Change one measurement of folder

disturbance-control-system/index.org

@@ -1,4 +1,4 @@
-#+TITLE:Measurements
+#+TITLE:Effect on the control system of each stages on the vibration of the station
 :DRAWER:
 #+STARTUP: overview
 
@@ -398,7 +398,11 @@ All the control systems are turned OFF, then, they are turned on one at a time.
 
 Each measurement are done during 100s.
 
-The settings of the voltage amplifier are shown on figure [[fig:amplifier_settings]].
+The settings of the voltage amplifier are shown on figure [[fig:amplifier_settings]]:
+- gain of 60dB
+- AC/DC option set on DC
+- Low pass filter set at 1kHz
+
 A first order low pass filter with a cut-off frequency of 1kHz is added before the voltage amplifier.
 
 #+name: tab:control_system_on_off
@@ -444,22 +448,44 @@ We load the data of the z axis of two geophones.
   d_he = load('mat/data_018.mat', 'data'); d_he = d_he.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 = 60; % [dB]
+
+  d_of(:, 1) = voltageToVelocityL22(d_of(:, 1), d_of(:, 3), gain);
+  d_ty(:, 1) = voltageToVelocityL22(d_ty(:, 1), d_ty(:, 3), gain);
+  d_ry(:, 1) = voltageToVelocityL22(d_ry(:, 1), d_ry(:, 3), gain);
+  d_sr(:, 1) = voltageToVelocityL22(d_sr(:, 1), d_sr(:, 3), gain);
+  d_rz(:, 1) = voltageToVelocityL22(d_rz(:, 1), d_rz(:, 3), gain);
+  d_he(:, 1) = voltageToVelocityL22(d_he(:, 1), d_he(:, 3), gain);
+
+  d_of(:, 2) = voltageToVelocityL22(d_of(:, 2), d_of(:, 3), gain);
+  d_ty(:, 2) = voltageToVelocityL22(d_ty(:, 2), d_ty(:, 3), gain);
+  d_ry(:, 2) = voltageToVelocityL22(d_ry(:, 2), d_ry(:, 3), gain);
+  d_sr(:, 2) = voltageToVelocityL22(d_sr(:, 2), d_sr(:, 3), gain);
+  d_rz(:, 2) = voltageToVelocityL22(d_rz(:, 2), d_rz(:, 3), gain);
+  d_he(:, 2) = voltageToVelocityL22(d_he(:, 2), d_he(:, 3), gain);
+#+end_src
+
 ** Analysis - Time Domain
 First, we can look at the time domain data and compare all the measurements:
 - comparison for the geophone at the sample location (figure [[fig:time_domain_sample_lpf]])
 - comparison for the geophone on the granite (figure [[fig:time_domain_marble_lpf]])
+- relative displacement of the sample with respect to the marble (figure [[fig:time_domain_marble_lpf]])
 
-#+begin_src matlab :results none
+#+begin_src matlab
   figure;
   hold on;
-  plot(d_of(:, 3), d_of(:, 2), 'DisplayName', 'All OFF';
+  plot(d_of(:, 3), d_of(:, 2), 'DisplayName', 'All OFF');
   plot(d_ty(:, 3), d_ty(:, 2), 'DisplayName', 'Ty ON');
   plot(d_ry(:, 3), d_ry(:, 2), 'DisplayName', 'Ry ON');
   plot(d_sr(:, 3), d_sr(:, 2), 'DisplayName', 'S-R ON');
   plot(d_rz(:, 3), d_rz(:, 2), 'DisplayName', 'Rz ON');
   plot(d_he(:, 3), d_he(:, 2), 'DisplayName', 'Hexa ON');
   hold off;
-  xlabel('Time [s]'); ylabel('Voltage [V]');
+  xlabel('Time [s]'); ylabel('Velocity [m/s]');
   xlim([0, 50]);
   legend('Location', 'bestoutside');
 #+end_src
@@ -476,7 +502,7 @@ First, we can look at the time domain data and compare all the measurements:
 [[file:figs/time_domain_sample_lpf.png]]
 
 
-#+begin_src matlab :results none
+#+begin_src matlab
   figure;
   hold on;
   plot(d_of(:, 3), d_of(:, 1), 'DisplayName', 'All OFF');
@@ -486,7 +512,7 @@ First, we can look at the time domain data and compare all the measurements:
   plot(d_rz(:, 3), d_rz(:, 1), 'DisplayName', 'Rz ON');
   plot(d_he(:, 3), d_he(:, 1), 'DisplayName', 'Hexa ON');
   hold off;
-  xlabel('Time [s]'); ylabel('Voltage [V]');
+  xlabel('Time [s]'); ylabel('Velocity [m/s]');
   xlim([0, 50]);
   legend('Location', 'bestoutside');
 #+end_src
@@ -502,6 +528,32 @@ First, we can look at the time domain data and compare all the measurements:
 #+RESULTS: fig:time_domain_marble_lpf
 [[file:figs/time_domain_marble_lpf.png]]
 
+#+begin_src matlab
+  figure;
+  hold on;
+  plot(d_of(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_of(:, 2)-d_of(:, 1), d_of(:, 3)), 'DisplayName', 'All OFF');
+  plot(d_ty(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_ty(:, 2)-d_ty(:, 1), d_ty(:, 3)), 'DisplayName', 'Ty ON');
+  plot(d_ry(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_ry(:, 2)-d_ry(:, 1), d_ry(:, 3)), 'DisplayName', 'Ry ON');
+  plot(d_sr(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_sr(:, 2)-d_sr(:, 1), d_sr(:, 3)), 'DisplayName', 'S-R ON');
+  plot(d_rz(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_rz(:, 2)-d_rz(:, 1), d_rz(:, 3)), 'DisplayName', 'Rz ON');
+  plot(d_he(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_he(:, 2)-d_he(:, 1), d_he(:, 3)), 'DisplayName', 'Hexa ON');
+  hold off;
+  xlabel('Time [s]'); ylabel('Relative Displacement [$\mu m$]');
+  xlim([0, 50]);
+  legend('Location', 'bestoutside');
+#+end_src
+
+#+NAME: fig:time_domain_relative_disp
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/time_domain_relative_disp.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:time_domain_relative_disp
+#+CAPTION: Relative displacement of the sample with respect to the marble
+#+RESULTS: fig:time_domain_relative_disp
+[[file:figs/time_domain_relative_disp.png]]
+
 ** Analysis - Frequency Domain
 #+begin_src matlab :results none
   dt = d_of(2, 3) - d_of(1, 3);
@@ -534,7 +586,7 @@ And we compare all the signals (figures [[fig:psd_sample_comp_lpf]] and [[fig:ps
   hold off;
   set(gca, 'xscale', 'log');
   set(gca, 'yscale', 'log');
-  xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
+  xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
   xlim([0.1, 500]);
   legend('Location', 'southwest');
 #+end_src
@@ -546,7 +598,7 @@ And we compare all the signals (figures [[fig:psd_sample_comp_lpf]] and [[fig:ps
 #+end_src
 
