nass-micro-station-measurements/disturbance-ty/index.org

#+TITLE: Vibrations induced by the translation stage motion
: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:shell  :eval no-export
:END:

* Measurement description
** Setup                                                             :ignore:
*Setup*:
Two geophone are use:
- One is on the marble (corresponding to the first column in the data)
- One at the sample location (corresponding to the second column in the data)

Two voltage amplifiers are used, their setup is:
- gain of 40dB (the gain at the be lowered from 60dB to 40dB to not saturate the voltage amplifiers)
- AC/DC switch on AC
- Low pass filter at 1kHz

A first order low pass filter is also added at the input of the voltage amplifiers.

Scans are done with the translation stage following sinus reference at 1Hz with amplitude of 600 000 cnt (= 3mm)
The scans are done with the ELMO software.

The North of the Geophones corresponds to the +Y direction and the East of the Geophones to the +X direction (see figure [[fig:experimental_setup_picture]]).

The spindle and slip-ring are turned ON. The Hexapod and the tilt-stage are OFF.

** Goal                                                              :ignore:
*Goal*:
- Determine the disturbances induced by the translation stage in the Z and X directions when scanning along the Y direction

** Measurements                                                      :ignore:
*Measurements*:
Three measurements are done:
| Measurement File   | Description                             |
|--------------------+-----------------------------------------|
| =mat/data_040.mat= | Z direction                             |
| =mat/data_041.mat= | E direction                             |
| =mat/data_042.mat= | E direction without any motion (Ty OFF) |

Each of the measurement =mat= file contains one =data= array with 3 columns:
| Column number | Description       |
|---------------+-------------------|
|             1 | Geophone - Marble |
|             2 | Geophone - Sample |
|             3 | Time              |

#+name: fig:experimental_setup_picture
#+caption: Picture of the experimental setup
#+attr_html: :width 500px
[[file:./img/IMG_20190513_163032.jpg]]

* Measurement Analysis
  :PROPERTIES:
  :header-args:matlab+: :tangle matlab/disturbance_ty.m
  :header-args:matlab+: :comments org :mkdirp yes
  :END:
  <<sec:disturbance_ty>>

** ZIP file containing the data and matlab files                     :ignore:
#+begin_src bash :exports none :results none
  if [ matlab/disturbance_ty.m -nt data/disturbance_ty.zip ]; then
    cp matlab/disturbance_ty.m disturbance_ty.m;
    zip data/disturbance_ty \
        mat/data_040.mat \
        mat/data_041.mat \
        mat/data_042.mat \
        mat/sin_elmo.csv \
        disturbance_ty.m
    rm disturbance_ty.m;
  fi
#+end_src

#+begin_note
  All the files (data and Matlab scripts) are accessible [[file:data/disturbance_ty.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>>
  addpath('../src');
#+end_src

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

** Load data
#+begin_src matlab
  z_ty = load('mat/data_040.mat', 'data'); z_ty = z_ty.data;
  e_ty = load('mat/data_041.mat', 'data'); e_ty = e_ty.data;
  e_of = load('mat/data_042.mat', 'data'); e_of = e_of.data;
#+end_src

** Voltage to Velocity
We convert the measured voltage to velocity using the function =voltageToVelocityL22= (accessible [[file:~/MEGA/These/meas/src/index.org][here]]).

#+begin_src matlab
  gain = 40; % [dB]

  z_ty(:, 1) = voltageToVelocityL22(z_ty(:, 1), z_ty(:, 3), gain);
  e_ty(:, 1) = voltageToVelocityL22(e_ty(:, 1), e_ty(:, 3), gain);
  e_of(:, 1) = voltageToVelocityL22(e_of(:, 1), e_of(:, 3), gain);

  z_ty(:, 2) = voltageToVelocityL22(z_ty(:, 2), z_ty(:, 3), gain);
  e_ty(:, 2) = voltageToVelocityL22(e_ty(:, 2), e_ty(:, 3), gain);
  e_of(:, 2) = voltageToVelocityL22(e_of(:, 2), e_of(:, 3), gain);
#+end_src

** Time domain plots
We plot the measured velocity of the marble and sample in the vertical direction (figure [[fig:ty_z_time]]) and in the X direction (figure [[fig:ty_e_time]]).

We also integrate the relative velocity to obtain the relative displacement (figure [[fig:x_relative_disp]] in the X direction and figure [[fig:z_relative_disp]] in the Z direction).

