Update analysis on control systems

disturbance-control-system/index.org

@@ -29,10 +29,16 @@
 #+PROPERTY: header-args:shell  :eval no-export
 :END:
 
-For all the measurements shown here:
-- geophones used are L22 with a resonance frequency of 1Hz
-- the signals are amplified with voltage amplifiers with a gain of 60dB
-- the voltage amplifiers include a low pass filter with a cut-off frequency at 1kHz
+
+This file is organized as follow:
+- Section [[sec:effect_control_all]]:
+  - One geophone on the marble and one at the sample location
+  - Each stage is turned on one by one
+- Section [[sec:effect_control_one]]:
+  - One geophone on the marble and one at the sample location
+  - Each stage is turned on one at a time
+- Section [[sec:effect_symetrie_driver]]:
+  - We check if the Symetrie driver induces some vibrations when placed on the marble
 
 * Effect of all the control systems on the Sample vibrations
   :PROPERTIES:
@@ -62,10 +68,15 @@ For all the measurements shown here:
 #+end_note
 
 ** Experimental Setup
-We here measure the signals of two geophones:
+We here measure the signals of two L22 geophones:
 - One is located on top of the Sample platform
 - One is located on the marble
 
+The signals are amplified with voltage amplifiers with the following settings:
+- gain of 60dB
+- AC/DC option set on AC
+- Low pass filter set at 1kHz
+
 The signal from the top geophone does not go trought the slip-ring.
 
 First, all the control systems are turned ON, then, they are turned one by one.
@@ -92,6 +103,7 @@ Each of the =mat= file contains one array =data= with 3 columns:
 ** Matlab Init                                              :noexport:ignore:
 #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
   <<matlab-dir>>
+  addpath('../src');
 #+end_src
 
 #+begin_src matlab :exports none :results silent :noweb yes
@@ -100,7 +112,7 @@ Each of the =mat= file contains one array =data= with 3 columns:
 
 ** Load data
 We load the data of the z axis of two geophones.
-#+begin_src matlab :results none
+#+begin_src matlab
   d3 = load('mat/data_003.mat', 'data'); d3 = d3.data;
   d4 = load('mat/data_004.mat', 'data'); d4 = d4.data;
   d5 = load('mat/data_005.mat', 'data'); d5 = d5.data;
@@ -114,15 +126,15 @@ 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]])
 - comparison for the geophone on the granite (figure [[fig:time_domain_marble]])
 
-#+begin_src matlab :results none
+#+begin_src matlab
   figure;
   hold on;
-  plot(d3(:, 3), d3(:, 2), 'DisplayName', 'All ON');
-  plot(d4(:, 3), d4(:, 2), 'DisplayName', 'Ty OFF');
-  plot(d5(:, 3), d5(:, 2), 'DisplayName', 'Ry OFF');
-  plot(d6(:, 3), d6(:, 2), 'DisplayName', 'S-R OFF');
-  plot(d7(:, 3), d7(:, 2), 'DisplayName', 'Rz OFF');
-  plot(d8(:, 3), d8(:, 2), 'DisplayName', 'Hexa OFF');
+  plot(d3(:, 3), d3(:, 2), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
+  plot(d4(:, 3), d4(:, 2), 'DisplayName', 'Hexa, Rz, SR, Ry');
+  plot(d5(:, 3), d5(:, 2), 'DisplayName', 'Hexa, Rz, SR');
+  plot(d6(:, 3), d6(:, 2), 'DisplayName', 'Hexa, Rz');
+  plot(d7(:, 3), d7(:, 2), 'DisplayName', 'Hexa');
+  plot(d8(:, 3), d8(:, 2), 'DisplayName', 'All OFF');
   hold off;
   xlabel('Time [s]'); ylabel('Voltage [V]');
   xlim([0, 50]);
@@ -140,16 +152,15 @@ First, we can look at the time domain data and compare all the measurements:
 #+RESULTS: fig:time_domain_sample
 [[file:figs/time_domain_sample.png]]
 
