapod_identification_damp_comp_simscape_both.svg
+++ b/paper/figs/nano_hexapod_identification_damp_comp_simscape_both.svg
--- a/paper/figs/nano_hexapod_identification_damp_comp_simscape_diag.pdf
+++ b/paper/figs/nano_hexapod_identification_damp_comp_simscape_diag.pdf
--- a/paper/figs/nano_hexapod_identification_damp_comp_simscape_diag.svg
+++ b/paper/figs/nano_hexapod_identification_damp_comp_simscape_diag.svg
--- a/paper/figs/nano_hexapod_identification_damp_comp_simscape_off_diag.pdf
+++ b/paper/figs/nano_hexapod_identification_damp_comp_simscape_off_diag.pdf
--- a/paper/figs/nano_hexapod_identification_damp_comp_simscape_off_diag.svg
+++ b/paper/figs/nano_hexapod_identification_damp_comp_simscape_off_diag.svg
--- a/paper/ref.bib
+++ b/paper/ref.bib
@ -47,8 +47,7 @@

@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
-                  Edition},
+  title           = {The Design of High Performance Mechatronics},
  year            = 2020,
  publisher       = {Ios Press},
 }
--- a/paper/submission/TUIO02.bib
+++ b/paper/submission/TUIO02.bib
@ -0,0 +1,119 @@
+@inproceedings{dehaeze18_sampl_stabil_for_tomog_exper,
+  author          = {Thomas Dehaeze and M. Magnin Mattenet and Christophe
+                  Collette},
+  title           = {Sample Stabilization For Tomography Experiments In Presence
+                  Of Large Plant Uncertainty},
+  booktitle       = {MEDSI'18},
+  year            = 2018,
+  doi             = {10.18429/JACoW-MEDSI2018-WEOAMA02},
+  month           = 12,
+}
+
+@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,
+}
+
+@article{souleille18_concep_activ_mount_space_applic,
+  author          = {Souleille, Adrien and Lampert, Thibault and Lafarga, V and
+                  Hellegouarch, Sylvain and Rondineau, Alan and Rodrigues,
+                  Gon{\c{c}}alo and Collette, Christophe},
+  title           = {A Concept of Active Mount for Space Applications},
+  journal         = {CEAS Space Journal},
+  year            = 2018,
+}
+
+@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,
+}
+
+@phdthesis{rankers98_machin,
+  author          = {Rankers, Adrian Mathias},
+  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},
+}
+
+@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},
+  title           = {Omny-A Tomography Nano Cryo Stage},
+  journal         = {Review of Scientific Instruments},
+  year            = 2018,
+  doi             = {10.1063/1.5020247},
+}
+
+@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
+++ b/paper/submission/TUIO02_f4a.pdf
--- 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
+++ b/paper/submission/TUIO02_f7a.pdf
--- 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
--- a/paper/submission/TUIO02_f9b.pdf
+++ b/paper/submission/TUIO02_f9b.pdf
--- a/paper/submission/jacow.cls
+++ b/paper/submission/jacow.cls
@ -0,0 +1,503 @@
+%%
+%% This file has been developed as a common template for papers
+%% destined for electronic production for Accelerator Conferences
+%%
+%% See the JACoW website for more information
+%%
+%%       http://jacow.org/
+%%
+%% This work may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either
+%% version 1.3c of this license or (at your option) any later
+%% version. This version of this license is in
+%%    http://www.latex-project.org/lppl/lppl-1-3c.txt
+%% and the latest version of this license is in
+%%    http://www.latex-project.org/lppl.txt
+%% and version 1.3 or later is part of all distributions of
+%% LaTeX version 2005/12/01 or later.
+%% 
+%% This work has the LPPL maintenance status "maintained".
+%% 
+%% This Current Maintainer of this work is Volker RW Schaa.
+%% 
+%% This work consists of the following files
+%%    jacow.cls               this class file
+%%    JACoW_LaTeX_A4.tex      A4/letter templates to demonstrate the 
+%%    JACoW_LaTeX_Letter.tex  .. use and explain the various parameters
+%%                            .. and settings for a submission to
+%%                            .. a JACoW conference proceedings
+%%    JACoW_LaTeX_A4.pdf      template in format A4 and European 
+%%                            settings (citation and hyphenation)
+%%    JACoW_LaTeX_Letter.pdf  template in format letter and American
+%%                            setting (citation and hyphenation)
+%%    annexes-A4.tex          Annexes A-C which are included in "JACoW_LaTeX_A4.tex"
+%%    annexes-Letter.tex      Annexes A-C which are included in "JACoW_LaTeX_Letter.tex"
+%%
+%%    JACpic_mc.pdf           a graphic showing the JACoW page format
+%%    JACpic2.jpg             a graphic for a full width figure and
+%%                            multiline caption
+%%    jacow-collaboration.tex  an example title page showing the
+%%    jacow-collaboration.pdf  JACoW Colloaboration, the responsible
+%%                             editors for the various platform
+%%                            dependent templates (LaTeX, Word on PC and
+%%                            Mac, ODF). The PDF is included in the template
+%% 
+%
+%  v0.1 to 1.3 : JAC2000.cls
+%  Special thanks to John Jowett and Michel Goossens from CERN and
+%  Martin Comyn at TRIUMF for their significant contributions to
+%  this class file over the period 1996 to 2000.
+%                                                 John Poole
+%                                                 March 2000
+%  v1.4 : JAC2001.cls
+%  JAC2001.cls is a modified version of JAC2000.cls to produce indented
+%  first paragraphs after section, subsection and subsubsection headings.
+%                                                 Martin Comyn  April 2001
+%
+%  v1.5 : JAC2003.cls
+%  This is a modified version of JAC2003.cls to adjust space around
+%  section and subsection headers to be more consistent with JACoW Word
+%  templates.                                     Todd Satogata  March 2011
+%
+% v 1.6 : jacow.cls
+% This is a complectly rewritten version of JAC2003.cls which needs a current
+% TeX-System to run.
+%                                                 Ulrike Fischer, November 2013
+%
+% v 1.7
+% - small change to correct the text block inside JACoW's magic red borders for
+%   a4paper (aca4); top has been set 18.5mm (19mm is defined in the template but
+%   leaves descenders outside the lower y margin).
+% - duplicate {boxit} removed
+%                                                 Volker RW Schaa, 14 April 2014
+%
+% v1.8
+% - added setup for \micro sign which disappears when using XeTeX or LuaTeX
+%   with unicode-math.                             Ulrike Fischer, 21 April 2014
+%
+% v1.9
+% - fixed the pdfLaTeX warnings for the text/math-micro hack
+%                                                  Ulrike Fischer, 22 April 2014
+%
+% v1.91
+% - Ligatures=TeX switch introduced to accommodate
+%                                                  Ulrike Fischer, 22 April 2014
+%
+% v1.92
+% - settings for top margin have to be different in A4 and letter to accommodate
