834 lines
31 KiB
Org Mode
834 lines
31 KiB
Org Mode
#+TITLE:Effect on the control system of each stages on the vibration of the station
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:DRAWER:
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#+STARTUP: overview
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#+LANGUAGE: en
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#+EMAIL: dehaeze.thomas@gmail.com
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#+AUTHOR: Dehaeze Thomas
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#+HTML_LINK_HOME: ../index.html
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#+HTML_LINK_UP: ../index.html
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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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#+HTML_MATHJAX: align: center tagside: right font: TeX
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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 none
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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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#+PROPERTY: header-args:shell :eval no-export
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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 all the control systems on the Sample vibrations
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:PROPERTIES:
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:header-args:matlab+: :tangle matlab/effect_control_all.m
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:header-args:matlab+: :comments org :mkdirp yes
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:END:
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<<sec:effect_control_all>>
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** ZIP file containing the data and matlab files :ignore:
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#+begin_src bash :exports none :results none
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if [ matlab/effect_control_all.m -nt data/effect_control_all.zip ]; then
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cp matlab/effect_control_all.m effect_control_all.m;
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zip data/effect_control_all \
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mat/data_003.mat \
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mat/data_004.mat \
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mat/data_005.mat \
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mat/data_006.mat \
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mat/data_007.mat \
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mat/data_008.mat \
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effect_control_all.m;
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rm effect_control_all.m;
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fi
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#+end_src
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#+begin_note
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All the files (data and Matlab scripts) are accessible [[file:data/effect_control_all.zip][here]].
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#+end_note
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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 :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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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('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
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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: Amplitude Spectral Density 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: Amplitude Spectral Density 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 Amplitude Spectral Densities (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('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
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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: Amplitude Spectral Density 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: Amplitude Spectral Density 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);
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plot(f, mod(180+180/pi*phase(T8), 360)-180);
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hold off;
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set(gca, 'xscale', 'log');
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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xlabel('Frequency [Hz]'); ylabel('Phase');
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linkaxes([ax1,ax2],'x');
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xlim([1, 500]);
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#+end_src
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#+NAME: fig:trans_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/trans_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:trans_comp
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#+CAPTION: Comparison of the transfer function from the geophone on the marble to the geophone at the sample location
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#+RESULTS: fig:trans_comp
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[[file:figs/trans_comp.png]]
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** Conclusion
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#+begin_important
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- The control system of the Ty stage induces a lot of vibrations of the marble
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#+end_important
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#+begin_note
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- 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?
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#+end_note
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* Effect of all the control systems on the Sample vibrations - One stage at a time
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:PROPERTIES:
|
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:header-args:matlab+: :tangle matlab/effect_control_one.m
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:header-args:matlab+: :comments org :mkdirp yes
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:END:
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<<sec:effect_control_one>>
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** ZIP file containing the data and matlab files :ignore:
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|
#+begin_src bash :exports none :results none
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|
if [ matlab/effect_control_one.m -nt data/effect_control_one.zip ]; then
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cp matlab/effect_control_one.m effect_control_one.m;
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zip data/effect_control_one \
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mat/data_013.mat \
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mat/data_014.mat \
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mat/data_015.mat \
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mat/data_016.mat \
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mat/data_017.mat \
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mat/data_018.mat \
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effect_control_one.m
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rm effect_control_one.m;
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fi
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#+end_src
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#+begin_note
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All the files (data and Matlab scripts) are accessible [[file:data/effect_control_one.zip][here]].
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#+end_note
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|
|
|
** Experimental Setup
|
|
We here measure the signals of two geophones:
|
|
- One is located on top of the Sample platform
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|
- One is located on the marble
|
|
|
|
The signal from the top geophone does go trought the slip-ring.
|
|
|
|
All the control systems are turned OFF, then, they are turned on one at a time.
|
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|
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Each measurement are done during 100s.
