#+TITLE: Tomography Experiment
:DRAWER:
#+STARTUP: overview

#+LANGUAGE: en
#+EMAIL: dehaeze.thomas@gmail.com
#+AUTHOR: Dehaeze Thomas

#+HTML_LINK_HOME: ../index.html
#+HTML_LINK_UP: ../index.html

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#+PROPERTY: header-args:matlab  :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :results none
#+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :eval no-export
#+PROPERTY: header-args:matlab+ :output-dir figs
#+PROPERTY: header-args:matlab+ :tangle matlab/tomo_exp.m
#+PROPERTY: header-args:matlab+ :mkdirp yes

#+PROPERTY: header-args:shell  :eval no-export

#+PROPERTY: header-args:latex  :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/}{config.tex}")
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
#+PROPERTY: header-args:latex+ :results raw replace :buffer no
#+PROPERTY: header-args:latex+ :eval no-export
#+PROPERTY: header-args:latex+ :exports both
#+PROPERTY: header-args:latex+ :mkdirp yes
#+PROPERTY: header-args:latex+ :output-dir figs
:END:

* Introduction                                                       :ignore:
The goal here is to simulate some scientific experiments with the tuned Simscape model when no control is applied to the nano-hexapod.

This has several goals:
- Validate the model
- Estimate the expected error motion for the experiments
- Estimate the stroke that we may need for the nano-hexapod

The document in organized as follow:
- In section [[sec:simscape_model]] the Simscape model is initialized
- In section [[sec:tomo_no_dist]] a tomography experiment is performed where the sample is aligned with the rotation axis. No disturbance is included
- In section [[sec:tomo_dist]], the same is done but with disturbance included
- In section [[sec:tomo_hexa_trans]] the micro-hexapod translate the sample such that its center of mass is no longer aligned with the rotation axis. No disturbance is included
- In section [[sec:ty_scans]], scans with the translation stage are simulated with no perturbation included

* Matlab Init                                               :noexport:ignore:
#+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 :tangle no
  simulinkproject('../');
#+end_src

* Simscape Model
<<sec:simscape_model>>

#+begin_src matlab
  open('nass_model.slx');
#+end_src

We load the shared simulink configuration and we set the =StopTime=.
#+begin_src matlab
  load('mat/conf_simulink.mat');
  set_param(conf_simulink, 'StopTime', '5');
#+end_src

We first initialize all the stages.
#+begin_src matlab
  initializeGround();
  initializeGranite();
  initializeTy();
  initializeRy();
  initializeRz();
  initializeMicroHexapod();
  initializeAxisc();
  initializeMirror();
  initializeNanoHexapod('actuator', 'piezo');
  initializeSample('mass', 1);
#+end_src

We initialize the reference path for all the stages.
All stage is set to its zero position except the Spindle which is rotating at 60rpm.
#+begin_src matlab
  initializeReferences('Rz_type', 'rotating', 'Rz_period', 1);
#+end_src

* Tomography Experiment with no disturbances
<<sec:tomo_no_dist>>
** Introduction                                                     :ignore:

** Simulation Setup
And we initialize the disturbances to be equal to zero.
#+begin_src matlab
  initializeDisturbances(...
      'Dwx', false, ... % Ground Motion - X direction
      'Dwy', false, ... % Ground Motion - Y direction
      'Dwz', false, ... % Ground Motion - Z direction
      'Fty_x', false, ... % Translation Stage - X direction
      'Fty_z', false, ... % Translation Stage - Z direction
      'Frz_z', false  ... % Spindle - Z direction
      );
#+end_src

We simulate the model.
#+begin_src matlab
  sim('nass_model');
#+end_src

And we save the obtained data.
#+begin_src matlab
  tomo_align_no_dist = struct('t', t, 'MTr', MTr);
  save('experiment_tomography/mat/experiment.mat', 'tomo_align_no_dist', '-append');
#+end_src

** Analysis
#+begin_src matlab
  load('experiment_tomography/mat/experiment.mat', 'tomo_align_no_dist');
  t = tomo_align_no_dist.t;
  MTr = tomo_align_no_dist.MTr;
#+end_src

