832 lines
28 KiB
Org Mode
832 lines
28 KiB
Org Mode
#+TITLE:Measurements
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:DRAWER:
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#+STARTUP: overview
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/>
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/>
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/zenburn.css"/>
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#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.min.js"></script>
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#+HTML_HEAD: <script type="text/javascript" src="../js/bootstrap.min.js"></script>
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#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.stickytableheaders.min.js"></script>
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#+HTML_HEAD: <script type="text/javascript" src="../js/readtheorg.js"></script>
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#+PROPERTY: header-args:matlab :session *MATLAB*
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#+PROPERTY: header-args:matlab+ :comments org
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#+PROPERTY: header-args:matlab+ :results output
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#+PROPERTY: header-args:matlab+ :exports both
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#+PROPERTY: header-args:matlab+ :eval no-export
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#+PROPERTY: header-args:matlab+ :output-dir figs
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:END:
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For all the measurements shown here:
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- geophones used are L22 with a resonance frequency of 1Hz
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- the signals are amplified with voltage amplifiers with a gain of 60dB
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- the voltage amplifiers include a low pass filter with a cut-off frequency at 1kHz
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* Effect of the Slip-Ring on the signal
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** Experimental Setup
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Two measurements are made with the control systems of all the stages turned OFF.
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One geophone is located on the marble while the other is located at the sample location (figure [[fig:setup_slipring]]).
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#+name: fig:setup_slipring
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#+caption: Experimental Setup
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#+attr_html: :width 500px
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[[file:./img/IMG_20190430_112615.jpg]]
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The two measurements are:
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| Measurement File | Description |
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|------------------+------------------------------------------------------------------|
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| =meas_008.mat= | Signal from the top geophone does not goes through the Slip-ring |
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| =meas_009.mat= | Signal goes through the Slip-ring (as shown on the figure above) |
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Each of the measurement =mat= file contains one =data= array with 3 columns:
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| Column number | Description |
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|---------------+-------------------|
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| 1 | Geophone - Marble |
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| 2 | Geophone - Sample |
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| 3 | Time |
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** Matlab Init :noexport:ignore:
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#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init>>
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#+end_src
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** Load data
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We load the data of the z axis of two geophones.
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#+begin_src matlab :results none
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d8 = load('mat/data_008.mat', 'data'); d8 = d8.data;
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d9 = load('mat/data_009.mat', 'data'); d9 = d9.data;
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#+end_src
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** Analysis - Time Domain
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First, we compare the time domain signals for the two experiments (figure [[fig:slipring_time]]).
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(d9(:, 3), d9(:, 2), 'DisplayName', 'Slip-Ring');
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plot(d8(:, 3), d8(:, 2), 'DisplayName', 'Wire');
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hold off;
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xlabel('Time [s]'); ylabel('Voltage [V]');
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xlim([0, 50]);
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legend('location', 'northeast');
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#+end_src
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#+NAME: fig:slipring_time
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/slipring_time.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:slipring_time
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#+CAPTION: Effect of the Slip-Ring on the measured signal - Time domain
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#+RESULTS: fig:slipring_time
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[[file:figs/slipring_time.png]]
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** Analysis - Frequency Domain
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We then compute the Power Spectral Density of the two signals and we compare them (figure [[fig:slipring_asd]]).
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#+begin_src matlab :results none
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dt = d8(2, 3) - d8(1, 3);
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Fs = 1/dt;
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win = hanning(ceil(1*Fs));
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#+end_src
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#+begin_src matlab :results none
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[pxx8, f] = pwelch(d8(:, 2), win, [], [], Fs);
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[pxx9, ~] = pwelch(d9(:, 2), win, [], [], Fs);
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#+end_src
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(f, sqrt(pxx9), 'DisplayName', 'Slip-Ring');
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plot(f, sqrt(pxx8), 'DisplayName', 'Wire');
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hold off;
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set(gca, 'xscale', 'log');
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set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD [V/sqrt(Hz)]')
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xlim([1, 500]);
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legend('Location', 'southwest');
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#+end_src
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#+NAME: fig:slipring_asd
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/slipring_asd.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:slipring_asd
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#+CAPTION: Effect of the Slip-Ring on the measured signal - Frequency domain
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#+RESULTS: fig:slipring_asd
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[[file:figs/slipring_asd.png]]
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** Conclusion
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#+begin_important
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- Connecting the geophone through the Slip-Ring seems to induce a lot of noise.