+%   JACoW's PitStop Action List. This was found after receiving Plamen Hopchev's
+%   email about margins and testing the workflow with cropping the bounding box
+%   which starts at the lower left edge and not at the top (see graphic JACpic_mc
+%   in the template for measures).
+%                                                 Volker RW Schaa, 29 April 2014
+% v1.93
+% - setting the bottom margin (19mm) without top solves the problem for different
+%   A4/Letter settings. This was already the default in v1.6. Pointed out by
+%   Plamen Hopchev. To accommodate the descenders the bottom margin has been set
+%   to 56pt now.
+%                                                   Volker RW Schaa, 01 May 2014
+%
+% v1.94
+% - the micro sign in UTF-8 prevents ASCII format of the cls file. Ulrike pointed
+%   out a hack in http://tex.stackexchange.com/questions/172968/hide-notation-from-pdftex
+%   which is now introduced.
+%                                                   Volker RW Schaa, 02 May 2014
+%
+% v1.95
+% - only change to the version 1.94 are the extended documenation and license
+%   statement (lppl1.3c) as preparation for publication on CTAN.
+%                                                   Volker RW Schaa, 02 May 2014
+%
+% v1.96
+% - modification of bibatex style information. Since the JACoW template Feb-2016 
+%   the bibliography requires the IEEEtran style. Heine provided an adapted
+%   version using the required values of the template:
+%   + ieee biblatex style instead of numeric-compv
+%   + doi field is cleared for all entries
+%   + et al. is used when there are > 6 authors (maxnames=6). In that case, 
+%     only the first author is mentioned (minnames=1)
+%   + url field is cleared for articles and inproceedings
+%   + giveninits=true reduces all given names to initials
+%                                            Heine Dølrath Thomsen, 30 June 2016
+%
+% v2.00
+% - after using v1.96 during conferences where DOIs/URLs were present in biblio-
+%   graphic records, the following changes to Heine's version have been made:
+%   + doi field allowed
+%   + url field allowed
+%                                                 Volker RW Schaa, 02 May 2014
+% v2.1 new options introduced
+% flushend: new: keeplastbox
+% siunitx:  new: binary-units=true
+% BibLaTeX: changed: style=ieee => bibstyle=ieee, citestyle=numeric-comp
+%           new: dashed=false
+%           removed: doi=false
+%                                                 Volker RW Schaa, 02 May 2014
+%
+% v2.2
+% - adapted to the changes of template version 2018-02
+% - made this one official
+%                                                  Volker RW Schaa, 23 Feb 2018
+%
+% v2.3
+% - font for tt switched to newtxtt with option zerostyle=d (dotted 0)
+%                                                  Volker RW Schaa, 15 Jan 2019
+%
+% v2.4
+% - version 2.3 did not work for XeTeX/LuaTeX, therefore font change using
+%   \def\UrlFont and switching the fontencoding to T1 (suggested by Ulrike Fischer)
+% - package amsmath included to provide 
+%                                                  Volker RW Schaa, 01 Apr 2019
+%
+\def\fileversion{2.4}
+\def\filedate{2019/04/01}
+\def\docdate {2019/04/01}
+
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesClass{jacow}[\filedate\space Version \fileversion]
+
+\typeout{------------------------------------------------------------------------}
+\typeout{LaTeX2e Class file for Accelerator Conference publication for LaTeX2e users}
+\typeout{ }
+\typeout{Use the boxit option to draw a box on page showing the correct margins}
+\typeout{ }
+\typeout{Itemize, Enumerate and Description environments are compact versions}
+\typeout{------------------------------------------------------------------------}
+\typeout{ }
+
+\newif\ifjacowbiblatex
+\newif\ifjacowrefpage
+
+\DeclareOption{acus}{%
+   \PassOptionsToPackage{paper=letterpaper}{geometry}
+   \typeout{Setup for US LETTER PAPER}}
+
+\DeclareOption{letterpaper}{%
+   \PassOptionsToPackage{paper=letterpaper}{geometry}
+   \typeout{Setup for US LETTER PAPER}}
+
+\DeclareOption{a4paper}{%
+    \PassOptionsToPackage{paper=a4paper}{geometry}
+    \typeout{Setup for A4 PAPER}}
+
+\DeclareOption{aca4}{%
+    \PassOptionsToPackage{paper=a4paper}{geometry}
+    \typeout{Setup for A4 PAPER}}
+
+\DeclareOption{boxit}{\PassOptionsToPackage{showframe}{geometry}}
+
+\DeclareOption{biblatex}{\jacowbiblatextrue}
+
+\DeclareOption{refpage}{\jacowrefpagetrue}
+
+\DeclareOption*{\PassOptionsToClass{\CurrentOption}{article}}
+
+\ExecuteOptions{aca4}
+\ProcessOptions
+
+\RequirePackage{fix-cm}
+\LoadClass[10pt,twocolumn]{article}
+\RequirePackage[keeplastbox]{flushend} %% modified
+% Tools:
+\RequirePackage{etoolbox}
+\RequirePackage{ifxetex}
+\RequirePackage{ifluatex}
+\RequirePackage{textcase}
+%
+%Add thanks to the list of "\@nonchangecase"-commands from textcase:
+\def\@uclcnotmath#1#2#3#4{\begingroup
+      #1%
+      \def\({$}\let\)\(%
+      \def\NoCaseChange##1{\noexpand\NoCaseChange{\noexpand##1}}%
+      \@nonchangecase\label
+      \@nonchangecase\ref
+      \@nonchangecase\ensuremath
+      \@nonchangecase\thanks %new
+      \@nonchangecase\si %new
+      \@nonchangecase\SI %new
+      \def\cite##1##{\toks@{\noexpand\cite##1}\@citex}%
+      \def\@citex##1{\NoCaseChange{\the\toks@{##1}}}%
+      \def\reserved@a##1##2{\let#2\reserved@a}%
+      \expandafter\reserved@a\@uclclist\reserved@b{\reserved@b\@gobble}%
+      \protected@edef\reserved@a{\endgroup
+          \noexpand\@skipmath#3#4$\valign$}%
+      \reserved@a}
+
+\RequirePackage[detect-mode,detect-weight, binary-units=true]{siunitx}
+\RequirePackage{graphicx}
+\RequirePackage{booktabs}
+\RequirePackage[figureposition=bottom,tableposition=top,skip=5pt]{caption}
+\RequirePackage{xcolor}
+\RequirePackage{amsmath}
+\AtEndPreamble{\RequirePackage[autostyle]{csquotes}}
+
+
+% Page layout:
+\RequirePackage[%
+  textwidth=170mm,
+  textheight=241mm,
+  heightrounded,
+  left=20mm,
+  bottom=56pt,
+  columnsep=5mm,
+  noheadfoot,
+  nomarginpar,
+  twocolumn]
+  {geometry}
+
+\columnseprule 0pt
+\usepackage[hang]{footmisc}
+\setlength{\footnotemargin}{.6em}
+
+
+\pagestyle{empty}
+
+\RequirePackage{url}
+%
+% redefine the default Typewriter Font to newtxtt with dotted zeros (v2.3)
+%
+\RequirePackage[zerostyle=d]{newtxtt}
+\newcommand\urlZDtxt{\fontencoding{T1}\fontfamily{newtxtt}\selectfont}
+\def\UrlFont{\urlZDtxt}
+
+\ifboolexpr{bool{xetex} or bool{luatex}}
+ {}
+ { \catcode`\^^^=9
+ }
+ 
+\ifboolexpr{bool{xetex} or bool{luatex}}
+ { \let\ori@vdots\vdots
+   \RequirePackage{unicode-math}
+   \AtBeginDocument{\let\vdots\ori@vdots}
+   \setmainfont[Ligatures=TeX]{TeX Gyre Termes}
+   \setmathfont{TeX Gyre Termes Math}
+   \sisetup{
+     math-micro = \text{^^^^03bc},
+     text-micro = ^^^^03bc
+      }
+ }
+ {
+  % Fonts: Times clones
+  \RequirePackage{textcomp}
+  \RequirePackage[T1]{fontenc}
+  \RequirePackage{lmodern}
+  \RequirePackage{tgtermes}