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|
|
|
The settings of the voltage amplifier are shown on figure [[fig:amplifier_settings]]:
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- gain of 60dB
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- AC/DC option set on DC
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- Low pass filter set at 1kHz
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|
|
A first order low pass filter with a cut-off frequency of 1kHz is added before the voltage amplifier.
|
|
|
|
#+name: tab:control_system_on_off
|
|
#+caption: Summary of the measurements and the states of the control systems
|
|
| Ty | Ry | Slip Ring | Spindle | Hexapod | Meas. file |
|
|
|------+------+-----------+---------+---------+----------------|
|
|
| OFF | OFF | OFF | OFF | OFF | =meas_013.mat= |
|
|
| *ON* | OFF | OFF | OFF | OFF | =meas_014.mat= |
|
|
| OFF | *ON* | OFF | OFF | OFF | =meas_015.mat= |
|
|
| OFF | OFF | *ON* | OFF | OFF | =meas_016.mat= |
|
|
| OFF | OFF | OFF | *ON* | OFF | =meas_017.mat= |
|
|
| OFF | OFF | OFF | OFF | *ON* | =meas_018.mat= |
|
|
|
|
Each of the =mat= file contains one array =data= with 3 columns:
|
|
| Column number | Description |
|
|
|---------------+-------------------|
|
|
| 1 | Geophone - Marble |
|
|
| 2 | Geophone - Sample |
|
|
| 3 | Time |
|
|
|
|
#+name: fig:amplifier_settings
|
|
#+caption: Voltage amplifier settings for the measurement
|
|
#+attr_html: :width 500px
|
|
[[file:./img/IMG_20190507_101459.jpg]]
|
|
|
|
** Matlab Init :noexport:ignore:
|
|
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
|
<<matlab-dir>>
|
|
#+end_src
|
|
|
|
#+begin_src matlab :exports none :results silent :noweb yes
|
|
<<matlab-init>>
|
|
#+end_src
|
|
|
|
** Load data
|
|
We load the data of the z axis of two geophones.
|
|
#+begin_src matlab :results none
|
|
d_of = load('mat/data_013.mat', 'data'); d_of = d_of.data;
|
|
d_ty = load('mat/data_014.mat', 'data'); d_ty = d_ty.data;
|
|
d_ry = load('mat/data_015.mat', 'data'); d_ry = d_ry.data;
|
|
d_sr = load('mat/data_016.mat', 'data'); d_sr = d_sr.data;
|
|
d_rz = load('mat/data_017.mat', 'data'); d_rz = d_rz.data;
|
|
d_he = load('mat/data_018.mat', 'data'); d_he = d_he.data;
|
|
#+end_src
|
|
|
|
** Voltage to Velocity
|
|
We convert the measured voltage to velocity using the function =voltageToVelocityL22= (accessible [[file:~/MEGA/These/meas/src/index.org][here]]).