#+begin_src matlab
  Edx = squeeze(MTr(1, 4, :));
  Edy = squeeze(MTr(2, 4, :));
  Edz = squeeze(MTr(3, 4, :));
  % The angles obtained are u-v-w Euler angles (rotations in the moving frame)
  Ery = atan2( squeeze(MTr(1, 3, :)),           squeeze(sqrt(MTr(1, 1, :).^2 + MTr(1, 2, :).^2)));
  Erx = atan2(-squeeze(MTr(2, 3, :))./cos(Ery), squeeze(MTr(3, 3, :))./cos(Ery));
  Erz = atan2(-squeeze(MTr(1, 2, :))./cos(Ery), squeeze(MTr(1, 1, :))./cos(Ery));
#+end_src

#+begin_src matlab :exports none
  figure;
  ax1 = subplot(1, 3, 1);
  plot(t, Edx, 'DisplayName', '$\epsilon_{x}$')
  ylabel('Displacement [m]');
  legend('location', 'northeast');

  ax2 = subplot(1, 3, 2);
  plot(t, Edy, 'DisplayName', '$\epsilon_{y}$')
  xlabel('Time [s]');
  legend('location', 'northeast');

  ax3 = subplot(1, 3, 3);
  plot(t, Edz, 'DisplayName', '$\epsilon_{z}$')
  legend('location', 'northeast');

  linkaxes([ax1,ax2,ax3],'x');
  xlim([2, inf]);
#+end_src

#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/exp_tomo_without_dist_trans.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:exp_tomo_without_dist_trans
#+CAPTION: X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances ([[./figs/exp_tomo_without_dist_trans.png][png]], [[./figs/exp_tomo_without_dist_trans.pdf][pdf]])
[[file:figs/exp_tomo_without_dist_trans.png]]

#+begin_src matlab :exports none
  figure;
  ax1 = subplot(1, 3, 1);
  plot(t, Erx, 'DisplayName', '$\epsilon_{\theta x}$')
  ylabel('Rotation [rad]');
  legend('location', 'northeast');

  ax2 = subplot(1, 3, 2);
  plot(t, Ery, 'DisplayName', '$\epsilon_{\theta y}$')
  xlabel('Time [s]');
  legend('location', 'northeast');

  ax3 = subplot(1, 3, 3);
  plot(t, Erz, 'DisplayName', '$\epsilon_{\theta z}$')
  legend('location', 'northeast');

  linkaxes([ax1,ax2,ax3],'x');
  xlim([2, inf]);
#+end_src

#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/exp_tomo_without_dist_rot.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:exp_tomo_without_dist_rot
#+CAPTION: X-Y-Z rotations of the sample w.r.t. granite when performing tomography experiment with no disturbances ([[./figs/exp_tomo_without_dist_rot.png][png]], [[./figs/exp_tomo_without_dist_rot.pdf][pdf]])
[[file:figs/exp_tomo_without_dist_rot.png]]

** Conclusion

#+begin_important
  When everything is aligned, the resulting error motion is very small (nm range) and is quite negligible with respect to the error when disturbances are included.
  This residual error motion probably comes from a small misalignment somewhere.
#+end_important

* Tomography Experiment with included perturbations
<<sec:tomo_dist>>
** Introduction                                                     :ignore:

** Simulation Setup
We now activate the disturbances.
#+begin_src matlab
  initializeDisturbances(...
      'Dwx', true, ... % Ground Motion - X direction
      'Dwy', true, ... % Ground Motion - Y direction
      'Dwz', true, ... % Ground Motion - Z direction
      'Fty_x', true, ... % Translation Stage - X direction
      'Fty_z', true, ... % Translation Stage - Z direction
      'Frz_z', true  ... % Spindle - Z direction
      );
#+end_src

We simulate the model.
#+begin_src matlab
  sim('nass_model');
#+end_src

And we save the obtained data.
#+begin_src matlab
  tomo_align_dist = struct('t', t, 'MTr', MTr);
  save('experiment_tomography/mat/experiment.mat', 'tomo_align_dist', '-append');
#+end_src

** Analysis
#+begin_src matlab
  load('experiment_tomography/mat/experiment.mat', 'tomo_align_dist');
  t = tomo_align_dist.t;
  MTr = tomo_align_dist.MTr;
#+end_src

