#+TITLE: Nano Active Stabilization System - Introduction
:DRAWER:
#+LANGUAGE: en
#+EMAIL: dehaeze.thomas@gmail.com
#+AUTHOR: Dehaeze Thomas

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* Build                                                             :noexport:
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* Notes                                                             :noexport:

Prefix is =introduction=

** TODO [#C] Synchrotron moore laws
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>>
#+end_src

#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init>>
#+end_src

#+begin_src matlab
brilliances = [1e7, 1e8, 5e11, 2e12, 1e14, 1e15, 1e19, 1e21, 2e22, ]
#+end_src


** TODO [#C] Complete list of Synchrotrons

| Name                   | Country          | Generation | Energy | Brightness | Status |
|------------------------+------------------+------------+--------+------------+--------|
| ESRF                   | France, Grenoble | 4th        |        |            |        |
| Soleil                 | France, Paris    | 3rd        |        |            |        |
| Diamond                | UK, Oxfordshire  | 3rd        | 3GeV   |            |        |
| ALS                    | US               |            |        |            |        |
| SLAC                   | US               |            |        |            |        |
| APS                    | US               | 4th        |        |            |        |
| NSLS II                | US, New York     | 3rd        | 3GeV   |      10^21 |        |
| Alba                   | Spain            |            |        |            |        |
| PSI                    | Switzerland      |            |        |            |        |
| Elettra                | Italy            |            |        |            |        |
| Max IV                 | Sweden           | 4th        | 3GeV   |            |        |
| DESY                   | Germany          |            |        |            |        |
| BESSY                  | Germany          |            |        |            |        |
| SESAME                 | Jordan           |            |        |            |        |
| LNLS                   | Brazil           | 4th        |        |            |        |
| HEPS                   | China            |            |        |            |        |
| NSRL                   | China            |            |        |            |        |
| SSRF                   | China            |            |        |            |        |
| Spring 8               | Japan            |            |        |            |        |
| Australian Synchrotron | Australy         |            |        |            |        |
| Canadian Light Source  | Canada           |            |        |            |        |


** TODO [#C] Review about Stewart platforms

# [[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/bibliography.org]]

- [ ] cite:li01_simul_fault_vibrat_isolat_point
- [ ] cite:bishop02_devel_precis_point_contr_vibrat
- [ ] cite:hanieh03_activ_stewar
- [ ] cite:afzali-far16_vibrat_dynam_isotr_hexap_analy_studies
- [ ] cite:naves20_desig

** TODO [#C] Review about Stewart platform control

Based on [[file:~/Cloud/work-projects/ID31-NASS/matlab/stewart-simscape/org/bibliography.org]]

Broad subject (MIMO control), maybe talk only about vibration control based on external metrology.

- Active Damping
- Decentralized
- Centralized
- Manually tuned: PID, lead lag, etc...
- Automatic / Optimal: LQG, H-Infinity

** TODO [#C] Review of two stage control

[[elisp:(helm-bibtex nil nil "Two Stage Actuator ")][Two Stage Actuator]]:
- [X] cite:&xu12_desig_devel_flexur_based_dual
- [ ] cite:&pahk01_ultra_precis_posit_system_servo_motor
- [ ] cite:&kobayashi03_phase_stabil_servo_contr_dual
  disk drive
- [ ] cite:&michellod06_strat_contr_dual_nano_system_singl_metrol
- [ ] cite:&woody06_desig_perfor_dual_drive_system
- [ ] cite:&chassagne07_nano_posit_system_with_sub
- [ ] cite:&schitter08_dual
- [X] cite:&buice09_desig_evaluat_singl_axis_precis
- [X] cite:&liu10_desig_contr_long_travel_nano_posit_stage
- [ ] cite:&ting11_contr_desig_high_frequen_cuttin
- [ ] cite:&okazaki12_dual_servo_mechan_stage_contin_posit
- [ ] cite:&ito13_high_precis_posit_system_using
- [ ] cite:&yamaguchi13_advan_high_perfor_motion_contr_mechat_system
- [ ] cite:&kim13_desig_contr_singl_stage_dual
- [ ] cite:&wu13_desig
- [ ] cite:&parmar14_large_dynam_range_nanop_using
- [ ] cite:&ito15_low_stiff_dual_stage_actuat
- [ ] cite:&qingsong16_desig_implem_large_range_compl_microp_system
- [ ] cite:&zhu17_flexur_based_paral_actuat_dual
- [ ] cite:&wang17_devel_contr_long_strok_precis_stage
- [ ] cite:&okyay18_modal_analy_metrol_error_budget
- [ ] cite:&csencsics18_system_contr_desig_voice_coil
- [ ] cite:&okyay18_mechat_desig_actuat_optim_contr
- [ ] cite:&kong18_vibrat_isolat_dual_stage_actuat
- [ ] cite:&du19_multi_actuat_system_contr
- [ ] cite:&yun20_inves_two_stage_vibrat_suppr
- [ ] cite:&mukherjee20_hybrid_contr_precis_posit_applic
- [ ] cite:&barros21_feedf_contr_piezoel_dual_actuat_system

*To read in details*:
- [X] cite:&choi08_desig_contr_nanop_xy_theta_scann
  *top*
- [X] [[cite:&buice09_desig_evaluat_singl_axis_precis]]
- [X] cite:&shinno11_newly_devel_long_range_posit
- [ ] cite:&okazaki12_dual_servo_mechan_stage_contin_posit
- [ ] cite:&shan15_contr_review
  *good review*
- [X] cite:&okyay16_mechat_desig_dynam_contr_metrol
  *Good review*
  #+begin_quote
  The alternative, sliding contact bearings are limited to 2-10 [μm] motion resolution, due to stick-slip motion [[cite:&slocum92_precis_machin_desig]], hence they are not preferred.
Stick-slip occurs due to the difference between static and dynamic coefficients of friction in such bearings, which results in an impact-like disturbance in the control system during motion reversal.
  #+end_quote
- [X] cite:&kong18_vibrat_isolat_dual_stage_actuat
  *only found example of dual stage with hexapod*
  #+begin_quote
  The coarse stage is usually actuated by VCMs or other linear motors, and the fine stage is usually actuated by piezoelectric actuators or VCMs.
  #+end_quote

#+name: tab:introduction_dual_stages
#+caption: for each example, interferometers are used as the measured stage position (and signal feedback for the short stroke actuator).
#+attr_latex: :environment tabularx :width \linewidth :align lXX
#+attr_latex: :center t :booktabs t
| DoF    | Long Stroke                     | Short Stroke  | Bandwidth     |                                                      |
|--------+---------------------------------+---------------+---------------+------------------------------------------------------|
| X,Y    | 2 axis, linear motor            | 2 piezo       |               | cite:&chassagne07_nano_posit_system_with_sub         |
| X,Y,Rz | 1 axis, iron core linear motor  | 4 VCM         | 85Hz          | cite:&choi08_desig_contr_nanop_xy_theta_scann        |
| X      | 1 axis, DC motor, feedscrew     | 1 PZT         |               | cite:&buice09_desig_evaluat_singl_axis_precis        |
| X,Y,Rz | 1 axis, ballscrew, rotary motor | 3 piezo       | 3 PID, few Hz | cite:&liu10_desig_contr_long_travel_nano_posit_stage |
| X      | 1 axis, Servo motor, ball screw | 1 VCM         |               | cite:&shinno11_newly_devel_long_range_posit          |
| X      | 1 axis, VCM                     | 1 piezo stack |               | cite:&xu12_desig_devel_flexur_based_dual             |