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#+end_important
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#+begin_note
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*Remaining questions to answer*:
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- Why is there a sharp peak at 300Hz?
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- Why the use of the Slip-Ring does induce a noise?
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- Can the capacitive/inductive properties of the wires in the Slip-ring does not play well with the geophone? (resonant RLC circuit)
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#+end_note
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* Effect of all the control systems on the Sample vibrations
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** Experimental Setup
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We here measure the signals of two geophones:
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- One is located on top of the Sample platform
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- One is located on the marble
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The signal from the top geophone does not go trought the slip-ring.
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First, all the control systems are turned ON, then, they are turned one by one.
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Each measurement are done during 50s.
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#+name: tab:control_system_on_off
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#+caption: Summary of the measurements and the states of the control systems
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| Ty | Ry | Slip Ring | Spindle | Hexapod | Meas. file |
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|------+------+-----------+---------+---------+----------------|
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| *ON* | *ON* | *ON* | *ON* | *ON* | =meas_003.mat= |
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| OFF | *ON* | *ON* | *ON* | *ON* | =meas_004.mat= |
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| OFF | OFF | *ON* | *ON* | *ON* | =meas_005.mat= |
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| OFF | OFF | OFF | *ON* | *ON* | =meas_006.mat= |
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| OFF | OFF | OFF | OFF | *ON* | =meas_007.mat= |
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| OFF | OFF | OFF | OFF | OFF | =meas_008.mat= |
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Each of the =mat= file contains one array =data= with 3 columns:
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| Column number | Description |
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|---------------+-------------------|
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| 1 | Geophone - Marble |
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| 2 | Geophone - Sample |
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| 3 | Time |
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** Matlab Init :noexport:ignore:
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#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init>>
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#+end_src
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** Load data
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We load the data of the z axis of two geophones.
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#+begin_src matlab :results none
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d3 = load('mat/data_003.mat', 'data'); d3 = d3.data;
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d4 = load('mat/data_004.mat', 'data'); d4 = d4.data;
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d5 = load('mat/data_005.mat', 'data'); d5 = d5.data;
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d6 = load('mat/data_006.mat', 'data'); d6 = d6.data;
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d7 = load('mat/data_007.mat', 'data'); d7 = d7.data;
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d8 = load('mat/data_008.mat', 'data'); d8 = d8.data;
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#+end_src
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** Analysis - Time Domain
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First, we can look at the time domain data and compare all the measurements:
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- comparison for the geophone at the sample location (figure [[fig:time_domain_sample]])
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- comparison for the geophone on the granite (figure [[fig:time_domain_marble]])
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(d3(:, 3), d3(:, 2), 'DisplayName', 'All ON');
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plot(d4(:, 3), d4(:, 2), 'DisplayName', 'Ty OFF');
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plot(d5(:, 3), d5(:, 2), 'DisplayName', 'Ry OFF');
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plot(d6(:, 3), d6(:, 2), 'DisplayName', 'S-R OFF');
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plot(d7(:, 3), d7(:, 2), 'DisplayName', 'Rz OFF');
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plot(d8(:, 3), d8(:, 2), 'DisplayName', 'Hexa OFF');
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hold off;
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xlabel('Time [s]'); ylabel('Voltage [V]');
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xlim([0, 50]);
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legend('Location', 'bestoutside');
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#+end_src
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#+NAME: fig:time_domain_sample
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/time_domain_sample.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:time_domain_sample
