Update figures to gain some space

paper/dehaeze21_mechatronics_approach_nass.org

@@ -77,30 +77,15 @@ The presented development approach is foreseen to be applied more frequently to
 #+end_abstract
 
 * INTRODUCTION
-** Establish Significance                                            :ignore:
+With the new $4^\text{th}$ generation machines, there is an increasing need of fast and accurate positioning systems cite:dimper15_esrf_upgrad_progr_phase_ii.
 
-A good overview of the mechatronic approach is given in cite:schmidt20_desig_high_perfor_mechat_third_revis_edition.
+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.
 
-Need of high precision systems with high control bandwidth
-=> the static behavior of the system is not enough, dynamical models are required
-Also include actuators, sensors, control electronics
-=> mechatronic approach
+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 "mechatronic 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.
+Such design methodology was recently used for the development of several systems used by the synchrotron community cite:geraldes17_mechat_concep_new_high_dynam_dcm_sirius,holler18_omny_tomog_nano_cryo_stage,brendike19_esrf_doubl_cryst_monoc_protot.
 
-** Previous and/or current research and contributions                :ignore:
-
-Such mechatronic approach is widely used in the dutch industry cite:rankers98_machin
-
-Systems at Synchrotron using mechatronic approach:
-cite:geraldes17_mechat_concep_new_high_dynam_dcm_sirius
-cite:holler18_omny_tomog_nano_cryo_stage
-cite:brendike19_esrf_doubl_cryst_monoc_protot
-
-** Locate a gap in the research / problem / question / prediction    :ignore:
-
-** The present work                                                  :ignore:
-
-This work shows how the mechatronic approach was used for the development of a nano active stabilization system at the ESRF.
-cite:dehaeze18_sampl_stabil_for_tomog_exper
+In this paper, such approach is described for the design of a Nano Active Stabilization System (NASS).
 
 * NASS - MECHATRONIC APPROACH
 ** The ID31 Micro-Station
@@ -109,7 +94,7 @@ It is composed of several stacked stages (represented in yellow in Fig.\nbsp{}re
 Such architecture allows to obtain high mobility, however, this however limits the position accuracy to tens of $\mu m$.
 
 ** The Nano Active Stabilization System
-The Nano Active Stabilization System (NASS) is a system whose goal is to improve the positioning accuracy of the micro-station.
+The NASS is a system whose goal is to improve the positioning accuracy of the micro-station.
 It is represented in Fig.\nbsp{}ref:fig:nass_concept_schematic and consists of three main elements:
 - A nano-hexapod located between the sample to be positioned and the micro-station
 - An interferometric metrology system measuring the sample's position with respect to the focusing optics
@@ -117,7 +102,7 @@ It is represented in Fig.\nbsp{}ref:fig:nass_concept_schematic and consists of t
 
 #+name: fig:nass_concept_schematic
 #+attr_latex: :scale 0.9
-#+caption: Nano Active Stabilization System - Schematic representation. 1) micro-station, 2) nano-hexapod, 3) sample, 4) metrology system
+#+caption: NASS - Schematic representation. 1) Micro-station, 2) Nano-hexapod, 3) Sample, 4) Metrology system
 [[file:figs/nass_concept_schematic.pdf]]
 
 ** Mechatronic Approach - Overview
@@ -125,7 +110,7 @@ In order to design the NASS in a predictive way, a mechatronic approach, schemat
 
 #+name: fig:nass_mechatronics_approach
 #+attr_latex: :float multicolumn :width 0.9\linewidth
-#+caption: Overview of the mechatronic approach
+#+caption: Overview of the mechatronic approach used for the design of the NASS
 [[file:figs/nass_mechatronics_approach.pdf]]
 
 It consists of three main phases:
@@ -151,7 +136,7 @@ Indeed, several models are used throughout the design with increasing level of c
   \hfill
   \begin{subfigure}[t]{0.48\linewidth}
     \centering
-    \includegraphics[width=0.89\linewidth]{figs/nass_simscape_3d.png}
+    \includegraphics[width=0.89\linewidth]{figs/nass_simscape_3d.pdf}
     \caption{\label{fig:nass_simscape_3d} Multi Body Model}
   \end{subfigure}
   \hfill
@@ -195,12 +180,25 @@ Therefore, an alternative configuration with the encoders fixed to the plates wa
 ** Nano-Hexapod Specifications
 The nano-hexapod should have a maximum height of $95\,mm$, support samples up to $50\,kg$ and have a stroke of $\approx 100\,\mu m$.
 Has shown in Fig.\nbsp{}ref:fig:nano_hexapod_elements, it only has few parts: two plates and 6 active struts in between.
-Each strut is composed of one flexible joint at each end, and one actuator in between (Fig.\nbsp{}ref:fig:picture_nano_hexapod_strut).
+Each strut is composed of one flexible joint at each end, and one actuator in between (Fig.\nbsp{}ref:fig:nano_heaxpod_strut_picture).
 