** TODO [#C] Make all the figures

1. [ ] [[file:figs/introduction_esrf_schematic.svg]]
   highlight Linac, Booster, Storage ring, ID31 beamline
2. [ ] Good Picture of ESRF: =introduction_esrf_picture=
3. [ ] Map with all the Synchrotrons in the World: =introduction_synchrotrons=
   Show Synchrotron going to 4th generation, Highlight ESRF
4. [ ] Synchrotron Moore law =introduction_moore_law=
5. [ ] Picture of the beam =introduction_beam_3rd_generation= and =introduction_beam_4th_generation=
6. [ ] ID31/typical beamline layout with: =introduction_id31_layout=
   - Insertion device
7. [ ] CAD view of the ID31 EH: =introduction_id31_cad=
   - Highlight focussing optics, positioning station, sample, detector
   - Show X-Y-Z vectors
8. [ ] Micro-Station with each stage in different color and associated motions
   =introduction_id31_microstation_cad=
   =introduction_id31_microstation_picture=
9. [ ] Typical experiment (ideally from ID31 experiments):
   - [ ] tomography: =introduction_exp_tomography= and =introduction_exp_tomography_image=
   - [ ] scanning: =introduction_exp_scanning= and =introduction_exp_scanning_image=
10. [ ] Typical linear stage =introduction_linear_stage=
    - Show: stepper motor, ball screw, linear guides
    - Show: straightness, flatness, etc...
11. [ ] Flexure based stage =introduction_flexure_stage=
12. [ ] NASS concept: =introduction_nass_concept_schematic=
    - 4 elements: micro-station, nano-hexapod, metrology, control system
13. [ ] NASS metrology schematic: =introduction_nass_metrology=
    - Nano-hexapod, sample, spherical mirror with flat bottom surface
    - several fiber interferometers with tracking systems (arrows showing that they can move in Rx/Ry)
14. [ ] Show some passive end-stations =introduction_pass_stations=
    - ID16b
    - ID11
15. [ ] Show active passive end-stations =introduction_acti_stations=
    - ID16a
16. [ ] Two stage control =introduction_two_stage_control=
    Schematic with the long stroke, short stroke, metrology and control architecture: trajectory generation => long stroke & short stroke + feedback on the short stroke
17. [ ] Examples of two stage control:
    - =introduction_two_stage_control_h_bridge= from [[cite:&schmidt20_desig_high_perfor_mechat_third_revis_edition]]
    - =introduction_two_stage_control_example= from [[cite:&shinno11_newly_devel_long_range_posit]]
18. [ ] Serial VS Parallel: comparison of X-Y-Rz stages
    - =introduction_kinematics_serial=
    - =introduction_kinematics_parallel=
19. [ ] Stewart platform architecture =introduction_stewart_platform=
    Maybe two pose to show that by changing the length of each strut, it is possible to change the relative position between the two plates?
    Maybe do that with Matlab and then editing with Inkscape
20. [ ] Different model types
    - =introduction_model_lumped=
    - =introduction_model_fem=
    - =introduction_model_multi_body=
21. [ ] Feedback System / Closed loop simulations =introduction_close_loop=
    - feedback model with: controller, plant, disturbances (plant output), sensor with noise, actuator with noise
22. [ ] Dynamic Error Budgeting =introduction_dyn_error_budget=
    - PSD + CPS ? => understand what are the limitations?, similar to what is in [[cite:&schmidt20_desig_high_perfor_mechat_third_revis_edition]] ?
    - Use the same signals than for the previous figure
23. [ ] About Stewart platform control? Centralized / Decentralized? MIMO / 6 SISO?

** DONE [#B] Check these papers for literature review
CLOSED: [2024-05-05 Sun 16:22]

Check these papers:
- [[elisp:(helm-bibtex nil nil "nass ")][Nano Active Stabilization System]]
- [[elisp:(helm-bibtex nil nil "esrf ")][ESRF]]
- [[elisp:(helm-bibtex nil nil "nanostage ")][Nano Positioning Stage]]


NASS:
- [X] cite:&wang12_autom_marker_full_field_hard
  Calibration of spindle run-out errors, and correct the errors in post processing, for tomography
- [X] cite:&stankevic17_inter_charac_rotat_stages_x_ray_nanot
- [X] cite:&schroer17_ptynam
- [X] cite:&nazaretski17_desig_perfor_x_ray_scann
- [X] cite:&nazaretski15_pushin_limit
- [X] cite:nazaretski22_new_kirkp_baez_based_scann

- [X] cite:&naves20_t_flex
- [X] cite:&kim13_compac_protot_appar_reduc_circl
- [X] cite:&khaled18_pract_desig_applic_model_predic_contr
- [X] cite:&holler18_omny_tomog_nano_cryo_stage
- [X] cite:&holler17_omny_pin_versat_sampl_holder
- [X] cite:&engblom18_nanop_resul
- [X] cite:&dehaeze18_sampl_stabil_for_tomog_exper
- [X] HXN [[cite:&xu23_high_nsls_ii]]
  Laser interferometers on reference ring (on top of rotary stage).
  Used to trigger the detectors (ptychography, microscope)

ESRF:
- [X] cite:raimondi21_commis_hybrid_multib_achrom_lattic
- [X] cite:cotte17_id21_x_ray_infrar_micros
- [X] cite:martinez-criado16_id16b
- [X] cite:villar18_nanop_esrf_id16a_nano_imagin_beaml
- [X] cite:riekel10_progr_micro_nano_diffr_at
- [X] cite:wright20_new_oppor_at_mater_scien
- [X] cite:leake19_nanod_beaml_id01
- [X] cite:versteegen23_inser_devic_contr
- [X] cite:marion04_hexap_esrf
- [X] cite:fajardo95_contr_six_degree_paral_manip
- [X] cite:cammarata09_chopp_system_time_resol_exper
- [X] cite:dabin02_mechan_desig_high_precis_posit
- [X] cite:dabin03_precis_mechan_high_accur_beaml
- [X] cite:guijarro17_bliss_exper_contr_esrf_ebs_beaml
- [X] cite:janvier13_icepap
- [X] cite:baker18_esrf_doubl_cryst_monoc_protot_projec
- [X] cite:dabin04_mecan
- [X] cite:reichert21_stiff_hexap
- [X] cite:dehaeze21_mechat_approac_devel_nano_activ_stabil_system
- [X] cite:brumund21_multib_simul_reduc_order_flexib_bodies_fea
- [X] cite:dehaeze21_activ_dampin_rotat_platf_using
- [X] cite:zhang96_groun_vibrat_orme_meris_super_esrf
- [X] cite:zelenika04_flexur_use_elast_sr_instr_desig
- [X] cite:youness20_concep
- [X] cite:ravy18_shinin_light_synch_light
- [X] cite:dimper15_esrf_upgrad_progr_phase_ii
- [X] cite:dehaeze18_sampl_stabil_for_tomog_exper
- [X] cite:dabin04_mecan
- [X] cite:brendike19_esrf_doubl_cryst_monoc_protot_contr_concep

nanostage:
- [X] cite:&yong16_mechan_desig_high_speed_nanop_system
- [X] cite:&lee17_compac_compl_paral_xy_nano
- [X] cite:&awtar13_desig_large_range_xy_nanop_system
- [X] cite:&liu18_desig_trajec_track_contr_piezoel
- [X] cite:&yong09_desig_ident_contr_flexur_based
- [X] cite:&fleming10_integ_strain_force_feedb_high
- [X] cite:&barillot99_desig_funct_tests_xy_piezoel