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#+CAPTION: Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location
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#+RESULTS: fig:time_domain_sample
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[[file:figs/time_domain_sample.png]]
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(d3(:, 3), d3(:, 1), 'DisplayName', 'All ON');
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plot(d4(:, 3), d4(:, 1), 'DisplayName', 'Ty OFF');
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plot(d5(:, 3), d5(:, 1), 'DisplayName', 'Ry OFF');
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plot(d6(:, 3), d6(:, 1), 'DisplayName', 'S-R OFF');
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plot(d7(:, 3), d7(:, 1), 'DisplayName', 'Rz OFF');
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plot(d8(:, 3), d8(:, 1), 'DisplayName', 'Hexa OFF');
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hold off;
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xlabel('Time [s]'); ylabel('Voltage [V]');
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xlim([0, 50]);
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legend('Location', 'bestoutside');
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#+end_src
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#+NAME: fig:time_domain_marble
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/time_domain_marble.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:time_domain_marble
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#+CAPTION: Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble
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#+RESULTS: fig:time_domain_marble
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[[file:figs/time_domain_marble.png]]
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** Analysis - Frequency Domain
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#+begin_src matlab :results none
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dt = d3(2, 3) - d3(1, 3);
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Fs = 1/dt;
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win = hanning(ceil(10*Fs));
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#+end_src
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*** Vibrations at the sample location
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First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
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#+begin_src matlab :results none
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[px3, f] = pwelch(d3(:, 2), win, [], [], Fs);
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[px4, ~] = pwelch(d4(:, 2), win, [], [], Fs);
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[px5, ~] = pwelch(d5(:, 2), win, [], [], Fs);
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[px6, ~] = pwelch(d6(:, 2), win, [], [], Fs);
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[px7, ~] = pwelch(d7(:, 2), win, [], [], Fs);
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[px8, ~] = pwelch(d8(:, 2), win, [], [], Fs);
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#+end_src
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And we compare all the signals (figures [[fig:psd_sample_comp]] and [[fig:psd_sample_comp_high_freq]]).
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(f, sqrt(px3), 'DisplayName', 'All ON');
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plot(f, sqrt(px4), 'DisplayName', 'Ty OFF');
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plot(f, sqrt(px5), 'DisplayName', 'Ry OFF');
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plot(f, sqrt(px6), 'DisplayName', 'S-R OFF');
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plot(f, sqrt(px7), 'DisplayName', 'Rz OFF');
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plot(f, sqrt(px8), 'DisplayName', 'Hexa OFF');
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hold off;
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set(gca, 'xscale', 'log');
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set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD [V/sqrt(Hz)]')
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xlim([0.1, 500]);
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legend('Location', 'southwest');
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#+end_src
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#+NAME: fig:psd_sample_comp
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/psd_sample_comp.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:psd_sample_comp
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#+CAPTION: PSD of the signal coming from the top geophone
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#+RESULTS: fig:psd_sample_comp
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[[file:figs/psd_sample_comp.png]]
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#+begin_src matlab :results none :tangle no :exports none
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xlim([80, 500]);
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#+end_src
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#+NAME: fig:psd_sample_comp_high_freq
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/psd_sample_comp_high_freq.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:psd_sample_comp_high_freq
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#+CAPTION: PSD of the signal coming from the top geophone (zoom at high frequencies)
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#+RESULTS: fig:psd_sample_comp_high_freq
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[[file:figs/psd_sample_comp_high_freq.png]]
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*** Vibrations on the marble
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Now we plot the same curves for the geophone located on the marble.
