Figure update + re-read all the paper

paper/dehaeze21_mechatronics_approach_nass.org

@@ -17,13 +17,15 @@
 #+AUTHOR: @@latex:\\@@
 #+AUTHOR: \textsuperscript{1}also at Precision Mechatronics Laboratory, University of Liege, Belgium
 
-#+LATEX_HEADER: \usepackage{pdfpages,multirow,ragged2e}
+#+latex_header: \usepackage{graphicx}
-#+LATEX_HEADER: \usepackage{graphicx,tabularx,booktabs}
+#+latex_header: \usepackage{tabularx}
-#+LATEX_HEADER: \usepackage{blindtext,bm}
+#+latex_header: \usepackage{booktabs}
+#+LATEX_HEADER: \usepackage{bm}
 #+LATEX_HEADER: \usepackage{subcaption}
 #+LATEX_HEADER: \usepackage{siunitx}
 #+LATEX_HEADER: \usepackage[USenglish]{babel}
-#+LATEX_HEADER: \setcounter{footnote}{1}
+#+LATEX_HEADER_EXTRA: \setcounter{footnote}{1}
+#+LATEX_HEADER_EXTRA: \setlist[itemize]{noitemsep}
 #+LATEX_HEADER_EXTRA: \usepackage[colorlinks=true, allcolors=blue]{hyperref}
 #+LATEX_HEADER_EXTRA: \addbibresource{ref.bib}
 :END:
@@ -50,10 +52,8 @@
 
 (add-to-list 'org-export-filter-headline-functions
              'my-latex-filter-removeOrgAutoLabels)
-#+end_src
 
-In order to compile this document, just use the =latexmk= command.
+;; Function to compile to PDF
-#+begin_src emacs-lisp
 (defun my-compile-to-pdf ()
   (interactive)
   (org-latex-export-to-latex)
@@ -61,12 +61,8 @@ In order to compile this document, just use the =latexmk= command.
     (async-shell-command "latexmk")))
 #+end_src
 
-#+RESULTS:
-: #<window 72 on *Async Shell Command*>
-: #<window 64 on *Async Shell Command*>
-
 * ABSTRACT                                                           :ignore:
-#+BEGIN_abstract
+#+begin_abstract
 With the growing number of fourth generation light sources, there is an increased need of fast positioning end-stations with nanometric precision.
 Such systems are usually including dedicated control strategies, and many factors may limit their performances.
 In order to design such complex systems in a predictive way, a mechatronic design approach also known as "model based design", may be utilized.
@@ -78,51 +74,60 @@ Several test benches were used to validate the models and to gain confidence on
 Measured nano-hexapod's dynamics was shown to be in very good agreement with the models.
 Further tests should be done in order to confirm that the performances of the system match the predicted one.
 The presented development approach is foreseen to be applied more frequently to future mechatronic system design at the ESRF.
-#+END_abstract
+#+end_abstract
 
 * INTRODUCTION
 ** Establish Significance                                            :ignore:
 
+A good overview of the mechatronic approach is given in cite:schmidt20_desig_high_perfor_mechat_third_revis_edition.
+
+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
 
 ** 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:
 
-Such mechatronic approach is widely used in the dutch industry cite:rankers98_machin and much less in the Synchrotron's world.
-
 ** The present work                                                  :ignore:
 
-In this paper, is presented how the mechatronic approach is used for the development of a nano active stabilization system.
+This work shows how the mechatronic approach was used for the development of a nano active stabilization system at the ESRF.
-
-cite:dehaeze21_activ_dampin_rotat_platf_using
-cite:souleille18_concep_activ_mount_space_applic
-cite:brumund21_multib_simul_reduc_order_flexib_bodies_fea
 cite:dehaeze18_sampl_stabil_for_tomog_exper
-cite:schmidt20_desig_high_perfor_mechat_third_revis_edition
 
 * NASS - MECHATRONIC APPROACH
-** The ID31 Micro Station
+** The ID31 Micro-Station
-The ID31 Micro Station is used to position samples along complex trajectories cite:dehaeze18_sampl_stabil_for_tomog_exper.
+The ID31 micro-station is used to position samples along complex trajectories cite:dehaeze18_sampl_stabil_for_tomog_exper.
 It is composed of several stacked stages (represented in yellow in Fig.\nbsp{}ref:fig:nass_concept_schematic).
-This allows this station to have high mobility, however, this limits the position accuracy to tens of $\mu m$.
+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 ID31 Micro Station.
+The Nano Active Stabilization System (NASS) is a system whose goal is to improve the positioning accuracy of the micro-station.
-
 It is represented in Fig.\nbsp{}ref:fig:nass_concept_schematic and consists of three main elements:
-- a nano-hexapod located between the sample to be positioned and the micro-station.
+- A nano-hexapod located between the sample to be positioned and the micro-station
-- a interferometric metrology system measuring the sample's position with respect to the focusing optics
+- An interferometric metrology system measuring the sample's position with respect to the focusing optics
-- a control system (not represented), which base on the measured position, properly actuates the nano-hexapod in order to stabilize the sample's position
+- A control system (not represented), which based on the measured position, properly actuates the nano-hexapod in order to stabilize the sample's position.
 
 #+name: fig:nass_concept_schematic
-#+attr_latex: :scale 1
+#+attr_latex: :scale 0.9
 #+caption: Nano Active Stabilization System - Schematic representation. 1) micro-station, 2) nano-hexapod, 3) sample, 4) metrology system
 [[file:figs/nass_concept_schematic.pdf]]
 
 ** Mechatronic Approach - Overview
 In order to design the NASS in a predictive way, a mechatronic approach, schematically represented in Fig.\nbsp{}ref:fig:nass_mechatronics_approach, is used.
 
+#+name: fig:nass_mechatronics_approach
+#+attr_latex: :float multicolumn :width 0.9\linewidth
+#+caption: Overview of the mechatronic approach
+[[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.
@@ -132,11 +137,6 @@ 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.
 
-#+name: fig:nass_mechatronics_approach
-#+attr_latex: :float multicolumn :width \linewidth
-#+caption: Overview of the mechatronic approach
-[[file:figs/nass_mechatronics_approach.pdf]]
-
 ** Models
 As shown in Fig.\nbsp{}ref:fig:nass_mechatronics_approach, the models are at the core of the mechatronic approach.
 Indeed, several models are used throughout the design with increasing level of complexity (Fig.\nbsp{}ref:fig:nass_models).
@@ -166,26 +166,26 @@ 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 are used (Fig.\nbsp{}ref:fig:mass_spring_damper_hac_lac) in order to easily try different concepts.
+At the beginning of the conceptual phase, simple "mass-spring-dampers" models (Fig.\nbsp{}ref:fig:mass_spring_damper_hac_lac) are used in order to easily study different 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.
 Also, including a force sensor in series with the nano-hexapod's actuators can be used to actively damp the resonances using the "Integral Force Feedback" (IFF) strategy.
 The goal is to obtain a "plant" dynamics which is easy to control in a robust way.
 