#+begin_src matlab
  Edx = squeeze(MTr(1, 4, :));
  Edy = squeeze(MTr(2, 4, :));
  Edz = squeeze(MTr(3, 4, :));
  % The angles obtained are u-v-w Euler angles (rotations in the moving frame)
  Ery = atan2( squeeze(MTr(1, 3, :)),           squeeze(sqrt(MTr(1, 1, :).^2 + MTr(1, 2, :).^2)));
  Erx = atan2(-squeeze(MTr(2, 3, :))./cos(Ery), squeeze(MTr(3, 3, :))./cos(Ery));
  Erz = atan2(-squeeze(MTr(1, 2, :))./cos(Ery), squeeze(MTr(1, 1, :))./cos(Ery));
#+end_src

#+begin_src matlab :exports none
  figure;
  ax1 = subplot(1, 3, 1);
  plot(t, Edx, 'DisplayName', '$\epsilon_{x}$')
  ylabel('Displacement [m]');
  legend('location', 'northeast');

  ax2 = subplot(1, 3, 2);
  plot(t, Edy, 'DisplayName', '$\epsilon_{y}$')
  xlabel('Time [s]');
  legend('location', 'northeast');

  ax3 = subplot(1, 3, 3);
  plot(t, Edz, 'DisplayName', '$\epsilon_{z}$')
  legend('location', 'northeast');

  linkaxes([ax1,ax2,ax3],'x');
  xlim([2, inf]);
#+end_src

#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/exp_tomo_dist_trans.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:exp_tomo_dist_trans
#+CAPTION: X-Y-Z translation of the sample w.r.t. the granite when performing tomography experiment with disturbances ([[./figs/exp_tomo_dist_trans.png][png]], [[./figs/exp_tomo_dist_trans.pdf][pdf]])
[[file:figs/exp_tomo_dist_trans.png]]

#+begin_src matlab :exports none
  figure;
  ax1 = subplot(1, 3, 1);
  plot(t, Erx, 'DisplayName', '$\epsilon_{\theta x}$')
  ylabel('Rotation [rad]');
  legend('location', 'northeast');

  ax2 = subplot(1, 3, 2);
  plot(t, Ery, 'DisplayName', '$\epsilon_{\theta y}$')
  xlabel('Time [s]');
  legend('location', 'northeast');

  ax3 = subplot(1, 3, 3);
  plot(t, Erz, 'DisplayName', '$\epsilon_{\theta z}$')
  legend('location', 'northeast');

  linkaxes([ax1,ax2,ax3],'x');
  xlim([2, inf]);
#+end_src

#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/exp_tomo_dist_rot.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:exp_tomo_dist_rot
#+CAPTION: X-Y-Z rotations of the sample w.r.t. the granite when performing tomography experiment with disturbances ([[./figs/exp_tomo_dist_rot.png][png]], [[./figs/exp_tomo_dist_rot.pdf][pdf]])
[[file:figs/exp_tomo_dist_rot.png]]

** Conclusion

#+begin_important
  Error motion is what expected from the disturbance measurements.
#+end_important

* Tomography when the micro-hexapod is not centered
<<sec:tomo_hexa_trans>>
** Introduction                                                     :ignore:

** Simulation Setup
We first set the wanted translation of the Micro Hexapod.
#+begin_src matlab
  P_micro_hexapod = [0.01; 0; 0]; % [m]
#+end_src

We initialize the reference path.
#+begin_src matlab
  initializeReferences('Dh_pos', [P_micro_hexapod; 0; 0; 0], 'Rz_type', 'rotating', 'Rz_period', 1);
#+end_src

We initialize the stages.
#+begin_src matlab
  initializeMicroHexapod('AP', P_micro_hexapod);
#+end_src

And we initialize the disturbances to zero.
#+begin_src matlab
  initializeDisturbances(...
      'Dwx', false, ... % Ground Motion - X direction
      'Dwy', false, ... % Ground Motion - Y direction
      'Dwz', false, ... % Ground Motion - Z direction
      'Fty_x', false, ... % Translation Stage - X direction
      'Fty_z', false, ... % Translation Stage - Z direction
      'Frz_z', false  ... % Spindle - Z direction
      );
#+end_src

