Submitted paper

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 and Y. Benyakhlef for their help throughout the project.
 
 * REFERENCES                                                          :ignore:
 \printbibliography{}

paper/dehaeze21_mechatronics_approach_nass.tex

@@ -1,6 +1,6 @@
-% Created 2021-07-16 ven. 00:05
+% Created 2021-07-26 lun. 20:38
 % 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 and Y. Benyakhlef for their help throughout the project.
 
 \printbibliography{}
 \end{document}