-#+name: fig:nano_hexapod_elements
-#+attr_latex: :float multicolumn :width 0.9\linewidth
-#+caption: CAD view of the nano-hexapod with key elements
-[[file:figs/nano_hexapod_elements.pdf]]
+#+begin_export latex
+\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}
+  \end{subfigure}
+  \hfill
+  \begin{subfigure}[t]{0.19\linewidth}
+    \centering
+    \includegraphics[width=0.95\linewidth]{figs/nano_heaxpod_strut_picture.pdf}
+    \caption{\label{fig:nano_heaxpod_strut_picture} Mounted strut}
+  \end{subfigure}
+  \caption{\label{fig:nano_hexapod}Nano-hexapod}
+  \centering
+\end{figure*}
+#+end_export
 
 Based on the models used throughout the mechatronic approach, several specifications was obtained in order to maximize the performances of the system:
 - Actuator: axial stiffness $\approx \SI{2}{N/\um}$.
@@ -217,16 +215,11 @@ The top plate geometry was manually optimized to maximize its flexible modes.
 First flexible modes at around $\SI{700}{Hz}$ could be obtained.
 
 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:picture_nano_hexapod_strut).
+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 $\approx \SI{1.8}{\um}$.
 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 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.
 
-#+name: fig:picture_nano_hexapod_strut
-#+attr_latex: :width 0.9\linewidth
-#+caption: Picture of a nano-hexapod's strut
-[[file:figs/picture_nano_hexapod_strut.pdf]]
-
 ** Nano-Hexapod Mounting
 A bench were developed to help the mounting of the struts such that the APA and the two flexible joints are well aligned.
 This helped reducing the effects of flexible modes of the APA.
@@ -238,7 +231,7 @@ The nano-hexapod fixed on top of the micro-station is shown in Fig.\nbsp{}ref:fi
 #+name: fig:nano_hexapod_picture
 #+attr_latex: :width 0.9\linewidth
 #+caption: Nano-hexapod on top of the ID31 micro-station
-[[file:figs/nano_hexapod_picture.jpg]]
+[[file:figs/nano_hexapod_picture.pdf]]
 
 * TEST-BENCHES
 ** Flexible Joints and Instrumentation
@@ -347,22 +340,17 @@ Even the off-diagonal elements (effect of one actuator on the encoder fixed to a
 #+end_export
 
 * CONCLUSION
+The mechatronic 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.
 
-A mechatronic approach used for the development of a nano active stabilization system was presented.
-This allows to design the system in a predictive way, can help
+Measurements made on the nano-hexapod were found to match very well with the models indicating proper design.
+The current performance limitation is coming from the flexible modes of the top platform and future work will focus on overcoming this limitation.
 
-This design methodology can be easily transposed to other complex mechatronic systems.
-
-One main limitation is the flexible modes of the top platform.
-Active damping techniques
-
-- actively damp the top plate flexible modes
-- make the controller robust to change of payload mass
-- integrate it on top of the micro-station
+This design methodology can be easily transposed to other complex mechatronic systems and are foreseen to be applied for future mechatronic systems at the ESRF.
 
 * ACKNOWLEDGMENTS
 This research was made possible by a grant from the FRIA.
-The authors wish to thank Damien Coulon, Philipp Brumund, Marc Lesourd and Youness Benyakhlef.
+The authors wish to thank L. Ducotte, D. Coulon, P. Brumund, M. Lesourd and Y. Benyakhlef for their help throughout the project.
 
 * REFERENCES                                                          :ignore:
 \printbibliography{}

paper/dehaeze21_mechatronics_approach_nass.tex

@@ -1,4 +1,4 @@
-% Created 2021-07-15 jeu. 15:35
+% Created 2021-07-15 jeu. 21:33
 % Intended LaTeX compiler: pdflatex
 \documentclass[a4paper, keeplastbox, biblatex, boxit]{jacow}
 
@@ -35,20 +35,15 @@ The presented development approach is foreseen to be applied more frequently to
 \end{abstract}
 
 \section{INTRODUCTION}
-A good overview of the mechatronic approach is given in \cite{schmidt20_desig_high_perfor_mechat_third_revis_edition}.
+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}.
 