 #+NAME: fig:psd_sample_comp_lpf
-#+CAPTION: Amplitude Spectral Density of the signal coming from the top geophone
+#+CAPTION: Amplitude Spectral Density of the sample velocity
 #+RESULTS: fig:psd_sample_comp_lpf
 [[file:figs/psd_sample_comp_lpf.png]]
 
@@ -562,7 +614,7 @@ And we compare all the signals (figures [[fig:psd_sample_comp_lpf]] and [[fig:ps
 #+end_src
 
 #+NAME: fig:psd_sample_comp_high_freq_lpf
-#+CAPTION: Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)
+#+CAPTION: Amplitude Spectral Density of the sample velocity (zoom at high frequencies)
 #+RESULTS: fig:psd_sample_comp_high_freq_lpf
 [[file:figs/psd_sample_comp_high_freq_lpf.png]]
 
@@ -590,7 +642,7 @@ And we compare the Amplitude Spectral Densities (figures [[fig:psd_marble_comp_l
   hold off;
   set(gca, 'xscale', 'log');
   set(gca, 'yscale', 'log');
-  xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
+  xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
   xlim([0.1, 500]);
   legend('Location', 'northeast');
 #+end_src
@@ -602,7 +654,7 @@ And we compare the Amplitude Spectral Densities (figures [[fig:psd_marble_comp_l
 #+end_src
 
 #+NAME: fig:psd_marble_comp_lpf
-#+CAPTION: Amplitude Spectral Density of the signal coming from geophone located on the marble
+#+CAPTION: Amplitude Spectral Density of the marble velocity
 #+RESULTS: fig:psd_marble_comp_lpf
 [[file:figs/psd_marble_comp_lpf.png]]
 
@@ -619,7 +671,7 @@ And we compare the Amplitude Spectral Densities (figures [[fig:psd_marble_comp_l
 #+end_src
 
 #+NAME: fig:psd_marble_comp_lpf_high_freq
-#+CAPTION: Amplitude Spectral Density of the signal coming from the geophone located on the marble (zoom at high frequencies)
+#+CAPTION: Amplitude Spectral Density of the marble velocity (zoom at high frequencies)
 #+RESULTS: fig:psd_marble_comp_lpf_high_freq
 [[file:figs/psd_marble_comp_lpf_high_freq.png]]
 
