Complete measurement analysis of 07/05

static-measurements/index.org

@@ -108,7 +108,7 @@ We then compute the Power Spectral Density of the two signals and we compare the
   hold off;
   set(gca, 'xscale', 'log');
   set(gca, 'yscale', 'log');
-  xlabel('Frequency [Hz]'); ylabel('ASD [V/sqrt(Hz)]')
+  xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
   xlim([1, 500]);
   legend('Location', 'southwest');
 #+end_src
@@ -271,7 +271,7 @@ And we compare all the signals (figures [[fig:psd_sample_comp]] and [[fig:psd_sa
   hold off;
   set(gca, 'xscale', 'log');
   set(gca, 'yscale', 'log');
-  xlabel('Frequency [Hz]'); ylabel('ASD [V/sqrt(Hz)]')
+  xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
   xlim([0.1, 500]);
   legend('Location', 'southwest');
 #+end_src
@@ -283,7 +283,7 @@ And we compare all the signals (figures [[fig:psd_sample_comp]] and [[fig:psd_sa
 #+end_src
 
 #+NAME: fig:psd_sample_comp
-#+CAPTION: PSD of the signal coming from the top geophone
+#+CAPTION: Amplitude Spectral Density of the signal coming from the top geophone
 #+RESULTS: fig:psd_sample_comp
 [[file:figs/psd_sample_comp.png]]
 
@@ -299,7 +299,7 @@ And we compare all the signals (figures [[fig:psd_sample_comp]] and [[fig:psd_sa
 #+end_src
 
 #+NAME: fig:psd_sample_comp_high_freq
-#+CAPTION: PSD of the signal coming from the top geophone (zoom at high frequencies)
+#+CAPTION: Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)
 #+RESULTS: fig:psd_sample_comp_high_freq
 [[file:figs/psd_sample_comp_high_freq.png]]
 
@@ -314,7 +314,7 @@ Now we plot the same curves for the geophone located on the marble.
   [px8, ~] = pwelch(d8(:, 1), win, [], [], Fs);
 #+end_src
 
-And we compare the ASD (figures [[fig:psd_marble_comp]] and [[fig:psd_marble_comp_high_freq]])
+And we compare the Amplitude Spectral Densities (figures [[fig:psd_marble_comp]] and [[fig:psd_marble_comp_high_freq]])
 #+begin_src matlab :results none
   figure;
   hold on;
@@ -327,7 +327,7 @@ And we compare the ASD (figures [[fig:psd_marble_comp]] and [[fig:psd_marble_com
   hold off;
   set(gca, 'xscale', 'log');
   set(gca, 'yscale', 'log');
-  xlabel('Frequency [Hz]'); ylabel('ASD [V/sqrt(Hz)]')
+  xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
   xlim([0.1, 500]);
   legend('Location', 'northeast');
 #+end_src
@@ -339,7 +339,7 @@ And we compare the ASD (figures [[fig:psd_marble_comp]] and [[fig:psd_marble_com
 #+end_src
 
 #+NAME: fig:psd_marble_comp
-#+CAPTION: PSD of the signal coming from the top geophone
+#+CAPTION: Amplitude Spectral Density of the signal coming from the top geophone
 #+RESULTS: fig:psd_marble_comp
 [[file:figs/psd_marble_comp.png]]
 
@@ -356,7 +356,7 @@ And we compare the ASD (figures [[fig:psd_marble_comp]] and [[fig:psd_marble_com
 #+end_src
 
 #+NAME: fig:psd_marble_comp_high_freq
-#+CAPTION: PSD of the signal coming from the top geophone (zoom at high frequencies)
+#+CAPTION: Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)
 #+RESULTS: fig:psd_marble_comp_high_freq
 [[file:figs/psd_marble_comp_high_freq.png]]
 ** Effect of the control system on the transmissibility from ground to sample
@@ -576,7 +576,7 @@ 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('ASD [V/sqrt(Hz)]')
+  xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
   xlim([0.1, 500]);
   legend('Location', 'southwest');
 #+end_src
@@ -588,7 +588,7 @@ And we compare all the signals (figures [[fig:psd_sample_comp_lpf]] and [[fig:ps
 #+end_src
 
 #+NAME: fig:psd_sample_comp_lpf
-#+CAPTION: PSD of the signal coming from the top geophone
+#+CAPTION: Amplitude Spectral Density of the signal coming from the top geophone
 #+RESULTS: fig:psd_sample_comp_lpf
 [[file:figs/psd_sample_comp_lpf.png]]
 
@@ -604,7 +604,7 @@ 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: PSD of the signal coming from the top geophone (zoom at high frequencies)
+#+CAPTION: Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)
 #+RESULTS: fig:psd_sample_comp_high_freq_lpf
 [[file:figs/psd_sample_comp_high_freq_lpf.png]]
 
