Add data analysis

Library/index.org

@@ -18,34 +18,671 @@
 #+PROPERTY: header-args:matlab+ :output-dir figs
 :END:
 
-For all the measurements here, the geophones are L22.
-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.
-
-* Effect of the control system of each stage
+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
 
+* Effect of the Slip-Ring on the signal
 ** Experimental Setup
-One geophone is on the marble, the other at the sample location (see figures below).
+Two measurements are made with the control systems of all the stages turned OFF.
 
-The signal from the top geophone goes through the slip-ring.
+One geophone is located on the marble while the other is located at the sample location (figure [[fig:setup_slipring]]).
 
-The signals from the geophones are amplified by a voltage amplifier with a gain of 60dB.
-The voltage amplifier also include a low pass filter with a corner frequency of 1kHz.
-
-#+name: fig:setup_ty_1
-#+caption: Figure caption
-#+attr_html: :width 500px
-[[file:./img/IMG_20190430_112613.jpg]]
-
-#+name: fig:setup_ty_2
-#+caption: Figure caption
+#+name: fig:setup_slipring
+#+caption: Experimental Setup
 #+attr_html: :width 500px
 [[file:./img/IMG_20190430_112615.jpg]]
 
-#+name: fig:setup_ty_3
-#+caption: Figure caption
+The two measurements are:
+| Measurement File | Description                                                      |
+|------------------+------------------------------------------------------------------|
+| =meas_008.mat=   | Signal from the top geophone does not goes through the Slip-ring |
+| =meas_009.mat=   | Signal goes through the Slip-ring (as shown on the figure above) |
+
+Each of the measurement =mat= file contains one =data= array 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
+  d8 = load('mat/data_008.mat', 'data'); d8 = d8.data;
+  d9 = load('mat/data_009.mat', 'data'); d9 = d9.data;
+#+end_src
+
+** Analysis - Time Domain
+First, we compare the time domain signals for the two experiments (figure [[fig:slipring_time]]).
+
+
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(d9(:, 3), d9(:, 2), 'DisplayName', 'Slip-Ring');
+  plot(d8(:, 3), d8(:, 2), 'DisplayName', 'Wire');
+  hold off;
+  xlabel('Time [s]'); ylabel('Voltage [V]');
+  xlim([0, 50]);
+  legend('location', 'northeast');
+#+end_src
+
+#+NAME: fig:slipring_time
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/slipring_time.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:slipring_time
+#+CAPTION: Effect of the Slip-Ring on the measured signal - Time domain
+#+RESULTS: fig:slipring_time
+[[file:figs/slipring_time.png]]
+
+** Analysis - Frequency Domain
+We then compute the Power Spectral Density of the two signals and we compare them (figure [[fig:slipring_asd]]).
+#+begin_src matlab :results none
+  dt = d8(2, 3) - d8(1, 3);
+  Fs = 1/dt;
+
+  win = hanning(ceil(1*Fs));
+#+end_src
+
+#+begin_src matlab :results none
+  [pxx8, f] = pwelch(d8(:, 2), win, [], [], Fs);
+  [pxx9, ~] = pwelch(d9(:, 2), win, [], [], Fs);
+#+end_src
+
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(f, sqrt(pxx9), 'DisplayName', 'Slip-Ring');
+  plot(f, sqrt(pxx8), 'DisplayName', 'Wire');
+  hold off;
+  set(gca, 'xscale', 'log');
+  set(gca, 'yscale', 'log');
+  xlabel('Frequency [Hz]'); ylabel('ASD [V/sqrt(Hz)]')
+  xlim([1, 500]);
+  legend('Location', 'southwest');
+#+end_src
+
+#+NAME: fig:slipring_asd
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/slipring_asd.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:slipring_asd
+#+CAPTION: Effect of the Slip-Ring on the measured signal - Frequency domain
+#+RESULTS: fig:slipring_asd
+[[file:figs/slipring_asd.png]]
+
+** Conclusion
+#+begin_important
+- Connecting the geophone through the Slip-Ring seems to induce a lot of noise.
+#+end_important
+
+#+begin_note
+*Remaining questions to answer*:
+- Why is there a sharp peak at 300Hz?
+- Why the use of the Slip-Ring does induce a noise?
+- Can the capacitive/inductive properties of the wires in the Slip-ring does not play well with the geophone? (resonant RLC circuit)
+#+end_note
+
+* Effect of all the control systems on the Sample vibrations
+** 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 not go trought the slip-ring.
+
+First, all the control systems are turned ON, then, they are turned one by one.
+Each measurement are done during 50s.
+
+#+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     |
+|------+------+-----------+---------+---------+----------------|
+| *ON* | *ON* | *ON*      | *ON*    | *ON*    | =meas_003.mat= |
+| OFF  | *ON* | *ON*      | *ON*    | *ON*    | =meas_004.mat= |
+| OFF  | OFF  | *ON*      | *ON*    | *ON*    | =meas_005.mat= |
+| OFF  | OFF  | OFF       | *ON*    | *ON*    | =meas_006.mat= |
+| OFF  | OFF  | OFF       | OFF     | *ON*    | =meas_007.mat= |