|
|
|
|
#+begin_src matlab
|
|
gain = 60; % [dB]
|
|
|
|
d_of(:, 1) = voltageToVelocityL22(d_of(:, 1), d_of(:, 3), gain);
|
|
d_ty(:, 1) = voltageToVelocityL22(d_ty(:, 1), d_ty(:, 3), gain);
|
|
d_ry(:, 1) = voltageToVelocityL22(d_ry(:, 1), d_ry(:, 3), gain);
|
|
d_sr(:, 1) = voltageToVelocityL22(d_sr(:, 1), d_sr(:, 3), gain);
|
|
d_rz(:, 1) = voltageToVelocityL22(d_rz(:, 1), d_rz(:, 3), gain);
|
|
d_he(:, 1) = voltageToVelocityL22(d_he(:, 1), d_he(:, 3), gain);
|
|
|
|
d_of(:, 2) = voltageToVelocityL22(d_of(:, 2), d_of(:, 3), gain);
|
|
d_ty(:, 2) = voltageToVelocityL22(d_ty(:, 2), d_ty(:, 3), gain);
|
|
d_ry(:, 2) = voltageToVelocityL22(d_ry(:, 2), d_ry(:, 3), gain);
|
|
d_sr(:, 2) = voltageToVelocityL22(d_sr(:, 2), d_sr(:, 3), gain);
|
|
d_rz(:, 2) = voltageToVelocityL22(d_rz(:, 2), d_rz(:, 3), gain);
|
|
d_he(:, 2) = voltageToVelocityL22(d_he(:, 2), d_he(:, 3), gain);
|
|
#+end_src
|
|
|
|
** Analysis - Time Domain
|
|
First, we can look at the time domain data and compare all the measurements:
|
|
- comparison for the geophone at the sample location (figure [[fig:time_domain_sample_lpf]])
|
|
- comparison for the geophone on the granite (figure [[fig:time_domain_marble_lpf]])
|
|
- relative displacement of the sample with respect to the marble (figure [[fig:time_domain_marble_lpf]])
|
|
|
|
#+begin_src matlab
|
|
figure;
|
|
hold on;
|
|
plot(d_of(:, 3), d_of(:, 2), 'DisplayName', 'All OFF');
|
|
plot(d_ty(:, 3), d_ty(:, 2), 'DisplayName', 'Ty ON');
|
|
plot(d_ry(:, 3), d_ry(:, 2), 'DisplayName', 'Ry ON');
|
|
plot(d_sr(:, 3), d_sr(:, 2), 'DisplayName', 'S-R ON');
|
|
plot(d_rz(:, 3), d_rz(:, 2), 'DisplayName', 'Rz ON');
|
|
plot(d_he(:, 3), d_he(:, 2), 'DisplayName', 'Hexa ON');
|
|
hold off;
|
|
xlabel('Time [s]'); ylabel('Velocity [m/s]');
|
|
xlim([0, 50]);
|
|
legend('Location', 'bestoutside');
|
|
#+end_src
|
|
|
|
#+NAME: fig:time_domain_sample_lpf
|
|
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
|
#+begin_src matlab :var filepath="figs/time_domain_sample_lpf.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
|
<<plt-matlab>>
|
|
#+end_src
|
|
|
|
#+NAME: fig:time_domain_sample_lpf
|
|
#+CAPTION: Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location
|
|
#+RESULTS: fig:time_domain_sample_lpf
|
|
[[file:figs/time_domain_sample_lpf.png]]
|
|
|
|
|
|
#+begin_src matlab
|
|
figure;
|
|
hold on;
|
|
plot(d_of(:, 3), d_of(:, 1), 'DisplayName', 'All OFF');
|
|
plot(d_ty(:, 3), d_ty(:, 1), 'DisplayName', 'Ty ON');
|
|
plot(d_ry(:, 3), d_ry(:, 1), 'DisplayName', 'Ry ON');
|
|
plot(d_sr(:, 3), d_sr(:, 1), 'DisplayName', 'S-R ON');
|
|
plot(d_rz(:, 3), d_rz(:, 1), 'DisplayName', 'Rz ON');
|
|
plot(d_he(:, 3), d_he(:, 1), 'DisplayName', 'Hexa ON');
|
|
hold off;
|
|
xlabel('Time [s]'); ylabel('Velocity [m/s]');