-Rapidly, a more sophisticated multi-body model (Fig.\nbsp{}ref:fig:nass_simscape_3d) has been used.
+Rapidly, a more sophisticated and more realistic multi-body model (Fig.\nbsp{}ref:fig:nass_simscape_3d) was used.
 This model is based on the 3D representation of the micro-station as well as on extensive dynamical measurements.
 Time domain simulations can then be performed with each stage moving with the associated positioning errors and disturbances.
-Such model is more realistic and permits to study effects which were not modeled with the previous model such as the coupling between directions and effect of the rotation of the spindle on the nano-hexapod's dynamics (gyroscopic effects cite:dehaeze21_activ_dampin_rotat_platf_using).
+Such model permits 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 can be developed and tested.
 
-During the detail design phase, the nano-hexapod model is updated by importing the 3D parts exported from the CAD software.
+During the detail design phase, the nano-hexapod model is updated using 3D parts exported from the CAD software as the mechanical design progresses.
-The key elements of the nano-hexapod such as the flexible joints and the APA are optimized using a Finite Element Software.
+The key elements of the nano-hexapod such as the flexible joints and the APA are optimized using a Finite Element Analysis (FEA) Software.
-As the flexible modes of the system are what generally limit the controller bandwidth, they are important to model in order to understand which ones are problematic and should be maximized.
+As the flexible modes of the mechanics are what generally limit the controller bandwidth, they are important to model in order to understand which ones are problematic and should be maximized.
-In order to do so, a "super-element" can be exported using a finite element analysis software and imported in Simscape (Fig.\nbsp{}ref:fig:super_element_simscape).
+To do so, a "super-element" can be exported using a FEA software and then imported in Simscape (Fig.\nbsp{}ref:fig:super_element_simscape).
 Such process is described in cite:brumund21_multib_simul_reduc_order_flexib_bodies_fea.
-The multi-body model with included flexible elements can be used to obtain very accurately the dynamics of the system.
+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 non practical to perform time domain simulations.
 
-Finally, during the experimental phase, the models are refined using experimental system identification.
+Finally, during the experimental phase, the models are refined using experimental system identification data.
 These models can be used 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 (Fig.\nbsp{}ref:fig:nano_hexapod_elements), several flexible modes of the APA were appearing in the dynamics which render the control using the encoders very complex.
@@ -193,10 +193,9 @@ Therefore, an alternative configuration with the encoders fixed to the plates wa
 
 * NANO-HEXAPOD DESIGN
 ** Nano-Hexapod Specifications
-The Nano-Hexapod must have a maximum height of $95\,mm$, support samples up to $50\,kg$ and have a stroke of $\approx 100\,\mu m$.
+The nano-hexapod should have a maximum height of $95\,mm$, support samples up to $50\,kg$ and have a stroke of $\approx 100\,\mu m$.
-it have few parts: two plates and 6 active struts in between.
+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 (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:picture_nano_hexapod_strut).
-A 3D view of the nano-hexapod is shown in Fig.\nbsp{}ref:fig:nano_hexapod_elements.
 
 #+name: fig:nano_hexapod_elements
 #+attr_latex: :float multicolumn :width 0.9\linewidth
@@ -204,24 +203,24 @@ A 3D view of the nano-hexapod is shown in Fig.\nbsp{}ref:fig:nano_hexapod_elemen
 [[file:figs/nano_hexapod_elements.pdf]]
 
 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 $\approx \SI{2}{\um}$
+- Actuator: axial stiffness $\approx \SI{2}{N/\um}$.
-- Flexible joints: bending stiffness $< \SI{100}{Nm/rad}$ and axial stiffness $> \SI{100}{N/\um}$
+- Flexible joints: bending stiffness $< \SI{100}{Nm/rad}$ and axial stiffness $> \SI{100}{N/\um}$.
-- Precise positioning of the $b_i$ and $\hat{s}_i$
+- 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
+- Flexible modes of the top-plate as high as possible to increase the control robustness.
-- Integration of a force sensor in each strut
+- Integration of a force sensor in each strut for active damping purposes.
 
 ** Parts' Optimization
 The geometry of the flexible joint could be optimized using a finite element software.
 The obtained stiffnesses are compliance with the requirements and the model was updated.
 
-The top plate was manually optimized to maximize its flexible modes.
+The top plate geometry was manually optimized to maximize its flexible modes.
-Flexible modes at around $\SI{700}{Hz}$ could be obtained.
+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).
 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.
-The main benefits is the good "collocation" of the sensor stack with the actuator stacks, meaning that the active damping controller will easily be made robust.
+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
@@ -229,40 +228,39 @@ The main benefits is the good "collocation" of the sensor stack with the actuato
 [[file:figs/picture_nano_hexapod_strut.pdf]]
 
 ** Nano-Hexapod Mounting
-After each element
+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.
 
-# Mounting bench for the struts
+A second mounting tool were used to fix the six struts to the two plates without inducing too much strain in the flexible joints.
-# Mounting tool for the nano-hexapod
 
-The nano-hexapod mounted on top of the micro-station is shown in Fig.\nbsp{}ref:fig:nano_hexapod_picture.
+The nano-hexapod fixed on top of the micro-station is shown in Fig.\nbsp{}ref:fig:nano_hexapod_picture.
 
 #+name: fig:nano_hexapod_picture
 #+attr_latex: :width 0.9\linewidth
-#+caption: Nano-Hexapod on top of the ID31 micro-station
+#+caption: Nano-hexapod on top of the ID31 micro-station
 [[file:figs/nano_hexapod_picture.jpg]]
 
 * TEST-BENCHES
 ** Flexible Joints and Instrumentation
-Several test benches were used to characterize the individual elements of the NASS.
+Before adding the NASS to the micro-station, several test benches were used to characterize the individual elements of the NASS.
 
-The bending stiffness of the flexible joints was measured by applying a (measured) force to one end of the joint while measuring its deflection at the same time.
+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 not compliant with the requirement and pair the remaining ones.
 
 The transfer function from input to output voltage of the voltage amplifier[fn:1] as well as its output noise was measured.
 Similarly, the measurement noise of the encoders[fn:2] was also measured.
 