+| OFF  | OFF  | OFF       | OFF     | OFF     | =meas_008.mat= |
+
+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
+  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;
+  d6 = load('mat/data_006.mat', 'data'); d6 = d6.data;
+  d7 = load('mat/data_007.mat', 'data'); d7 = d7.data;
+  d8 = load('mat/data_008.mat', 'data'); d8 = d8.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]])
+- comparison for the geophone on the granite (figure [[fig:time_domain_marble]])
+
+#+begin_src matlab :results none
+  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');
+  hold off;
+  xlabel('Time [s]'); ylabel('Voltage [V]');
+  xlim([0, 50]);
+  legend('Location', 'bestoutside');
+#+end_src
+
+#+NAME: fig:time_domain_sample
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/time_domain_sample.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:time_domain_sample
+#+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
+[[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');
+  hold off;
+  xlabel('Time [s]'); ylabel('Voltage [V]');
+  xlim([0, 50]);
+  legend('Location', 'bestoutside');
+#+end_src
+
+#+NAME: fig:time_domain_marble
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/time_domain_marble.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:time_domain_marble
+#+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
+[[file:figs/time_domain_marble.png]]
+
+** Analysis - Frequency Domain
+#+begin_src matlab :results none
+  dt = d3(2, 3) - d3(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
+  [px3, f] = pwelch(d3(:, 2), win, [], [], Fs);
+  [px4, ~] = pwelch(d4(:, 2), win, [], [], Fs);
+  [px5, ~] = pwelch(d5(:, 2), win, [], [], Fs);
+  [px6, ~] = pwelch(d6(:, 2), win, [], [], Fs);
+  [px7, ~] = pwelch(d7(:, 2), win, [], [], Fs);
+  [px8, ~] = pwelch(d8(:, 2), win, [], [], Fs);
+#+end_src
+
+And we compare all the signals (figures [[fig:psd_sample_comp]] and [[fig:psd_sample_comp_high_freq]]).
+#+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');
+  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
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/psd_sample_comp.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:psd_sample_comp
+#+CAPTION: PSD of the signal coming from the top geophone
+#+RESULTS: fig:psd_sample_comp
+[[file:figs/psd_sample_comp.png]]
+
+
+#+begin_src matlab :results none :tangle no :exports none
+  xlim([80, 500]);
+#+end_src
+
+#+NAME: fig:psd_sample_comp_high_freq
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/psd_sample_comp_high_freq.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:psd_sample_comp_high_freq
+#+CAPTION: PSD 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]]
+
+*** Vibrations on the marble
+Now we plot the same curves for the geophone located on the marble.
+#+begin_src matlab :results none
+  [px3, f] = pwelch(d3(:, 1), win, [], [], Fs);
+  [px4, ~] = pwelch(d4(:, 1), win, [], [], Fs);
+  [px5, ~] = pwelch(d5(:, 1), win, [], [], Fs);
+  [px6, ~] = pwelch(d6(:, 1), win, [], [], Fs);
+  [px7, ~] = pwelch(d7(:, 1), win, [], [], Fs);
+  [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]])
+#+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');
+  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
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/psd_marble_comp.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:psd_marble_comp
+#+CAPTION: PSD of the signal coming from the top geophone
+#+RESULTS: fig:psd_marble_comp
+[[file:figs/psd_marble_comp.png]]
+
+
+#+begin_src matlab :results none :tangle no :exports none
+  legend('Location', 'southwest');
+  xlim([80, 500]);
+#+end_src
+
+#+NAME: fig:psd_marble_comp_high_freq
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/psd_marble_comp_high_freq.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:psd_marble_comp_high_freq
+#+CAPTION: PSD 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
+#+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
+
+* Transfer function from one stage to the other
+** 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_112620.jpg]]
+[[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 :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
+
+* 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          |
@@ -53,7 +690,7 @@ Two measurements are done:
 | Control of Ty is on  | =mat/data_001.mat= |
 | Control of Ty is off | =mat/data_002.mat= |
 
-For each of the measurements
+For each of the measurements, the data are:
 | Variable | Description                                                        |
 |----------+--------------------------------------------------------------------|
 | =t=      | Time Vector                                                        |
@@ -74,7 +711,7 @@ We load the data of the z axis of two geophones.
   tyOff = load('mat/data_002.mat', 't', 'x1', 'x2');
 #+end_src
 