@@ -619,7 +619,7 @@ Now we plot the same curves for the geophone located on the marble.
   [px_he, ~] = pwelch(d_he(:, 1), win, [], [], Fs);
 #+end_src
 
-And we compare the ASD (figures [[fig:psd_marble_comp_lpf]] and [[fig:psd_marble_comp_lpf_high_freq]])
+And we compare the Amplitude Spectral Densities (figures [[fig:psd_marble_comp_lpf]] and [[fig:psd_marble_comp_lpf_high_freq]])
 #+begin_src matlab :results none
   figure;
   hold on;
@@ -632,7 +632,7 @@ And we compare the ASD (figures [[fig:psd_marble_comp_lpf]] and [[fig:psd_marble
   hold off;
   set(gca, 'xscale', 'log');
   set(gca, 'yscale', 'log');
-  xlabel('Frequency [Hz]'); ylabel('ASD [V/sqrt(Hz)]')
+  xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
   xlim([0.1, 500]);
   legend('Location', 'northeast');
 #+end_src
@@ -644,7 +644,7 @@ And we compare the ASD (figures [[fig:psd_marble_comp_lpf]] and [[fig:psd_marble
 #+end_src
 
 #+NAME: fig:psd_marble_comp_lpf
-#+CAPTION: PSD of the signal coming from the top geophone
+#+CAPTION: Amplitude Spectral Density of the signal coming from geophone located on the marble
 #+RESULTS: fig:psd_marble_comp_lpf
 [[file:figs/psd_marble_comp_lpf.png]]
 
@@ -661,14 +661,141 @@ And we compare the ASD (figures [[fig:psd_marble_comp_lpf]] and [[fig:psd_marble
 #+end_src
 
 #+NAME: fig:psd_marble_comp_lpf_high_freq
-#+CAPTION: PSD of the signal coming from the top geophone (zoom at high frequencies)
+#+CAPTION: Amplitude Spectral Density of the signal coming from the geophone located on the marble (zoom at high frequencies)
 #+RESULTS: fig:psd_marble_comp_lpf_high_freq
 [[file:figs/psd_marble_comp_lpf_high_freq.png]]
 
-** TODO Conclusion
+** Conclusion
 #+begin_important
+  - The Ty stage induces vibrations of the marble and at the sample location above 100Hz
+  - The hexapod stage induces vibrations at the sample position above 220Hz
 #+end_note
 
+* Effect of the Symetrie Driver
+** Experimental Setup
+We here measure the signals of two geophones:
+- One is located on top of the Sample platform
+- One is located on the marble
+
+The signal from the top geophone does go trought the slip-ring.
+
+All the control systems are turned OFF except the Hexapod one.
+
+Each measurement are done during 100s.
+
+The settings of the voltage amplifier are:
+- DC
+- 60dB
+- 1kHz
+
+A first order low pass filter with a cut-off frequency of 1kHz is added before the voltage amplifier.
+
+The measurements are:
+- =meas_018.mat=: Hexapod's driver on the granite
+- =meas_019.mat=: Hexapod's driver on the ground
+
+Each of the =mat= file contains one array =data= with 3 columns:
+| Column number | Description       |
+|---------------+-------------------|
+|             1 | Geophone - Marble |
+|             2 | Geophone - Sample |
+|             3 | Time              |
+
+** Matlab Init                                              :noexport:ignore:
+#+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
+  d_18 = load('mat/data_018.mat', 'data'); d_18 = d_18.data;
+  d_19 = load('mat/data_019.mat', 'data'); d_19 = d_19.data;
+#+end_src
+
+** Analysis - Time Domain
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(d_19(:, 3), d_19(:, 1), 'DisplayName', 'Driver - Ground');
+  plot(d_18(:, 3), d_18(:, 1), 'DisplayName', 'Driver - Granite');
+  hold off;
+  xlabel('Time [s]'); ylabel('Voltage [V]');
+  xlim([0, 50]);
+  legend('Location', 'bestoutside');
+#+end_src
+
+#+NAME: fig:time_domain_hexa_driver
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/time_domain_hexa_driver.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:time_domain_hexa_driver
+#+CAPTION: Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location
+#+RESULTS: fig:time_domain_hexa_driver
+[[file:figs/time_domain_hexa_driver.png]]
+
+** Analysis - Frequency Domain
+#+begin_src matlab :results none
+  dt = d_18(2, 3) - d_18(1, 3);
+
+  Fs = 1/dt;
+  win = hanning(ceil(10*Fs));
+#+end_src
+
+*** Vibrations at the sample location
+First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
+#+begin_src matlab :results none
+  [px_18, f] = pwelch(d_18(:, 1), win, [], [], Fs);
+  [px_19, ~] = pwelch(d_19(:, 1), win, [], [], Fs);
+#+end_src
+
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(f, sqrt(px_19), 'DisplayName', 'Driver - Ground');
+  plot(f, sqrt(px_18), 'DisplayName', 'Driver - Granite');
+  hold off;
+  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]);
+  legend('Location', 'southwest');
+#+end_src
+
+#+NAME: fig:psd_hexa_driver
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/psd_hexa_driver.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:psd_hexa_driver
+#+CAPTION: Amplitude Spectral Density of the signal coming from the top geophone
+#+RESULTS: fig:psd_hexa_driver
+[[file:figs/psd_hexa_driver.png]]
+
+
+#+begin_src matlab :results none :tangle no :exports none
+  xlim([80, 500]);
+#+end_src
+
+#+NAME: fig:psd_hexa_driver_high_freq
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/psd_hexa_driver_high_freq.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:psd_hexa_driver_high_freq
+#+CAPTION: Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)
+#+RESULTS: fig:psd_hexa_driver_high_freq
+[[file:figs/psd_hexa_driver_high_freq.png]]
+
+** Conclusion
+#+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
 ** Experimental Setup
 For all the measurements in this section:
@@ -909,6 +1036,9 @@ First, we compute the transfer function estimate between the two geophones for t
 [[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
@@ -956,23 +1086,36 @@ We load the data of the z axis of two geophones.
 