We simulate the model.
#+begin_src matlab
  sim('nass_model');
#+end_src

And we save the obtained data.
#+begin_src matlab
  tomo_not_align = struct('t', t, 'MTr', MTr);
  save('experiment_tomography/mat/experiment.mat', 'tomo_not_align', '-append');
#+end_src

** Analysis
#+begin_src matlab
  load('experiment_tomography/mat/experiment.mat', 'tomo_not_align');
  t = tomo_not_align.t;
  MTr = tomo_not_align.MTr;
#+end_src

#+begin_src matlab
  Edx = squeeze(MTr(1, 4, :));
  Edy = squeeze(MTr(2, 4, :));
  Edz = squeeze(MTr(3, 4, :));
  % The angles obtained are u-v-w Euler angles (rotations in the moving frame)
  Ery = atan2( squeeze(MTr(1, 3, :)),           squeeze(sqrt(MTr(1, 1, :).^2 + MTr(1, 2, :).^2)));
  Erx = atan2(-squeeze(MTr(2, 3, :))./cos(Ery), squeeze(MTr(3, 3, :))./cos(Ery));
  Erz = atan2(-squeeze(MTr(1, 2, :))./cos(Ery), squeeze(MTr(1, 1, :))./cos(Ery));
#+end_src

#+begin_src matlab :exports none
  figure;
  ax1 = subplot(1, 3, 1);
  plot(t, Edx, 'DisplayName', '$\epsilon_{x}$')
  ylabel('Displacement [m]');
  legend('location', 'northeast');

  ax2 = subplot(1, 3, 2);
  plot(t, Edy, 'DisplayName', '$\epsilon_{y}$')
  xlabel('Time [s]');
  legend('location', 'northeast');

  ax3 = subplot(1, 3, 3);
  plot(t, Edz, 'DisplayName', '$\epsilon_{z}$')
  legend('location', 'northeast');

  linkaxes([ax1,ax2,ax3],'x');
  xlim([2, inf]);
#+end_src

#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/exp_tomo_offset_trans.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:exp_tomo_offset_trans
#+CAPTION: X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances ([[./figs/exp_tomo_offset_trans.png][png]], [[./figs/exp_tomo_offset_trans.pdf][pdf]])
[[file:figs/exp_tomo_offset_trans.png]]

#+begin_src matlab :exports none
  figure;
  ax1 = subplot(1, 3, 1);
  plot(t, Erx, 'DisplayName', '$\epsilon_{\theta x}$')
  ylabel('Rotation [rad]');
  legend('location', 'northeast');

  ax2 = subplot(1, 3, 2);
  plot(t, Ery, 'DisplayName', '$\epsilon_{\theta y}$')
  xlabel('Time [s]');
  legend('location', 'northeast');

  ax3 = subplot(1, 3, 3);
  plot(t, Erz, 'DisplayName', '$\epsilon_{\theta z}$')
  legend('location', 'northeast');

  linkaxes([ax1,ax2,ax3],'x');
  xlim([2, inf]);
#+end_src

#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/exp_tomo_offset_rot.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:exp_tomo_offset_rot
#+CAPTION: X-Y-Z rotations of the sample w.r.t. granite when performing tomography experiment with no disturbances ([[./figs/exp_tomo_offset_rot.png][png]], [[./figs/exp_tomo_offset_rot.pdf][pdf]])
[[file:figs/exp_tomo_offset_rot.png]]

** Conclusion

#+begin_important
  The main motions are translations in the X direction of the mobile platform (corresponds to the eccentricity of the micro-hexapod) and rotations along the rotating Y axis.
#+end_important

* Raster Scans with the translation stage
<<sec:ty_scans>>
** Introduction                                                     :ignore:

** Simulation Setup
We set the reference path.
#+begin_src matlab
  initializeReferences('Dy_type', 'triangular', 'Dy_amplitude', 10e-3, 'Dy_period', 1);
#+end_src

We initialize the stages.
#+begin_src matlab
  initializeGround();
  initializeGranite();
  initializeTy();
  initializeRy();
  initializeRz();
  initializeMicroHexapod();
  initializeAxisc();
  initializeMirror();
  initializeNanoHexapod('actuator', 'piezo');
  initializeSample('mass', 1);
#+end_src