-Need of high precision systems with high control bandwidth
-=> the static behavior of the system is not enough, dynamical models are required
-Also include actuators, sensors, control electronics
-=> mechatronic approach
-Such mechatronic approach is widely used in the dutch industry \cite{rankers98_machin}
+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.
 
-Systems at Synchrotron using mechatronic approach:
-\cite{geraldes17_mechat_concep_new_high_dynam_dcm_sirius}
-\cite{holler18_omny_tomog_nano_cryo_stage}
-\cite{brendike19_esrf_doubl_cryst_monoc_protot}
-This work shows how the mechatronic approach was used for the development of a nano active stabilization system at the ESRF.
-\cite{dehaeze18_sampl_stabil_for_tomog_exper}
+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 ``mechatronic 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}.
+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).
 
 \section{NASS - MECHATRONIC APPROACH}
 \subsection{The ID31 Micro-Station}
@@ -57,7 +52,7 @@ It is composed of several stacked stages (represented in yellow in Fig.~\ref{fig
 Such architecture allows to obtain high mobility, however, this however limits the position accuracy to tens of \(\mu m\).
 
 \subsection{The Nano Active Stabilization System}
-The Nano Active Stabilization System (NASS) is a system whose goal is to improve the positioning accuracy of the micro-station.
+The NASS is a system whose goal is to improve the positioning accuracy of the micro-station.
 It is represented in Fig.~\ref{fig:nass_concept_schematic} and consists of three main elements:
 \begin{itemize}
 \item A nano-hexapod located between the sample to be positioned and the micro-station
@@ -68,7 +63,7 @@ It is represented in Fig.~\ref{fig:nass_concept_schematic} and consists of three
 \begin{figure}[htbp]
 \centering
 \includegraphics[scale=1,scale=0.9]{figs/nass_concept_schematic.pdf}
-\caption{\label{fig:nass_concept_schematic}Nano Active Stabilization System - Schematic representation. 1) micro-station, 2) nano-hexapod, 3) sample, 4) metrology system}
+\caption{\label{fig:nass_concept_schematic}NASS - Schematic representation. 1) Micro-station, 2) Nano-hexapod, 3) Sample, 4) Metrology system}
 \end{figure}
 
 \subsection{Mechatronic Approach - Overview}
@@ -77,7 +72,7 @@ In order to design the NASS in a predictive way, a mechatronic approach, schemat
 \begin{figure*}
 \centering
 \includegraphics[scale=1,width=0.9\linewidth]{figs/nass_mechatronics_approach.pdf}
-\caption{\label{fig:nass_mechatronics_approach}Overview of the mechatronic approach}
+\caption{\label{fig:nass_mechatronics_approach}Overview of the mechatronic approach used for the design of the NASS}
 \end{figure*}
 
 It consists of three main phases:
@@ -104,7 +99,7 @@ Indeed, several models are used throughout the design with increasing level of c
   \hfill
   \begin{subfigure}[t]{0.48\linewidth}
     \centering
-    \includegraphics[width=0.89\linewidth]{figs/nass_simscape_3d.png}
+    \includegraphics[width=0.89\linewidth]{figs/nass_simscape_3d.pdf}
     \caption{\label{fig:nass_simscape_3d} Multi Body Model}
   \end{subfigure}
   \hfill
@@ -147,12 +142,22 @@ Therefore, an alternative configuration with the encoders fixed to the plates wa
 \subsection{Nano-Hexapod Specifications}
 The nano-hexapod should have a maximum height of \(95\,mm\), support samples up to \(50\,kg\) and have a stroke of \(\approx 100\,\mu m\).
 Has shown in Fig.~\ref{fig:nano_hexapod_elements}, it only has few parts: two plates and 6 active struts in between.
-Each strut is composed of one flexible joint at each end, and one actuator in between (Fig.~\ref{fig:picture_nano_hexapod_strut}).
+Each strut is composed of one flexible joint at each end, and one actuator in between (Fig.~\ref{fig:nano_heaxpod_strut_picture}).
 