#+begin_src matlab
  figure;
  hold on;
  plot(z_ty(:, 3), z_ty(:, 1), 'DisplayName', 'Marble - Z');
  plot(z_ty(:, 3), z_ty(:, 2), 'DisplayName', 'Sample - Z');
  hold off;
  xlabel('Time [s]'); ylabel('Velocity [m/s]');
  xlim([0, 2]);
  legend('Location', 'northeast');
#+end_src

#+NAME: fig:ty_z_time
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ty_z_time.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:ty_z_time
#+CAPTION: Z velocity of the sample and marble when scanning with the translation stage
#+RESULTS: fig:ty_z_time
[[file:figs/ty_z_time.png]]

#+begin_src matlab
  figure;
  hold on;
  plot(e_ty(:, 3), e_ty(:, 1), 'DisplayName', 'Marble - X');
  plot(e_ty(:, 3), e_ty(:, 2), 'DisplayName', 'Sample - X');
  hold off;
  xlabel('Time [s]'); ylabel('Velocity [m/s]');
  xlim([0, 2]);
  legend('Location', 'northeast');
#+end_src

#+NAME: fig:ty_e_time
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ty_e_time.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:ty_e_time
#+CAPTION: Velocity of the sample and marble in the east direction when scanning with the translation stage
#+RESULTS: fig:ty_e_time
[[file:figs/ty_e_time.png]]

#+begin_src matlab
  figure;
  plot(e_ty(:, 3), 1e6*lsim(1/s, e_ty(:, 2)-e_ty(:, 1), e_ty(:, 3)));
  xlabel('Time [s]'); ylabel('X Relative Displacement [$\mu m$]');
  xlim([0, 2]);
#+end_src

#+NAME: fig:x_relative_disp
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/x_relative_disp.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:x_relative_disp
#+CAPTION: X relative displacement of the sample with respect to the marble
#+RESULTS: fig:x_relative_disp
[[file:figs/x_relative_disp.png]]

#+begin_src matlab
  figure;
  plot(z_ty(:, 3), 1e6*lsim(1/s, z_ty(:, 2)-z_ty(:, 1), z_ty(:, 3)));
  xlabel('Time [s]'); ylabel('Z Relative Displacement [$\mu m$]');
  xlim([0, 2]);
#+end_src

#+NAME: fig:z_relative_disp
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/z_relative_disp.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:z_relative_disp
#+CAPTION: Z relative disp of the sample with respect to the marble
#+RESULTS: fig:z_relative_disp
[[file:figs/z_relative_disp.png]]

** Frequency Domain analysis
We get the typical ground velocity to compare with the velocities measured.
#+begin_src matlab
  [pxx_gm, f_gm] = getPSDGroundVelocity();
#+end_src

We first compute some parameters that will be used for the PSD computation.
#+begin_src matlab
  dt = z_ty(2, 3)-z_ty(1, 3);

  Fs = 1/dt; % [Hz]

  win = hanning(ceil(10*Fs));
#+end_src

Then we compute the Power Spectral Density using =pwelch= function.

First for the geophone located on the marble
#+begin_src matlab
  [pxz_ty_m, f] = pwelch(z_ty(:, 1), win, [], [], Fs);
  [pxe_ty_m, ~] = pwelch(e_ty(:, 1), win, [], [], Fs);
  [pxe_of_m, ~] = pwelch(e_of(:, 1), win, [], [], Fs);
#+end_src

And for the geophone located at the sample position.
#+begin_src matlab
  [pxz_ty_s, ~] = pwelch(z_ty(:, 2), win, [], [], Fs);
  [pxe_ty_s, ~] = pwelch(e_ty(:, 2), win, [], [], Fs);
  [pxe_of_s, ~] = pwelch(e_of(:, 2), win, [], [], Fs);
#+end_src

And finally for the relative velocity between the sample and the marble.
#+begin_src matlab
  [pxz_ty_r, ~] = pwelch(z_ty(:, 2)-z_ty(:, 1), win, [], [], Fs);
  [pxe_ty_r, ~] = pwelch(e_ty(:, 2)-e_ty(:, 1), win, [], [], Fs);
  [pxe_of_r, ~] = pwelch(e_of(:, 2)-e_of(:, 1), win, [], [], Fs);
#+end_src

And we plot the ASD of the measured velocities:
- figure [[fig:asd_east_marble]] compares the marble velocity in the east direction when scanning and when Ty is OFF
- figure [[fig:asd_east_sample]] compares the sample velocity in the east direction when scanning and when Ty is OFF
- figure [[fig:asd_z_direction]] shows the marble and sample velocities in the Z direction when scanning with the translation stage
- figure [[fig:asd_e_relative]] shows the relative velocity of the sample with respect to the granite in the X direction when the translation stage is OFF and when it is scanning at 1Hz

#+begin_src matlab
  figure;
  hold on;
  plot(f, sqrt(pxe_ty_m), 'DisplayName', 'Ty 1Hz - Marble - X');
  plot(f, sqrt(pxe_of_m), 'DisplayName', 'Ty OFF - Marble - X');
  plot(f_gm, sqrt(pxx_gm), 'k--', 'DisplayName', 'Ground Motion');
  hold off;
  set(gca, 'xscale', 'log');
  set(gca, 'yscale', 'log');
  xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
  legend('Location', 'northwest');
  xlim([0.1, 500]);
#+end_src