|
|
xlim([0, 50]);
|
|
legend('Location', 'bestoutside');
|
|
#+end_src
|
|
|
|
#+NAME: fig:time_domain_marble_lpf
|
|
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
|
#+begin_src matlab :var filepath="figs/time_domain_marble_lpf.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
|
<<plt-matlab>>
|
|
#+end_src
|
|
|
|
#+NAME: fig:time_domain_marble_lpf
|
|
#+CAPTION: Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble
|
|
#+RESULTS: fig:time_domain_marble_lpf
|
|
[[file:figs/time_domain_marble_lpf.png]]
|
|
|
|
#+begin_src matlab
|
|
figure;
|
|
hold on;
|
|
plot(d_of(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_of(:, 2)-d_of(:, 1), d_of(:, 3)), 'DisplayName', 'All OFF');
|
|
plot(d_ty(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_ty(:, 2)-d_ty(:, 1), d_ty(:, 3)), 'DisplayName', 'Ty ON');
|
|
plot(d_ry(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_ry(:, 2)-d_ry(:, 1), d_ry(:, 3)), 'DisplayName', 'Ry ON');
|
|
plot(d_sr(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_sr(:, 2)-d_sr(:, 1), d_sr(:, 3)), 'DisplayName', 'S-R ON');
|
|
plot(d_rz(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_rz(:, 2)-d_rz(:, 1), d_rz(:, 3)), 'DisplayName', 'Rz ON');
|
|
plot(d_he(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_he(:, 2)-d_he(:, 1), d_he(:, 3)), 'DisplayName', 'Hexa ON');
|
|
hold off;
|
|
xlabel('Time [s]'); ylabel('Relative Displacement [$\mu m$]');
|
|
xlim([0, 50]);
|
|
legend('Location', 'bestoutside');
|
|
#+end_src
|
|
|
|
#+NAME: fig:time_domain_relative_disp
|
|
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
|
#+begin_src matlab :var filepath="figs/time_domain_relative_disp.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
|
<<plt-matlab>>
|
|
#+end_src
|
|
|
|
#+NAME: fig:time_domain_relative_disp
|
|
#+CAPTION: Relative displacement of the sample with respect to the marble
|
|
#+RESULTS: fig:time_domain_relative_disp
|
|
[[file:figs/time_domain_relative_disp.png]]
|
|
|
|
** Analysis - Frequency Domain
|
|
#+begin_src matlab :results none
|
|
dt = d_of(2, 3) - d_of(1, 3);
|
|
|
|
Fs = 1/dt;
|
|
win = hanning(ceil(10*Fs));
|
|
#+end_src
|
|
|
|
*** Vibrations at the sample location
|
|
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
|
|
#+begin_src matlab :results none
|
|
[px_of, f] = pwelch(d_of(:, 2), win, [], [], Fs);
|
|
[px_ty, ~] = pwelch(d_ty(:, 2), win, [], [], Fs);
|
|
[px_ry, ~] = pwelch(d_ry(:, 2), win, [], [], Fs);
|
|
[px_sr, ~] = pwelch(d_sr(:, 2), win, [], [], Fs);
|
|
[px_rz, ~] = pwelch(d_rz(:, 2), win, [], [], Fs);
|
|
[px_he, ~] = pwelch(d_he(:, 2), win, [], [], Fs);
|
|
#+end_src
|
|
|
|
And we compare all the signals (figures [[fig:psd_sample_comp_lpf]] and [[fig:psd_sample_comp_high_freq_lpf]]).
