#+TITLE: Identification
: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/modal_frf_coh.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}")
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#+PROPERTY: header-args:latex+ :exports both
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#+PROPERTY: header-args:latex+ :output-dir figs
:END:

* Introduction                                                       :ignore:
The goal here is to make an identification of the *micro-station* in order to compare the model with the measurements on the real micro-station.

In order to do so:
- Decide where to virtually excite the station and where to measure its motion
- Extract transfer functions from the excitation forces to the measured motion
- Compare those transfer functions with the modal analysis

For the excitation, we can choose the same excitation points as the one used for the modal test.
For the measurement points, we can choose the Center of Mass of each solid body.
The center of mass of each solid body is not easily defined using Simscape.
Indeed, we can define the center of mass of any solid body but not of multiple solid bodies. However, one solid body is composed of multiple STEP files.
One solution could be to use one STEP file for one solid body.
However, the position of the center of mass can be exported using simulink and then defined on Simscape.

* Identification of the Micro-Station
** Introduction                                                     :ignore:

** 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

** Compute the transfer functions
We first define some parameters for the identification.
The simulink file for the identification is =sim_micro_station_id.slx=.

#+begin_src matlab
  open 'simscape/sim_micro_station_id.slx'
#+end_src

#+begin_src matlab
%% Options for Linearized
options = linearizeOptions;
options.SampleTime = 0;

%% Name of the Simulink File
mdl = 'sim_micro_station_id';
#+end_src

#+begin_src matlab
%% Micro-Hexapod
% Input/Output definition
io(1) = linio([mdl, '/Micro-Station/Fm_ext'],1,'openinput');
io(2) = linio([mdl, '/Micro-Station/Fg_ext'],1,'openinput');
io(3) = linio([mdl, '/Micro-Station/Dm_inertial'],1,'output');
io(4) = linio([mdl, '/Micro-Station/Ty_inertial'],1,'output');
io(5) = linio([mdl, '/Micro-Station/Ry_inertial'],1,'output');
io(6) = linio([mdl, '/Micro-Station/Dg_inertial'],1,'output');
#+end_src

#+begin_src matlab
% Run the linearization
G_ms = linearize(mdl, io, 0);

% Input/Output names
G_ms.InputName  = {'Fmx', 'Fmy', 'Fmz',...
                   'Fgx', 'Fgy', 'Fgz'};
G_ms.OutputName = {'Dmx', 'Dmy', 'Dmz', ...
                   'Tyx', 'Tyy', 'Tyz', ...
                   'Ryx', 'Ryy', 'Ryz', ...
                   'Dgx', 'Dgy', 'Dgz'};
#+end_src

#+begin_src matlab
%% Save the obtained transfer functions
save('./mat/id_micro_station.mat', 'G_ms');
#+end_src


** Plots the transfer functions

** Compare with the measurements


* Modal Analysis of the Micro-Station
** 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
#+begin_src matlab
  open 'simscape/sim_micro_station_modal_analysis.slx'
#+end_src

#+begin_src matlab
%% Options for Linearized
options = linearizeOptions;
options.SampleTime = 0;

%% Name of the Simulink File
mdl = 'sim_micro_station_modal_analysis';
#+end_src

#+begin_src matlab
%% Micro-Hexapod
% Input/Output definition
io(1) = linio([mdl, '/Micro-Station/F_hammer'],1,'openinput');
io(2) = linio([mdl, '/Micro-Station/acc9'],1,'output');
io(3) = linio([mdl, '/Micro-Station/acc10'],1,'output');
io(4) = linio([mdl, '/Micro-Station/acc11'],1,'output');
io(5) = linio([mdl, '/Micro-Station/acc12'],1,'output');
#+end_src

#+begin_src matlab
  % Run the linearization
  G_ms = linearize(mdl, io, 0);

  % Input/Output names
  G_ms.InputName  = {'Fx', 'Fy', 'Fz'};
  G_ms.OutputName = {'x9', 'y9', 'z9', ...
                     'x10', 'y10', 'z10', ...
                     'x11', 'y11', 'z11', ...
                     'x12', 'y12', 'z12'};
#+end_src

** Plot Results
#+begin_src matlab
figure;
hold on;
plot(freqs, abs(squeeze(freqresp(G_ms('x9', 'Fx'), freqs, 'Hz'))));
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]');
hold off;
#+end_src

** Compare with measurements
#+begin_src matlab
  load('../meas/modal-analysis/mat/frf_coh_matrices.mat', 'FRFs', 'COHs', 'freqs');
#+end_src

#+begin_src matlab
  dirs = {'x', 'y', 'z'};

  n_acc = 9;
  n_dir = 1; % x, y, z
  n_exc = 1; % x, y, z

  figure;
  hold on;
  plot(freqs, abs(squeeze(FRFs(3*(n_acc-1) + n_dir, n_exc, :)))./((2*pi*freqs).^2)');
  plot(freqs, abs(squeeze(freqresp(G_ms([dirs{n_dir}, num2str(n_acc)], ['F', dirs{n_dir}]), freqs, 'Hz'))));
  set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
  ylabel('Amplitude [m/N]');
  hold off;
#+end_src