@@ -779,404 +831,3 @@ First, we compute the Power Spectral Density of the signals coming from the Geop
 #+begin_important
   Even tough the Hexapod's driver vibrates quite a lot, it does not generate significant vibrations of the granite when either placed on the granite or on the ground.
 #+end_important
-
-* Transfer function from one stage to the other
-  :PROPERTIES:
-  :header-args:matlab+: :tangle matlab/tf_stages_geophone.m
-  :header-args:matlab+: :comments org :mkdirp yes
-  :END:
-  <<sec:tf_stages_geophone>>
-
-** ZIP file containing the data and matlab files                     :ignore:
-#+begin_src bash :exports none :results none
-  if [ matlab/tf_stages_geophone.m -nt data/tf_stages_geophone.zip ]; then
-    cp matlab/tf_stages_geophone.m tf_stages_geophone.m;
-    zip data/tf_stages_geophone \
-        mat/data_010.mat \
-        mat/data_011.mat \
-        mat/data_012.mat \
-        tf_stages_geophone.m
-    rm tf_stages_geophone.m;
-  fi
-#+end_src
-
-#+begin_note
-  All the files (data and Matlab scripts) are accessible [[file:data/tf_stages_geophone.zip][here]].
-#+end_note
-
-** Experimental Setup
-For all the measurements in this section:
-- all the control stages are OFF.
-- the measurements are on the $z$ direction
-
-*** From Marble to Ty - =mat/meas_010.mat=
-One geophone is on the marble, one is on the Ty stage (see figures [[fig:setup_m_ty]], [[fig:setup_m_ty_zoom]] and [[fig:setup_m_ty_top]]).
-
-The =data= array contains the following columns:
-| Column | Description |
-|--------+-------------|
-|      1 | Ground      |
-|      2 | Ty          |
-|      3 | Time        |
-
-#+name: fig:setup_m_ty
-#+caption: Setup with one geophone on the marble and one on top of the translation stage
-#+attr_html: :width 500px
-[[file:./img/IMG_20190430_155330.jpg]]
-
-#+name: fig:setup_m_ty_zoom
-#+caption: Setup with one geophone on the marble and one on top of the translation stage - Close up view
-#+attr_html: :width 500px
-[[file:./img/IMG_20190430_155335.jpg]]
-
-#+name: fig:setup_m_ty_top
-#+caption: Setup with one geophone on the marble and one on top of the translation stage - Top view
-#+attr_html: :width 500px
-[[file:./img/IMG_20190430_155342.jpg]]
-
-*** From Marble to Ry - =mat/meas_011.mat=
-One geophone is on the marble, one is on the Ry stage (see figure [[fig:setup_m_ry]])
-
-The =data= array contains the following columns:
-| Column | Description |
-|--------+-------------|
-|      1 | Ground      |
-|      2 | Ry          |
-|      3 | Time        |
-
-#+name: fig:setup_m_ry
-#+caption: Setup with one geophone on the marble and one on top of the Tilt Stage
-#+attr_html: :width 500px
-[[file:./img/IMG_20190430_163919.jpg]]
-
-*** From Ty to Ry - =mat/meas_012.mat=
-One geophone is on the Ty stage, one is on the Ry stage (see figures [[fig:setup_ty_ry]], [[fig:setup_ty_ry_top]] and [[fig:setup_ty_ry_zoom]])
-One geophone on the Ty stage, one geophone on the Ry stage.
-
-The =data= array contains the following columns:
-| Column | Description |
-|--------+-------------|
-|      1 | Ty          |
-|      2 | Ry          |
-|      3 | Time        |
-
-#+name: fig:setup_ty_ry
-#+caption: Setup with one geophone on the translation stage and one on top of the Tilt Stage
-#+attr_html: :width 500px
-[[file:./img/IMG_20190430_170405.jpg]]
-
-#+name: fig:setup_ty_ry_top
-#+caption: Setup with one geophone on the translation stage and one on top of the Tilt Stage - Top view
-#+attr_html: :width 500px
-[[file:./img/IMG_20190430_170418.jpg]]
-
-#+name: fig:setup_ty_ry_zoom
-#+caption: Setup with one geophone on the translation stage and one on top of the Tilt Stage - Close up view
-#+attr_html: :width 500px
-[[file:./img/IMG_20190430_170425.jpg]]
-
-** 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
-
-** Load data
-We load the data of the z axis of two geophones.
-#+begin_src matlab :results none
-  m_ty  = load('mat/data_010.mat', 'data'); m_ty  = m_ty.data;
-  m_ry  = load('mat/data_011.mat', 'data'); m_ry  = m_ry.data;
-  ty_ry = load('mat/data_012.mat', 'data'); ty_ry = ty_ry.data;
-#+end_src
-
-** Analysis - Time Domain
-First, we can look at the time domain data.
-
-#+begin_src matlab :results none
-  figure;
-  hold on;
-  plot(m_ty(:, 3), m_ty(:, 1), 'DisplayName', 'Marble');
-  plot(m_ty(:, 3), m_ty(:, 2), 'DisplayName', 'Ty');
-  hold off;
-  xlabel('Time [s]'); ylabel('Voltage [V]');
-  legend('Location', 'northeast');
-  xlim([0, 500]);
-#+end_src
-
-#+NAME: fig:time_domain_m_ty
-#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
-#+begin_src matlab :var filepath="figs/time_domain_m_ty.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
-  <<plt-matlab>>
-#+end_src
-
-#+NAME: fig:time_domain_m_ty
-#+CAPTION: Time domain - Marble and translation stage
-#+RESULTS: fig:time_domain_m_ty
-[[file:figs/time_domain_m_ty.png]]
-
-
-#+begin_src matlab :results none
-  figure;
-  hold on;
-  plot(m_ry(:, 3), m_ry(:, 1), 'DisplayName', 'Marble');
-  plot(m_ry(:, 3), m_ry(:, 2), 'DisplayName', 'Ty');
-  hold off;
-  xlabel('Time [s]'); ylabel('Voltage [V]');
-  legend('Location', 'northeast');
-  xlim([0, 500]);
-#+end_src
-
-#+NAME: fig:time_domain_m_ry
-#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
-#+begin_src matlab :var filepath="figs/time_domain_m_ry.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
-  <<plt-matlab>>
-#+end_src
-
-#+NAME: fig:time_domain_m_ry
-#+CAPTION: Time domain - Marble and tilt stage
-#+RESULTS: fig:time_domain_m_ry
-[[file:figs/time_domain_m_ry.png]]
-
-#+begin_src matlab :results none
-  figure;
-  hold on;
-  plot(ty_ry(:, 3), ty_ry(:, 1), 'DisplayName', 'Ty');
-  plot(ty_ry(:, 3), ty_ry(:, 2), 'DisplayName', 'Ry');
-  hold off;
-  xlabel('Time [s]'); ylabel('Voltage [V]');
-  legend('Location', 'northeast');
-  xlim([0, 500]);
-#+end_src
-
-#+NAME: fig:time_domain_ty_ry
-#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
-#+begin_src matlab :var filepath="figs/time_domain_ty_ry.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
-  <<plt-matlab>>
-#+end_src
-
-#+NAME: fig:time_domain_ty_ry
-#+CAPTION: Time domain - Translation stage and tilt stage
-#+RESULTS: fig:time_domain_ty_ry
-[[file:figs/time_domain_ty_ry.png]]
-
-** Analysis - Frequency Domain
-#+begin_src matlab :results none
-  dt = m_ty(2, 3) - m_ty(1, 3);
-
-  Fs = 1/dt;
-  win = hanning(ceil(1*Fs));
-#+end_src
-
-First, we compute the transfer function estimate between the two geophones for the 3 experiments (figure [[fig:compare_tf_geophones]]). We also plot their coherence (figure [[fig:coherence_two_geophones]]).
-#+begin_src matlab :results none