-\begin{figure*}
-\centering
-\includegraphics[scale=1,width=0.9\linewidth]{figs/nano_hexapod_elements.pdf}
-\caption{\label{fig:nano_hexapod_elements}CAD view of the nano-hexapod with key elements}
+\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}
+  \end{subfigure}
+  \hfill
+  \begin{subfigure}[t]{0.19\linewidth}
+    \centering
+    \includegraphics[width=0.95\linewidth]{figs/nano_heaxpod_strut_picture.pdf}
+    \caption{\label{fig:nano_heaxpod_strut_picture} Mounted strut}
+  \end{subfigure}
+  \caption{\label{fig:nano_hexapod}Nano-hexapod}
+  \centering
 \end{figure*}
 
 Based on the models used throughout the mechatronic approach, several specifications was obtained in order to maximize the performances of the system:
@@ -172,17 +177,11 @@ The top plate geometry was manually optimized to maximize its flexible modes.
 First flexible modes at around \(\SI{700}{Hz}\) could be obtained.
 
 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:picture_nano_hexapod_strut}).
+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 \(\approx \SI{1.8}{\um}\).
 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 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}.
 
-\begin{figure}[htbp]
-\centering
-\includegraphics[scale=1,width=0.9\linewidth]{figs/picture_nano_hexapod_strut.pdf}
-\caption{\label{fig:picture_nano_hexapod_strut}Picture of a nano-hexapod's strut}
-\end{figure}
-
 \subsection{Nano-Hexapod Mounting}
 A bench were developed to help the mounting of the struts such that the APA and the two flexible joints are well aligned.
 This helped reducing the effects of flexible modes of the APA.
@@ -193,7 +192,7 @@ The nano-hexapod fixed on top of the micro-station is shown in Fig.~\ref{fig:nan
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1,width=0.9\linewidth]{figs/nano_hexapod_picture.jpg}
+\includegraphics[scale=1,width=0.9\linewidth]{figs/nano_hexapod_picture.pdf}
 \caption{\label{fig:nano_hexapod_picture}Nano-hexapod on top of the ID31 micro-station}
 \end{figure}
 
@@ -296,24 +295,17 @@ Even the off-diagonal elements (effect of one actuator on the encoder fixed to a
 \end{figure}
 
 \section{CONCLUSION}
+The mechatronic 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.
 
-A mechatronic approach used for the development of a nano active stabilization system was presented.
-This allows to design the system in a predictive way, can help
+Measurements made on the nano-hexapod were found to match very well with the models indicating proper design.
+The current performance limitation is coming from the flexible modes of the top platform and future work will focus on overcoming this limitation.
 
-This design methodology can be easily transposed to other complex mechatronic systems.
-
-One main limitation is the flexible modes of the top platform.
-Active damping techniques
-
-\begin{itemize}
-\item actively damp the top plate flexible modes
-\item make the controller robust to change of payload mass
-\item integrate it on top of the micro-station
-\end{itemize}
+This design methodology can be easily transposed to other complex mechatronic systems and are foreseen to be applied for future mechatronic systems at the ESRF.
 
 \section{ACKNOWLEDGMENTS}
 This research was made possible by a grant from the FRIA.
-The authors wish to thank Damien Coulon, Philipp Brumund, Marc Lesourd and Youness Benyakhlef.
+The authors wish to thank L. Ducotte, D. Coulon, P. Brumund, M. Lesourd and Y. Benyakhlef for their help throughout the project.
 
 \printbibliography{}
 \end{document}

paper/figs/nano_hexapod_elements.svg

@@ -2,9 +2,9 @@
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    id="svg1689"
-   width="1007.2601"
+   width="972.76404"
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+   viewBox="0 0 972.76407 266.70194"
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      inkscape:label="Nano-Hexapod"
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+     transform="translate(-34.496044,-23.575987)">
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@@ -656,7 +656,7 @@
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+         x="-12.911611"
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-         style="text-align:end;text-anchor:end;fill:#d95218">Top flexible Joint</tspan></text>
+         style="text-align:end;text-anchor:end;fill:#d95218">Flexible Joint</tspan></text>
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paper/figs/super_element_simscape.svg

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paper/figs/super_element_simscape_alt.svg

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paper/ref.bib

@@ -87,3 +87,12 @@
   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,
+}

tikz/figures.org

@@ -24,13 +24,13 @@
 
 \begin{tikzpicture}
   % Styles
-  \tikzset{myblock/.style= {draw, dashed, fill=white, text width=3cm, align=center, minimum height=1.4cm}};
+  \tikzset{myblock/.style= {draw, thin, color=white!70!black, fill=white, text width=3cm, align=center, minimum height=1.4cm}};
   \tikzset{mylabel/.style= {anchor=north, below, font=\bfseries\small, color=black, text width=3cm, align=center}};
   \tikzset{mymodel/.style= {anchor=south, above, font=\small, color=black, text width=3cm, align=center}};
   \tikzset{mystep/.style=  {->, ultra thick}};
 