+  \RequirePackage{newtxmath}
+  \input{glyphtounicode}
+  \pdfgentounicode=1
+%  \RequirePackage{cmap}
+ }
+
+\RequirePackage{microtype}
+
+%Lists
+
+\RequirePackage{enumitem}
+\newenvironment{Enumerate}{\begin{enumerate}[nosep]}{\end{enumerate}}
+\newenvironment{Itemize}{\begin{itemize}[nosep]}{\end{itemize}}
+\newenvironment{Description}{\begin{description}[nosep]}{\end{description}}
+
+
+%Floatparameter:
+\renewcommand{\topfraction}{.95}
+\renewcommand{\bottomfraction}{.95}
+\renewcommand{\textfraction}{0.1}
+\renewcommand{\floatpagefraction}{0.8}
+
+
+%headings:
+% section: Uppercase only for text
+\renewcommand{\section}
+   {%
+    \@startsection{section}{1}{0mm}
+       {2.0ex plus 0.8ex minus .1ex}{1.0ex plus .2ex}
+       {\normalfont\large\bfseries\mathversion{bold}\centering\MakeTextUppercase}%
+   }%
+
+\renewcommand\subsection
+  {%
+   \@startsection{subsection}{2}{\z@}
+    {1.4ex plus .8ex minus .17ex}{0.8ex plus .17ex}
+    {\normalfont\large\itshape}%
+   }
+
+\renewcommand\subsubsection
+ {%
+  \@startsection{subsubsection}{3}{\parindent}
+  {2.5ex plus .7ex minus .17ex}{-1em}
+  {\normalfont\normalsize\bfseries}%
+ }
+
+\renewcommand\paragraph
+ {%
+  \@startsection{paragraph}{4}{\z@}
+  {2.5ex plus .7ex minus .17ex}{-1em}
+  {\normalfont\normalsize\itshape}%
+ }
+
+\renewcommand\subparagraph
+ {%
+  \@startsection{subparagraph}{4}{\parindent}
+  {2.25ex plus .7ex minus .17ex}{-1em}
+  {\normalfont\normalsize\bfseries}%
+ }
+
+\setcounter{secnumdepth}{0}
+
+% This definition of \maketitle taken from article.sty, and has been
+% somewhat modified.
+
+\def\maketitle{\par
+ \begingroup
+   \def\thefootnote{\fnsymbol{footnote}}
+   \def\@makefnmark{\hbox
+       to 5pt{$^{\@thefnmark}$\hss}}
+   \twocolumn[\@maketitle]
+   \@thanks
+ \endgroup
+ \enlargethispage{\jac@copyrightspace}%
+ \setcounter{footnote}{0}
+ \let\maketitle\relax
+ \let\@maketitle\relax
+ \gdef\@thanks{}\gdef\@author{}\gdef\@title{}\let\thanks\relax}
+
+\newlength{\titleblockheight}       % so user can change it if need be
+\setlength{\titleblockheight}{3.5cm}
+
+\newlength\titleblockstartskip
+\setlength\titleblockstartskip{3pt}
+
+
+\newlength\titleblockmiddleskip
+\setlength\titleblockmiddleskip{1em}
+
+\newlength\titleblockendskip
+\setlength\titleblockendskip{1em}
+
+
+\def\@maketitle{%
+  \vskip \titleblockstartskip \centering
+  {\Large\bfseries \MakeTextUppercase{\@title} \par}
+  \vskip \titleblockmiddleskip               % Vertical space after title.
+  {\large\begin{tabular}[t]{@{}c@{}}\@author \end{tabular}\par}
+  \vskip \titleblockendskip}
+
+
+% The \copyrightspace command is used to produce a blank space in the first
+% column where a copyright notice may go.  It works by producing
+% with \enlargethispage and is inserted by \maketitle.
+% The command should be issued in the preamble.
+
+\newcommand\jac@copyrightspace{0pt}
+\newcommand\copyrightspace[1][1cm]{\renewcommand\jac@copyrightspace{-#1}}
+
+\ifboolexpr{bool{@titlepage}}
+{\renewenvironment{abstract}
+ {\list{}{%
+    \setlength{\leftmargin}{\dimexpr\textwidth/2-0.75\columnwidth}%
+    \setlength{\rightmargin}{\dimexpr-0.75\columnwidth-\columnsep}%
+    \setlength{\listparindent}{\parindent}%
+    \setlength{\itemsep}{\parskip}%
+    \setlength{\itemindent}{\z@}%
+    \setlength{\topsep}{\z@}%
+    \setlength{\parsep}{\parskip}%
+    \setlength{\partopsep}{\z@}%
+    \let\makelabel\@gobble
+    \setlength{\labelwidth}{\z@}%
+    \advance\@listdepth\m@ne   }%
+   \item\relax\subsection*{Abstract}}
+ {\endlist\clearpage}
+}
+{%
+ \renewenvironment{abstract}
+  {\subsection*{Abstract}}
+  {\par}
+}
+\ifboolexpr{bool{jacowbiblatex}}
+%2.00 {\RequirePackage[style=ieee,sorting=none,giveninits=true,doi=false,maxnames=6,minnames=1]{biblatex}
+%2.1 {\RequirePackage[style=ieee,sorting=none,giveninits=true,maxnames=6,minnames=1]{biblatex}
+%2.2
+  {\RequirePackage[bibstyle=ieee,citestyle=numeric-comp,dashed=false,sorting=none,giveninits=true,maxnames=6,minnames=1]{biblatex}
+  \renewbibmacro*{url+urldate}{%
+    \iffieldundef{url}
+     {}
+     {\printfield{url}%
+      \nopunct}}%
+  \DeclareFieldFormat{url}{\url{#1}}
+  \DeclareFieldFormat{eprint}{#1}
+%% when to activate this? Paper format acus/letter
+%  \DefineBibliographyExtras{american}{\stdpunctuation} % mod
+  % Drop urls for article and inproceedings entries
+%2.00  \DeclareFieldFormat
+%2.00  [article,inproceedings]
+%2.00  {url}{}
+  %
+  \setlength\bibitemsep{0pt}
+  \setlength\bibparsep{0pt}
+  \setlength\biblabelsep{5pt}
+  \ifjacowrefpage\preto\blx@bibliography{\clearpage}\fi
+  \AtBeginBibliography{\small\clubpenalty4000\widowpenalty4000}%
+ }
+ {\RequirePackage{cite}
+  % Redefine to use smaller fonts
+  \def\thebibliography#1{\setlength{\itemsep}{0pt}\setlength{\parsep}{0pt}%
+  \ifjacowrefpage\clearpage\fi
+  \section*{REFERENCES\@mkboth
+  {REFERENCES}{REFERENCES}}\small\list
+  {[\arabic{enumi}]}{\settowidth\labelwidth{[#1]}\leftmargin\labelwidth
+    \advance\leftmargin\labelsep
+    \usecounter{enumi}}
+    \def\newblock{\hskip .11em plus .33em minus .07em}
+    \sloppy\clubpenalty4000\widowpenalty4000
+    \sfcode`\.=1000\relax}
+   \let\endthebibliography=\endlist
+  }
+
+
+%\sloppy
+\clubpenalty10000\widowpenalty10000
+\flushbottom
+%-----------------------------------------------------------------------
+
+%avoid bug of fixltx2e:
+%http://www.latex-project.org/cgi-bin/ltxbugs2html?pr=latex/4023
+\RequirePackage{fixltx2e}%
+\def\@outputdblcol{%
+  \if@firstcolumn
+    \global\@firstcolumnfalse
+    \global\setbox\@leftcolumn\copy\@outputbox
+    \splitmaxdepth\maxdimen
+    \vbadness\maxdimen
+    \setbox\@outputbox\vbox{\unvbox\@outputbox\unskip}%new
+    \setbox\@outputbox\vsplit\@outputbox to\maxdimen
+    \toks@\expandafter{\topmark}%
+    \xdef\@firstcoltopmark{\the\toks@}%
+    \toks@\expandafter{\splitfirstmark}%
+    \xdef\@firstcolfirstmark{\the\toks@}%
+    \ifx\@firstcolfirstmark\@empty
+      \global\let\@setmarks\relax
+    \else
+      \gdef\@setmarks{%
+        \let\firstmark\@firstcolfirstmark
+        \let\topmark\@firstcoltopmark}%
+    \fi
+  \else
+    \global\@firstcolumntrue
+    \setbox\@outputbox\vbox{%
+     \hb@xt@\textwidth{%
+        \hb@xt@\columnwidth{\box\@leftcolumn \hss}%
+        \hfil
+        \vrule \@width\columnseprule
+        \hfil
+       \hb@xt@\columnwidth{\box\@outputbox \hss}}}%
+  \@combinedblfloats
+    \@setmarks
+    \@outputpage
+    \begingroup
+      \@dblfloatplacement
+      \@startdblcolumn
+      \@whilesw\if@fcolmade \fi{\@outputpage\@startdblcolumn}%
+    \endgroup
+  \fi}
+
+\endinput
--- a/talk/dehaeze21_mechatronics_approach_nass_talk.org
+++ b/talk/dehaeze21_mechatronics_approach_nass_talk.org
@ -1,11 +1,11 @@
 #+TITLE: Mechatronics Approach for the Development of a Nano-Active-Stabilization-System
 :DRAWER:
-#+AUTHOR:    Dehaeze Thomas, Bonnefoy Julien and Collette Christophe
+#+AUTHOR:
 #+SUBTITLE:  MEDSI2020, July 26-29, 2021
 #+EMAIL:     dehaeze.thomas@gmail.com
 #+DATE:

-#+LATEX_HEADER_EXTRA: \author[shortname]{Thomas Dehaeze \inst{1,2}, Julien Bonnefoy \inst{1} \and Christophe Collette \inst{2,3}}
+#+LATEX_HEADER_EXTRA: \author[shortname]{Thomas Dehaeze \inst{1,2}, Julien Bonnefoy \inst{1} and Christophe Collette \inst{2,3}}
 #+LATEX_HEADER_EXTRA: \institute[shortinst]{\inst{1} European Synchrotron Radiation Facility, Grenoble, France \and %
 #+LATEX_HEADER_EXTRA:                       \inst{2} Precision Mechatronics Laboratory, University of Liege, Belgium \and %
 #+LATEX_HEADER_EXTRA:                       \inst{3} BEAMS Department, Free University of Brussels, Belgium}
@ -86,7 +86,7 @@ CLOSED: [2021-07-21 mer. 21:46]
 \end{tikzpicture}
 #+end_export

-** DONE Introduction - The Nano Active Stabilization System
+** DONE Introduction - The Nano Active Stabilization System (NASS)
 CLOSED: [2021-07-06 mar. 22:48]
 :PROPERTIES:
 :UNNUMBERED: notoc
@ -201,10 +201,10 @@ CLOSED: [2021-07-08 jeu. 09:46]
 #+attr_latex: :width \linewidth
 [[file:figs/control_bandwidth_2_above_res.pdf]]