-  [T_m_ty,  f] = tfestimate(m_ty(:, 1),  m_ty(:, 2),  win, [], [], Fs);
-  [T_m_ry,  ~] = tfestimate(m_ry(:, 1),  m_ry(:, 2),  win, [], [], Fs);
-  [T_ty_ry, ~] = tfestimate(ty_ry(:, 1), ty_ry(:, 2), win, [], [], Fs);
-#+end_src
-
-#+begin_src matlab :results none
-  figure;
-  ax1 = subplot(2, 1, 1);
-  hold on;
-  plot(f, abs(T_m_ty),  'DisplayName', 'Marble - Ty');
-  plot(f, abs(T_m_ry),  'DisplayName', 'Marble - Ry');
-  plot(f, abs(T_ty_ry), 'DisplayName', 'Ty - Ry');
-  hold off;
-  set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
-  set(gca, 'XTickLabel',[]);
-  ylabel('Magnitude');
-  legend('Location', 'northwest');
-
-  ax2 = subplot(2, 1, 2);
-  hold on;
-  plot(f, mod(180+180/pi*phase(T_m_ty),  360)-180);
-  plot(f, mod(180+180/pi*phase(T_m_ry),  360)-180);
-  plot(f, mod(180+180/pi*phase(T_ty_ry), 360)-180);
-  hold off;
-  set(gca, 'xscale', 'log');
-  ylim([-180, 180]);
-  yticks([-180, -90, 0, 90, 180]);
-  xlabel('Frequency [Hz]'); ylabel('Phase');
-
-  linkaxes([ax1,ax2],'x');
-  xlim([10, 500]);
-#+end_src
-
-#+NAME: fig:compare_tf_geophones
-#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
-#+begin_src matlab :var filepath="figs/compare_tf_geophones.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
-  <<plt-matlab>>
-#+end_src
-
-#+NAME: fig:compare_tf_geophones
-#+CAPTION: Transfer function from the first geophone to the second geophone for the three experiments
-#+RESULTS: fig:compare_tf_geophones
-[[file:figs/compare_tf_geophones.png]]
-
-
-#+begin_src matlab :results none
-  [coh_m_ty,  f] = mscohere(m_ty(:, 1),  m_ty(:, 2),  win, [], [], Fs);
-  [coh_m_ry,  ~] = mscohere(m_ry(:, 1),  m_ry(:, 2),  win, [], [], Fs);
-  [coh_ty_ry, ~] = mscohere(ty_ry(:, 1), ty_ry(:, 2), win, [], [], Fs);
-#+end_src
-
-#+begin_src matlab :results none :exports none
-  figure;
-  hold on;
-  plot(f, coh_m_ty,  'DisplayName', 'Marble - Ty');
-  plot(f, coh_m_ry,  'DisplayName', 'Marble - Ry');
-  plot(f, coh_ty_ry, 'DisplayName', 'Ty - Ry');
-  hold off;
-  set(gca, 'xscale', 'log');
-  xlabel('Frequency [Hz]'); ylabel('Coherence');
-  ylim([0, 1]); xlim([1, 500]);
-#+end_src
-
-#+NAME: fig:coherence_two_geophones
-#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
-#+begin_src matlab :var filepath="figs/coherence_two_geophones.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
-  <<plt-matlab>>
-#+end_src
-
-#+NAME: fig:coherence_two_geophones
-#+CAPTION: Coherence between the two geophones for the three experiments
-#+RESULTS: fig:coherence_two_geophones
-[[file:figs/coherence_two_geophones.png]]
-
-** Conclusion
-#+begin_important
-  These measurements are not relevant.
-#+end_important
-
-* Effect of the Ty Control System on the vibration of the Sample :noexport:ignore:
-** Experimental Setup
-One geophone is on the marble, the other at the sample location (see figures [[fig:setup_ty]]).
-
-The signal from the top geophone goes through the slip-ring.
-
-#+name: fig:setup_ty
-#+caption: Experimental Setup
-#+attr_html: :width 500px
-[[file:./img/IMG_20190430_112615.jpg]]
-
-Two measurements are done:
-| Setup                | Data File          |
-|----------------------+--------------------|
-| Control of Ty is on  | =mat/data_001.mat= |
-| Control of Ty is off | =mat/data_002.mat= |
-
-For each of the measurements, the data are:
-| Variable | Description                                                        |
-|----------+--------------------------------------------------------------------|
-| =t=      | Time Vector                                                        |
-| =x1=     | Voltage measured across the geophone placed on the marble          |
-| =x2=     | Voltage measured across the geophone placed at the sample location |
-
-Measurements are 50s long.
-
-** 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
-
-** Load data
-We load the data of the z axis of two geophones.
-#+begin_src matlab :results none
-  tyOn  = load('mat/data_001.mat', 't', 'x1', 'x2');
-  tyOff = load('mat/data_002.mat', 't', 'x1', 'x2');
-#+end_src
-
-** Analysis - Time Domain
-#+begin_src matlab :results none
-  dt = tyOn.t(2)-tyOn.t(1);
-  Fs = 1/dt;
-#+end_src
-
-#+begin_src matlab :results none
-  figure;
-  subplot(1, 2, 1);
-  hold on;
-  plot(tyOn.t, tyOn.x1, 'DisplayName', 'Ty ON - Marble');
-  plot(tyOff.t, tyOff.x1, 'DisplayName', 'Ty OFF - Marble');
-  hold off;
-  legend();
-  xlabel('Time [s]'); ylabel('Voltage [V]');
-  xlim([0, 50]);
-
-  subplot(1, 2, 2);
-  hold on;
-  plot(tyOn.t, tyOn.x2, 'DisplayName', 'Ty ON - Sample');
-  plot(tyOff.t, tyOff.x2, 'DisplayName', 'Ty OFF - Sample');
-  hold off;
-  legend();
-  xlabel('Time [s]'); ylabel('Voltage [V]');
-  xlim([0, 50]);
-#+end_src
-
-#+NAME: fig:time_domain_effect_ty
-#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
-#+begin_src matlab :var filepath="figs/time_domain_effect_ty.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
-  <<plt-matlab>>
-#+end_src
-
-#+NAME: fig:time_domain_effect_ty
-#+CAPTION: Effect of the Ty control system on the vibrations of the marble and sample
-#+RESULTS: fig:time_domain_effect_ty
-[[file:figs/time_domain_effect_ty.png]]
-
-** Analysis - Frequency Domain
-#+begin_src matlab :results none
-  Fs = 1/dt;
-  win = hanning(ceil(10*Fs));
-#+end_src
-
-#+begin_src matlab :results none
-  [pxOn1, f] = pwelch(tyOn.x1, win, [], [], Fs);
-  [pxOn2, ~] = pwelch(tyOn.x2, win, [], [], Fs);
-
-  [pxOff1, ~] = pwelch(tyOff.x1, win, [], [], Fs);
-  [pxOff2, ~] = pwelch(tyOff.x2, win, [], [], Fs);
-#+end_src
-
-#+begin_src matlab :results none
-  figure;
-  subplot(1, 2, 1);
-  hold on;
-  plot(f, sqrt(pxOn1), 'DisplayName', 'Ty ON - Marble');
-  plot(f, sqrt(pxOff1), 'DisplayName', 'Ty OFF - Marble');
-  hold off;
-  legend();
-  set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
-  xlim([0.1, 500]); ylim([1e-4, 1]);
-  xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
-
-  subplot(1, 2, 2);
-  hold on;
-  plot(f, sqrt(pxOn2), 'DisplayName', 'Ty ON - Sample');
-  plot(f, sqrt(pxOff2), 'DisplayName', 'Ty OFF - Sample');
-  hold off;
-  legend();
-  set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
-  xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
-  xlim([0.1, 500]); ylim([1e-4, 1]);
-#+end_src
-
-#+NAME: fig:psd_effect_ty
-#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
-#+begin_src matlab :var filepath="figs/psd_effect_ty.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
-  <<plt-matlab>>
-#+end_src
-
-#+NAME: fig:psd_effect_ty
-#+CAPTION: Amplitude Spectral Density - Effect of the Ty control system
-#+RESULTS: fig:psd_effect_ty
-[[file:figs/psd_effect_ty.png]]
-
-** Conclusion