|
|
#+begin_src matlab :results none
|
|
figure;
|
|
hold on;
|
|
plot(f, sqrt(px_of), 'DisplayName', 'All OFF');
|
|
plot(f, sqrt(px_ty), 'DisplayName', 'Ty ON');
|
|
plot(f, sqrt(px_ry), 'DisplayName', 'Ry ON');
|
|
plot(f, sqrt(px_sr), 'DisplayName', 'S-R ON');
|
|
plot(f, sqrt(px_rz), 'DisplayName', 'Rz ON');
|
|
plot(f, sqrt(px_he), 'DisplayName', 'Hexa ON');
|
|
hold off;
|
|
set(gca, 'xscale', 'log');
|
|
set(gca, 'yscale', 'log');
|
|
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
|
|
xlim([0.1, 500]);
|
|
legend('Location', 'southwest');
|
|
#+end_src
|
|
|
|
#+NAME: fig:psd_sample_comp_lpf
|
|
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
|
#+begin_src matlab :var filepath="figs/psd_sample_comp_lpf.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
|
<<plt-matlab>>
|
|
#+end_src
|
|
|
|
#+NAME: fig:psd_sample_comp_lpf
|
|
#+CAPTION: Amplitude Spectral Density of the sample velocity
|
|
#+RESULTS: fig:psd_sample_comp_lpf
|
|
[[file:figs/psd_sample_comp_lpf.png]]
|
|
|
|
|
|
#+begin_src matlab :results none :tangle no :exports none
|
|
xlim([80, 500]);
|
|
#+end_src
|
|
|
|
#+NAME: fig:psd_sample_comp_high_freq_lpf
|
|
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
|
#+begin_src matlab :var filepath="figs/psd_sample_comp_high_freq_lpf.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
|
<<plt-matlab>>
|
|
#+end_src
|
|
|
|
#+NAME: fig:psd_sample_comp_high_freq_lpf
|
|
#+CAPTION: Amplitude Spectral Density of the sample velocity (zoom at high frequencies)
|
|
#+RESULTS: fig:psd_sample_comp_high_freq_lpf
|
|
[[file:figs/psd_sample_comp_high_freq_lpf.png]]
|
|
|
|
*** Vibrations on the marble
|
|
Now we plot the same curves for the geophone located on the marble.
|
|
#+begin_src matlab :results none
|
|
[px_of, f] = pwelch(d_of(:, 1), win, [], [], Fs);
|
|
[px_ty, ~] = pwelch(d_ty(:, 1), win, [], [], Fs);
|
|
[px_ry, ~] = pwelch(d_ry(:, 1), win, [], [], Fs);
|
|
[px_sr, ~] = pwelch(d_sr(:, 1), win, [], [], Fs);
|
|
[px_rz, ~] = pwelch(d_rz(:, 1), win, [], [], Fs);
|
|
[px_he, ~] = pwelch(d_he(:, 1), win, [], [], Fs);
|
|
#+end_src
|
|
|
|
And we compare the Amplitude Spectral Densities (figures [[fig:psd_marble_comp_lpf]] and [[fig:psd_marble_comp_lpf_high_freq]])
|
|
#+begin_src matlab :results none
|
|
figure;
|
|
hold on;
|
|
plot(f, sqrt(px_of), 'DisplayName', 'All OFF');
|
|
plot(f, sqrt(px_ty), 'DisplayName', 'Ty ON');
|
|
plot(f, sqrt(px_ry), 'DisplayName', 'Ry ON');
|
|
plot(f, sqrt(px_sr), 'DisplayName', 'S-R ON');
|
|
plot(f, sqrt(px_rz), 'DisplayName', 'Rz ON');
|
|
plot(f, sqrt(px_he), 'DisplayName', 'Hexa ON');
|
|
hold off;
|
|
set(gca, 'xscale', 'log');
|
|
set(gca, 'yscale', 'log');
|
|
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
|
|
xlim([0.1, 500]);
|
|
legend('Location', 'northeast');
|
|
#+end_src
|
|
|
|
#+NAME: fig:psd_marble_comp_lpf
|
|
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
|
#+begin_src matlab :var filepath="figs/psd_marble_comp_lpf.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
|
<<plt-matlab>>
|
|
#+end_src
|
|
|
|
#+NAME: fig:psd_marble_comp_lpf
|
|
#+CAPTION: Amplitude Spectral Density of the marble velocity
|
|
#+RESULTS: fig:psd_marble_comp_lpf
|
|
[[file:figs/psd_marble_comp_lpf.png]]
|
|
|
|
|
|
#+begin_src matlab :results none :tangle no :exports none
|
|