-#+Beamer: }\only<3>{
+# #+Beamer: }\only<3>{

-#+attr_latex: :width \linewidth
-[[file:figs/control_bandwidth_3_next_gen.pdf]]
+# #+attr_latex: :width \linewidth
+# [[file:figs/control_bandwidth_3_next_gen.pdf]]

 #+Beamer: }

@ -234,13 +234,13 @@ Limited by complex dynamics\newline
 Model based controller
 #+end_tcolorbox

-#+Beamer: }\only<3>{
+# #+Beamer: }\only<3>{

-#+attr_latex: :options [title=Next-Gen Systems, fontupper=\small]
-#+begin_tcolorbox
-Active research topic\newline
-Complex controllers
-#+end_tcolorbox
+# #+attr_latex: :options [title=Next-Gen Systems, fontupper=\small]
+# #+begin_tcolorbox
+# Active research topic\newline
+# Complex controllers
+# #+end_tcolorbox

 #+Beamer: }

@ -273,14 +273,14 @@ CLOSED: [2021-07-09 ven. 13:37]
 #+Beamer: \onslide<1->{

 #+attr_latex: :width \linewidth
-[[file:figs/nass_example_alone.pdf]]
+[[file:figs/nass_example_alone_b.pdf]]

 \vspace{-2em}

 #+Beamer: }\onslide<2->{

 #+attr_latex: :width \linewidth
-[[file:figs/nass_example_support_uncertainty_d_L.pdf]]
+[[file:figs/nass_example_support_uncertainty_d_L_b.pdf]]

 #+Beamer: }

@ -317,7 +317,7 @@ CLOSED: [2021-07-09 ven. 15:51]
 #+attr_latex: :options [title=Low Authority Control]
 #+begin_tcolorbox
 - Collocated sensors/actuators
- Guaranteed Stability
+- Guaranteed Stability, simple $K$
 - Adds damping
 - $\searrow$ vibration near resonances
 #+end_tcolorbox
@ -331,8 +331,8 @@ CLOSED: [2021-07-09 ven. 15:51]
 #+begin_tcolorbox
 - Position sensors
 - Complex dynamics
- $\searrow$ vibration in the bandwidth
 - Use transformation matrices
+- $\searrow$ vibration in the bandwidth
 #+end_tcolorbox

 ** DONE Multi-Body Models - Simulations
@ -529,30 +529,30 @@ CLOSED: [2021-07-22 jeu. 10:12]
 \vspace{-2em}
 *** Column                                                           :BMCOL:
 :PROPERTIES:
-:BEAMER_col: 0.5
+:BEAMER_col: 0.45
 :END:

 #+attr_latex: :width 0.95\linewidth
 [[file:figs/received_flexible_joints.jpg]]

 #+attr_latex: :width 0.95\linewidth
-[[file:figs/soft_measure_flex_size.jpg]]
+[[file:figs/flexible_joint_bench.pdf]]