-These simple measurements on individual elements are useful to refine their models, found any problem as early as possible, and will help analyzing the results once the nano-hexapod is mounted and all elements combined.
+These simple measurements on individual elements are useful to refine their models, to found any problem as early as possible, and to help analyzing the results obtained with the nano-hexapod mounted and all 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.
-It consist of a $5\,\text{kg}$ granite vertical guided with an air bearing and fixed on top 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) is generated and applied to two of the piezoelectric stacks.
 Both the voltage generated by the third piezoelectric stack and the displacement measured by the encoder are recorded.
-The two obtained frequency response functions (FRF) can then be compared with the model (Fig.\nbsp{}ref:fig:apa_test_bench_results).
+The two obtained frequency response functions (FRF) are compared with the model in Fig.\nbsp{}ref:fig:apa_test_bench_results.
 
 The piezoelectric constants describing the conversion from the mechanical domain (force, strain) easily accessible on the model to the electrical domain (voltages, charges) easily measured can be estimated.
-With these constants, the match between the measured FRF and the model dynamics is very good (Fig.\nbsp{}ref:fig:apa_test_bench_results)
+With these constants, the match between the measured FRF and the model dynamics is very good (Fig.\nbsp{}ref:fig:apa_test_bench_results).
 
 The same bench was also used with the struts in order to study the added effects of the flexible joints.
 
@@ -276,13 +274,13 @@ The same bench was also used with the struts in order to study the added effects
   \begin{subfigure}[t]{0.48\linewidth}
     \centering
     \includegraphics[width=0.95\linewidth]{figs/apa_test_bench_results_de.pdf}
-    \caption{\label{fig:apa_test_bench_results_de} Encoder}
+    \caption{\label{fig:apa_test_bench_results_de} Encoder $d_e/V_a$}
   \end{subfigure}
   \hfill
   \begin{subfigure}[t]{0.48\linewidth}
     \centering
     \includegraphics[width=0.95\linewidth]{figs/apa_test_bench_results_Vs.pdf}
-    \caption{\label{fig:apa_test_bench_results_Vs} Force Sensor}
+    \caption{\label{fig:apa_test_bench_results_Vs} Force Sensor $V_s/V_a$}
   \end{subfigure}
   \caption{\label{fig:apa_test_bench_results}Measured Frequency Response functions compared with the Simscape model. From the actuator stacks voltage to the encoder (\subref{fig:apa_test_bench_results_de}) and to the force sensor stack (\subref{fig:apa_test_bench_results_Vs}).}
   \centering
@@ -291,21 +289,21 @@ The same bench was also used with the struts in order to study the added effects
 
 ** Nano-Hexapod
 
-Once the nano-hexapod is mounted, its dynamics is identified.
+Once the nano-hexapod is mounted, its dynamics is identified by individually exciting each of the actuators and simultaneously recording the six force sensors and six encoders signals.
-To do so, each actuator is individually excited and the six force sensors and six encoders signals are recorded each time.
 Two $6$ by $6$ FRF matrices are computed.
-The diagonal elements of these two matrices are shown in Fig.\nbsp{}ref:fig:nano_hexapod_identification_comp_simscape and compared with the model.
+Their diagonal elements are shown in Fig.\nbsp{}ref:fig:nano_hexapod_identification_comp_simscape and compared with the model.
 
-From Fig.\nbsp{}ref:fig:nano_hexapod_identification_comp_simscape_de one can observe the following modes:
+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 around $\SI{700}{Hz}$: flexible modes of the top plate, not modeled (taken as a rigid body)
+- At $\SI{700}{Hz}$: flexible modes of the top plate, not matching the FRF because it is modeled as a rigid body
 
-The transfer function from the actuator to the force sensors has alternating poles and zeros (Fig.\nbsp{}ref:fig:nano_hexapod_identification_comp_simscape_Vs) which is confirming the good "collocation" between the stacks.
+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.
-
+IFF is then applied individually on each pair of actuator/force sensor in order to actively damp the suspension modes.
-IFF is then applied individually on each pair of actuator/force sensor in order to actively damp the modes shown in Fig.\nbsp{}ref:fig:nano_hexapod_identification_comp_simscape_Vs.
+The optimal gain of the IFF controller is determined using the model.
-The optimal gain of the IFF controller is determined from the model.
 After applying the active damping technique, the $6$ by $6$ FRF matrix from the actuator to the encoders is 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).
 
 # #+name: fig:nass_hac_lac_schematic_test
 # #+attr_latex: :width \linewidth
@@ -317,15 +315,15 @@ After applying the active damping technique, the $6$ by $6$ FRF matrix from the
   \begin{subfigure}[t]{0.48\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}
+    \caption{\label{fig:nano_hexapod_identification_comp_simscape_de} Encoder: $d\mathcal{L}_i/u_i$}
   \end{subfigure}
   \hfill
   \begin{subfigure}[t]{0.48\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}
+    \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}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}).}
+  \caption{\label{fig:nano_hexapod_identification_comp_simscape}Comparison of the measured Frequency Response functions (FRF) with the Simscape model. From the excitation voltage to the associated encoder (\subref{fig:apa_test_bench_results_de}) and to the associated force sensor stack (\subref{fig:apa_test_bench_results_Vs}).}
   \centering
 \end{figure}
 #+end_export
@@ -335,32 +333,36 @@ After applying the active damping technique, the $6$ by $6$ FRF matrix from the
   \begin{subfigure}[t]{0.49\linewidth}
     \centering
     \includegraphics[height=5.5cm]{figs/nano_hexapod_identification_damp_comp_simscape_diag.pdf}
-    \caption{\label{fig:nano_hexapod_identification_damp_comp_simscape_diag} Diagonal}
+    \caption{\label{fig:nano_hexapod_identification_damp_comp_simscape_diag} Diagonal term}
   \end{subfigure}
   \hfill
   \begin{subfigure}[t]{0.49\linewidth}
     \centering
     \includegraphics[height=5.5cm]{figs/nano_hexapod_identification_damp_comp_simscape_off_diag.pdf}
-    \caption{\label{fig:nano_hexapod_identification_damp_comp_simscape_off_diag} Off-Diagonal}
+    \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}}
+  \caption{\label{fig:nano_hexapod_identification_damp_comp_simscape}Transfer functions from actuator to encoder with and without the active damping technique applied.}
   \centering
 \end{figure}
 #+end_export
 
 * CONCLUSION
 
-Future work:
+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
+
+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
 