-
 #+begin_src matlab :results none
   figure;
   hold on;
-  plot(d3(:, 3), d3(:, 1), 'DisplayName', 'All ON');
-  plot(d4(:, 3), d4(:, 1), 'DisplayName', 'Ty OFF');
-  plot(d5(:, 3), d5(:, 1), 'DisplayName', 'Ry OFF');
-  plot(d6(:, 3), d6(:, 1), 'DisplayName', 'S-R OFF');
-  plot(d7(:, 3), d7(:, 1), 'DisplayName', 'Rz OFF');
-  plot(d8(:, 3), d8(:, 1), 'DisplayName', 'Hexa OFF');
+  plot(d3(:, 3), d3(:, 1), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
+  plot(d4(:, 3), d4(:, 1), 'DisplayName', 'Hexa, Rz, SR, Ry');
+  plot(d5(:, 3), d5(:, 1), 'DisplayName', 'Hexa, Rz, SR');
+  plot(d6(:, 3), d6(:, 1), 'DisplayName', 'Hexa, Rz');
+  plot(d7(:, 3), d7(:, 1), 'DisplayName', 'Hexa');
+  plot(d8(:, 3), d8(:, 1), 'DisplayName', 'All OFF');
   hold off;
   xlabel('Time [s]'); ylabel('Voltage [V]');
   xlim([0, 50]);
@@ -168,7 +179,7 @@ First, we can look at the time domain data and compare all the measurements:
 [[file:figs/time_domain_marble.png]]
 
 ** Analysis - Frequency Domain
-#+begin_src matlab :results none
+#+begin_src matlab
   dt = d3(2, 3) - d3(1, 3);
 
   Fs = 1/dt;
@@ -190,12 +201,13 @@ And we compare all the signals (figures [[fig:psd_sample_comp]] and [[fig:psd_sa
 #+begin_src matlab :results none
   figure;
   hold on;
-  plot(f, sqrt(px3), 'DisplayName', 'All ON');
-  plot(f, sqrt(px4), 'DisplayName', 'Ty OFF');
-  plot(f, sqrt(px5), 'DisplayName', 'Ry OFF');
-  plot(f, sqrt(px6), 'DisplayName', 'S-R OFF');
-  plot(f, sqrt(px7), 'DisplayName', 'Rz OFF');
-  plot(f, sqrt(px8), 'DisplayName', 'Hexa OFF');
+  plot(f, sqrt(px3), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
+  plot(f, sqrt(px4), 'DisplayName', 'Hexa, Rz, SR, Ry');
+  plot(f, sqrt(px5), 'DisplayName', 'Hexa, Rz, SR');
+  plot(f, sqrt(px6), 'DisplayName', 'Hexa, Rz');
+  plot(f, sqrt(px7), 'DisplayName', 'Hexa');
+  plot(f, sqrt(px8), 'DisplayName', 'All OFF');
+  plot(fgm, sqrt(pxxgm), '-k', 'DisplayName', 'Ground Velocity');
   hold off;
   set(gca, 'xscale', 'log');
   set(gca, 'yscale', 'log');
@@ -246,12 +258,13 @@ And we compare the Amplitude Spectral Densities (figures [[fig:psd_marble_comp]]
 #+begin_src matlab :results none
   figure;
   hold on;
-  plot(f, sqrt(px3), 'DisplayName', 'All ON');
-  plot(f, sqrt(px4), 'DisplayName', 'Ty OFF');
-  plot(f, sqrt(px5), 'DisplayName', 'Ry OFF');
-  plot(f, sqrt(px6), 'DisplayName', 'S-R OFF');
-  plot(f, sqrt(px7), 'DisplayName', 'Rz OFF');
-  plot(f, sqrt(px8), 'DisplayName', 'Hexa OFF');
+  plot(f, sqrt(px3), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
+  plot(f, sqrt(px4), 'DisplayName', 'Hexa, Rz, SR, Ry');
+  plot(f, sqrt(px5), 'DisplayName', 'Hexa, Rz, SR');
+  plot(f, sqrt(px6), 'DisplayName', 'Hexa, Rz');
+  plot(f, sqrt(px7), 'DisplayName', 'Hexa');
+  plot(f, sqrt(px8), 'DisplayName', 'All OFF');
+  plot(fgm, sqrt(pxxgm), '-k', 'DisplayName', 'Ground Velocity');
   hold off;
   set(gca, 'xscale', 'log');
   set(gca, 'yscale', 'log');
@@ -287,79 +300,14 @@ And we compare the Amplitude Spectral Densities (figures [[fig:psd_marble_comp]]
 #+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
-As the feedback loops change the dynamics of the system, we should see differences on the transfer function from marble velocity to sample velocity when turning off the control systems (figure [[fig:trans_comp]]).
 