** DONE [#C] Table that compares nano positioning stations with metrology / feedback
CLOSED: [2024-05-05 Sun 11:55]

- [X] ID16a: capacitive sensors, short stroke, spindle above the fix hexapod, light samples [[cite:&villar18_nanop_esrf_id16a_nano_imagin_beaml]]
- [X] Soleil Nano probe [[cite:&engblom18_nanop_resul;&stankevic17_inter_charac_rotat_stages_x_ray_nanot]]
- [X] PSI OMNY [[cite:&holler18_omny_tomog_nano_cryo_stage;&holler17_omny_pin_versat_sampl_holder]]
  [[cite:&holler15_error_motion_compen_track_inter;&holler12_instr_x_ray_nano_imagin]]
- [X] DESY PETRA III /PtyNAMi/ [[cite:&schropp20_ptynam;&schroer17_ptynam;&schroeck01_compen_desig_linear_time_invar]]
  scanning microscope and tomography
  tracking the mechanical stability of optics relative to the sample scanner
  laser interferometer system to track the sample in the two directions transverse to the optical axis
  #+begin_quote
  For scanning microscopy and tomography it is essential to know where the beam hits the sample.
  Position uncertainties can arise from vibrations of the focusing optics and of the sample.
  The sample is scanned through the nanobeam, while the optics are kept fixed after initial alignment.
  #+end_quote
  Interferometers used for monitoring, not for closed-loop control
- [ ] APS/Diamond:
- [X] cite:&wang12_autom_marker_full_field_hard
  Calibration of spindle run-out errors, and correct the errors in post processing, for tomography
- [X] [[cite:&geraldes23_sapot_carnaub_sirius_lnls]]
  SIRIUS, LNLS
  #+begin_quote
Synchrotron scanning X-ray microscopes are generally based on piezo scanning stages, with motion range typically
limited to 100 µm, such that complementary long-stroke stages, with motion range of several millimeters, are often
required to comply with alignment and the search of regions of interest in typical millimeter-size samples or sample
mounts [3, 5–13, 15, 16]. However, potential limitations in this architecture include: 1) limited dynamics and stability,
with resonance modes in the order of 100 Hz (or less) resulting from multiple stacked stages; 2) parasitic motion
associated with coarse stages; and 3) deteriorated performance in continuous fly-scan beyond the piezo range, which
are caused by disturbances introduced by stepper motors or stick-slip piezos [43].
  #+end_quote
- [X] Delta robot, diamond [[cite:&kelly22_delta_robot_long_travel_nano]]

Bandwidth is rarely specified

Same table for nano positioning stages without integrated metrology?


* Context of this thesis
** Synchrotron Radiation Facilities
**** Accelerating electrons to produce intense X-ray

- Explain what is a Synchrotron: light source
- Say how many there are in the world (~50)

#+name: fig:introduction_synchrotrons
#+caption: 4th generation Synchrotrons in operation (red). Upgrade or new 4th generation projects (green). 3rd generation Synchrotrons (blue).
#+attr_latex: :width \linewidth
[[file:figs/introduction_synchrotrons.png]]

- Electron part: LINAC, Booster, Storage Ring ref:fig:introduction_esrf_schematic
- Synchrotron radiation: Insertion device / Bending magnet
- Many beamlines (large diversity in terms of instrumentation and science)
- Science that can be performed:
  - structural biology, structure of materials, matter at extreme, ...


**** The European Synchrotron Radiation Facility

#+name: fig:fig_label
#+caption: Caption with reference to sub figure (\subref{fig:fig_label_a})
#+attr_latex: :options [htbp]
#+begin_figure
#+attr_latex: :caption \subcaption{\label{fig:introduction_esrf_schematic}Schematic of the ESRF - Over 40 beamlines. Booster, Linac, storage ring}
#+attr_latex: :options {0.49\textwidth}
#+begin_subfigure
#+attr_latex: :width 0.95\linewidth
[[file:figs/introduction_esrf_schematic.png]]
#+end_subfigure
#+attr_latex: :caption \subcaption{\label{fig:introduction_esrf_picture}European Synchrotron Radiation Facility}
#+attr_latex: :options {0.49\textwidth}
#+begin_subfigure
#+attr_latex: :width 0.95\linewidth
[[file:figs/introduction_esrf_picture.jpg]]
#+end_subfigure
#+end_figure

**** 3rd and 4th generation Synchrotrons

Brilliance: figure of merit for synchrotron

- 4th generation light sources
  - [[cite:&raimondi21_commis_hybrid_multib_achrom_lattic]]
  - [ ] Picture of 3rd generation "beam source" vs 4th generation?
- [ ] Picture showing Synchrotron "moore's law"

#+name: fig:introduction_moore_law
#+caption: Figure caption
[[file:figs/introduction_moore_law.pdf]]



** The ID31 ESRF Beamline
**** Beamline Layout

- [ ] Beamline layout (OH, EH)
- ID31 and Micro Station (Figure ref:fig:introduction_id31_microstation_picture)
  Check https://www.esrf.fr/UsersAndScience/Experiments/StructMaterials/ID31
  https://www.wayforlight.eu/beamline/23244
- X-ray beam + detectors + sample stage (Figure ref:fig:introduction_id31_beamline_schematic)
- Focusing optics
- Optical schematic with: source, lens, sample and detector.
  Explain that what is the most important is the relative position between the sample and the lens.
- Explain the XYZ frame for all the thesis (ESRF convention: X: x-ray, Z gravity up)
  - [ ] Add XYZ on figure ref:fig:introduction_id31_cad

#+begin_src latex :file id31_microstation_picture.pdf
\begin{tikzpicture}
  \node[inner sep=0pt, anchor=south west] (photo) at (0,0)
  {\includegraphics[width=0.39\textwidth]{/home/thomas/Cloud/documents/reports/phd-thesis/figs/exp_setup_photo.png}};

  \coordinate[] (aheight) at (photo.north west);
  \coordinate[] (awidth)  at (photo.south east);

  \coordinate[] (granite) at ($0.1*(aheight)+0.1*(awidth)$);
  \coordinate[] (trans)   at ($0.5*(aheight)+0.4*(awidth)$);
  \coordinate[] (tilt)    at ($0.65*(aheight)+0.75*(awidth)$);
  \coordinate[] (hexapod) at ($0.7*(aheight)+0.5*(awidth)$);
  \coordinate[] (sample)  at ($0.9*(aheight)+0.55*(awidth)$);

  % Granite
  \node[labelc] at (granite) {1};
  % Translation stage
  \node[labelc] at (trans) {2};
  % Tilt Stage
  \node[labelc] at (tilt) {3};
  % Micro-Hexapod
  \node[labelc] at (hexapod) {4};
  % Sample
  \node[labelc] at (sample) {5};

  % Axis
  \begin{scope}[shift={($0.07*(aheight)+0.87*(awidth)$)}]
    \draw[->] (0, 0) -- ++(55:0.7) node[above] {$y$};
    \draw[->] (0, 0) -- ++(90:0.9) node[left] {$z$};
    \draw[->] (0, 0) -- ++(-20:0.7) node[above] {$x$};
  \end{scope}
\end{tikzpicture}
#+end_src