 *** Column                                                           :BMCOL:
 :PROPERTIES:
 :BEAMER_col: 0.55
 :END:

-\vspace{-1.5em}
-
-#+attr_latex: :width 0.8\linewidth
-[[file:figs/flexible_joint_bench.pdf]]
-
-\vspace{-1em}
-
 #+attr_latex: :width 0.9\linewidth
 [[file:figs/flex_joint_meas_example_F_d_lin_fit.pdf]]

+#+attr_latex: :options [title=Other Measurement Benches]
+#+begin_tcolorbox
+- Amplifier Output Noise and Bandwidth
+- Encoder Measurement Noise
+- DAC Output Noise
+#+end_tcolorbox
+
 ** DONE Amplified Piezoelectric Actuator - Test Bench
 CLOSED: [2021-07-21 mer. 15:26]

@ -574,7 +574,7 @@ CLOSED: [2021-07-21 mer. 15:26]
 \end{tikzpicture}
 #+end_export

-** DONE Amplified Piezoelectric Actuator - Extracted Model
+** DONE Amplified Piezoelectric Actuator - Measured FRF and Extracted Model
 CLOSED: [2021-07-21 mer. 15:27]

 #+attr_latex: :width \linewidth
@ -700,7 +700,7 @@ CLOSED: [2021-07-21 mer. 17:43]
 #+attr_latex: :width \linewidth
 [[file:figs/mounted_nano_hexapod_picture.jpg]]

-** DONE Nano-Hexapod - Identified Dynamics
+** DONE Nano-Hexapod - Identified Dynamics (Diagonal elements)
 CLOSED: [2021-07-22 jeu. 16:17]

 \vspace{-1em}
--- a/talk/dehaeze21_mechatronics_approach_nass_talk.pdf
+++ b/talk/dehaeze21_mechatronics_approach_nass_talk.pdf
--- a/talk/dehaeze21_mechatronics_approach_nass_talk.tex
+++ b/talk/dehaeze21_mechatronics_approach_nass_talk.tex
@ -1,4 +1,4 @@
-% Created 2021-07-22 jeu. 23:48
+% Created 2021-07-27 mar. 08:42
 % Intended LaTeX compiler: pdflatex
 \documentclass[aspectratio=169, t]{clean-beamer}
 \usepackage[utf8]{inputenc}
@ -21,7 +21,7 @@
 \usepackage{array}
 \usepackage{siunitx}
 \usepackage{mathtools}
-\author[shortname]{Thomas Dehaeze \inst{1,2}, Julien Bonnefoy \inst{1} \and Christophe Collette \inst{2,3}}
+\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}
@ -45,12 +45,11 @@
 \setbeamertemplate{bibliography item}[text]
 \DeclareSIUnit\rms{rms}
 \usetheme{default}
-\author{Dehaeze Thomas, Bonnefoy Julien and Collette Christophe}
 \date{}
 \title{Mechatronics Approach for the Development of a Nano-Active-Stabilization-System}
 \subtitle{MEDSI2020, July 26-29, 2021}
 \hypersetup{
- pdfauthor={Dehaeze Thomas, Bonnefoy Julien and Collette Christophe},
+ pdfauthor={},
 pdftitle={Mechatronics Approach for the Development of a Nano-Active-Stabilization-System},
 pdfkeywords={},
 pdfsubject={},
@ -61,8 +60,8 @@
 \maketitle

 \section*{Introduction}
-\label{sec:org2f2f7e5}
-\begin{frame}[label={sec:org7a284a6}]{The ID31 Micro Station}
+\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}
@ -73,7 +72,7 @@
 \end{tikzpicture}
 \end{frame}

-\begin{frame}[label={sec:org5dbf487}]{Introduction - The Nano Active Stabilization System}
+\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''

@ -82,21 +81,21 @@
 \end{center}
 \end{frame}

-\begin{frame}[label={sec:org8665237}]{Overview of the Mechatronic Approach - Model Based Design}
+\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:org0e45181}
-\begin{frame}[label={sec:org66fab8a}]{Outline - 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:org5582b03}]{Feedback Control - The Control Loop}
+\begin{frame}[label={sec:orgf99643e}]{Feedback Control - The Control Loop}
 \vspace{-1em}

 \begin{center}
@ -127,7 +126,7 @@
 \end{columns}
 \end{frame}

-\begin{frame}[label={sec:org95d167f}]{Noise Budgeting and Required Control Bandwidth}
+\begin{frame}[label={sec:orge603014}]{Noise Budgeting and Required Control Bandwidth}
 \vspace{-1em}

 \begin{center}
@ -135,7 +134,7 @@
 \end{center}
 \end{frame}

-\begin{frame}[label={sec:orgce8e920}]{Limitation of the Controller Bandwidth?}
+\begin{frame}[label={sec:org1a8d575}]{Limitation of the Controller Bandwidth?}
 \begin{columns}
 \begin{column}{0.6\columnwidth}
 \vspace{-2em}
@ -152,12 +151,6 @@
 \includegraphics[scale=1,width=\linewidth]{figs/control_bandwidth_2_above_res.pdf}
 \end{center}

-}\only<3>{
-
-\begin{center}
-\includegraphics[scale=1,width=\linewidth]{figs/control_bandwidth_3_next_gen.pdf}
-\end{center}
-
 }
 \end{column}

@ -182,19 +175,12 @@ Limited by complex dynamics\newline
 Model based controller
 \end{tcolorbox}

-}\only<3>{
-
-\begin{tcolorbox}[title=Next-Gen Systems, fontupper=\small]
-Active research topic\newline
-Complex controllers
-\end{tcolorbox}
-
 }
 \end{column}
 \end{columns}
 \end{frame}