* Compare with measurements at the CoM of each element
** 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

** Init
#+begin_src matlab :results none
%% Initialize Ground
initializeGround();

%% Initialize Granite
initializeGranite();

%% Initialize Translation stage
initializeTy();

%% Initialize Tilt Stage
initializeRy();

%% Initialize Spindle
initializeRz();

%% Initialize Hexapod Symétrie
initializeMicroHexapod();

%% Initialize Center of gravity compensation
initializeAxisc();
#+end_src

** Center of Mass of each solid body

|        | granite bot | granite top |   ty |   ry |   rz | hexa |
|--------+-------------+-------------+------+------+------+------|
| X [mm] |          45 |          52 |    0 |    0 |    0 |   -4 |
| Y [mm] |         144 |         258 |   14 |   -5 |    0 |    6 |
| Z [mm] |       -1251 |        -778 | -600 | -628 | -580 | -319 |

#+begin_src matlab
  open 'simscape/sim_micro_station_modal_analysis_com.slx'
#+end_src

** Simscape Model
#+begin_src matlab
  %% Options for Linearized
  options = linearizeOptions;
  options.SampleTime = 0;

  %% Name of the Simulink File
  mdl = 'sim_micro_station_modal_analysis_com';
#+end_src

#+begin_src matlab
  %% Micro-Hexapod
  % Input/Output definition
  io(1) = linio([mdl, '/Micro-Station/F_hammer'],1,'openinput');
  io(2) = linio([mdl, '/Micro-Station/acc_gtop'],1,'output');
  io(3) = linio([mdl, '/Micro-Station/acc_ty'],1,'output');
  io(4) = linio([mdl, '/Micro-Station/acc_ry'],1,'output');
  io(5) = linio([mdl, '/Micro-Station/acc_rz'],1,'output');
  io(6) = linio([mdl, '/Micro-Station/acc_hexa'],1,'output');
#+end_src

#+begin_src matlab
  % Run the linearization
  G_ms = linearize(mdl, io, 0);

  % Input/Output names
  G_ms.InputName  = {'Fx', 'Fy', 'Fz'};
  G_ms.OutputName = {'gtop_x', 'gtop_y', 'gtop_z', 'gtop_rx', 'gtop_ry', 'gtop_rz', ...
                     'ty_x', 'ty_y', 'ty_z', 'ty_rx', 'ty_ry', 'ty_rz', ...
                     'ry_x', 'ry_y', 'ry_z', 'ry_rx', 'ry_ry', 'ry_rz', ...
                     'rz_x', 'rz_y', 'rz_z', 'rz_rx', 'rz_ry', 'rz_rz', ...
                     'hexa_x', 'hexa_y', 'hexa_z', 'hexa_rx', 'hexa_ry', 'hexa_rz'};
#+end_src

** Compare with measurements
#+begin_src matlab
  load('../meas/modal-analysis/mat/frf_coh_matrices.mat', 'freqs');
  load('../meas/modal-analysis/mat/frf_com.mat', 'FRFs_CoM');
#+end_src

#+begin_src matlab
  dirs = {'x', 'y', 'z', 'rx', 'ry', 'rz'};
  stages = {'gbot', 'gtop', 'ty', 'ry', 'rz', 'hexa'}

  n_stg = 2;
  n_dir = 2; % x, y, z, Rx, Ry, Rz
  n_exc = 2; % x, y, z

  f = logspace(1, 3, 1000);

  figure;
  hold on;
  plot(freqs, abs(squeeze(FRFs_CoM(6*(n_stg-1) + n_dir, n_exc, :)))./((2*pi*freqs).^2)');
  plot(f, abs(squeeze(freqresp(G_ms([stages{n_stg}, '_', dirs{n_dir}], ['F', dirs{n_exc}]), f, 'Hz'))));
  set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
  ylabel('Amplitude [m/N]');
  hold off;
  xlim([10, 1000]);
#+end_src

#+begin_src matlab
  dirs = {'x', 'y', 'z', 'rx', 'ry', 'rz'};
  stages = {'gtop', 'ty', 'ry', 'rz', 'hexa'}

  f = logspace(1, 3, 1000);

  figure;
  for n_stg = 1:2
    for n_dir = 1:3
      subplot(3, 2, (n_dir-1)*2 + n_stg);
      title(['F ', dirs{n_dir}, ' to ', stages{n_stg}, ' ', dirs{n_dir}]);
      hold on;
      plot(freqs, abs(squeeze(FRFs_CoM(6*(n_stg) + n_dir, n_dir, :)))./((2*pi*freqs).^2)');
      plot(f, abs(squeeze(freqresp(G_ms([stages{n_stg}, '_', dirs{n_dir}], ['F', dirs{n_dir}]), f, 'Hz'))));
      set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
      ylabel('Amplitude [m/N]');
      hold off;
      xlim([10, 1000]);
      ylim([1e-12, 1e-6]);
    end
  end
#+end_src