#+NAME: fig:asd_east_marble
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/asd_east_marble.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:asd_east_marble
#+CAPTION: Amplitude spectral density of the measured velocities corresponding to the geophone in the east direction located on the marble when the translation stage is OFF and when it is scanning at 1Hz
#+RESULTS: fig:asd_east_marble
[[file:figs/asd_east_marble.png]]


#+begin_src matlab
  figure;
  hold on;
  plot(f, sqrt(pxe_ty_s), 'DisplayName', 'Ty 1Hz - Sample - X');
  plot(f, sqrt(pxe_of_s), 'DisplayName', 'Ty OFF - Sample - X');
  plot(f_gm, sqrt(pxx_gm), 'k--', 'DisplayName', 'Ground Motion');
  hold off;
  set(gca, 'xscale', 'log');
  set(gca, 'yscale', 'log');
  xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
  legend('Location', 'northwest');
  xlim([0.1, 500]);
#+end_src

#+NAME: fig:asd_east_sample
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/asd_east_sample.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:asd_east_sample
#+CAPTION: Amplitude spectral density of the measured velocities corresponding to the geophone in the east direction located at the sample location when the translation stage is OFF and when it is scanning at 1Hz
#+RESULTS: fig:asd_east_sample
[[file:figs/asd_east_sample.png]]


#+begin_src matlab
  figure;
  hold on;
  plot(f, sqrt(pxz_ty_m), 'DisplayName', 'Ty 1Hz - Marble - Z');
  plot(f, sqrt(pxz_ty_s), 'DisplayName', 'Ty 1Hz - Sample - Z');
  plot(f_gm, sqrt(pxx_gm), 'k--', 'DisplayName', 'Ground Motion');
  hold off;
  set(gca, 'xscale', 'log');
  set(gca, 'yscale', 'log');
  xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
  legend('Location', 'northwest');
  xlim([0.1, 500]);
#+end_src

#+NAME: fig:asd_z_direction
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/asd_z_direction.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:asd_z_direction
#+CAPTION: Amplitude spectral density of the measure velocity corresponding to the geophone in the vertical direction located on the granite and at the sample location when the translation stage is scanning at 1Hz
#+RESULTS: fig:asd_z_direction
[[file:figs/asd_z_direction.png]]


#+begin_src matlab
  figure;
  hold on;
  plot(f, sqrt(pxe_of_r), 'DisplayName', 'Ty OFF - Relative - E');
  plot(f, sqrt(pxe_ty_r), 'DisplayName', 'Ty 1Hz - Relative - E');
  hold off;
  set(gca, 'xscale', 'log');
  set(gca, 'yscale', 'log');
  xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
  legend('Location', 'northwest');
  xlim([0.1, 500]);
#+end_src

#+NAME: fig:asd_e_relative
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/asd_e_relative.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:asd_e_relative
#+CAPTION: Amplitude spectral density of the measured relative velocity in the X direction
#+RESULTS: fig:asd_e_relative
[[file:figs/asd_e_relative.png]]

** Transfer function from marble motion in the East direction to sample motion in the East direction
Let's compute the transfer function for the marble velocity in the east direction to the sample velocity in the east direction.

We first plot the time domain motions when every stage is off (figure [[fig:east_marble_sample]]).

#+begin_src matlab
  figure;
  hold on;
  plot(e_of(:, 3), e_of(:, 2), 'DisplayName', 'Sample - X');
  plot(e_of(:, 3), e_of(:, 1), 'DisplayName', 'Marble - X');
  hold off;
  xlabel('Time [s]'); ylabel('Velocity [m/s]');
  xlim([0, 100]);
  legend('Location', 'southwest');
#+end_src

#+NAME: fig:east_marble_sample
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/east_marble_sample.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:east_marble_sample
#+CAPTION: Velocity in the east direction of the marble and sample when all the stages are OFF
#+RESULTS: fig:east_marble_sample
[[file:figs/east_marble_sample.png]]


We then compute the transfer function using =tfestimate=.
#+begin_src matlab
  dt = e_of(2, 3)-e_of(1, 3);
  Fs = 1/dt; % [Hz]
  win = hanning(ceil(10*Fs));