-\begin{frame}[label={sec:orge61676f}]{Soft or Stiff \(\nu\text{-hexapod}\) ? Interaction with the \(\mu\text{-station}\)}
+\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}
@ -217,7 +203,7 @@ Complex controllers
 \onslide<1->{

 \begin{center}
-\includegraphics[scale=1,width=\linewidth]{figs/nass_example_alone.pdf}
+\includegraphics[scale=1,width=\linewidth]{figs/nass_example_alone_b.pdf}
 \end{center}

 \vspace{-2em}
@ -225,7 +211,7 @@ Complex controllers
 }\onslide<2->{

 \begin{center}
-\includegraphics[scale=1,width=\linewidth]{figs/nass_example_support_uncertainty_d_L.pdf}
+\includegraphics[scale=1,width=\linewidth]{figs/nass_example_support_uncertainty_d_L_b.pdf}
 \end{center}

 }
@ -233,7 +219,7 @@ Complex controllers
 \end{columns}
 \end{frame}

-\begin{frame}[label={sec:orgfa52d1c}]{Complexity of the Micro-Station Dynamics (Model Analysis)}
+\begin{frame}[label={sec:orgeb9ee99}]{Complexity of the Micro-Station Dynamics (Model Analysis)}
 \vspace{-1em}

 \begin{center}
@ -246,7 +232,7 @@ Complex controllers
 \end{tikzpicture}
 \end{frame}

-\begin{frame}[label={sec:org82c9a46}]{Control Strategy: HAC-LAC}
+\begin{frame}[label={sec:orgb8ddd28}]{Control Strategy: HAC-LAC}
 \vspace{-0.5em}

 \begin{center}
@ -260,7 +246,7 @@ Complex controllers
 \begin{tcolorbox}[title=Low Authority Control]
 \begin{itemize}
 \item Collocated sensors/actuators
-\item Guaranteed Stability
+\item Guaranteed Stability, simple \(K\)
 \item Adds damping
 \item \(\searrow\) vibration near resonances
 \end{itemize}
@ -272,15 +258,15 @@ Complex controllers
 \begin{itemize}
 \item Position sensors
 \item Complex dynamics
-\item \(\searrow\) vibration in the bandwidth
 \item Use transformation matrices
+\item \(\searrow\) vibration in the bandwidth
 \end{itemize}
 \end{tcolorbox}
 \end{column}
 \end{columns}
 \end{frame}

-\begin{frame}[label={sec:org8694100}]{Multi-Body Models - Simulations}
+\begin{frame}[label={sec:org0579a05}]{Multi-Body Models - Simulations}
 \begin{center}
 \includegraphics[scale=1,width=\linewidth]{figs/simscape_simulation.jpg}
 \end{center}
@ -302,14 +288,14 @@ Complex controllers
 \end{frame}

 \section{Detail Design Phase}
-\label{sec:orgff27fa3}
-\begin{frame}[label={sec:orgf7e1c30}]{Outline - 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:org133ceaa}]{Nano-Hexapod Overview - Key elements}
+\begin{frame}[label={sec:org1f20e49}]{Nano-Hexapod Overview - Key elements}
 \vspace{-1.5em}

 \begin{center}
@ -329,7 +315,7 @@ Complex controllers
 \end{tcolorbox}
 \end{frame}

-\begin{frame}[label={sec:org276a69c}]{Choice of Actuator and Flexible Joint Design}
+\begin{frame}[label={sec:orge2a3011}]{Choice of Actuator and Flexible Joint Design}
 \vspace{-2em}
 \begin{columns}
 \begin{column}{0.5\columnwidth}
@ -384,7 +370,7 @@ Bending Stroke & \SI{> 1}{\milli\radian} & 20\\
 \end{columns}
 \end{frame}

-\begin{frame}[label={sec:org27824a6}]{Instrumentation}
+\begin{frame}[label={sec:orgc5a1632}]{Instrumentation}
 \vspace{-1em}

 \begin{columns}
@ -475,43 +461,43 @@ All elements could be chosen/design based on the models
 \end{frame}

 \section{Experimental Phase}
-\label{sec:orgbc8949c}
-\begin{frame}[label={sec:org6e7483a}]{Outline - 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:org2b19437}]{Flexible Joints - Measurements}
+\begin{frame}[label={sec:orge94eaf3}]{Flexible Joints - Measurements}
 \vspace{-2em}
 \begin{columns}
-\begin{column}{0.5\columnwidth}
+\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/soft_measure_flex_size.jpg}
+\includegraphics[scale=1,width=0.95\linewidth]{figs/flexible_joint_bench.pdf}
 \end{center}
 \end{column}

 \begin{column}{0.55\columnwidth}
-\vspace{-1.5em}
-
-\begin{center}
-\includegraphics[scale=1,width=0.8\linewidth]{figs/flexible_joint_bench.pdf}
-\end{center}
-
-\vspace{-1em}
-
 \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:org96a6b68}]{Amplified Piezoelectric Actuator - Test Bench}
+\begin{frame}[label={sec:org518f2db}]{Amplified Piezoelectric Actuator - Test Bench}
 \vspace{-1em}

 \begin{center}
@ -530,13 +516,13 @@ All elements could be chosen/design based on the models
 \end{tikzpicture}
 \end{frame}

-\begin{frame}[label={sec:orge87ad99}]{Amplified Piezoelectric Actuator - Extracted Model}
+\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:org7af7fba}]{Amplified Piezoelectric Actuator - Integral Force Feedback}
+\begin{frame}[label={sec:org1d672c7}]{Amplified Piezoelectric Actuator - Integral Force Feedback}
 \vspace{-3em}
 \begin{columns}
 \begin{column}{0.62\columnwidth}
@ -557,7 +543,7 @@ All elements could be chosen/design based on the models
 \end{columns}
 \end{frame}