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#+begin_src matlab :results none
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[px3, f] = pwelch(d3(:, 1), win, [], [], Fs);
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[px4, ~] = pwelch(d4(:, 1), win, [], [], Fs);
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[px5, ~] = pwelch(d5(:, 1), win, [], [], Fs);
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[px6, ~] = pwelch(d6(:, 1), win, [], [], Fs);
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[px7, ~] = pwelch(d7(:, 1), win, [], [], Fs);
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[px8, ~] = pwelch(d8(:, 1), win, [], [], Fs);
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#+end_src
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And we compare the ASD (figures [[fig:psd_marble_comp]] and [[fig:psd_marble_comp_high_freq]])
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(f, sqrt(px3), 'DisplayName', 'All ON');
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plot(f, sqrt(px4), 'DisplayName', 'Ty OFF');
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plot(f, sqrt(px5), 'DisplayName', 'Ry OFF');
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plot(f, sqrt(px6), 'DisplayName', 'S-R OFF');
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plot(f, sqrt(px7), 'DisplayName', 'Rz OFF');
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plot(f, sqrt(px8), 'DisplayName', 'Hexa OFF');
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hold off;
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set(gca, 'xscale', 'log');
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set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD [V/sqrt(Hz)]')
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xlim([0.1, 500]);
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legend('Location', 'northeast');
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#+end_src
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#+NAME: fig:psd_marble_comp
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/psd_marble_comp.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:psd_marble_comp
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#+CAPTION: PSD of the signal coming from the top geophone
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#+RESULTS: fig:psd_marble_comp
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[[file:figs/psd_marble_comp.png]]
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#+begin_src matlab :results none :tangle no :exports none
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legend('Location', 'southwest');
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xlim([80, 500]);
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#+end_src
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#+NAME: fig:psd_marble_comp_high_freq
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/psd_marble_comp_high_freq.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:psd_marble_comp_high_freq
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#+CAPTION: PSD of the signal coming from the top geophone (zoom at high frequencies)
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#+RESULTS: fig:psd_marble_comp_high_freq
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[[file:figs/psd_marble_comp_high_freq.png]]
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** Effect of the control system on the transmissibility from ground to sample
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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]]).
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#+begin_src matlab :results none
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dt = d3(2, 3) - d3(1, 3);
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Fs = 1/dt;
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win = hanning(ceil(1*Fs));
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#+end_src
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First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
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#+begin_src matlab :results none
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[T3, f] = tfestimate(d3(:, 1), d3(:, 2), win, [], [], Fs);
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[T4, ~] = tfestimate(d4(:, 1), d4(:, 2), win, [], [], Fs);
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[T5, ~] = tfestimate(d5(:, 1), d5(:, 2), win, [], [], Fs);
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[T6, ~] = tfestimate(d6(:, 1), d6(:, 2), win, [], [], Fs);
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[T7, ~] = tfestimate(d7(:, 1), d7(:, 2), win, [], [], Fs);
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[T8, ~] = tfestimate(d8(:, 1), d8(:, 2), win, [], [], Fs);
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#+end_src
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#+begin_src matlab :results none
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figure;
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ax1 = subplot(2, 1, 1);
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hold on;
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plot(f, abs(T3), 'DisplayName', 'All ON');
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plot(f, abs(T4), 'DisplayName', 'Ty OFF');
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plot(f, abs(T5), 'DisplayName', 'Ry OFF');
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plot(f, abs(T6), 'DisplayName', 'S-R OFF');
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plot(f, abs(T7), 'DisplayName', 'Rz OFF');
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plot(f, abs(T8), 'DisplayName', 'Hexa OFF');
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hold off;
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set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
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set(gca, 'XTickLabel',[]);
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ylabel('Magnitude');
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legend('Location', 'northwest');
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ax2 = subplot(2, 1, 2);
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hold on;
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plot(f, mod(180+180/pi*phase(T3), 360)-180);
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plot(f, mod(180+180/pi*phase(T4), 360)-180);
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plot(f, mod(180+180/pi*phase(T5), 360)-180);
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plot(f, mod(180+180/pi*phase(T6), 360)-180);
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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_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 |
|
|
|----------------------+--------------------|
|
|
| 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 :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;
|
|
hold on;
|
|
plot(tyOn.t, tyOn.x1);
|
|
plot(tyOn.t, tyOn.x2);
|
|
hold off;
|
|
legend({'x1 - ON', 'x2 - ON'});
|
|
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'});
|
|
#+end_src
|
|
|
|
** 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;
|
|
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));
|
|
hold off;
|
|
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
|
set(gca, 'XTickLabel',[]);
|
|
ylabel('Magnitude');
|
|
|
|
ax2 = subplot(2, 1, 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);
|
|
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
|