other-measurements/matlab/tf_stages_geophone.m

@@ -0,0 +1,124 @@
+%% Clear Workspace and Close figures
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+% Load data
+% We load the data of the z axis of two geophones.
+
+m_ty  = load('mat/data_010.mat', 'data'); m_ty  = m_ty.data;
+m_ry  = load('mat/data_011.mat', 'data'); m_ry  = m_ry.data;
+ty_ry = load('mat/data_012.mat', 'data'); ty_ry = ty_ry.data;
+
+% Analysis - Time Domain
+% First, we can look at the time domain data.
+
+
+figure;
+hold on;
+plot(m_ty(:, 3), m_ty(:, 1), 'DisplayName', 'Marble');
+plot(m_ty(:, 3), m_ty(:, 2), 'DisplayName', 'Ty');
+hold off;
+xlabel('Time [s]'); ylabel('Voltage [V]');
+legend('Location', 'northeast');
+xlim([0, 500]);
+
+
+
+% #+NAME: fig:time_domain_m_ty
+% #+CAPTION: Time domain - Marble and translation stage
+% #+RESULTS: fig:time_domain_m_ty
+% [[file:figs/time_domain_m_ty.png]]
+
+
+
+figure;
+hold on;
+plot(m_ry(:, 3), m_ry(:, 1), 'DisplayName', 'Marble');
+plot(m_ry(:, 3), m_ry(:, 2), 'DisplayName', 'Ty');
+hold off;
+xlabel('Time [s]'); ylabel('Voltage [V]');
+legend('Location', 'northeast');
+xlim([0, 500]);
+
+
+
+% #+NAME: fig:time_domain_m_ry
+% #+CAPTION: Time domain - Marble and tilt stage
+% #+RESULTS: fig:time_domain_m_ry
+% [[file:figs/time_domain_m_ry.png]]
+
+
+figure;
+hold on;
+plot(ty_ry(:, 3), ty_ry(:, 1), 'DisplayName', 'Ty');
+plot(ty_ry(:, 3), ty_ry(:, 2), 'DisplayName', 'Ry');
+hold off;
+xlabel('Time [s]'); ylabel('Voltage [V]');
+legend('Location', 'northeast');
+xlim([0, 500]);
+
+% Analysis - Frequency Domain
+
+dt = m_ty(2, 3) - m_ty(1, 3);
+
+Fs = 1/dt;
+win = hanning(ceil(1*Fs));
+
+
+
+% First, we compute the transfer function estimate between the two geophones for the 3 experiments (figure [[fig:compare_tf_geophones]]). We also plot their coherence (figure [[fig:coherence_two_geophones]]).
+
+[T_m_ty,  f] = tfestimate(m_ty(:, 1),  m_ty(:, 2),  win, [], [], Fs);
+[T_m_ry,  ~] = tfestimate(m_ry(:, 1),  m_ry(:, 2),  win, [], [], Fs);
+[T_ty_ry, ~] = tfestimate(ty_ry(:, 1), ty_ry(:, 2), win, [], [], Fs);
+
+figure;
+ax1 = subplot(2, 1, 1);
+hold on;
+plot(f, abs(T_m_ty),  'DisplayName', 'Marble - Ty');
+plot(f, abs(T_m_ry),  'DisplayName', 'Marble - Ry');
+plot(f, abs(T_ty_ry), 'DisplayName', 'Ty - Ry');
+hold off;
+set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+set(gca, 'XTickLabel',[]);
+ylabel('Magnitude');
+legend('Location', 'northwest');
+
+ax2 = subplot(2, 1, 2);
+hold on;
+plot(f, mod(180+180/pi*phase(T_m_ty),  360)-180);
+plot(f, mod(180+180/pi*phase(T_m_ry),  360)-180);
+plot(f, mod(180+180/pi*phase(T_ty_ry), 360)-180);
+hold off;
+set(gca, 'xscale', 'log');
+ylim([-180, 180]);
+yticks([-180, -90, 0, 90, 180]);
+xlabel('Frequency [Hz]'); ylabel('Phase');
+
+linkaxes([ax1,ax2],'x');
+xlim([10, 500]);
+
+
+
+% #+NAME: fig:compare_tf_geophones
+% #+CAPTION: Transfer function from the first geophone to the second geophone for the three experiments
+% #+RESULTS: fig:compare_tf_geophones
+% [[file:figs/compare_tf_geophones.png]]
+
+
+
+[coh_m_ty,  f] = mscohere(m_ty(:, 1),  m_ty(:, 2),  win, [], [], Fs);
+[coh_m_ry,  ~] = mscohere(m_ry(:, 1),  m_ry(:, 2),  win, [], [], Fs);
+[coh_ty_ry, ~] = mscohere(ty_ry(:, 1), ty_ry(:, 2), win, [], [], Fs);
+
+figure;
+hold on;
+plot(f, coh_m_ty,  'DisplayName', 'Marble - Ty');
+plot(f, coh_m_ry,  'DisplayName', 'Marble - Ry');
+plot(f, coh_ty_ry, 'DisplayName', 'Ty - Ry');
+hold off;
+set(gca, 'xscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Coherence');
+ylim([0, 1]); xlim([1, 500]);