#+name: fig:introduction_id31_cad
#+caption: CAD view of the optical hutch with the nano-focusing optics, the micro-station
#+attr_latex: :width 0.8\linewidth
[[file:figs/introduction_id31_cad.jpg]]

**** Positioning End Station: The Micro-Station

Micro-Station:
- DoF with strokes: Ty, Ry, Rz, Hexapod
- Experiments: tomography, reflectivity, truncation rod, ...
  Make a table to explain the different "experiments"
- Explain how it is used (positioning, scans), what it does. But not about the performances
- Different sample environments

#+begin_src latex :file id31_beamline_schematic.pdf
  \begin{tikzpicture}
    % Parameters
    \def\blockw{6.0cm}
    \def\blockh{1.2cm}

    \def\tiltdeg{3}
    \coordinate[] (rotationpoint) at (0, 4.5*\blockh);

    \begin{scope}[rotate around={\tiltdeg:(rotationpoint)}]
      % Tilt
      \path[] ([shift=(-120:4*\blockh)]rotationpoint) coordinate(beginarc) arc (-120:-110:4*\blockh) %
      -- ([shift=(-70:4*\blockh)]rotationpoint) arc (-70:-60:4*\blockh)%
      |- ++(-0.15*\blockw, 0.6*\blockh) coordinate (spindlene)%
      |- ($(beginarc) + (0.15*\blockw, 0.2*\blockh)$) coordinate (spindlesw) -- ++(0, 0.4*\blockh) coordinate(tiltte) -| cycle;

      % Spindle
      \coordinate[] (spindlese) at (spindlesw-|spindlene);
      \draw[fill=black!30] ($(spindlese)+(-0.1,0.1)+(-0.1*\blockw, 0)$) -| ($(spindlene)+(-0.1, 0)$) -| coordinate[pos=0.25](spindletop) ($(spindlesw)+(0.1,0.1)$) -| ++(0.1*\blockw, -\blockh) -| coordinate[pos=0.25](spindlebot) cycle;

      % \draw[dashed, color=black!60] ($(spindletop)+(0, 0.2)$) -- ($(spindlebot)+(0,-0.2)$);

      % Tilt
      \draw[fill=black!60] ([shift=(-120:4*\blockh)]rotationpoint) coordinate(beginarc) arc (-120:-110:4*\blockh) %
      -- ([shift=(-70:4*\blockh)]rotationpoint) arc (-70:-60:4*\blockh)%
      |- coordinate (tiltne) ++(-0.15*\blockw, 0.6*\blockh) coordinate (spindlene)%
      |- ($(beginarc) + (0.15*\blockw, 0.2*\blockh)$) coordinate (spindlesw) -- ++(0, 0.4*\blockh) -| cycle;

      % Micro-Hexapod
      \begin{scope}[shift={(spindletop)}]
        % Parameters definitions
        \def\baseh{0.22*\blockh} % Height of the base
        \def\naceh{0.18*\blockh} % Height of the nacelle
        \def\baser{0.22*\blockw} % Radius of the base
        \def\nacer{0.18*\blockw} % Radius of the nacelle

        \def\armr{0.2*\blockh} % Radius of the arms
        \def\basearmborder{0.2}
        \def\nacearmborder{0.2}

        \def\xnace{0} \def\ynace{\blockh-\naceh} \def\anace{0}
        \def\xbase{0} \def\ybase{0} \def\abase{0}

        % Hexapod1
        \begin{scope}[shift={(\xbase, \ybase)}, rotate=\abase]
          % Base
          \draw[fill=white] (-\baser, 0) coordinate[](uhexabot) rectangle (\baser, \baseh);

          \coordinate[] (armbasel) at (-\baser+\basearmborder+\armr, \baseh);
          \coordinate[] (armbasec) at (0, \baseh);
          \coordinate[] (armbaser) at (\baser-\basearmborder-\armr, \baseh);

          \begin{scope}[shift={(\xnace, \ynace)}, rotate=\anace]
            \draw[fill=white] (-\nacer, 0) rectangle (\nacer, \naceh);
            \coordinate[] (uhexatop) at (0, \naceh);
            \coordinate[] (armnacel) at (-\nacer+\nacearmborder+\armr, 0);
            \coordinate[] (armnacec) at (0, 0);
            \coordinate[] (armnacer) at (\nacer-\nacearmborder-\armr, 0);
          \end{scope}

          \draw[] (armbasec) -- (armnacer);
          \draw[] (armbasec) -- (armnacel);
          \draw[] (armbasel) -- coordinate(mhexaw) (armnacel);
          \draw[] (armbasel) -- (armnacec);
          \draw[] (armbaser) -- (armnacec);
          \draw[] (armbaser) -- coordinate(mhexae) (armnacer);
        \end{scope}
      \end{scope}

      % Sample
      \begin{scope}[shift={(uhexatop)}]
        \draw[fill=white] (-0.1*\blockw, 0) coordinate[](samplebot) rectangle coordinate[pos=0.5](samplecenter) node[pos=0.5, above]{Sample} (0.1*\blockw, \blockh) coordinate[](samplene);
        \coordinate[](samplenw) at (-0.1*\blockw, \blockh);
      \end{scope}
    \end{scope}

    \begin{scope}[shift={(0, -0.3*\blockh)}]
      % Translation Stage - fixed part
      \draw[fill=black!40] (-0.5*\blockw, 0) coordinate[](tyb) rectangle (0.5*\blockw, 0.15*\blockh);
      \coordinate[] (measposbot) at (0.5*\blockw, 0);

      % Translation Stage - mobile part
      \draw[fill=black!10, fill opacity=0.5] (-0.5*\blockw, 0.2*\blockh) -- (-0.5*\blockw, 1.5*\blockh) coordinate[](tyt) -- (0.5*\blockw, 1.5*\blockh) -- (0.5*\blockw, 0.2*\blockh) -- (0.35*\blockw, 0.2*\blockh) -- (0.35*\blockw, 0.8*\blockh) -- (-0.35*\blockw, 0.8*\blockh) -- (-0.35*\blockw, 0.2*\blockh) -- cycle;

      % Translation Guidance
      \draw[dashed, color=black!60] ($(-0.5*\blockw, 0)+( 0.075*\blockw,0.5*\blockh)$) circle (0.2*\blockh);
      \draw[dashed, color=black!60] ($( 0.5*\blockw, 0)+(-0.075*\blockw,0.5*\blockh)$) circle (0.2*\blockh);

      % Tilt Guidance
      \draw[dashed, color=black!60] ([shift=(-107:4.1*\blockh)]rotationpoint) arc (-107:-120:4.1*\blockh);
      \draw[dashed, color=black!60] ([shift=( -73:4.1*\blockh)]rotationpoint) arc (-73:-60:4.1*\blockh);
    \end{scope}

    % % Vertical line
    % \draw[dashed, color=black] (samplecenter) -- ++(0, -4*\blockh);
    % \begin{scope}[rotate around={\tiltdeg:(samplecenter)}]
    %   \draw[dashed, color=black] (samplecenter) -- ++(0, -4*\blockh);
    %   \node[] at ($(samplecenter)+(0, -2.3*\blockh)$) {\AxisRotator[rotate=-90]};
    %   \node[right, shift={(0.3,0)}] at ($(samplecenter)+(0, -2.3*\blockh)$) {$\theta_z$};
    % \end{scope}
    % \draw[->] ([shift=(-90:3.6*\blockh)]samplecenter) arc (-90:-87:3.6*\blockh) node[right]{$\theta_y$};