-\begin{frame}[label={sec:orgc496afb}]{Strut - Mounting Tool}
+\begin{frame}[label={sec:org7b5008c}]{Strut - Mounting Tool}
 \vspace{-2.5em}
 \begin{columns}
 \begin{column}{0.63\columnwidth}
@ -578,7 +564,7 @@ All elements could be chosen/design based on the models
 \end{column}
 \end{columns}
 \end{frame}
-\begin{frame}[label={sec:orgaec0a8a}]{Strut - Dynamical Measurements}
+\begin{frame}[label={sec:orgc1ecd2e}]{Strut - Dynamical Measurements}
 \vspace{-1em}

 \begin{center}
@ -598,7 +584,7 @@ All elements could be chosen/design based on the models
 \end{tikzpicture}
 \end{frame}

-\begin{frame}[label={sec:org965cd42}]{Strut - Encoders Output and Spurious Modes}
+\begin{frame}[label={sec:org8ce2d42}]{Strut - Encoders Output and Spurious Modes}
 \vspace{-3em}
 \begin{columns}
 \begin{column}{0.43\columnwidth}
@ -624,7 +610,7 @@ All elements could be chosen/design based on the models
 \end{columns}
 \end{frame}

-\begin{frame}[label={sec:orgda21de8}]{Nano-Hexapod Mounting Tool}
+\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}
@ -635,7 +621,7 @@ All elements could be chosen/design based on the models
 \end{tikzpicture}
 \end{frame}

-\begin{frame}[label={sec:org79abb20}]{Mounted Nano-Hexapod}
+\begin{frame}[label={sec:org281520e}]{Mounted Nano-Hexapod}
 \vspace{-1em}

 \begin{center}
@ -643,7 +629,7 @@ All elements could be chosen/design based on the models
 \end{center}
 \end{frame}

-\begin{frame}[label={sec:orgf59950c}]{Nano-Hexapod - Identified Dynamics}
+\begin{frame}[label={sec:org351990a}]{Nano-Hexapod - Identified Dynamics (Diagonal elements)}
 \vspace{-1em}

 \begin{center}
@ -651,7 +637,7 @@ All elements could be chosen/design based on the models
 \end{center}
 \end{frame}

-\begin{frame}[label={sec:org00f7894}]{Nano-Hexapod - Damped Dynamics}
+\begin{frame}[label={sec:org18b6334}]{Nano-Hexapod - Damped Dynamics}
 \vspace{-1em}

 \begin{center}
@ -659,7 +645,7 @@ All elements could be chosen/design based on the models
 \end{center}
 \end{frame}

-\begin{frame}[label={sec:org89187a0}]{The Nano-Hexapod on top of the Micro-Station}
+\begin{frame}[label={sec:org79d4d53}]{The Nano-Hexapod on top of the Micro-Station}
 \vspace{-0.5em}

 \only<1>{
@ -678,8 +664,8 @@ All elements could be chosen/design based on the models
 \end{frame}

 \section{Conclusion}
-\label{sec:orgcce0f41}
-\begin{frame}[label={sec:org905c81b}]{Conclusion}
+\label{sec:org5c1e008}
+\begin{frame}[label={sec:orgd50b8eb}]{Conclusion}
 \begin{columns}
 \begin{column}{0.4\columnwidth}
 \textbf{Mechatronics Approach}:
--- a/talk/figs/apa_comp_model_frf.pdf
+++ b/talk/figs/apa_comp_model_frf.pdf
--- a/talk/figs/apa_comp_model_frf.svg
+++ b/talk/figs/apa_comp_model_frf.svg
--- a/talk/figs/control_bandwidth_1_classical.pdf
+++ b/talk/figs/control_bandwidth_1_classical.pdf
--- a/talk/figs/control_bandwidth_2_above_res.pdf
+++ b/talk/figs/control_bandwidth_2_above_res.pdf
--- a/talk/figs/identification_control_noise_budget.pdf
+++ b/talk/figs/identification_control_noise_budget.pdf
--- a/talk/figs/identification_control_noise_budget.red.pdf
+++ b/talk/figs/identification_control_noise_budget.red.pdf
--- a/talk/figs/identification_control_noise_budget.svg
+++ b/talk/figs/identification_control_noise_budget.svg
--- a/talk/figs/nano_hexapod_damped_bode_plot.pdf
+++ b/talk/figs/nano_hexapod_damped_bode_plot.pdf
--- a/talk/figs/nano_hexapod_damped_bode_plot.svg
+++ b/talk/figs/nano_hexapod_damped_bode_plot.svg
--- a/talk/figs/nano_hexapod_enc_iff_bode_plot.pdf
+++ b/talk/figs/nano_hexapod_enc_iff_bode_plot.pdf
--- a/talk/figs/nano_hexapod_enc_iff_bode_plot.svg
+++ b/talk/figs/nano_hexapod_enc_iff_bode_plot.svg
--- a/talk/figs/nass_example_alone_b.pdf
+++ b/talk/figs/nass_example_alone_b.pdf
--- a/talk/figs/nass_example_support_uncertainty_d_L_b.pdf
+++ b/talk/figs/nass_example_support_uncertainty_d_L_b.pdf
--- a/talk/figs/nass_example_support_uncertainty_d_L_b.svg
+++ b/talk/figs/nass_example_support_uncertainty_d_L_b.svg
--- a/talk/figs/nass_example_uncertainty_support.pdf
+++ b/talk/figs/nass_example_uncertainty_support.pdf
--- a/tikz/figures.org
+++ b/tikz/figures.org
@ -279,7 +279,7 @@
  \draw[->] (iff.south)    -- (ctrladd.north);
  \draw[->] (ctrladd.west) -- (f.east) node[above right]{$u$};
  \draw[->] (d.west)       -| (ctrl.south);
-  \draw[->] (ctrl.north)   -- (ctrladd.south);
+  \draw[->] (ctrl.north)   -- (ctrladd.south) node[below right]{$u^\prime$};
  % ====================
 \end{tikzpicture}
 #+end_src
Author	SHA1	Message	Date
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