#+begin_src matlab
  dirs = {'x', 'y', 'z', 'rx', 'ry', 'rz'};
  stages = {'ry', 'rz', 'hexa'}

  f = logspace(1, 3, 1000);

  figure;
  for n_stg = 1:2
    for n_dir = 1:3
      subplot(3, 2, (n_dir-1)*2 + n_stg);
      title(['F ', dirs{n_dir}, ' to ', stages{n_stg}, ' ', dirs{n_dir}]);
      hold on;
      plot(freqs, abs(squeeze(FRFs_CoM(6*(n_stg+2) + n_dir, n_dir, :)))./((2*pi*freqs).^2)');
      plot(f, abs(squeeze(freqresp(G_ms([stages{n_stg}, '_', dirs{n_dir}], ['F', dirs{n_dir}]), f, 'Hz'))));
      set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
      ylabel('Amplitude [m/N]');
      hold off;
      xlim([10, 1000]);
      ylim([1e-12, 1e-6]);
    end
  end
#+end_src

#+begin_src matlab
  dirs = {'x', 'y', 'z', 'rx', 'ry', 'rz'};
  stages = {'hexa'}

  f = logspace(1, 3, 1000);

  figure;
  for n_stg = 1
    for n_dir = 1:3
      subplot(3, 2, (n_dir-1)*2 + n_stg);
      title(['F ', dirs{n_dir}, ' to ', stages{n_stg}, ' ', dirs{n_dir}]);
      hold on;
      plot(freqs, abs(squeeze(FRFs_CoM(6*(n_stg+4) + n_dir, n_dir, :)))./((2*pi*freqs).^2)');
      plot(f, abs(squeeze(freqresp(G_ms([stages{n_stg}, '_', dirs{n_dir}], ['F', dirs{n_dir}]), f, 'Hz'))));
      set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
      ylabel('Amplitude [m/N]');
      hold off;
      xlim([10, 1000]);
      ylim([1e-12, 1e-6]);
    end
  end
#+end_src

** Bis
#+begin_src matlab :results none
  %% Initialize Ground
  initializeGround();

  %% Initialize Granite
  initializeGranite(struct('rigid', false));

  %% Initialize Translation stage
  initializeTy(struct('rigid', false));

  %% Initialize Tilt Stage
  initializeRy(struct('rigid', false));

  %% Initialize Spindle
  initializeRz(struct('rigid', false));

  %% Initialize Hexapod Symétrie
  initializeMicroHexapod(struct('rigid', false));

  %% Initialize Center of gravity compensation
  initializeAxisc();
#+end_src

For Granite Fx to Tx/Ty/Tz/Rx/Ry/Rz
#+begin_src matlab
  dirs = {'x', 'y', 'z', 'rx', 'ry', 'rz'};
  stages = {'gtop', 'ty', 'ry', 'rz', 'hexa'}

  n_stg = 5;
  n_exc = 3;

  f = logspace(0, 3, 1000);

  figure;
  for n_dir = 1:6
    subplot(2, 3, n_dir);
    title(['F', dirs{n_exc}, ' to ', stages{n_stg}, ' ', dirs{n_dir}]);
    hold on;
    plot(freqs, abs(squeeze(FRFs_CoM(6*(n_stg) + n_dir, n_exc, :)))./((2*pi*freqs).^2)');
    plot(f, abs(squeeze(freqresp(G_ms([stages{n_stg}, '_', dirs{n_dir}], ['F', dirs{n_exc}]), f, 'Hz'))));
    set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
    ylabel('Amplitude [m/N]');
    hold off;
    xlim([10, 1000]);
    ylim([1e-12, 1e-6]);
  end
#+end_src

* ZIP file containing the data and matlab files                      :ignore:
#+begin_src bash :exports none :results none
  if [ matlab/identification_micro_station.m -nt data/identification_micro_station.zip ]; then
    cp matlab/identification_micro_station.m identification_micro_station.m;
    zip data/identification_micro_station \
        mat/data.mat \
        identification_micro_station.m
    rm identification_micro_station.m;
  fi
#+end_src

#+begin_note
  All the files (data and Matlab scripts) are accessible [[file:data/identification_micro_station.zip][here]].
#+end_note

* 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

* Identification of the micro-station
#+begin_src matlab
  simulinkproject('../');
#+end_src

#+begin_src matlab
  open sim_micro_station_id.slx
#+end_src

* Plot the obtained transfer functions
* Compare with the modal measurements
* Modal Identification of the micro station