 * ACKNOWLEDGMENTS
 This research was made possible by a grant from the FRIA.
-Damien Coulomb
+The authors wish to thank Damien Coulon, Philipp Brumund, Marc Lesourd and Youness Benyakhlef.
-Youness Benya
-Marc Lesourd
-Philipp Brumund
 
 * REFERENCES                                                          :ignore:
 \printbibliography{}

paper/dehaeze21_mechatronics_approach_nass.tex

@@ -1,18 +1,20 @@
-% Created 2021-07-14 mer. 18:47
+% Created 2021-07-15 jeu. 15:35
 % Intended LaTeX compiler: pdflatex
 \documentclass[a4paper, keeplastbox, biblatex, boxit]{jacow}
 
-\usepackage{pdfpages,multirow,ragged2e}
+\usepackage{graphicx}
-\usepackage{graphicx,tabularx,booktabs}
+\usepackage{tabularx}
-\usepackage{blindtext,bm}
+\usepackage{booktabs}
+\usepackage{bm}
 \usepackage{subcaption}
 \usepackage{siunitx}
 \usepackage[USenglish, english]{babel}
 \setcounter{footnote}{1}
+\setlist[itemize]{noitemsep}
 \usepackage[colorlinks=true, allcolors=blue]{hyperref}
 \addbibresource{ref.bib}
 \author{T. Dehaeze\textsuperscript{1,}\thanks{thomas.dehaeze@esrf.fr}, J. Bonnefoy, ESRF, Grenoble, France \\ C. Collette\textsuperscript{1}, Université Libre de Bruxelles, BEAMS department, Brussels, Belgium \\ \textsuperscript{1}also at Precision Mechatronics Laboratory, University of Liege, Belgium}
-\date{2021-07-14}
+\date{2021-07-15}
 \title{MECHATRONICS APPROACH FOR THE DEVELOPMENT OF A NANO-ACTIVE-STABILIZATION-SYSTEM}
 \begin{document}
 
@@ -33,40 +35,51 @@ The presented development approach is foreseen to be applied more frequently to
 \end{abstract}
 
 \section{INTRODUCTION}
-Such mechatronic approach is widely used in the dutch industry \cite{rankers98_machin} and much less in the Synchrotron's world.
+A good overview of the mechatronic approach is given in \cite{schmidt20_desig_high_perfor_mechat_third_revis_edition}.
-In this paper, is presented how the mechatronic approach is used for the development of a nano active stabilization system.
 
-\cite{dehaeze21_activ_dampin_rotat_platf_using}
+Need of high precision systems with high control bandwidth
-\cite{souleille18_concep_activ_mount_space_applic}
+=> the static behavior of the system is not enough, dynamical models are required
-\cite{brumund21_multib_simul_reduc_order_flexib_bodies_fea}
+Also include actuators, sensors, control electronics
+=> mechatronic approach
+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}
+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}
-\cite{schmidt20_desig_high_perfor_mechat_third_revis_edition}
 
 \section{NASS - MECHATRONIC APPROACH}
-\subsection{The ID31 Micro Station}
+\subsection{The ID31 Micro-Station}
-The ID31 Micro Station is used to position samples along complex trajectories \cite{dehaeze18_sampl_stabil_for_tomog_exper}.
+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}).
-This allows this station to have high mobility, however, this limits the position accuracy to tens of \(\mu m\).
+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 ID31 Micro Station.
+The Nano Active Stabilization System (NASS) is a system whose goal is to improve the positioning accuracy of the micro-station.
-
 It is represented in Fig.~\ref{fig:nass_concept_schematic} and consists of three main elements:
 \begin{itemize}
-\item a nano-hexapod located between the sample to be positioned and the micro-station.
+\item A nano-hexapod located between the sample to be positioned and the micro-station
-\item a interferometric metrology system measuring the sample's position with respect to the focusing optics
+\item An interferometric metrology system measuring the sample's position with respect to the focusing optics
-\item a control system (not represented), which base on the measured position, properly actuates the nano-hexapod in order to stabilize the sample's position
+\item A control system (not represented), which based on the measured position, properly actuates the nano-hexapod in order to stabilize the sample's position.
 \end{itemize}
 
 \begin{figure}[htbp]
 \centering
-\includegraphics[scale=1,scale=1]{figs/nass_concept_schematic.pdf}
+\includegraphics[scale=1,scale=0.9]{figs/nass_concept_schematic.pdf}
 \caption{\label{fig:nass_concept_schematic}Nano Active Stabilization System - Schematic representation. 1) micro-station, 2) nano-hexapod, 3) sample, 4) metrology system}
 \end{figure}
 
 \subsection{Mechatronic Approach - Overview}
 In order to design the NASS in a predictive way, a mechatronic approach, schematically represented in Fig.~\ref{fig:nass_mechatronics_approach}, is used.
 
+\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}
+\end{figure*}
+
 It consists of three main phases:
 \begin{enumerate}
 \item Conceptual phase: Simple models of both the micro-station and the nano-hexapod are used to first evaluate the performances of several concepts.
@@ -78,12 +91,6 @@ 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}
 
-\begin{figure*}
-\centering
-\includegraphics[scale=1,width=\linewidth]{figs/nass_mechatronics_approach.pdf}
-\caption{\label{fig:nass_mechatronics_approach}Overview of the mechatronic approach}
-\end{figure*}
-
 \subsection{Models}
 As shown in Fig.~\ref{fig:nass_mechatronics_approach}, the models are at the core of the mechatronic approach.
 Indeed, several models are used throughout the design with increasing level of complexity (Fig.~\ref{fig:nass_models}).
@@ -111,26 +118,26 @@ Indeed, several models are used throughout the design with increasing level of c
   \centering
 \end{figure*}
 
-At the beginning of the conceptual phase, simple ``mass-spring-dampers'' models are used (Fig.~\ref{fig:mass_spring_damper_hac_lac}) in order to easily try different concepts.
+At the beginning of the conceptual phase, simple ``mass-spring-dampers'' models (Fig.~\ref{fig:mass_spring_damper_hac_lac}) are used in order to easily study different 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.
 Also, including a force sensor in series with the nano-hexapod's actuators can be used to actively damp the resonances using the ``Integral Force Feedback'' (IFF) strategy.
 The goal is to obtain a ``plant'' dynamics which is easy to control in a robust way.
 