other-measurements/tf_geophone_stages.html

@@ -0,0 +1,686 @@
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+ <a accesskey="h" href="../index.html"> UP </a>
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+</div><div id="content">
+<h1 class="title">Transfer function from velocity of one stage to the velocity of another stage using geophones</h1>
+<div id="table-of-contents">
+<h2>Table of Contents</h2>
+<div id="text-table-of-contents">
+<ul>
+<li><a href="#orgbdb27eb">1. Experimental Setup</a>
+<ul>
+<li><a href="#org8dbd49b">1.1. From Marble to Ty - <code>mat/meas_010.mat</code></a></li>
+<li><a href="#orgf538b5e">1.2. From Marble to Ry - <code>mat/meas_011.mat</code></a></li>
+<li><a href="#orga48e2bc">1.3. From Ty to Ry - <code>mat/meas_012.mat</code></a></li>
+</ul>
+</li>
+<li><a href="#org3ea309e">2. Measurement Analysis</a>
+<ul>
+<li><a href="#org1638277">2.1. Load data</a></li>
+<li><a href="#org0d3cc48">2.2. Analysis - Time Domain</a></li>
+<li><a href="#org65a5a79">2.3. Analysis - Frequency Domain</a></li>
+<li><a href="#orgbbc525b">2.4. Conclusion</a></li>
+</ul>
+</li>
+</ul>
+</div>
+</div>
+
+<div id="outline-container-orgbdb27eb" class="outline-2">
+<h2 id="orgbdb27eb"><span class="section-number-2">1</span> Experimental Setup</h2>
+<div class="outline-text-2" id="text-1">
+<p>
+For all the measurements in this section:
+</p>
+<ul class="org-ul">
+<li>all the control stages are OFF.</li>
+<li>the measurements are on the \(z\) direction</li>
+</ul>
+</div>
+
+<div id="outline-container-org8dbd49b" class="outline-3">
+<h3 id="org8dbd49b"><span class="section-number-3">1.1</span> From Marble to Ty - <code>mat/meas_010.mat</code></h3>
+<div class="outline-text-3" id="text-1-1">
+<p>
+One geophone is on the marble, one is on the Ty stage (see figures <a href="#orgee9d1f3">1</a>, <a href="#org0acaa0d">2</a> and <a href="#orgec4ad6b">3</a>).
+</p>
+
+<p>
+The <code>data</code> array contains the following columns:
+</p>
+<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
+
+
+<colgroup>
+<col  class="org-right" />
+
+<col  class="org-left" />
+</colgroup>
+<thead>
+<tr>
+<th scope="col" class="org-right">Column</th>
+<th scope="col" class="org-left">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="org-right">1</td>
+<td class="org-left">Ground</td>
+</tr>
+
+<tr>
+<td class="org-right">2</td>
+<td class="org-left">Ty</td>
+</tr>
+
+<tr>
+<td class="org-right">3</td>
+<td class="org-left">Time</td>
+</tr>
+</tbody>
+</table>
+
+
+<div id="orgee9d1f3" class="figure">
+<p><img src="./img/IMG_20190430_155330.jpg" alt="IMG_20190430_155330.jpg" width="500px" />
+</p>
+<p><span class="figure-number">Figure 1: </span>Setup with one geophone on the marble and one on top of the translation stage</p>
+</div>
+
+
+<div id="org0acaa0d" class="figure">
+<p><img src="./img/IMG_20190430_155335.jpg" alt="IMG_20190430_155335.jpg" width="500px" />
+</p>
+<p><span class="figure-number">Figure 2: </span>Setup with one geophone on the marble and one on top of the translation stage - Close up view</p>
+</div>
+
+
+<div id="orgec4ad6b" class="figure">
+<p><img src="./img/IMG_20190430_155342.jpg" alt="IMG_20190430_155342.jpg" width="500px" />
+</p>
+<p><span class="figure-number">Figure 3: </span>Setup with one geophone on the marble and one on top of the translation stage - Top view</p>
+</div>
+</div>
+</div>
+
+<div id="outline-container-orgf538b5e" class="outline-3">
+<h3 id="orgf538b5e"><span class="section-number-3">1.2</span> From Marble to Ry - <code>mat/meas_011.mat</code></h3>
+<div class="outline-text-3" id="text-1-2">
+<p>
+One geophone is on the marble, one is on the Ry stage (see figure <a href="#orgd643390">4</a>)
+</p>
+
+<p>
+The <code>data</code> array contains the following columns:
+</p>
+<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
+
+
+<colgroup>
+<col  class="org-right" />
+
+<col  class="org-left" />
+</colgroup>
+<thead>
+<tr>
+<th scope="col" class="org-right">Column</th>
+<th scope="col" class="org-left">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="org-right">1</td>
+<td class="org-left">Ground</td>
+</tr>
+
+<tr>
+<td class="org-right">2</td>
+<td class="org-left">Ry</td>
+</tr>
+
+<tr>
+<td class="org-right">3</td>
+<td class="org-left">Time</td>
+</tr>
+</tbody>
+</table>
+
+
+<div id="orgd643390" class="figure">
+<p><img src="./img/IMG_20190430_163919.jpg" alt="IMG_20190430_163919.jpg" width="500px" />
+</p>
+<p><span class="figure-number">Figure 4: </span>Setup with one geophone on the marble and one on top of the Tilt Stage</p>
+</div>
+</div>
+</div>
+
+<div id="outline-container-orga48e2bc" class="outline-3">
+<h3 id="orga48e2bc"><span class="section-number-3">1.3</span> From Ty to Ry - <code>mat/meas_012.mat</code></h3>
+<div class="outline-text-3" id="text-1-3">
+<p>
+One geophone is on the Ty stage, one is on the Ry stage (see figures <a href="#org4038125">5</a>, <a href="#orge841934">6</a> and <a href="#org7715257">7</a>)
+One geophone on the Ty stage, one geophone on the Ry stage.
+</p>
+
+<p>
+The <code>data</code> array contains the following columns:
+</p>
+<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
+
+
+<colgroup>
+<col  class="org-right" />
+
+<col  class="org-left" />
+</colgroup>
+<thead>
+<tr>
+<th scope="col" class="org-right">Column</th>
+<th scope="col" class="org-left">Description</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="org-right">1</td>
+<td class="org-left">Ty</td>
+</tr>
+
+<tr>
+<td class="org-right">2</td>
+<td class="org-left">Ry</td>
+</tr>
+
+<tr>
+<td class="org-right">3</td>
+<td class="org-left">Time</td>
+</tr>
+</tbody>
+</table>
+
+
+<div id="org4038125" class="figure">
+<p><img src="./img/IMG_20190430_170405.jpg" alt="IMG_20190430_170405.jpg" width="500px" />
+</p>
+<p><span class="figure-number">Figure 5: </span>Setup with one geophone on the translation stage and one on top of the Tilt Stage</p>
+</div>
+
+
+<div id="orge841934" class="figure">
+<p><img src="./img/IMG_20190430_170418.jpg" alt="IMG_20190430_170418.jpg" width="500px" />
+</p>
+<p><span class="figure-number">Figure 6: </span>Setup with one geophone on the translation stage and one on top of the Tilt Stage - Top view</p>
+</div>
+
+
+<div id="org7715257" class="figure">
+<p><img src="./img/IMG_20190430_170425.jpg" alt="IMG_20190430_170425.jpg" width="500px" />
+</p>
+<p><span class="figure-number">Figure 7: </span>Setup with one geophone on the translation stage and one on top of the Tilt Stage - Close up view</p>
+</div>
+</div>
+</div>
+</div>
+
+<div id="outline-container-org3ea309e" class="outline-2">
+<h2 id="org3ea309e"><span class="section-number-2">2</span> Measurement Analysis</h2>
+<div class="outline-text-2" id="text-2">
+<p>
+<a id="org88007a9"></a>
+</p>
+<div class="note">
+<p>
+All the files (data and Matlab scripts) are accessible <a href="data/tf_stages_geophone.zip">here</a>.
+</p>
+
+</div>
+</div>
+
+<div id="outline-container-org1638277" class="outline-3">
+<h3 id="org1638277"><span class="section-number-3">2.1</span> Load data</h3>
+<div class="outline-text-3" id="text-2-1">
+<p>
+We load the data of the z axis of two geophones.
+</p>
+<div class="org-src-container">
+<pre class="src src-matlab">m_ty  = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_010.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; m_ty  = m_ty.data;
+m_ry  = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_011.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; m_ry  = m_ry.data;