    % Laser
    \begin{scope}[shift={(samplecenter)}]
      \draw[color=red, -<-=0.3] (samplecenter) node[circle, fill=red, inner sep=0pt, minimum size=3pt]{} -- node[pos=0.3, above, color=black]{X-ray} ($(samplecenter)+(1.2*\blockw,0)$);
    \end{scope}

    % Axis
    \begin{scope}[shift={(-0.35*\blockw, 3*\blockh)}]
      \def\axissize{0.8cm}
      \draw[->] (0, 0) -- ++(0, \axissize) node[right]{$z$};
      \draw[->] (0, 0) -- ++(-\axissize, 0) node[above]{$x$};
      \draw[fill, color=black] (0, 0) circle (0.05*\axissize);
      \node[draw, circle, inner sep=0pt, minimum size=0.4*\axissize, label=right:$y$] (yaxis) at (0, 0){};
      % \node[draw, circle, inner sep=0pt, cross, minimum size=0.4*\axissize, label=left:$y$] (yaxis) at (0, 0){};
    \end{scope}

    \node[fit={($(-0.6*\blockw, -0.5*\blockh)$) ($(0.6*\blockw, 4*\blockh)$)}, inner sep=0pt, draw, dashed, color=gray, label={Positioning Station}] (possystem) {};

    \draw[fill=black!30] ($(tyb)+(-5, -1)$) coordinate[](granitesw) rectangle node[pos=0.5]{Granite Frame} ($(measposbot)+(5, 0)$) coordinate[](granitene);

    % Focusing Optics
    \draw[fill=black!20] ($(granitene)+(-1.5, 3)$) rectangle ++(-1, 2);
    \draw[spring] ($(granitene)+(-2, 0)$) -- ++(0, 3);

    \node[fit={($(granitene)+(-2.8, -0.2)$) ($(granitene)+(-1.2, 5.2)$)}, inner sep=0pt, draw, dashed, color=gray, label={Focusing Optics}] () {};

    % Measurement Optics
    \draw[fill=black!20] ($(granitesw)+(1.5, 4)$) rectangle ++(1, 2);
    \draw[spring] ($(granitesw)+(2, 1)$) -- ++(0, 3);

    \node[fit={($(granitesw)+(2.8, 0.8)$) ($(granitesw)+(1.2, 6.2)$)}, inner sep=0pt, draw, dashed, color=gray, label={Imagery System}] () {};
  \end{tikzpicture}
#+end_src

- Alternative: =id31_microstation_cad_view.png= (CAD view)

#+name: fig:introduction_id31_microstation_picture
#+caption: Picture of the ID31 Micro-Station with annotations
#+attr_latex: :width 0.49\linewidth
#+RESULTS:
[[file:figs/introduction_id31_microstation_picture.png]]

**** Science performed on ID31

- Few words about science made on ID31 and why nano-meter accuracy is required
- Typical experiments (tomography, ...), various samples (up to 50kg), sample environments (high temp, cryo, etc..)
  - Alignment of the sample, then
  - Reflectivity
  - Tomography
  - Diffraction tomography: most critical
- Example of picture obtained (Figure ref:fig:introduction_id31_tomography_result) with resolution


=introduction_exp_scanning= and =introduction_exp_scanning_image=

#+name: fig:introduction_id31_tomography_result
#+caption: Image obtained on the ID31 beamline
#+attr_latex: :width 0.49\linewidth
[[file:example-image-c.png]]

** Need of accurate positioning end stations with high dynamics
**** A push towards brighter and smaller beams...

Improvement of both the light source and the instrumentation:
- EBS: smaller source + higher flux ref:fig:introduction_beam_ebs

#+name: fig:introduction_beam_ebs
#+caption: View of the ESRF X-ray beam before the EBS upgrade (top) and after the EBS upgrade (bottom)
[[file:figs/introduction_beam_ebs.png]]


- Better focusing optic (add some links): beam size in the order of 10 to 20nm FWHM (reference) ref:fig:introduction_moore_law_focus
  crossed silicon compound refractive lenses, KB mirrors [17], zone plates [18], or multilayer Laue lenses [19]
  [[cite:&barrett16_reflec_optic_hard_x_ray]]

#+name: fig:introduction_moore_law_focus
#+caption: Figure caption
[[file:figs/introduction_moore_law_focus.png]]

Higher flux density (+high energy of the ID31 beamline) => Radiation damage: needs to scan the sample quite fast with respect to the focused beam

- Allowed by better detectors: higher sampling rates and lower noise => possible to scan fast
  [[cite:&hatsui15_x_ray_imagin_detec_synch_xfel_sourc]]

**** ...Requires the use of dynamical positioning
"from traditional step by step scans to /fly-scan/"

Fast scans + needs of high accuracy and stability => need mechatronics system with:
- accurate metrology
- multi degree of freedom positioning systems
- fast feedback loops

Shift from step by step scan to /fly-scan/ cite:huang15_fly_scan_ptych
- Much lower pixel size + large image => takes of lot of time if captured step by step.
  Explain what is step by step scanning: move motors from point A to point B, stops, start detector acquisition, open shutter , close the shutter, move to point C, ...

[[cite:&xu23_high_nsls_ii]]
#+begin_quote
In traditional step scan mode, each exposure position requires the system to stop prior to data acquisition, which may become a limiting factor when fast data collection is required.
Fly-scanning is chosen as a preferred solution that helps overcome such speed limitations [5, 6].
In fly-scan mode, the sample keeps moving and a triggering system generates trigger signals based on the position of the sample or the time elapsed.
The trigger signals are used to control detector exposure.
#+end_quote

- [ ] Make picture representing a typical experiment (maybe YZ scan?) with:
  Probably already shown earlier =introduction_exp_scanning=
  - nano focusing optics (see the beam focused)
  - positioning stage with displayed YZ motion (pixel by pixel in the YZ plane)
  - detector

Subject of this thesis: design of high performance positioning station with high dynamics and nanometer accuracy

* Challenge definition
** Multi DoF, Highly accurate, and Long stroke positioning end station?
**** Performance limitation of "stacked stages" end-stations

Typical positioning end station:
- stacked stages
- ballscrew, linear guides, rotary motor


Explain the limitation of performances:
- Backlash, play, thermal expansion, guiding imperfections, ...
- Give some numbers: straightness of the Ty stage for instance, change of $0.1^oC$ with steel gives x nm of motion
- Vibrations
- Explain that this micro-station can only have ~10um of accuracy due to physical limitation
- Possibility to have linear/rotary encoders that correct the motion in the considered DoF, but does not change anything to the other 5DoF


Talk about flexure based positioning stations?
Advantages: no backlash, etc...
But: limited to short stroke
Picture of schematic of one positioning station based on flexure

**** The ID31 Micro-Station

Presentation of the Micro-Station in details ref:fig:introduction_id31_microstation_cad:
- Goal of each stage (e.g. micro-hexapod: static positioning, Ty and Rz: scans, ...)
- Stroke
- Initial design objectives: as stiff as possible, smallest errors as possible

**** New positioning requirements

- To benefits from nano-focusing optics, new source, etc... new positioning requirements
- Positioning requirements on ID31:
  - Maybe make a table with the requirements and the associated performances of the micro-station
  - Make tables with the wanted motion, stroke, accuracy in different DoF, etc..
- Sample masses

The goal in this thesis is to increase the positioning accuracy of the micro-station to fulfil the initial positioning requirements.

