Add analysis on the new measurements

static-measurements/index.org

@@ -432,6 +432,243 @@ First, we compute the Power Spectral Density of the signals coming from the Geop
 - Why it seems that the measurement noise at high frequency is the limiting factor when the slip ring is ON but not when it is OFF?
 #+end_note
 
+* Effect of all the control systems on the Sample vibrations - One stage at a time
+** 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, 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]].
+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
+#+caption: Summary of the measurements and the states of the control systems
+| Ty   | Ry   | Slip Ring | Spindle | Hexapod | Meas. file     |
+|------+------+-----------+---------+---------+----------------|
+| OFF  | OFF  | OFF       | OFF     | OFF     | =meas_013.mat= |
+| *ON* | OFF  | OFF       | OFF     | OFF     | =meas_014.mat= |
+| OFF  | *ON* | OFF       | OFF     | OFF     | =meas_015.mat= |
+| OFF  | OFF  | *ON*      | OFF     | OFF     | =meas_016.mat= |
+| OFF  | OFF  | OFF       | *ON*    | OFF     | =meas_017.mat= |
+| OFF  | OFF  | OFF       | OFF     | *ON*    | =meas_018.mat= |
+
+Each of the =mat= file contains one array =data= with 3 columns:
+| Column number | Description       |
+|---------------+-------------------|
+|             1 | Geophone - Marble |
+|             2 | Geophone - Sample |
+|             3 | Time              |
+
+#+name: fig:amplifier_settings
+#+caption: Voltage amplifier settings for the measurement
+#+attr_html: :width 500px
+[[file:./img/IMG_20190507_101459.jpg]]
+
+** 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_of = load('mat/data_013.mat', 'data'); d_of = d_of.data;
+  d_ty = load('mat/data_014.mat', 'data'); d_ty = d_ty.data;
+  d_ry = load('mat/data_015.mat', 'data'); d_ry = d_ry.data;
+  d_sr = load('mat/data_016.mat', 'data'); d_sr = d_sr.data;
+  d_rz = load('mat/data_017.mat', 'data'); d_rz = d_rz.data;
+  d_he = load('mat/data_018.mat', 'data'); d_he = d_he.data;
+#+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]])
+
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  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]');
+  xlim([0, 50]);
+  legend('Location', 'bestoutside');
+#+end_src
+
+#+NAME: fig:time_domain_sample_lpf
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/time_domain_sample_lpf.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:time_domain_sample_lpf
+#+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_sample_lpf
+[[file:figs/time_domain_sample_lpf.png]]
+
+
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(d_of(:, 3), d_of(:, 1), 'DisplayName', 'All OFF');
+  plot(d_ty(:, 3), d_ty(:, 1), 'DisplayName', 'Ty ON');
+  plot(d_ry(:, 3), d_ry(:, 1), 'DisplayName', 'Ry ON');
+  plot(d_sr(:, 3), d_sr(:, 1), 'DisplayName', 'S-R ON');
+  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]');
+  xlim([0, 50]);
+  legend('Location', 'bestoutside');
+#+end_src
+
+#+NAME: fig:time_domain_marble_lpf
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/time_domain_marble_lpf.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:time_domain_marble_lpf
+#+CAPTION: Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble
+#+RESULTS: fig:time_domain_marble_lpf
+[[file:figs/time_domain_marble_lpf.png]]
+
+** Analysis - Frequency Domain
+#+begin_src matlab :results none
+  dt = d_of(2, 3) - d_of(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_of, f] = pwelch(d_of(:, 2), win, [], [], Fs);
+  [px_ty, ~] = pwelch(d_ty(:, 2), win, [], [], Fs);
+  [px_ry, ~] = pwelch(d_ry(:, 2), win, [], [], Fs);
+  [px_sr, ~] = pwelch(d_sr(:, 2), win, [], [], Fs);
+  [px_rz, ~] = pwelch(d_rz(:, 2), win, [], [], Fs);
+  [px_he, ~] = pwelch(d_he(:, 2), win, [], [], Fs);
+#+end_src
+
+And we compare all the signals (figures [[fig:psd_sample_comp_lpf]] and [[fig:psd_sample_comp_high_freq_lpf]]).