+ty_ry = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_012.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ty_ry = ty_ry.data;
+</pre>
+</div>
+</div>
+</div>
+
+<div id="outline-container-org0d3cc48" class="outline-3">
+<h3 id="org0d3cc48"><span class="section-number-3">2.2</span> Analysis - Time Domain</h3>
+<div class="outline-text-3" id="text-2-2">
+<p>
+First, we can look at the time domain data.
+</p>
+
+<div class="org-src-container">
+<pre class="src src-matlab"><span class="org-type">figure</span>;
+hold on;
+plot<span class="org-rainbow-delimiters-depth-1">(</span>m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+plot<span class="org-rainbow-delimiters-depth-1">(</span>m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+hold off;
+xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+</pre>
+</div>
+
+
+<div id="org6d8a0eb" class="figure">
+<p><img src="figs/time_domain_m_ty.png" alt="time_domain_m_ty.png" />
+</p>
+<p><span class="figure-number">Figure 8: </span>Time domain - Marble and translation stage</p>
+</div>
+
+
+<div class="org-src-container">
+<pre class="src src-matlab"><span class="org-type">figure</span>;
+hold on;
+plot<span class="org-rainbow-delimiters-depth-1">(</span>m_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+plot<span class="org-rainbow-delimiters-depth-1">(</span>m_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+hold off;
+xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+</pre>
+</div>
+
+
+<div id="org8700a74" class="figure">
+<p><img src="figs/time_domain_m_ry.png" alt="time_domain_m_ry.png" />
+</p>
+<p><span class="figure-number">Figure 9: </span>Time domain - Marble and tilt stage</p>
+</div>
+
+<div class="org-src-container">
+<pre class="src src-matlab"><span class="org-type">figure</span>;
+hold on;
+plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ry'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+hold off;
+xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+</pre>
+</div>
+
+
+<div id="orgcb2e12d" class="figure">
+<p><img src="figs/time_domain_ty_ry.png" alt="time_domain_ty_ry.png" />
+</p>
+<p><span class="figure-number">Figure 10: </span>Time domain - Translation stage and tilt stage</p>
+</div>
+</div>
+</div>
+
+<div id="outline-container-org65a5a79" class="outline-3">
+<h3 id="org65a5a79"><span class="section-number-3">2.3</span> Analysis - Frequency Domain</h3>
+<div class="outline-text-3" id="text-2-3">
+<div class="org-src-container">
+<pre class="src src-matlab">dt = m_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> m_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+
+Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt;
+win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+</pre>
+</div>
+
+<p>
+First, we compute the transfer function estimate between the two geophones for the 3 experiments (figure <a href="#orgc25589d">11</a>). We also plot their coherence (figure <a href="#org6b84c12">12</a>).
+</p>
+<div class="org-src-container">
+<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>T_m_ty,  f<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>,  m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>,  win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
+<span class="org-rainbow-delimiters-depth-1">[</span>T_m_ry,  <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>m_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>,  m_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>,  win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
+<span class="org-rainbow-delimiters-depth-1">[</span>T_ty_ry, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>ty_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
+</pre>
+</div>
+
+<div class="org-src-container">
+<pre class="src src-matlab"><span class="org-type">figure</span>;
+ax1 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+hold on;
+plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T_m_ty<span class="org-rainbow-delimiters-depth-2">)</span>,  <span class="org-string">'DisplayName', 'Marble - Ty'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T_m_ry<span class="org-rainbow-delimiters-depth-2">)</span>,  <span class="org-string">'DisplayName', 'Marble - Ry'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T_ty_ry<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty - Ry'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+hold off;
+<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XTickLabel'</span>,<span class="org-rainbow-delimiters-depth-2">[]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Magnitude'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+
+ax2 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+hold on;
+plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T_m_ty<span class="org-rainbow-delimiters-depth-3">)</span>,  <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T_m_ry<span class="org-rainbow-delimiters-depth-3">)</span>,  <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T_ty_ry<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+hold off;
+<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+yticks<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-type">-</span><span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Phase'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+
+linkaxes<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>ax1,ax2<span class="org-rainbow-delimiters-depth-2">]</span>,<span class="org-string">'x'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">10</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
+</pre>
+</div>
+
+
+<div id="orgc25589d" class="figure">
+<p><img src="figs/compare_tf_geophones.png" alt="compare_tf_geophones.png" />
+</p>
+<p><span class="figure-number">Figure 11: </span>Transfer function from the first geophone to the second geophone for the three experiments</p>
+</div>
+
+
+<div class="org-src-container">
+<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>coh_m_ty,  f<span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>,  m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>,  win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
+<span class="org-rainbow-delimiters-depth-1">[</span>coh_m_ry,  <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>m_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>,  m_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>,  win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
+<span class="org-rainbow-delimiters-depth-1">[</span>coh_ty_ry, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>ty_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
+</pre>
+</div>
+
+
+<div id="org6b84c12" class="figure">
+<p><img src="figs/coherence_two_geophones.png" alt="coherence_two_geophones.png" />
+</p>
+<p><span class="figure-number">Figure 12: </span>Coherence between the two geophones for the three experiments</p>
+</div>
+</div>
+</div>
+
+<div id="outline-container-orgbbc525b" class="outline-3">
+<h3 id="orgbbc525b"><span class="section-number-3">2.4</span> Conclusion</h3>
+<div class="outline-text-3" id="text-2-4">
+<div class="important">
+<p>
+These measurements are not relevant.
+</p>
+
+</div>
+</div>
+</div>
+</div>
+</div>
+<div id="postamble" class="status">
+<p class="author">Author: Dehaeze Thomas</p>
+<p class="date">Created: 2019-05-15 mer. 17:22</p>
+<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
+</div>
+</body>
+</html>