*Goal*: Improve accuracy of 6DoF long stroke position platform

** The Nano Active Stabilization System
**** NASS Concept

Briefly describe the NASS concept.
4 parts:
- Micro Station
- multi-DoF positioning system with good dynamics
- 5DoF metrology system
- Control system and associated instrumentation

6DoF vibration control platform on top of a complex positioning platform that correct positioning errors based on an external metrology

- [ ] Add the control system in the schematic

#+name: fig:introduction_nass_concept_schematic
#+caption: Nass Concept. 1: micro-station, 2: nano-hexapod, 3: sample, 4: 5DoF metrology
[[file:figs/introduction_nass_concept_schematic.png]]

**** Metrology system

Requirements:
- 5 DoF
- long stroke
- nano-meter accurate
- high bandwidth

The accuracy of the NASS will only depend on the accuracy of the metrology system.

Concept:
- Fiber interferometers
- Spherical reflector with flat bottom
- Tracking system

Complex mechatronics system on its own.

This metrology system is not further discussed in this thesis as it is still under active development.

In the following of this thesis, it is supposed that the metrology system is accurate, etc..

- Say that there are several high precision sensors, but only interferometers for long stroke / high accuracy?

**** Multi-DoF Positioning stage for error compensation

- 5 DoF
- High dynamics
- nano-meter capable (no backlash,)
- Accept payloads up to 50kg

**** MIMO robust control strategies

Explain the robustness need?
- 24 7/7 ...
- That is why most of end-stations are based on well-proven design (stepper motors, linear guides, ball bearing, ...)
- Plant uncertainty: many different samples, use cases, rotating velocities, etc...

Trade-off between robustness and performance in the design of feedback system.

** Predictive Design

- The performances of the system will depend on many factors:
  - sensors
  - actuators
  - mechanical design
  - achievable bandwidth
  - ...
- Need to evaluate the different concepts, and predict the performances to guide the design
- The goal is to design, built and test this system such that it work as expected the first time.
  Very costly system, so much be correct.

** Control Challenge

High bandwidth, 6 DoF system for vibration control, fixed on top of a complex multi DoF positioning station, robust, ...

- Many different configurations (tomography, Ty scans, slow fast, ...)
- Complex MIMO system. Dynamics of the system could be coupled to the complex dynamics of the micro station
- Rotation aspect, gyroscopic effects, actuators are rotating with respect to the sensors
- Robustness to payload change: very critical.
  Say that high performance systems (lithography machines, etc...) works with calibrated payloads.
  Being robust to change of payload inertia means large stability margins and therefore less performance.

* Literature Review
** Nano Positioning end-stations
**** End Station with Stacked Stages

Stacked stages:
- errors are combined

To have acceptable performances / stability:
- limited number of stages
- high performances stages (air bearing etc...)

Examples:
- ID16b [[cite:&martinez-criado16_id16b]]
- ID13 [[cite:&riekel10_progr_micro_nano_diffr_at]]
- ID11 cite:wright20_new_oppor_at_mater_scien
- ID01 [[cite:&leake19_nanod_beaml_id01]]
- [ ] Maybe make a table to compare stations

Explain limitations => Thermal drifts, run-out errors of spindles (improved by using air bearing), straightness of translation stages, ...

**** Online Metrology and Active Control of Positioning Errors

The idea of having an external metrology to correct for errors is not new.

- To have even better performances: online metrology are required.
- Several strategies:
  - only used for measurements (post processing)
  - for calibration
  - for triggering detectors
  - for real time positioning control



- [ ] HXN [[cite:&xu23_high_nsls_ii]]
  Laser interferometers on reference ring (on top of rotary stage).
  Used to trigger the detectors (ptychography, microscope)
  Similar to cite:&wang12_autom_marker_full_field_hard

#+name: tab:introduction_sample_stages
#+caption: Table caption
#+attr_latex: :environment tabularx :width \linewidth :align lllllllX
#+attr_latex: :center t :booktabs t
| Architecture                                  | Sensors and measured DoFs            | Actuators and controlled DoFs | Institute, BL  | OL/CL (bandwidth)   | Stroke, DoF           | Samples      | Ref                                                                              |
|-----------------------------------------------+--------------------------------------+-------------------------------+----------------+---------------------+-----------------------+--------------+----------------------------------------------------------------------------------|
| XYZ, Spherical retroreflector, Sample         | 3 interferometers[fn:1], Y,Z         | YZ piezo stages               | PETRA III, P06 | OL                  | 100um                 | light        | [[cite:&schroer17_ptynam;&schropp20_ptynam]]                                         |
| Spindle / Metrology Ring / XYZ Stage / Sample | 3 Capacitive, Y,Z,Rx                 |                               | NSLS, X8C      | OL, post processing |                       | micron scale | cite:&wang12_autom_marker_full_field_hard                                        |
| *Hexapod* / Spindle / Metrology Ring / Sample | 12 Capacitive[fn:4], X,Y,Z,Rx,Ry     | Piezo (Hexapod)               | ESRF, ID16a    | CL, 10Hz bandwidth  | 50um, 500urad         | light        | [[cite:&villar18_nanop_esrf_id16a_nano_imagin_beaml]]                                |
| XYZ, Rz, XY, Cylindrical reference            | 5 interferometers[fn:3], X,Y,Z,Rx,Ry | XYZ linear motors             | Soleil         | CL                  |                       | light        | [[cite:&engblom18_nanop_resul;&stankevic17_inter_charac_rotat_stages_x_ray_nanot]]   |
| XYZ, Rz, XYZ Spherical reference              | 3 Interferometers[fn:2], Y,Z,Rx      | XYZ parallel piezo stage      | PSI, OMNY      | CL                  | 400um                 | light        | [[cite:&holler18_omny_tomog_nano_cryo_stage;&holler17_omny_pin_versat_sampl_holder]] |
| XYZ, mirrors/sample                           | 3 interferometers[fn:3], XYZ         | XYZ piezo stage               | APS            | CL, 3 PID           | 3mm                   | light        | [[cite:&nazaretski15_pushin_limit]]                                                  |
| Rz, Parallel XYZ stage                        | 3 interferometers[fn:1]              | 3xVCM parallel stage          | LNLS, CARNAUBA | CL, 100Hz bandwidth | YZ: 3mm, Rz: +-110deg | light        | [[cite:&geraldes23_sapot_carnaub_sirius_lnls]]                                       |
| Parallel XYZ stage                            | 3 interferometers[fn:2], XYZ         | 3xVCM parallel stage          | Diamond, I14   | CL, 100Hz bandwidth | XYZ: 3mm              | up to 350g   | [[cite:&kelly22_delta_robot_long_travel_nano]]                                       |

- [ ] Figure with different stages
- [ ] Compared to the existing stages (see table), what are the challenges here? Rotation, large stroke, light to heavy payloads, lots of DoF (5 to be controlled)
- [ ] Comparison with NASS?
| Architecture            | Sensors            | Actuators | Institute, BL | OL/CL (bandwidth) | Stroke, DoF      | Samples    | Ref |
|-------------------------+--------------------+-----------+---------------+-------------------+------------------+------------+-----|
| Ty,Ry,Rz,Hexapod,Sample | 6+ Interferometers |           | ESRF, ID31    | CL                | Ty, Ry, Rz, Hexa | up to 50kg |     |


**** Long Stroke - Short Stroke architecture

Speak about two stage control?
- Long stroke + short stroke
- Usually applied to 1dof, 3dof (show some examples: disk drive, wafer scanner)
- Any application in 6DoF? Maybe new!
- In the table, say which ones are long stroke / short stroke. Some new stages are just long stroke (voice coil)

** Multi-DoF dynamical positioning stations
**** Serial and Parallel Kinematics

Example of several dynamical stations:
- XYZ piezo stages
- Delta robot? Octoglide?
- Stewart platform

Serial vs parallel kinematics (table?)