-** Analysis
+** Analysis - Time Domain
 #+begin_src matlab :results none
   dt = tyOn.t(2)-tyOn.t(1);
   Fs = 1/dt;
@@ -87,6 +724,7 @@ We load the data of the z axis of two geophones.
   plot(tyOn.t, tyOn.x2);
   hold off;
   legend({'x1 - ON', 'x2 - ON'});
+  xlim([0, 50]);
 #+end_src
 
 #+begin_src matlab :results none
@@ -98,6 +736,7 @@ We load the data of the z axis of two geophones.
   legend({'x1 - OFF', 'x2 - OFF'});
 #+end_src
 
+** Analysis - Frequency Domain
 #+begin_src matlab :results none
   Fs = 1/dt;
   win = hanning(ceil(10*Fs));
@@ -190,110 +829,3 @@ We load the data of the z axis of two geophones.
   linkaxes([ax1,ax2],'x');
   xlim([1, 500]);
 #+end_src
-* Effect of the Slip-Ring on the signal
-** Experimental Setup
-Two measurements are made where the control of all the stages are OFF.
-
-One geophone is located on the marble while the other is located at the sample location.
-
-The two measurements are:
-| Measurement File | Description                                                      |
-|------------------+------------------------------------------------------------------|
-| =meas_008.mat=   | Signal from the top geophone does not goes through the Slip-ring |
-| =meas_009.mat=   | Signal goes through the Slip-ring                                |
-
-Each of the measurement =mat= file contains one =data= array 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
-  data8 = load('mat/data_008.mat', 'data');
-  data9 = load('mat/data_009.mat', 'data');
-#+end_src
-
-** Analysis - Time Domain
-#+begin_src matlab :results none
-  figure;
-  hold on;
-  plot(data9.data(:, 3), data9.data(:, 2), 'DisplayName', 'Slip-Ring');
-  plot(data8.data(:, 3), data8.data(:, 2), 'DisplayName', 'Wire');
-  hold off;
-  xlabel('Time [s]'); ylabel('Voltage [V]');
-  xlim([0, 50]);
-  legend();
-#+end_src
-
-#+NAME: fig:slipring_time
-#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
-#+begin_src matlab :var filepath="figs/slipring_time.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
-  <<plt-matlab>>
-#+end_src
-
-#+NAME: fig:slipring_time
-#+CAPTION: Effect of the Slip-Ring on the measured signal - Time domain
-#+RESULTS: fig:slipring_time
-[[file:figs/slipring_time.png]]
-
-** Analysis - Frequency Domain
-#+begin_src matlab :results none
-  dt = data8.data(2, 3) - data8.data(1, 3);
-
-  Fs = 1/dt;
-  win = hanning(ceil(1*Fs));
-#+end_src
-
-#+begin_src matlab :results none
-  [pxx8, f] = pwelch(data8.data(:, 2), win, [], [], Fs);
-  [pxx9, ~] = pwelch(data9.data(:, 2), win, [], [], Fs);
-#+end_src
-
-#+begin_src matlab :results none
-  figure;
-  hold on;
-  plot(f, sqrt(pxx9), 'DisplayName', 'Slip-Ring');
-  plot(f, sqrt(pxx8), 'DisplayName', 'Wire');
-  hold off;
-  set(gca, 'xscale', 'log');
-  set(gca, 'yscale', 'log');
-  xlabel('Frequency [Hz]'); ylabel('ASD [V/sqrt(Hz)]')
-  xlim([1, 500]);
-  legend('Location', 'southwest');
-#+end_src
-
-#+NAME: fig:slipring_asd
-#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
-#+begin_src matlab :var filepath="figs/slipring_asd.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
-  <<plt-matlab>>
-#+end_src
-
-#+NAME: fig:slipring_asd
-#+CAPTION: Effect of the Slip-Ring on the measured signal - Frequency domain
-#+RESULTS: fig:slipring_asd
-[[file:figs/slipring_asd.png]]
-
-** Conclusion
-*Remaining questions to answer*:
-- Why is there a sharp peak at 300Hz?
-- Why the use of the Slip-Ring does induce a noise?
-- Can the capacitive/inductive properties of the wires in the Slip-ring does not play well with the geophone? (resonant RLC circuit)
-
-* Measurement when signal from top geophone does not go trought the slip-ring
-
-| Ty   | Ry   | Slip Ring | Spindle | Hexapod | Meas. file     |
-|------+------+-----------+---------+---------+----------------|
-| *ON* | *ON* | *ON*      | *ON*    | *ON*    | =meas_003.mat= |
-| OFF  | *ON* | *ON*      | *ON*    | *ON*    | =meas_004.mat= |
-| OFF  | OFF  | *ON*      | *ON*    | *ON*    | =meas_005.mat= |
-| OFF  | OFF  | OFF       | *ON*    | *ON*    | =meas_006.mat= |
-| OFF  | OFF  | OFF       | OFF     | *ON*    | =meas_007.mat= |
-| OFF  | OFF  | OFF       | OFF     | OFF     | =meas_008.mat= |