 #+begin_src matlab :results none
   figure;
+  subplot(1, 2, 1);
   hold on;
-  plot(tyOn.t, tyOn.x1);
-  plot(tyOn.t, tyOn.x2);
+  plot(tyOn.t, tyOn.x1, 'DisplayName', 'Ty ON - Marble');
+  plot(tyOff.t, tyOff.x1, 'DisplayName', 'Ty OFF - Marble');
   hold off;
-  legend({'x1 - ON', 'x2 - ON'});
+  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
 
-#+begin_src matlab :results none
-  figure;
-  hold on;
-  plot(tyOff.t, tyOff.x1);
-  plot(tyOff.t, tyOff.x2);
-  hold off;
-  legend({'x1 - OFF', 'x2 - OFF'});
+#+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;
@@ -989,80 +1132,36 @@ We load the data of the z axis of two geophones.
 
 #+begin_src matlab :results none
   figure;
+  subplot(1, 2, 1);
   hold on;
-  plot(f, sqrt(pxOn1));
-  plot(f, sqrt(pxOn2));
-  hold off;
-  set(gca, 'xscale', 'log');
-  set(gca, 'yscale', 'log');
-  xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
-  % xlim([2, 500]);
-#+end_src
-
-#+begin_src matlab :results none
-  figure;
-  hold on;
-  plot(f, sqrt(pxOn1));
-  plot(f, sqrt(pxOff1));
-  hold off;
-  set(gca, 'xscale', 'log');
-  set(gca, 'yscale', 'log');
-  xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
-  % xlim([2, 500]);
-#+end_src
-
-#+begin_src matlab :results none
-  figure;
-  hold on;
-  plot(f, sqrt(pxOn2));
-  plot(f, sqrt(pxOff2));
-  hold off;
-  set(gca, 'xscale', 'log');
-  set(gca, 'yscale', 'log');
-  xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
-  % xlim([2, 500]);
-#+end_src
-
-#+begin_src matlab :results none
-  [T_off, ~]   = tfestimate(tyOff.x1, tyOff.x2, win, [], [], Fs);
-  [coh_off, ~] = mscohere(tyOff.x1, tyOff.x2, win, [], [], Fs);
-
-  [T_on, ~]   = tfestimate(tyOn.x1, tyOn.x2, win, [], [], Fs);
-  [coh_on, ~] = mscohere(tyOn.x1, tyOn.x2, win, [], [], Fs);
-#+end_src
-
-#+begin_src matlab :results none :exports none
-  figure;
-  hold on;
-  plot(f, coh_on);
-  plot(f, coh_off);
-  hold off;
-  set(gca, 'xscale', 'log');
-  xlabel('Frequency [Hz]'); ylabel('Coherence');
-  ylim([0,1]); xlim([1, 500]);
-#+end_src
-
-#+begin_src matlab :results none :exports none
-  figure;
-  ax1 = subplot(2, 1, 1);
-  hold on;
-  plot(f, abs(T_on));
-  plot(f, abs(T_off));
+  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');
-  set(gca, 'XTickLabel',[]);
-  ylabel('Magnitude');
+  xlim([0.1, 500]); ylim([1e-4, 1]);
+  xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
 
-  ax2 = subplot(2, 1, 2);
+  subplot(1, 2, 2);
   hold on;
-  plot(f, mod(180+180/pi*phase(T_on), 360)-180);
-  plot(f, mod(180+180/pi*phase(T_off), 360)-180);
+  plot(f, sqrt(pxOn2), 'DisplayName', 'Ty ON - Sample');
+  plot(f, sqrt(pxOff2), 'DisplayName', 'Ty OFF - Sample');
   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([1, 500]);
+  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