**** Stewart platforms

- [ ] Explain the normal stewart platform architecture
- [ ] Make a table that compares the different stewart platforms for vibration control.
  Geometry (cubic), Actuator (soft, stiff), Sensor, Flexible joints, etc.

#+name: fig:introduction_stewart_platform_examples
#+caption: Examples of Stewart Platforms
#+begin_figure
#+name: fig:introduction_stewart_platform_a
#+attr_latex: :caption \subcaption{Stewart platform based on voice coil actuators}
#+attr_latex: :options {0.49\textwidth}
#+begin_subfigure
#+attr_latex: :width 0.8\linewidth
[[file:example-image-a.png]]
#+end_subfigure
#+name: fig:introduction_stewart_platform_a
#+attr_latex: :options {0.49\textwidth}
#+attr_latex: :caption \subcaption{Stewart platform based on piezoelectric actuators}
#+begin_subfigure
#+attr_latex: :width 0.8\linewidth
[[file:example-image-b.png]]
#+end_subfigure
#+end_figure

** Mechatronics approach
**** Predicting performances using models

- [[cite:&monkhorst04_dynam_error_budget]]
  #+begin_quote
  high costs of the design process: the designed system must be *first time right*.
  When the system is finally build, its performance level should satisfy the specifications.
  No significant changes are allowed in the post design phase.
  Because of this, the designer wants to be able to predict the performance of the system a-priori and gain insight in the performance limiting factors of the system.
  #+end_quote


Can use several models:
- Lumped mass-spring-damper models
  cite:rankers98_machin
- Multi-Body Models
- Finite element models
  Sub structuring?

**** Closed-Loop Simulations

[[cite:&schmidt20_desig_high_perfor_mechat_third_revis_edition]]

Say what can limit the performances for a complex mechatronics systems as this one:
- disturbances
- measurement noise
- DAC / amplifier noise (actuator)
- feedback system / bandwidth

Simulations can help evaluate the behavior of the system.

**** Dynamic Error Budgeting

- [[cite:&monkhorst04_dynam_error_budget]]
  #+begin_quote
  high costs of the design process: the designed system must be *first time right*.
  When the system is finally build, its performance level should satisfy the specifications.
  No significant changes are allowed in the post design phase.
  Because of this, the designer wants to be able to predict the performance of the system a-priori and gain insight in the performance limiting factors of the system.
  #+end_quote
- cite:jabben07_mechat
- [[cite:&okyay16_mechat_desig_dynam_contr_metrol]]
  #+begin_quote
Error budgets [23] are frequently used in the design of precision machines, in order to assess the
contributions of different factors such as parasitic motions, thermal expansion, and servo accuracy, on
the positioning accuracy of a machine. Dynamic Error Budgeting (DEB) or ‘Spectral Analysis’
extends this concept to the realm of feedback control. Recognizing that the controller can provide
only a finite attenuation of disturbance signals interfering with the servo, DEB provides a
methodology for predicting the cumulative effect of such signals on the control error as a function of
their spectral (frequency) content. The method can be used to predict the control accuracy of a system
implemented using a set of certain devices under certain conditions before it is realized. Furthermore,
as it is formulated in the frequency domain, it can be used to optimize the controller design as well,
typically leading to an H2 - optimal control framework. In DEB, the disturbance signals are modeled
with their power spectral density (PSD), assuming that they are stationary stochastic processes which
are not correlated with each other. Then, these PSD’s are transmitted to the performance goal, most
often the positioning error, using linear time invariant (LTI) system theory. The transmitted PSD’s are
summed up into the variance of the performance goal, which constitutes a comparative measure of
performance. Most importantly, the influence of different dynamic factors and disturbance sources,
which have the greatest impact on the achievable performance (e.g., accuracy) can be easily spotted
and improved, through this kind of analysis. An approach similar to DEB was followed to decompose
the contribution of different noise sources on the hard disk position error in [1], [2], [45]. DEB has
been used to assess the performance of a geophone and a vibration isolation system in [75]. Jabben
[49] has used DEB in the mechatronic design of a magnetically suspended rotating platform. Aguirre
et al. [3] have analyzed the performance of active aerostatic thrust bearings using DEB.
  #+end_quote

** TODO Control architecture

Maybe make a simple review of control strategies for Stewart platform control.

* Original Contributions
**** Introduction                                                  :ignore:

This thesis proposes several contributions in the fields of Control, Mechatronics Design and Experimental validation.

**** Active Damping of rotating mechanical systems using Integral Force Feedback

[[cite:&dehaeze20_activ_dampin_rotat_platf_integ_force_feedb;&dehaeze21_activ_dampin_rotat_platf_using]]
#+begin_quote
This paper investigates the use of Integral Force Feedback (IFF) for the active damping of rotating mechanical systems.
Guaranteed stability, typical benefit of IFF, is lost as soon as the system is rotating due to gyroscopic effects.
To overcome this issue, two modifications of the classical IFF control scheme are proposed.
The first consists of slightly modifying the control law while the second consists of adding springs in parallel with the force sensors.
Conditions for stability and optimal parameters are derived.
The results reveal that, despite their different implementations, both modified IFF control scheme have almost identical damping authority on the suspension modes.
#+end_quote

**** Design of complementary filters using $\mathcal{H}_\infty$ Synthesis and sensor fusion

[[cite:&dehaeze19_compl_filter_shapin_using_synth]]
[[cite:&verma20_virtual_sensor_fusion_high_precis_contr]]
[[cite:&tsang22_optim_sensor_fusion_method_activ]]

- Several uses (link to some papers).
- For the NASS, they could be use to further improve the robustness of the system.