-Rapidly, a more sophisticated multi-body model (Fig.~\ref{fig:nass_simscape_3d}) has been used.
+Rapidly, a more sophisticated and more realistic multi-body model (Fig.~\ref{fig:nass_simscape_3d}) was used.
 This model is based on the 3D representation of the micro-station as well as on extensive dynamical measurements.
 Time domain simulations can then be performed with each stage moving with the associated positioning errors and disturbances.
-Such model is more realistic and permits to study effects which were not modeled with the previous model such as the coupling between directions and effect of the rotation of the spindle on the nano-hexapod's dynamics (gyroscopic effects \cite{dehaeze21_activ_dampin_rotat_platf_using}).
+Such model permits 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 can be developed and tested.
 
-During the detail design phase, the nano-hexapod model is updated by importing the 3D parts exported from the CAD software.
+During the detail design phase, the nano-hexapod model is updated using 3D parts exported from the CAD software as the mechanical design progresses.
-The key elements of the nano-hexapod such as the flexible joints and the APA are optimized using a Finite Element Software.
+The key elements of the nano-hexapod such as the flexible joints and the APA are optimized using a Finite Element Analysis (FEA) Software.
-As the flexible modes of the system are what generally limit the controller bandwidth, they are important to model in order to understand which ones are problematic and should be maximized.
+As the flexible modes of the mechanics are what generally limit the controller bandwidth, they are important to model in order to understand which ones are problematic and should be maximized.
-In order to do so, a ``super-element'' can be exported using a finite element analysis software and imported in Simscape (Fig.~\ref{fig:super_element_simscape}).
+To do so, a ``super-element'' can be exported using a FEA software and then imported in Simscape (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 obtain very accurately the dynamics of the system.
+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 non practical to perform time domain simulations.
 
-Finally, during the experimental phase, the models are refined using experimental system identification.
+Finally, during the experimental phase, the models are refined using experimental system identification data.
 These models can be used 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 (Fig.~\ref{fig:nano_hexapod_elements}), several flexible modes of the APA were appearing in the dynamics which render the control using the encoders very complex.
@@ -138,10 +145,9 @@ Therefore, an alternative configuration with the encoders fixed to the plates wa
 
 \section{NANO-HEXAPOD DESIGN}
 \subsection{Nano-Hexapod Specifications}
-The Nano-Hexapod must have a maximum height of \(95\,mm\), support samples up to \(50\,kg\) and have a stroke of \(\approx 100\,\mu m\).
+The nano-hexapod should have a maximum height of \(95\,mm\), support samples up to \(50\,kg\) and have a stroke of \(\approx 100\,\mu m\).
-it have few parts: two plates and 6 active struts in between.
+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 (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:picture_nano_hexapod_strut}).
-A 3D view of the nano-hexapod is shown in Fig.~\ref{fig:nano_hexapod_elements}.
 
 \begin{figure*}
 \centering
@@ -151,25 +157,25 @@ A 3D view of the nano-hexapod is shown in Fig.~\ref{fig:nano_hexapod_elements}.
 
 Based on the models used throughout the mechatronic approach, several specifications was obtained in order to maximize the performances of the system:
 \begin{itemize}
-\item Actuator: axial stiffness \(\approx \SI{2}{\um}\)
+\item Actuator: axial stiffness \(\approx \SI{2}{N/\um}\).
-\item Flexible joints: bending stiffness \(< \SI{100}{Nm/rad}\) and axial stiffness \(> \SI{100}{N/\um}\)
+\item Flexible joints: bending stiffness \(< \SI{100}{Nm/rad}\) and axial stiffness \(> \SI{100}{N/\um}\).
-\item Precise positioning of the \(b_i\) and \(\hat{s}_i\)
+\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
+\item Flexible modes of the top-plate as high as possible to increase the control robustness.
-\item Integration of a force sensor in each strut
+\item Integration of a force sensor in each strut for active damping purposes.
 \end{itemize}
 
 \subsection{Parts' Optimization}
 The geometry of the flexible joint could be optimized using a finite element software.
 The obtained stiffnesses are compliance with the requirements and the model was updated.
 
-The top plate was manually optimized to maximize its flexible modes.
+The top plate geometry was manually optimized to maximize its flexible modes.
-Flexible modes at around \(\SI{700}{Hz}\) could be obtained.
+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}).
 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.
-The main benefits is the good ``collocation'' of the sensor stack with the actuator stacks, meaning that the active damping controller will easily be made robust.
+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
@@ -178,38 +184,40 @@ The main benefits is the good ``collocation'' of the sensor stack with the actua
 \end{figure}
 
 \subsection{Nano-Hexapod Mounting}
-After each element
+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.
 
-The nano-hexapod mounted on top of the micro-station is shown in Fig.~\ref{fig:nano_hexapod_picture}.
+A second mounting tool were used to fix the six struts to the two plates without inducing too much strain in the flexible joints.
+
+The nano-hexapod fixed on top of the micro-station is shown in Fig.~\ref{fig:nano_hexapod_picture}.
 
 \begin{figure}[htbp]
 \centering
 \includegraphics[scale=1,width=0.9\linewidth]{figs/nano_hexapod_picture.jpg}
-\caption{\label{fig:nano_hexapod_picture}Nano-Hexapod on top of the ID31 micro-station}
+\caption{\label{fig:nano_hexapod_picture}Nano-hexapod on top of the ID31 micro-station}
 \end{figure}
 
 \section{TEST-BENCHES}
 \subsection{Flexible Joints and Instrumentation}
-Several test benches were used to characterize the individual elements of the NASS.
+Before adding the NASS to the micro-station, several test benches were used to characterize the individual elements of the NASS.
 
-The bending stiffness of the flexible joints was measured by applying a (measured) force to one end of the joint while measuring its deflection at the same time.
+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 not compliant with the requirement and pair the remaining ones.
 
 The transfer function from input to output voltage of the voltage amplifier\footnote{PD200 from PiezoDrive} as well as its output noise was measured.
 Similarly, the measurement noise of the encoders\footnote{Vionic from Renishaw} was also measured.
 
-These simple measurements on individual elements are useful to refine their models, found any problem as early as possible, and will help analyzing the results once the nano-hexapod is mounted and all elements combined.
+These simple measurements on individual elements are useful to refine their models, to found any problem as early as possible, and to help analyzing the results obtained with the nano-hexapod mounted and all 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.
-It consist of a \(5\,\text{kg}\) granite vertical guided with an air bearing and fixed on top 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) is generated and applied to two of the piezoelectric stacks.
 Both the voltage generated by the third piezoelectric stack and the displacement measured by the encoder are recorded.
-The two obtained frequency response functions (FRF) can then be compared with the model (Fig.~\ref{fig:apa_test_bench_results}).
+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})
+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.
 