And we initialize the disturbances to zero.
#+begin_src matlab
  initializeDisturbances(...
      'Dwx', false, ... % Ground Motion - X direction
      'Dwy', false, ... % Ground Motion - Y direction
      'Dwz', false, ... % Ground Motion - Z direction
      'Fty_x', false, ... % Translation Stage - X direction
      'Fty_z', false, ... % Translation Stage - Z direction
      'Frz_z', false  ... % Spindle - Z direction
      );
#+end_src

We simulate the model.
#+begin_src matlab
  sim('nass_model');
#+end_src

And we save the obtained data.
#+begin_src matlab
  ty_scan = struct('t', t, 'MTr', MTr);
  save('experiment_tomography/mat/experiment.mat', 'ty_scan', '-append');
#+end_src

** Analysis
#+begin_src matlab
  load('experiment_tomography/mat/experiment.mat', 'ty_scan');
  t = ty_scan.t;
  MTr = ty_scan.MTr;
#+end_src

#+begin_src matlab
  Edx = squeeze(MTr(1, 4, :));
  Edy = squeeze(MTr(2, 4, :));
  Edz = squeeze(MTr(3, 4, :));
  % The angles obtained are u-v-w Euler angles (rotations in the moving frame)
  Ery = atan2( squeeze(MTr(1, 3, :)),           squeeze(sqrt(MTr(1, 1, :).^2 + MTr(1, 2, :).^2)));
  Erx = atan2(-squeeze(MTr(2, 3, :))./cos(Ery), squeeze(MTr(3, 3, :))./cos(Ery));
  Erz = atan2(-squeeze(MTr(1, 2, :))./cos(Ery), squeeze(MTr(1, 1, :))./cos(Ery));
#+end_src

#+begin_src matlab :exports none
  figure;
  ax1 = subplot(1, 3, 1);
  plot(t, Edx, 'DisplayName', '$\epsilon_{x}$')
  ylabel('Displacement [m]');
  legend('location', 'northeast');

  ax2 = subplot(1, 3, 2);
  plot(t, Edy, 'DisplayName', '$\epsilon_{y}$')
  xlabel('Time [s]');
  legend('location', 'northeast');

  ax3 = subplot(1, 3, 3);
  plot(t, Edz, 'DisplayName', '$\epsilon_{z}$')
  legend('location', 'northeast');

  linkaxes([ax1,ax2,ax3],'x');
  xlim([2, inf]);
#+end_src

#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/exp_ty_scan_trans.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:exp_ty_scan_trans
#+CAPTION: X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances ([[./figs/exp_ty_scan_trans.png][png]], [[./figs/exp_ty_scan_trans.pdf][pdf]])
[[file:figs/exp_ty_scan_trans.png]]

#+begin_src matlab :exports none
  figure;
  ax1 = subplot(1, 3, 1);
  plot(t, Erx, 'DisplayName', '$\epsilon_{\theta x}$')
  ylabel('Rotation [rad]');
  legend('location', 'northeast');

  ax2 = subplot(1, 3, 2);
  plot(t, Ery, 'DisplayName', '$\epsilon_{\theta y}$')
  xlabel('Time [s]');
  legend('location', 'northeast');

  ax3 = subplot(1, 3, 3);
  plot(t, Erz, 'DisplayName', '$\epsilon_{\theta z}$')
  legend('location', 'northeast');

  linkaxes([ax1,ax2,ax3],'x');
  xlim([2, inf]);
#+end_src

#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/exp_ty_scan_rot.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:exp_ty_scan_rot
#+CAPTION: X-Y-Z rotations of the sample w.r.t. granite when performing tomography experiment with no disturbances ([[./figs/exp_ty_scan_rot.png][png]], [[./figs/exp_ty_scan_rot.pdf][pdf]])
[[file:figs/exp_ty_scan_rot.png]]

** Conclusion

#+begin_important
  This is logic that the main error moving is translation along the Y axis and rotation along the X axis.
  In order to reduce the errors, we can make a smoother reference path for the translation stage.
#+end_important