-#+begin_src matlab :results none
-  dt = d3(2, 3) - d3(1, 3);
-
-  Fs = 1/dt;
-  win = hanning(ceil(1*Fs));
-#+end_src
-
-First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
-#+begin_src matlab :results none
-  [T3, f] = tfestimate(d3(:, 1), d3(:, 2), win, [], [], Fs);
-  [T4, ~] = tfestimate(d4(:, 1), d4(:, 2), win, [], [], Fs);
-  [T5, ~] = tfestimate(d5(:, 1), d5(:, 2), win, [], [], Fs);
-  [T6, ~] = tfestimate(d6(:, 1), d6(:, 2), win, [], [], Fs);
-  [T7, ~] = tfestimate(d7(:, 1), d7(:, 2), win, [], [], Fs);
-  [T8, ~] = tfestimate(d8(:, 1), d8(:, 2), win, [], [], Fs);
-#+end_src
-
-#+begin_src matlab :results none
-  figure;
-  ax1 = subplot(2, 1, 1);
-  hold on;
-  plot(f, abs(T3), 'DisplayName', 'All ON');
-  plot(f, abs(T4), 'DisplayName', 'Ty OFF');
-  plot(f, abs(T5), 'DisplayName', 'Ry OFF');
-  plot(f, abs(T6), 'DisplayName', 'S-R OFF');
-  plot(f, abs(T7), 'DisplayName', 'Rz OFF');
-  plot(f, abs(T8), 'DisplayName', 'Hexa OFF');
-  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(T3), 360)-180);
-  plot(f, mod(180+180/pi*phase(T4), 360)-180);
-  plot(f, mod(180+180/pi*phase(T5), 360)-180);
-  plot(f, mod(180+180/pi*phase(T6), 360)-180);
-  plot(f, mod(180+180/pi*phase(T7), 360)-180);
-  plot(f, mod(180+180/pi*phase(T8), 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([1, 500]);
-#+end_src
-
-#+NAME: fig:trans_comp
-#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
-#+begin_src matlab :var filepath="figs/trans_comp.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
-  <<plt-matlab>>
-#+end_src
-
-#+NAME: fig:trans_comp
-#+CAPTION: Comparison of the transfer function from the geophone on the marble to the geophone at the sample location
-#+RESULTS: fig:trans_comp
-[[file:figs/trans_comp.png]]
 ** Conclusion
 #+begin_important
-- The control system of the Ty stage induces a lot of vibrations of the marble
+  - The control system of the Ty stage induces a lot of vibrations of the marble above 100Hz
+  - The hexapod control system add vibrations of the sample only above 200Hz
+  - When the Slip-Ring is ON, white noise appears at high frequencies. This is studied [[file:../slip-ring-electrical-noise/index.org][here]]
 #+end_important
 
-#+begin_note
-- 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
   :PROPERTIES:
   :header-args:matlab+: :tangle matlab/effect_control_one.m
@@ -716,9 +664,9 @@ 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
+- 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.