@@ -223,13 +231,13 @@ The same bench was also used with the struts in order to study the added effects
   \begin{subfigure}[t]{0.48\linewidth}
     \centering
     \includegraphics[width=0.95\linewidth]{figs/apa_test_bench_results_de.pdf}
-    \caption{\label{fig:apa_test_bench_results_de} Encoder}
+    \caption{\label{fig:apa_test_bench_results_de} Encoder $d_e/V_a$}
   \end{subfigure}
   \hfill
   \begin{subfigure}[t]{0.48\linewidth}
     \centering
     \includegraphics[width=0.95\linewidth]{figs/apa_test_bench_results_Vs.pdf}
-    \caption{\label{fig:apa_test_bench_results_Vs} Force Sensor}
+    \caption{\label{fig:apa_test_bench_results_Vs} Force Sensor $V_s/V_a$}
   \end{subfigure}
   \caption{\label{fig:apa_test_bench_results}Measured Frequency Response functions compared with the Simscape model. From the actuator stacks voltage to the encoder (\subref{fig:apa_test_bench_results_de}) and to the force sensor stack (\subref{fig:apa_test_bench_results_Vs}).}
   \centering
@@ -237,37 +245,37 @@ The same bench was also used with the struts in order to study the added effects
 
 \subsection{Nano-Hexapod}
 
-Once the nano-hexapod is mounted, its dynamics is identified.
+Once the nano-hexapod is mounted, its dynamics is identified by individually exciting each of the actuators and simultaneously recording the six force sensors and six encoders signals.
-To do so, each actuator is individually excited and the six force sensors and six encoders signals are recorded each time.
 Two \(6\) by \(6\) FRF matrices are computed.
-The diagonal elements of these two matrices are shown in Fig.~\ref{fig:nano_hexapod_identification_comp_simscape} and compared with the model.
+Their diagonal elements are shown in Fig.~\ref{fig:nano_hexapod_identification_comp_simscape} and compared with the model.
 
-From Fig.~\ref{fig:nano_hexapod_identification_comp_simscape_de} one can observe the following modes:
+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 around \(\SI{700}{Hz}\): flexible modes of the top plate, not modeled (taken as a rigid body)
+\item At \(\SI{700}{Hz}\): flexible modes of the top plate, not matching the FRF because it is modeled as a rigid body
 \end{itemize}
 
-The transfer function from the actuator to the force sensors has alternating poles and zeros (Fig.~\ref{fig:nano_hexapod_identification_comp_simscape_Vs}) which is confirming the good ``collocation'' between the stacks.
+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.
-
+IFF is then applied individually on each pair of actuator/force sensor in order to actively damp the suspension modes.
-IFF is then applied individually on each pair of actuator/force sensor in order to actively damp the modes shown in Fig.~\ref{fig:nano_hexapod_identification_comp_simscape_Vs}.
+The optimal gain of the IFF controller is determined using the model.
-The optimal gain of the IFF controller is determined from the model.
 After applying the active damping technique, the \(6\) by \(6\) FRF matrix from the actuator to the encoders is 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}).
 
 \begin{figure}[htbp]
   \begin{subfigure}[t]{0.48\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}
+    \caption{\label{fig:nano_hexapod_identification_comp_simscape_de} Encoder: $d\mathcal{L}_i/u_i$}
   \end{subfigure}
   \hfill
   \begin{subfigure}[t]{0.48\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}
+    \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}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}).}
+  \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}
 
@@ -275,21 +283,28 @@ After applying the active damping technique, the \(6\) by \(6\) FRF matrix from
   \begin{subfigure}[t]{0.49\linewidth}
     \centering
     \includegraphics[height=5.5cm]{figs/nano_hexapod_identification_damp_comp_simscape_diag.pdf}
-    \caption{\label{fig:nano_hexapod_identification_damp_comp_simscape_diag} Diagonal}
+    \caption{\label{fig:nano_hexapod_identification_damp_comp_simscape_diag} Diagonal term}
   \end{subfigure}
   \hfill
   \begin{subfigure}[t]{0.49\linewidth}
     \centering
     \includegraphics[height=5.5cm]{figs/nano_hexapod_identification_damp_comp_simscape_off_diag.pdf}
-    \caption{\label{fig:nano_hexapod_identification_damp_comp_simscape_off_diag} Off-Diagonal}
+    \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}}
+  \caption{\label{fig:nano_hexapod_identification_damp_comp_simscape}Transfer functions from actuator to encoder with and without the active damping technique applied.}
   \centering
 \end{figure}
 
 \section{CONCLUSION}
 
-Future work:
+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
+
+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
@@ -298,10 +313,7 @@ Future work:
 
 \section{ACKNOWLEDGMENTS}
 This research was made possible by a grant from the FRIA.
-Damien Coulomb
+The authors wish to thank Damien Coulon, Philipp Brumund, Marc Lesourd and Youness Benyakhlef.
-Youness Benya
-Marc Lesourd
-Philipp Brumund
 
 \printbibliography{}
 \end{document}

paper/ref.bib

@@ -5,18 +5,8 @@
                   Of Large Plant Uncertainty},
   booktitle       = {MEDSI'18},
   year            = 2018,
-  number          = 10,
-  pages           = {153--157},
   doi             = {10.18429/JACoW-MEDSI2018-WEOAMA02},
-  url             = {https://doi.org/10.18429/JACoW-MEDSI2018-WEOAMA02},
-  address         = {Geneva, Switzerland},
-  isbn            = {978-3-95450-207-3},
-  language        = {english},
   month           = 12,
-  publisher       = {JACoW Publishing},
-  series          = {Mechanical Engineering Design of Synchrotron Radiation
-                  Equipment and Instrumentation},
-  venue           = {Paris, France},
 }
 
 @inproceedings{brumund21_multib_simul_reduc_order_flexib_bodies_fea,
@@ -25,11 +15,7 @@
                   obtained by FEA},
   booktitle       = {MEDSI'20},
   year            = 2021,
-  language        = {english},
+  month           = 07,
-  publisher       = {JACoW Publishing},
-  series          = {Mechanical Engineering Design of Synchrotron Radiation
-                  Equipment and Instrumentation},
-  venue           = {Chicago, USA},
 }
 
 @article{souleille18_concep_activ_mount_space_applic,
@@ -38,9 +24,6 @@
                   Gon{\c{c}}alo and Collette, Christophe},
   title           = {A Concept of Active Mount for Space Applications},
   journal         = {CEAS Space Journal},
-  volume          = 10,
-  number          = 2,
-  pages           = {157--165},
   year            = 2018,
 }
 