other-measurements/tf_geophone_stages.org

@@ -0,0 +1,301 @@
+#+TITLE: Transfer function from velocity of one stage to the velocity of another stage using geophones
+:DRAWER:
+#+STARTUP: overview
+
+#+LANGUAGE: en
+#+EMAIL: dehaeze.thomas@gmail.com
+#+AUTHOR: Dehaeze Thomas
+
+#+HTML_LINK_HOME: ../index.html
+#+HTML_LINK_UP: ../index.html
+
+#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/>
+#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/>
+#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/zenburn.css"/>
+#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.min.js"></script>
+#+HTML_HEAD: <script type="text/javascript" src="../js/bootstrap.min.js"></script>
+#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.stickytableheaders.min.js"></script>
+#+HTML_HEAD: <script type="text/javascript" src="../js/readtheorg.js"></script>
+
+#+HTML_MATHJAX: align: center tagside: right font: TeX
+
+#+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:
+
+* Experimental Setup
+For all the measurements in this section:
+- all the control stages are OFF.
+- the measurements are on the $z$ direction
+
+** From Marble to Ty - =mat/meas_010.mat=
+One geophone is on the marble, one is on the Ty stage (see figures [[fig:setup_m_ty]], [[fig:setup_m_ty_zoom]] and [[fig:setup_m_ty_top]]).
+
+The =data= array contains the following columns:
+| Column | Description |
+|--------+-------------|
+|      1 | Ground      |
+|      2 | Ty          |
+|      3 | Time        |
+
+#+name: fig:setup_m_ty
+#+caption: Setup with one geophone on the marble and one on top of the translation stage
+#+attr_html: :width 500px
+[[file:./img/IMG_20190430_155330.jpg]]
+
+#+name: fig:setup_m_ty_zoom
+#+caption: Setup with one geophone on the marble and one on top of the translation stage - Close up view
+#+attr_html: :width 500px
+[[file:./img/IMG_20190430_155335.jpg]]
+
+#+name: fig:setup_m_ty_top
+#+caption: Setup with one geophone on the marble and one on top of the translation stage - Top view
+#+attr_html: :width 500px
+[[file:./img/IMG_20190430_155342.jpg]]
+
+** From Marble to Ry - =mat/meas_011.mat=
+One geophone is on the marble, one is on the Ry stage (see figure [[fig:setup_m_ry]])
+
+The =data= array contains the following columns:
+| Column | Description |
+|--------+-------------|
+|      1 | Ground      |
+|      2 | Ry          |
+|      3 | Time        |
+
+#+name: fig:setup_m_ry
+#+caption: Setup with one geophone on the marble and one on top of the Tilt Stage
+#+attr_html: :width 500px
+[[file:./img/IMG_20190430_163919.jpg]]
+
+** From Ty to Ry - =mat/meas_012.mat=
+One geophone is on the Ty stage, one is on the Ry stage (see figures [[fig:setup_ty_ry]], [[fig:setup_ty_ry_top]] and [[fig:setup_ty_ry_zoom]])
+One geophone on the Ty stage, one geophone on the Ry stage.
+
+The =data= array contains the following columns:
+| Column | Description |
+|--------+-------------|
+|      1 | Ty          |
+|      2 | Ry          |
+|      3 | Time        |
+
+#+name: fig:setup_ty_ry
+#+caption: Setup with one geophone on the translation stage and one on top of the Tilt Stage
+#+attr_html: :width 500px
+[[file:./img/IMG_20190430_170405.jpg]]
+
+#+name: fig:setup_ty_ry_top
+#+caption: Setup with one geophone on the translation stage and one on top of the Tilt Stage - Top view
+#+attr_html: :width 500px
+[[file:./img/IMG_20190430_170418.jpg]]
+
+#+name: fig:setup_ty_ry_zoom
+#+caption: Setup with one geophone on the translation stage and one on top of the Tilt Stage - Close up view
+#+attr_html: :width 500px
+[[file:./img/IMG_20190430_170425.jpg]]
+
+* Measurement Analysis
+  :PROPERTIES:
+  :header-args:matlab+: :tangle matlab/tf_stages_geophone.m
+  :header-args:matlab+: :comments org :mkdirp yes
+  :END:
+  <<sec:tf_stages_geophone>>
+
+** ZIP file containing the data and matlab files                     :ignore:
+#+begin_src bash :exports none :results none
+  if [ matlab/tf_stages_geophone.m -nt data/tf_stages_geophone.zip ]; then
+    cp matlab/tf_stages_geophone.m tf_stages_geophone.m;
+    zip data/tf_stages_geophone \
+        mat/data_010.mat \
+        mat/data_011.mat \
+        mat/data_012.mat \
+        tf_stages_geophone.m
+    rm tf_stages_geophone.m;
+  fi
+#+end_src
+
+#+begin_note
+  All the files (data and Matlab scripts) are accessible [[file:data/tf_stages_geophone.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
+
+** Load data
+We load the data of the z axis of two geophones.
+#+begin_src matlab :results none
+  m_ty  = load('mat/data_010.mat', 'data'); m_ty  = m_ty.data;
+  m_ry  = load('mat/data_011.mat', 'data'); m_ry  = m_ry.data;
+  ty_ry = load('mat/data_012.mat', 'data'); ty_ry = ty_ry.data;
+#+end_src
+
+** Analysis - Time Domain
+First, we can look at the time domain data.
+
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(m_ty(:, 3), m_ty(:, 1), 'DisplayName', 'Marble');
+  plot(m_ty(:, 3), m_ty(:, 2), 'DisplayName', 'Ty');
+  hold off;
+  xlabel('Time [s]'); ylabel('Voltage [V]');
+  legend('Location', 'northeast');
+  xlim([0, 500]);
+#+end_src
+
+#+NAME: fig:time_domain_m_ty
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/time_domain_m_ty.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:time_domain_m_ty
+#+CAPTION: Time domain - Marble and translation stage
+#+RESULTS: fig:time_domain_m_ty
+[[file:figs/time_domain_m_ty.png]]
+
+
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(m_ry(:, 3), m_ry(:, 1), 'DisplayName', 'Marble');
+  plot(m_ry(:, 3), m_ry(:, 2), 'DisplayName', 'Ty');
+  hold off;
+  xlabel('Time [s]'); ylabel('Voltage [V]');
+  legend('Location', 'northeast');
+  xlim([0, 500]);
+#+end_src
+
+#+NAME: fig:time_domain_m_ry
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/time_domain_m_ry.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:time_domain_m_ry
+#+CAPTION: Time domain - Marble and tilt stage
+#+RESULTS: fig:time_domain_m_ry
+[[file:figs/time_domain_m_ry.png]]
+
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(ty_ry(:, 3), ty_ry(:, 1), 'DisplayName', 'Ty');
+  plot(ty_ry(:, 3), ty_ry(:, 2), 'DisplayName', 'Ry');
+  hold off;
+  xlabel('Time [s]'); ylabel('Voltage [V]');
+  legend('Location', 'northeast');
+  xlim([0, 500]);
+#+end_src
+
+#+NAME: fig:time_domain_ty_ry
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/time_domain_ty_ry.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:time_domain_ty_ry
+#+CAPTION: Time domain - Translation stage and tilt stage
+#+RESULTS: fig:time_domain_ty_ry
+[[file:figs/time_domain_ty_ry.png]]
+
+** Analysis - Frequency Domain
+#+begin_src matlab :results none
+  dt = m_ty(2, 3) - m_ty(1, 3);
+
+  Fs = 1/dt;
+  win = hanning(ceil(1*Fs));
+#+end_src
+
+First, we compute the transfer function estimate between the two geophones for the 3 experiments (figure [[fig:compare_tf_geophones]]). We also plot their coherence (figure [[fig:coherence_two_geophones]]).
+#+begin_src matlab :results none
+  [T_m_ty,  f] = tfestimate(m_ty(:, 1),  m_ty(:, 2),  win, [], [], Fs);
+  [T_m_ry,  ~] = tfestimate(m_ry(:, 1),  m_ry(:, 2),  win, [], [], Fs);
+  [T_ty_ry, ~] = tfestimate(ty_ry(:, 1), ty_ry(:, 2), win, [], [], Fs);
+#+end_src
+
+#+begin_src matlab :results none
+  figure;
+  ax1 = subplot(2, 1, 1);
+  hold on;
+  plot(f, abs(T_m_ty),  'DisplayName', 'Marble - Ty');
+  plot(f, abs(T_m_ry),  'DisplayName', 'Marble - Ry');
+  plot(f, abs(T_ty_ry), 'DisplayName', 'Ty - Ry');
+  hold off;
+  set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+  set(gca, 'XTickLabel',[]);
+  ylabel('Magnitude');
+  legend('Location', 'northwest');
+
+  ax2 = subplot(2, 1, 2);
+  hold on;
+  plot(f, mod(180+180/pi*phase(T_m_ty),  360)-180);
+  plot(f, mod(180+180/pi*phase(T_m_ry),  360)-180);
+  plot(f, mod(180+180/pi*phase(T_ty_ry), 360)-180);
+  hold off;
+  set(gca, 'xscale', 'log');
+  ylim([-180, 180]);
+  yticks([-180, -90, 0, 90, 180]);
+  xlabel('Frequency [Hz]'); ylabel('Phase');
+
+  linkaxes([ax1,ax2],'x');
+  xlim([10, 500]);
+#+end_src
+
+#+NAME: fig:compare_tf_geophones
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/compare_tf_geophones.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:compare_tf_geophones
+#+CAPTION: Transfer function from the first geophone to the second geophone for the three experiments
+#+RESULTS: fig:compare_tf_geophones
+[[file:figs/compare_tf_geophones.png]]
+
+
+#+begin_src matlab :results none
+  [coh_m_ty,  f] = mscohere(m_ty(:, 1),  m_ty(:, 2),  win, [], [], Fs);
+  [coh_m_ry,  ~] = mscohere(m_ry(:, 1),  m_ry(:, 2),  win, [], [], Fs);
+  [coh_ty_ry, ~] = mscohere(ty_ry(:, 1), ty_ry(:, 2), win, [], [], Fs);
+#+end_src
+
+#+begin_src matlab :results none :exports none
+  figure;
+  hold on;
+  plot(f, coh_m_ty,  'DisplayName', 'Marble - Ty');
+  plot(f, coh_m_ry,  'DisplayName', 'Marble - Ry');
+  plot(f, coh_ty_ry, 'DisplayName', 'Ty - Ry');
+  hold off;
+  set(gca, 'xscale', 'log');
+  xlabel('Frequency [Hz]'); ylabel('Coherence');
+  ylim([0, 1]); xlim([1, 500]);
+#+end_src
+
+#+NAME: fig:coherence_two_geophones
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/coherence_two_geophones.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:coherence_two_geophones
+#+CAPTION: Coherence between the two geophones for the three experiments
+#+RESULTS: fig:coherence_two_geophones
+[[file:figs/coherence_two_geophones.png]]
+
+** Conclusion
+#+begin_important
+  These measurements are not relevant.
+#+end_important

src/index.org

@@ -76,7 +76,7 @@ This Matlab function is accessible [[file:voltageToDisplacementL22.m][here]].
 #+begin_src matlab
   velocity = voltageToVelocityL22(voltage, time, gain);
 
-  disp = lsim(1/s, velocity, time);
+  disp = lsim(1/(1+s/(2*pi*0.5)), velocity, time);
 #+end_src
 * getGroundVelocity
   :PROPERTIES:

src/voltageToDisplacementL22.m

@@ -15,4 +15,4 @@ s = zpk('s');
 
 velocity = voltageToVelocityL22(voltage, time, gain);
 
-disp = lsim(1/s, velocity, time);
+disp = lsim(1/(1+s/(2*pi*0.5)), velocity, time);