**** Multi-body simulations with reduced order flexible bodies obtained by FEA

[[cite:&brumund21_multib_simul_reduc_order_flexib_bodies_fea]]

Combined multi-body / FEA techniques and experimental validation on a Stewart platform containing amplified piezoelectric actuators
Super-element of amplified piezoelectric actuator / combined multibody-FEA technique, experimental validation on an amplified piezoelectric actuator and further validated on a complete stewart platform

#+begin_quote
We considered sub-components in the multi-body model as /reduced order flexible bodies/ representing the component’s modal behaviour with reduced mass and stiffness matrices obtained from finite element analysis (FEA) models.
These matrices were created from FEA models via modal reduction techniques, more specifically the /component mode synthesis/ (CMS).
This makes this design approach a combined multibody-FEA technique.
We validated the technique with a test bench that confirmed the good modelling capabilities using reduced order flexible body models obtained from FEA for an amplified piezoelectric actuator (APA).
#+end_quote

**** Robustness by design

- Design of a Stewart platform and associated control architecture that is robust to large plant uncertainties due to large variety of payload and experimental conditions.
- Instead of relying on complex controller synthesis (such as $\mathcal{H}_\infty$ synthesis or $\mu\text{-synthesis}$) to guarantee the robustness and performance.
- The approach here is to choose an adequate architecture (mechanics, sensors, actuators) such that controllers are robust by nature.
- Example: collocated actuator/sensor pair => controller can easily be made robust
- This is done by using models and using HAC-LAC architecture

**** Mechatronics design

Conduct a rigorous mechatronics design approach for a nano active stabilization system
[[cite:&dehaeze18_sampl_stabil_for_tomog_exper;&dehaeze21_mechat_approac_devel_nano_activ_stabil_system]]

Approach from start to finish:
- From first concepts using basic models, to concept validation
- Detailed design phase
- Experimental phase

Complete design with clear choices based on models.
Such approach, while not new, is here applied
This can be used for the design of future end-stations.

#+begin_src latex :file nass_mechatronics_approach.pdf
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  \node[myblock, fill=lightgreen, label={[mylabel] Nano 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  = 2pt of mechanical]  (instrumentation) {};
  \node[myblock, fill=lightyellow, label={[mylabel] FEM},             right = 2pt of mechanical]  (fem) {};

  \node[myblock, fill=lightred, label={[mylabel] Test Benches},   right = 3 of model.east]                          (testbenches) {};
  \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[anchor=south, above, text width=8cm, align=left] at (model.south) {Extensive use of models for:\begin{itemize}[noitemsep,topsep=5pt]\item Extraction of transfer functions \\ \item Choice of appropriate control architecture \\ \item Tuning of control laws \\ \item Closed loop simulations \\ \item Noise budgets / Evaluation of performances \\ \item Sensibility to parameters / disturbances\end{itemize}\centerline{Models are at the core the mecatronic approach!}};

  \node[mymodel] at (mustation.south)       {Multiple stages     \\ Complex dynamics};
  \node[mymodel] at (dist.south)            {Ground motion       \\ Position errors};
  \node[mymodel] at (nanohexapod.south)     {Different concepts  \\ Sensors, Actuators};

  \node[mymodel] at (instrumentation.south) {Sensors, Actuators  \\ Electronics};
  \node[mymodel] at (mechanical.south)      {Proper integration  \\ Ease of assembly};
  \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       \\ Micro Station};

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  \draw[->] ($(mounting.west-|model.east)+(0, 0.15)$) -- node[above, midway]{{\small Requirements}} ($(mounting.west)+(0, 0.15)$);
  \draw[<-] ($(mounting.west-|model.east)-(0, 0.15)$) -- node[below, midway]{{\small Model refinement}}   ($(mounting.west)-(0, 0.15)$);

  \draw[->] ($(testbenches.west-|model.east)+(0, 0.15)$) -- node[above, midway]{{\small Control Laws}} ($(testbenches.west)+(0, 0.15)$);
  \draw[<-] ($(testbenches.west-|model.east)-(0, 0.15)$) -- node[below, midway]{{\small Model refinement}}   ($(testbenches.west)-(0, 0.15)$);

  \draw[->] ($(implementation.west-|model.east)+(0, 0.15)$) -- node[above, midway]{{\small Control Laws}} ($(implementation.west)+(0, 0.15)$);
  \draw[<-] ($(implementation.west-|model.east)-(0, 0.15)$) -- node[below, midway]{{\small Model refinement}}   ($(implementation.west)-(0, 0.15)$);

  % Main steps
  \node[font=\bfseries, rotate=90, anchor=south, above] (conceptual_phase_node) at (dist.west) {1 - Conceptual Phase};
  \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) {3 - Experimental Phase};
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      \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, inner sep=2pt] (implementation_phase) {};
      % \node[above left] at (dob.south east) {DOB};
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  % Between main steps
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  % \node[inner sep=1pt, outer sep=6pt, anchor=north west, draw, fill=white, thin] (multibodymodel) at ($(model.north west) - (0, 0.5)$)
  %   {\includegraphics[width=5.6cm]{simscape_nano_hexapod.png}};

  % \node[inner sep=1pt, outer sep=6pt, anchor=south west, draw, fill=white, thin] (simscape) at (model.south west)
  %   {\includegraphics[width=5.6cm]{simscape_picture.jpg}};

  % % Feedback Model
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  % % FeedBack
  % \node[inner sep=3pt, outer sep=6pt, anchor=south east, draw, fill=white, thin] (feedback) at (model.south east)
  %   {\includegraphics[width=3.6cm]{classical_feedback_small.pdf}};
\end{tikzpicture}
#+end_src

#+name: fig:introduction_nass_mechatronics_approach
#+caption: Overview of the mechatronic approach used for the Nano-Active-Stabilization-System
#+attr_latex: :width \linewidth
#+RESULTS:
[[file:figs/nass_mechatronics_approach.png]]

**** 6DoF vibration control of a rotating platform

Vibration control in 5DoF of a rotating stage
To the author's knowledge, the use of a continuously rotating stewart platform for vibration control has not been proved in the literature.

**** Experimental validation of the Nano Active Stabilization System

Demonstration of the improvement of the the positioning accuracy of a complex multi DoF (the micro-station) by several orders of magnitude (Section ...) using ...

* Thesis Outline - Mechatronics Design Approach
**** Introduction                                                  :ignore:

#+name: fig:introduction_overview_chapters
#+caption: Overview of the sections
#+attr_latex: :width \linewidth
[[file:figs/introduction_overview_chapters.png]]

This thesis
- has a structure that follows the mechatronics design approach

Is structured in three chapters that corresponds to the three mains parts of the proposed mechatronics approach.

A brief overview of these three chapters is given bellow.

**** Conceptual design development

- Start with simple models for witch trade offs can be easily understood (uniaxial)
- Increase the model complexity if important physical phenomenon are to be modelled (cf the rotating model)
- Only when better understanding of the physical effects in play, and only if required, go for higher model complexity (here multi-body model)
- The system concept and main characteristics should be extracted from the different models and validated with closed-loop simulations with the most accurate model
- Once the concept is validated, the chosen concept can be design in mode details

**** Detailed design

- During this detailed design phase, models are refined from the obtained CAD and using FEM
- The models are used to assists the design and to optimize each element based on dynamical analysis and closed-loop simulations
- The requirements for all the associated instrumentation can be determined from a dynamical noise budgeting
- After converging to a detailed design that give acceptable performance based on the models, the different parts can be ordered and the experimental phase begins

**** Experimental validation

- It is advised that the important characteristics of the different elements are evaluated individually
  Systematic validation/refinement of models with experimental measurements
- The obtained characteristics can be used to refine the models
- Then, an accurate model of the system is obtained which can be used during experimental tests (for control synthesis for instance)


* Bibliography                                                        :ignore:
#+latex: \printbibliography[heading=bibintoc,title={Bibliography}]

* Footnotes
[fn:4]Capacitive sensors from Fogale Sensors
[fn:3]Attocube FPS3010 Fabry-Pérot interferometers
[fn:2]Attocube IDS3010 Fabry-Pérot interferometers
[fn:1]PicoScale SmarAct Michelson interferometers