@@ -51,8 +34,7 @@
   journal         = {Engineering Research Express},
   year            = 2021,
   doi             = {10.1088/2631-8695/abe803},
-  url             = {https://doi.org/10.1088/2631-8695/abe803},
+  month           = 2,
-  month           = {2},
 }
 
 @phdthesis{rankers98_machin,
@@ -70,3 +52,38 @@
   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},
+}

tikz/figures.org

@@ -24,75 +24,80 @@
 
 \begin{tikzpicture}
   % Styles
-  \tikzset{myblock/.style= {draw, fill=white, text width=3cm, align=center, minimum height=1.8cm}};
+  \tikzset{myblock/.style= {draw, dashed, 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, fill=lightblue, draw, label={[mylabel, text width=9.8cm] Dynamical Models / Simulations / Control}, minimum height = 6cm, text width = 9.8cm] (model) at (0, 0) {};
+  \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[myblock, fill=lightgreen, label={[mylabel] $\mu$ Station}, left = 3 of model.south west, anchor=south east] (mustation) {};
   \node[myblock, fill=lightgreen, label={[mylabel] Disturbances},  left = 3 of model.west]                          (dist) {};
-  \node[myblock, fill=lightgreen, label={[mylabel] $\nu$ Hexapod}, left = 3 of model.north west, anchor=north east] (nanohexapod) {};
+  \node[myblock, fill=lightgreen, label={[mylabel] $\mu$ Station}, below = 2pt of dist] (mustation) {};
+  \node[myblock, fill=lightgreen, label={[mylabel] $\nu$ Hexapod}, above = 2pt of dist] (nanohexapod) {};
 
   \node[myblock, fill=lightyellow, label={[mylabel] Mech. Design},    above = 1 of model.north] (mechanical) {};
-  \node[myblock, fill=lightyellow, label={[mylabel] Instrumentation}, left  = 1 of mechanical]  (instrumentation) {};
+  \node[myblock, fill=lightyellow, label={[mylabel] Instrumentation}, left  = 2pt of mechanical]  (instrumentation) {};
-  \node[myblock, fill=lightyellow, label={[mylabel] FEM},             right = 1 of mechanical]  (fem) {};
+  \node[myblock, fill=lightyellow, label={[mylabel] FEM},             right = 2pt of mechanical]  (fem) {};
 
-  \node[myblock, fill=lightred, label={[mylabel] Assembly},       right = 3 of model.north east, anchor=north west] (mounting) {};
   \node[myblock, fill=lightred, label={[mylabel] Test Benches},   right = 3 of model.east]                          (testbenches) {};
-  \node[myblock, fill=lightred, label={[mylabel] Implementation}, right = 3 of model.south east, anchor=south west] (implementation) {};
+  \node[myblock, fill=lightred, label={[mylabel] Assembly},       above = 2pt of testbenches] (mounting) {};
+  \node[myblock, fill=lightred, label={[mylabel] Implementation}, below = 2pt of testbenches] (implementation) {};
 
   % Text
-  \node[mymodel] at (mustation.south) {Multiple stages\\Complex dynamics\\Solid bodies};
+  \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[mymodel] at (dist.south) {Ground motion\\Vibrations\\Position errors};
-  \node[mymodel] at (nanohexapod.south) {Different concepts\\ Optimal geometry \\ Choice of sensors};
 
-  \node[mymodel] at (instrumentation.south) {Sensors, Actuators\\Amplifiers\\Control electronics};
+  \node[mymodel] at (mustation.south)       {Multiple stages     \\ Complex dynamics};
-  \node[mymodel] at (mechanical.south) {Parts optimization\\Proper integration\\Ease of assembly};
+  \node[mymodel] at (dist.south)            {Ground motion       \\ Position errors};
-  \node[mymodel] at (fem.south) {Optimize key parts:\\Flexible joints\\Plates};
+  \node[mymodel] at (nanohexapod.south)     {Different concepts  \\ Sensors, Actuators};
 
-  \node[mymodel] at (mounting.south) {Mounting Tools:\\Struts\\ Nano-Hexapod};
+  \node[mymodel] at (instrumentation.south) {Sensors, Actuators  \\ Electronics};
-  \node[mymodel] at (testbenches.south) {Instrumentation\\APA, Struts\\Hexapod};
+  \node[mymodel] at (mechanical.south)      {Proper integration  \\ Ease of assembly};
-  \node[mymodel] at (implementation.south) {Test Benches\\$\mu$ Station};
+  \node[mymodel] at (fem.south)             {Optimize key parts: \\ Joints, Plates, APA};
+
+  \node[mymodel] at (mounting.south)        {Struts              \\ Nano-Hexapod};
+  \node[mymodel] at (testbenches.south)     {Instrumentation     \\ APA, Struts};
+  \node[mymodel] at (implementation.south)  {Control tests       \\ $\mu$ Station};
 
   % Links
-  \draw[->] (dist.east) -- node[above, midway]{Measurements} node[below,midway]{} (dist.east-|model.west);
+  \draw[->] (dist.east)      -- node[above, midway]{{\small Measurements}} node[below,midway]{{\small Spectral Analysis}} (dist.east-|model.west);
-  \draw[->] (mustation.east) -- node[above, midway]{Measurements} node[below, midway]{CAD Model} (mustation.east-|model.west);
+  \draw[->] (mustation.east) -- node[above, midway]{{\small Measurements}} node[below, midway]{{\small CAD Model}} (mustation.east-|model.west);
 
-  \draw[->] ($(nanohexapod.east-|model.west)+(0, 0.2)$) -- node[above, midway]{Optimization} ($(nanohexapod.east)+(0, 0.2)$);
+  \draw[->] ($(nanohexapod.east-|model.west)-(0, 0.15)$) -- node[below, midway]{{\small Optimization}} ($(nanohexapod.east)-(0, 0.15)$);
-  \draw[<-] ($(nanohexapod.east-|model.west)-(0, 0.2)$) -- node[below, midway]{Model} ($(nanohexapod.east)-(0, 0.2)$);
+  \draw[<-] ($(nanohexapod.east-|model.west)+(0, 0.15)$) -- node[above, midway]{{\small Model}} ($(nanohexapod.east)+(0, 0.15)$);
 