   % Blocks
-  \node[myblock, solid, fill=lightblue, draw, label={[mylabel, text width=8.0cm] Dynamical Models}, minimum height = 4.5cm, text width = 8.0cm] (model) at (0, 0) {};
+  \node[draw, fill=lightblue, align=center, label={[mylabel, text width=8.0cm] Dynamical Models}, minimum height = 4.5cm, text width = 8.0cm] (model) at (0, 0) {};
 
   \node[myblock, fill=lightgreen, label={[mylabel] Disturbances},  left = 3 of model.west]                          (dist) {};
   \node[myblock, fill=lightgreen, label={[mylabel] $\mu$ Station}, below = 2pt of dist] (mustation) {};
@@ -45,7 +45,7 @@
   \node[myblock, fill=lightred, label={[mylabel] Implementation}, below = 2pt of testbenches] (implementation) {};
 
   % Text
-  \node[anchor=south, above, text width=8cm, align=left] at (model.south) {Extensive use of models for:\begin{itemize}[noitemsep,topsep=5pt]\item Extraction of transfer functions \\ \item Choice of control architecture \\ \item Tuning of control laws \\ \item Closed loop simulations \\ \item Noise budgets / Evaluation of performances \\ \item Sensibility to parameters / disturbances\end{itemize}Helpful for proper and predictive design!};
+  \node[anchor=south, above, text width=8cm, align=left] at (model.south) {Extensive use of models for:\begin{itemize}[noitemsep,topsep=5pt]\item Extraction of transfer functions \\ \item Choice of appropriate control architecture \\ \item Tuning of control laws \\ \item Closed loop simulations \\ \item Noise budgets / Evaluation of performances \\ \item Sensibility to parameters / disturbances\end{itemize}\centerline{Models are at the core the mecatronic approach!}};
 
   \node[mymodel] at (mustation.south)       {Multiple stages     \\ Complex dynamics};
   \node[mymodel] at (dist.south)            {Ground motion       \\ Position errors};
@@ -76,13 +76,13 @@
   \draw[<-] ($(instrumentation.south|-model.north)-(0.15, 0)$) -- node[left, midway]{{\small Model}}         ($(instrumentation.south)-(0.15,0)$);
 
   \draw[->] ($(mounting.west-|model.east)+(0, 0.15)$) -- node[above, midway]{{\small Requirements}} ($(mounting.west)+(0, 0.15)$);
-  \draw[<-] ($(mounting.west-|model.east)-(0, 0.15)$) -- node[below, midway]{{\small Refinement}}   ($(mounting.west)-(0, 0.15)$);
+  \draw[<-] ($(mounting.west-|model.east)-(0, 0.15)$) -- node[below, midway]{{\small Model refinement}}   ($(mounting.west)-(0, 0.15)$);
 
   \draw[->] ($(testbenches.west-|model.east)+(0, 0.15)$) -- node[above, midway]{{\small Control Laws}} ($(testbenches.west)+(0, 0.15)$);
-  \draw[<-] ($(testbenches.west-|model.east)-(0, 0.15)$) -- node[below, midway]{{\small Refinement}}   ($(testbenches.west)-(0, 0.15)$);
+  \draw[<-] ($(testbenches.west-|model.east)-(0, 0.15)$) -- node[below, midway]{{\small Model refinement}}   ($(testbenches.west)-(0, 0.15)$);
 
   \draw[->] ($(implementation.west-|model.east)+(0, 0.15)$) -- node[above, midway]{{\small Control Laws}} ($(implementation.west)+(0, 0.15)$);
-  \draw[<-] ($(implementation.west-|model.east)-(0, 0.15)$) -- node[below, midway]{{\small Refinement}}   ($(implementation.west)-(0, 0.15)$);
+  \draw[<-] ($(implementation.west-|model.east)-(0, 0.15)$) -- node[below, midway]{{\small Model refinement}}   ($(implementation.west)-(0, 0.15)$);
 
   % Main steps
   \node[font=\bfseries, rotate=90, anchor=south, above] (conceptual_phase_node) at (dist.west) {1 - Conceptual Phase};