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(f, sqrt(px_of), 'DisplayName', 'All OFF');
+  plot(f, sqrt(px_ty), 'DisplayName', 'Ty ON');
+  plot(f, sqrt(px_ry), 'DisplayName', 'Ry ON');
+  plot(f, sqrt(px_sr), 'DisplayName', 'S-R ON');
+  plot(f, sqrt(px_rz), 'DisplayName', 'Rz ON');
+  plot(f, sqrt(px_he), 'DisplayName', 'Hexa ON');
+  hold off;
+  set(gca, 'xscale', 'log');
+  set(gca, 'yscale', 'log');
+  xlabel('Frequency [Hz]'); ylabel('ASD [V/sqrt(Hz)]')
+  xlim([0.1, 500]);
+  legend('Location', 'southwest');
+#+end_src
+
+#+NAME: fig:psd_sample_comp_lpf
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/psd_sample_comp_lpf.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:psd_sample_comp_lpf
+#+CAPTION: PSD of the signal coming from the top geophone
+#+RESULTS: fig:psd_sample_comp_lpf
+[[file:figs/psd_sample_comp_lpf.png]]
+
+
+#+begin_src matlab :results none :tangle no :exports none
+  xlim([80, 500]);
+#+end_src
+
+#+NAME: fig:psd_sample_comp_high_freq_lpf
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/psd_sample_comp_high_freq_lpf.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:psd_sample_comp_high_freq_lpf
+#+CAPTION: PSD 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]]
+
+*** Vibrations on the marble
+Now we plot the same curves for the geophone located on the marble.
+#+begin_src matlab :results none
+  [px_of, f] = pwelch(d_of(:, 1), win, [], [], Fs);
+  [px_ty, ~] = pwelch(d_ty(:, 1), win, [], [], Fs);
+  [px_ry, ~] = pwelch(d_ry(:, 1), win, [], [], Fs);
+  [px_sr, ~] = pwelch(d_sr(:, 1), win, [], [], Fs);
+  [px_rz, ~] = pwelch(d_rz(:, 1), win, [], [], Fs);
+  [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]])
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(f, sqrt(px_of), 'DisplayName', 'All OFF');
+  plot(f, sqrt(px_ty), 'DisplayName', 'Ty ON');
+  plot(f, sqrt(px_ry), 'DisplayName', 'Ry ON');
+  plot(f, sqrt(px_sr), 'DisplayName', 'S-R ON');
+  plot(f, sqrt(px_rz), 'DisplayName', 'Rz ON');
+  plot(f, sqrt(px_he), 'DisplayName', 'Hexa ON');
+  hold off;
+  set(gca, 'xscale', 'log');
+  set(gca, 'yscale', 'log');
+  xlabel('Frequency [Hz]'); ylabel('ASD [V/sqrt(Hz)]')
+  xlim([0.1, 500]);
+  legend('Location', 'northeast');
+#+end_src
+
+#+NAME: fig:psd_marble_comp_lpf
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/psd_marble_comp_lpf.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:psd_marble_comp_lpf
+#+CAPTION: PSD of the signal coming from the top geophone
+#+RESULTS: fig:psd_marble_comp_lpf
+[[file:figs/psd_marble_comp_lpf.png]]
+
+
+#+begin_src matlab :results none :tangle no :exports none
+  legend('Location', 'southwest');
+  xlim([80, 500]);
+#+end_src
+
+#+NAME: fig:psd_marble_comp_lpf_high_freq
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/psd_marble_comp_lpf_high_freq.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:psd_marble_comp_lpf_high_freq
+#+CAPTION: PSD of the signal coming from the top geophone (zoom at high frequencies)
+#+RESULTS: fig:psd_marble_comp_lpf_high_freq
+[[file:figs/psd_marble_comp_lpf_high_freq.png]]
+
+** TODO Conclusion
+#+begin_important
+#+end_note
+
 * Transfer function from one stage to the other
 ** Experimental Setup
 For all the measurements in this section:

static-measurements/readme.org

@@ -58,13 +58,13 @@ The voltage amplifiers are: 60db, DC(!) and 1kHz
 Channel 1: marble motion
 Channel 2: Sample motion
 
-- All OFF meas_013.mat
-- Ty ON   meas_014.mat
-- Ry ON   meas_015.mat
-- SR ON   meas_016.mat
-- Rz ON   meas_017.mat
-- Hexa ON meas_018.mat
+- All OFF =meas_013.mat=
+- Ty ON   =meas_014.mat=
+- Ry ON   =meas_015.mat=
+- SR ON   =meas_016.mat=
+- Rz ON   =meas_017.mat=
+- Hexa ON =meas_018.mat=
 
 * Test without the Hexapod Driver on the granite
 
-- Hexa ON with on the ground meas_019.mat
+- Hexa ON with on the ground meas_019.mat