-  \draw[->] ($(fem.south|-model.north)+(0.2, 0)$) -- node[right, midway]{Specif.} ($(fem.south)+(0.2,0)$);
+  \draw[->] ($(fem.south|-model.north)+(0.15, 0)$) -- node[right, midway]{{\small Specif.}} ($(fem.south)+(0.15,0)$);
-  \draw[<-] ($(fem.south|-model.north)-(0.2, 0)$) -- node[left, midway,align=right]{Super\\Element}  ($(fem.south)-(0.2,0)$);
+  \draw[<-] ($(fem.south|-model.north)-(0.15, 0)$) -- node[left, midway,align=right]{{\small Super}\\{\small Element}}  ($(fem.south)-(0.15,0)$);
 
-  \draw[->] ($(mechanical.south|-model.north)+(0.2, 0)$) -- node[right, midway]{Specif.} ($(mechanical.south)+(0.2,0)$);
+  \draw[->] ($(mechanical.south|-model.north)+(0.15, 0)$) -- node[right, midway]{{\small Specif.}} ($(mechanical.south)+(0.15,0)$);
-  \draw[<-] ($(mechanical.south|-model.north)-(0.2, 0)$) -- node[left, midway]{3D parts}        ($(mechanical.south)-(0.2,0)$);
+  \draw[<-] ($(mechanical.south|-model.north)-(0.15, 0)$) -- node[left, midway,align=right]{{\small CAD}\\{\small model}}        ($(mechanical.south)-(0.15,0)$);
 
-  \draw[->] ($(instrumentation.south|-model.north)+(0.2, 0)$) -- node[right, midway]{Specif.} ($(instrumentation.south)+(0.2,0)$);
+  \draw[->] ($(instrumentation.south|-model.north)+(0.15, 0)$) -- node[right, midway]{{\small Specif.}} ($(instrumentation.south)+(0.15,0)$);
-  \draw[<-] ($(instrumentation.south|-model.north)-(0.2, 0)$) -- node[left, midway]{Model}         ($(instrumentation.south)-(0.2,0)$);
+  \draw[<-] ($(instrumentation.south|-model.north)-(0.15, 0)$) -- node[left, midway]{{\small Model}}         ($(instrumentation.south)-(0.15,0)$);
 
-  \draw[->] ($(testbenches.west-|model.east)+(0, 0.2)$) -- node[above, midway]{Control Laws} ($(testbenches.west)+(0, 0.2)$);
+  \draw[->] ($(mounting.west-|model.east)+(0, 0.15)$) -- node[above, midway]{{\small Requirements}} ($(mounting.west)+(0, 0.15)$);
-  \draw[<-] ($(testbenches.west-|model.east)-(0, 0.2)$) -- node[below, midway]{Refinement}   ($(testbenches.west)-(0, 0.2)$);
+  \draw[<-] ($(mounting.west-|model.east)-(0, 0.15)$) -- node[below, midway]{{\small Refinement}}   ($(mounting.west)-(0, 0.15)$);
 
-  \draw[->] ($(implementation.west-|model.east)+(0, 0.2)$) -- node[above, midway]{Control Laws} ($(implementation.west)+(0, 0.2)$);
+  \draw[->] ($(testbenches.west-|model.east)+(0, 0.15)$) -- node[above, midway]{{\small Control Laws}} ($(testbenches.west)+(0, 0.15)$);
-  \draw[<-] ($(implementation.west-|model.east)-(0, 0.2)$) -- node[below, midway]{Refinement}   ($(implementation.west)-(0, 0.2)$);
+  \draw[<-] ($(testbenches.west-|model.east)-(0, 0.15)$) -- node[below, midway]{{\small 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}}   ($(implementation.west)-(0, 0.15)$);
 
   % Main steps
-  \node[font=\bfseries, rotate=90, anchor=south, above] (conceptual_phase_node) at (dist.west) {Conceptual Phase};
+  \node[font=\bfseries, rotate=90, anchor=south, above] (conceptual_phase_node) at (dist.west) {1 - Conceptual Phase};
-  \node[font=\bfseries, above] (detailed_phase_node) at (mechanical.north) {Detail Design Phase};
+  \node[font=\bfseries, above] (detailed_phase_node) at (mechanical.north) {2 - Detail Design Phase};
-  \node[font=\bfseries, rotate=-90, anchor=south, above] (implementation_phase_node) at (testbenches.east) {Experimental Phase};
+  \node[font=\bfseries, rotate=-90, anchor=south, above] (implementation_phase_node) at (testbenches.east) {3 - Experimental Phase};
     \begin{scope}[on background layer]
-      \node[fit={(conceptual_phase_node.north|-nanohexapod.north) (mustation.south east)}, fill=lightgreen!50!white, draw, dashed, inner sep=2pt] (conceptual_phase) {};
+      \node[fit={(conceptual_phase_node.north|-nanohexapod.north) (mustation.south east)}, fill=lightgreen!50!white, draw, inner sep=2pt] (conceptual_phase) {};
-      \node[fit={(detailed_phase_node.north-|instrumentation.west) (fem.south east)}, fill=lightyellow!50!white, draw, dashed, inner sep=2pt] (detailed_phase) {};
+      \node[fit={(detailed_phase_node.north-|instrumentation.west) (fem.south east)}, fill=lightyellow!50!white, draw, inner sep=2pt] (detailed_phase) {};
-      \node[fit={(implementation_phase_node.north|-mounting.north) (implementation.south west)}, fill=lightred!50!white, draw, dashed, inner sep=2pt] (implementation_phase) {};
+      \node[fit={(implementation_phase_node.north|-mounting.north) (implementation.south west)}, fill=lightred!50!white, draw, inner sep=2pt] (implementation_phase) {};
       % \node[above left] at (dob.south east) {DOB};
     \end{scope}
 
   % Between main steps
-  \draw[mystep, dashed, postaction={decorate,decoration={raise=1ex,text along path,text align=center,text={Concept Validation}}}] (conceptual_phase.north) to[out=90, in=180] (detailed_phase.west);
+  \draw[mystep, postaction={decorate,decoration={raise=1ex,text along path,text align=center,text={Concept Validation}}}] (conceptual_phase.north) to[out=90, in=180] (detailed_phase.west);
-  \draw[mystep, dashed, postaction={decorate,decoration={raise=1ex,text along path,text align=center,text={Procurement}}}] (detailed_phase.east) to[out=0, in=90] (implementation_phase.north);
+  \draw[mystep, postaction={decorate,decoration={raise=1ex,text along path,text align=center,text={Procurement}}}] (detailed_phase.east) to[out=0, in=90] (implementation_phase.north);
 
   % % Inside Model
   % \node[inner sep=1pt, outer sep=6pt, anchor=north west, draw, fill=white, thin] (multibodymodel) at ($(model.north west) - (0, 0.5)$)