Library/readme.org

@@ -25,7 +25,6 @@ Meas009: everything off with signal goes through the slip-ring
 ** From Marble to Ty
 =meas_010.mat=
 Everything off, one geophone on the marble, one geophone on the Ty (measure on Z direction)
-=> Can be used to determine the vertical stiffness between the Granite and the Ty stage
 
 Channels:
 | 1 | Ground |
@@ -35,7 +34,6 @@ Channels:
 ** From Marble to Ry
 =meas_011.mat=
 Everything off, one geophone on the marble, one geophone on the Ry (measure on Z direction)
-=> Can be used to determine the vertical stiffness of the Ry Stage (by taking into account the Ty stiffness)
 
 Channels:
 | 1 | Ground |
@@ -45,7 +43,6 @@ Channels:
 ** From Ty to Ry
 =meas_012.mat=
 Everything off, one geophone on the Ty, one geophone on the Ry (measure on Z direction)
-=> Can be used to determine the vertical stiffness of the Ry stage
 
 Channels:
 | 1 | Ty   |

slip-ring-test/index.org

@@ -0,0 +1,108 @@
+#+TITLE:Effect of the rotation of the Slip-Ring
+:DRAWER:
+#+STARTUP: overview
+
+#+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>
+
+#+PROPERTY: header-args:matlab  :session *MATLAB*
+#+PROPERTY: header-args:matlab+ :comments org
+#+PROPERTY: header-args:matlab+ :results output
+#+PROPERTY: header-args:matlab+ :exports both
+#+PROPERTY: header-args:matlab+ :eval no-export
+#+PROPERTY: header-args:matlab+ :output-dir figs
+:END:
+
+* Measurement Description
+Random Signal is generated by one DAC of the SpeedGoat.
+
+The signal going out of the DAC is split into two:
+- one BNC cable is directly connected to one ADC of the SpeedGoat
+- one BNC cable goes two times in the Slip-Ring (from bottom to top and then from top to bottom) and then is connected to one ADC of the SpeedGoat
+
+Two measurements are done.
+| Data File          | Description           |
+|--------------------+-----------------------|
+| =mat/data_001.mat= | Slip-ring not turning |
+| =mat/data_002.mat= | Slip-ring turning     |
+
+For each measurement, the measured signals are:
+| Data File | Description                        |
+|-----------+------------------------------------|
+| =t=       | Time vector                        |
+| =x1=      | Direct signal                      |
+| =x2=      | Signal going through the Slip-Ring |
+
+The goal is to determine is the signal is altered when the spindle is rotating.
+
+Here, the rotation speed of the Slip-Ring is set to 1rpm.
+
+* 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
+  sr_off = load('mat/data_001.mat', 't', 'x1', 'x2');
+  sr_on  = load('mat/data_002.mat', 't', 'x1', 'x2');
+#+end_src
+
+* Analysis
+Let's first look at the signal produced by the DAC (figure [[fig:random_signal]]).
+
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(sr_on.t,  sr_on.x1);
+  hold off;
+  xlabel('Time [s]'); ylabel('Voltage [V]');
+  xlim([0 10]);
+#+end_src
+
+#+NAME: fig:random_signal
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/random_signal.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:random_signal
+#+CAPTION: Random signal produced by the DAC
+#+RESULTS: fig:random_signal
+[[file:figs/random_signal.png]]
+
+We now look at the difference between the signal directly measured by the ADC and the signal that goes through the slip-ring (figure [[fig:slipring_comp_signals]]).
+
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(sr_on.t,  sr_on.x1 - sr_on.x2,  'DisplayName', 'Slip-Ring - $\omega = 1rpm$');
+  plot(sr_off.t, sr_off.x1 - sr_off.x2,'DisplayName', 'Slip-Ring off');
+  hold off;
+  xlabel('Time [s]'); ylabel('Voltage [V]');
+  xlim([0 10]);
+  legend('Location', 'northeast');
+#+end_src
+
+#+NAME: fig:slipring_comp_signals
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/slipring_comp_signals.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:slipring_comp_signals
+#+CAPTION: Alteration of the signal when the slip-ring is turning
+#+RESULTS: fig:slipring_comp_signals
+[[file:figs/slipring_comp_signals.png]]
+
+* Conclusion
+
+*Remaining questions*:
+- Should the measurement be redone using voltage amplifiers?
+- Use higher rotation speed and measure for longer periods (to have multiple revolutions) ?

slip-ring-test/readme.org

@@ -1,2 +0,0 @@
-|data_001|slip-ring not turning|
-|data_002|slip-ring turning|