  [T, f] = tfestimate(e_of(:, 1), e_of(:, 2), win, [], [], Fs);
#+end_src


The result is shown on figure [[fig:tf_east_marble_sample]].
#+begin_src matlab :exports none
  figure;
  ax1 = subplot(2, 1, 1);
  hold on;
  plot(f, abs(T));
  hold off;
  set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
  set(gca, 'XTickLabel',[]);
  ylabel('Magnitude');

  ax2 = subplot(2, 1, 2);
  hold on;
  plot(f, mod(180+180/pi*phase(T), 360)-180);
  hold off;
  set(gca, 'xscale', 'log');
  ylim([-180, 180]);
  yticks([-180, -90, 0, 90, 180]);
  xlabel('Frequency [Hz]'); ylabel('Phase [deg]');

  linkaxes([ax1,ax2],'x');
  xlim([10, 100]);
#+end_src

#+NAME: fig:tf_east_marble_sample
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/tf_east_marble_sample.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:tf_east_marble_sample
#+CAPTION: Estimation of the transfer function from marble velocity in the east direction to sample velocity in the east direction
#+RESULTS: fig:tf_east_marble_sample
[[file:figs/tf_east_marble_sample.png]]

** Position of the translation stage and Current
The position of the translation and current flowing in its actuator are measured using the elmo software and saved as an csv file.

*** Data pre-processing
Let's look at at the start of the csv file.

#+begin_src bash :results output
  sed -n 1,30p mat/sin_elmo.csv | nl -ba -
#+end_src

#+RESULTS:
#+begin_example
     1	Elmo txt chart ver 2.0
     2
     3	[File Properties]
     4	Creation Time,2019-05-13 05:11:45
     5	Last Updated,2019-05-13 05:11:45
     6	Resolution,0.001
     7	Sampling Time,5E-05
     8	Recording Time,5.461
     9
    10	[Chart Properties]
    11	No.,Name,X Linear,X No.
    12	1,Chart #1,True,0
    13	2,Chart #2,True,0
    14
    15	[Chart Data]
    16	Display No.,X No.,Y No.,X Unit,Y Unit,Color,Style,Width
    17	1,1,2,sec,N/A,ff0000ff,Solid,TwoPoint
    18	2,1,3,sec,N/A,ff0000ff,Solid,TwoPoint
    19	2,1,4,sec,N/A,ff007f00,Solid,TwoPoint
    20
    21	[Signal Names]
    22	1,Time (sec)
    23	2,Position [cnt]
    24	3,Current Command [A]
    25	4,Total Current Command [A]
    26
    27	[Signals Data Group 1]
    28	1,2,3,4,
    29	0,1110769,-0.320872406596209,-0.320872406596209,
    30	0.001,1108743,-0.319658428261391,-0.319658428261391,
#+end_example

The real data starts at line 29.
We then load this =cvs= file starting at line 29.

#+begin_src matlab
  data = csvread("mat/sin_elmo.csv", 29, 0);
#+end_src

*** Time domain data
We plot the position of the translation stage measured by the encoders.
There is 200000 encoder count for each mm, we then divide by 200000 to obtain mm.
The result is shown on figure [[fig:ty_position_time]].

#+begin_src matlab
  figure;
  hold on;
  plot(data(:, 1), data(:, 2)/200000);
  hold off;
  xlim([0, 5]);
  xlabel('Time [s]'); ylabel('Position [mm]');
#+end_src

#+NAME: fig:ty_position_time
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ty_position_time.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:ty_position_time
#+CAPTION: Y position of the translation stage measured by the encoders
#+RESULTS: fig:ty_position_time
[[file:figs/ty_position_time.png]]

#+begin_src matlab :exports none :tangle no
  xlim([0, 1]);
#+end_src

#+NAME: fig:ty_position_time_zoom
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ty_position_time_zoom.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:ty_position_time_zoom
#+CAPTION: Y position of the translation stage measured by the encoders - Zoom
#+RESULTS: fig:ty_position_time_zoom
[[file:figs/ty_position_time_zoom.png]]

We also plot the current as function of the time on figure [[fig:current_time]].

#+begin_src matlab
  figure;
  hold on;
  plot(data(:, 1), data(:, 3));
  hold off;
  xlim([0, 5]); ylim([-10, 10]);
  xlabel('Time [s]'); ylabel('Current [A]');
#+end_src

#+NAME: fig:current_time
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/current_time.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:current_time
#+CAPTION: Current going through the actuator of the translation stage
#+RESULTS: fig:current_time
[[file:figs/current_time.png]]

#+begin_src matlab :exports none :tangle no
  xlim([0, 1]);
#+end_src

#+NAME: fig:current_time_zoom
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/current_time_zoom.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:current_time_zoom
#+CAPTION: Current going through the actuator of the translation stage - Zoom
#+RESULTS: fig:current_time_zoom
[[file:figs/current_time_zoom.png]]

** Conclusion
#+begin_important
  - The acquisition is done using the Speedgoat as well as using ELMO. The two acquisition are *not* synchronize
  - The value of the translation stage encoder can also be read with the speedgoat, this could permit to synchronize the measurements
#+end_important