legend('Location', 'southwest');
|
|
xlim([80, 500]);
|
|
#+end_src
|
|
|
|
#+NAME: fig:psd_marble_comp_lpf_high_freq
|
|
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
|
#+begin_src matlab :var filepath="figs/psd_marble_comp_lpf_high_freq.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
|
<<plt-matlab>>
|
|
#+end_src
|
|
|
|
#+NAME: fig:psd_marble_comp_lpf_high_freq
|
|
#+CAPTION: Amplitude Spectral Density of the marble velocity (zoom at high frequencies)
|
|
#+RESULTS: fig:psd_marble_comp_lpf_high_freq
|
|
[[file:figs/psd_marble_comp_lpf_high_freq.png]]
|
|
|
|
** Conclusion
|
|
#+begin_important
|
|
- The Ty stage induces vibrations of the marble and at the sample location above 100Hz
|
|
- The hexapod stage induces vibrations at the sample position above 220Hz
|
|
#+end_important
|
|
|
|
* Effect of the Symetrie Driver
|
|
:PROPERTIES:
|
|
:header-args:matlab+: :tangle matlab/effect_symetrie_driver.m
|
|
:header-args:matlab+: :comments org :mkdirp yes
|
|
:END:
|
|
<<sec:effect_symetrie_driver>>
|
|
|
|
** ZIP file containing the data and matlab files :ignore:
|
|
#+begin_src bash :exports none :results none
|
|
if [ matlab/effect_symetrie_driver.m -nt data/effect_symetrie_driver.zip ]; then
|
|
cp matlab/effect_symetrie_driver.m effect_symetrie_driver.m;
|
|
zip data/effect_symetrie_driver \
|
|
mat/data_018.mat \
|
|
mat/data_019.mat \
|
|
effect_symetrie_driver.m
|
|
rm effect_symetrie_driver.m;
|
|
fi
|
|
#+end_src
|
|
|
|
#+begin_note
|
|
All the files (data and Matlab scripts) are accessible [[file:data/effect_symetrie_driver.zip][here]].
|
|
#+end_note
|
|
|
|
** Experimental Setup
|
|
We here measure the signals of two geophones:
|
|
- One is located on top of the Sample platform
|
|
- One is located on the marble
|
|
|
|
The signal from the top geophone does go trought the slip-ring.
|
|
|
|
All the control systems are turned OFF except the Hexapod one.
|
|
|
|
Each measurement are done during 100s.
|
|
|
|
The settings of the voltage amplifier are:
|
|
- DC
|
|
- 60dB
|
|
- 1kHz
|
|
|
|
A first order low pass filter with a cut-off frequency of 1kHz is added before the voltage amplifier.
|
|
|
|
The measurements are:
|
|
- =meas_018.mat=: Hexapod's driver on the granite
|
|
- =meas_019.mat=: Hexapod's driver on the ground
|
|
|
|
Each of the =mat= file contains one array =data= with 3 columns:
|
|
| Column number | Description |
|
|
|---------------+-------------------|
|
|
| 1 | Geophone - Marble |
|
|
| 2 | Geophone - Sample |
|
|
| 3 | Time |
|
|
|
|
** Matlab Init :noexport:ignore:
|
|
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
|
<<matlab-dir>>
|
|
#+end_src
|
|
|
|
#+begin_src matlab :exports none :results silent :noweb yes
|
|
<<matlab-init>>
|
|
#+end_src
|
|
|
|
** Load data
|
|
We load the data of the z axis of two geophones.
|
|
#+begin_src matlab :results none
|
|
d_18 = load('mat/data_018.mat', 'data'); d_18 = d_18.data;
|
|
d_19 = load('mat/data_019.mat', 'data'); d_19 = d_19.data;
|
|
#+end_src
|
|
|
|
** Analysis - Time Domain
|
|
#+begin_src matlab :results none
|
|
figure;
|
|
hold on;
|
|
plot(d_19(:, 3), d_19(:, 1), 'DisplayName', 'Driver - Ground');
|
|
plot(d_18(:, 3), d_18(:, 1), 'DisplayName', 'Driver - Granite');
|
|
hold off;
|
|
xlabel('Time [s]'); ylabel('Voltage [V]');
|
|
xlim([0, 50]);
|
|
legend('Location', 'bestoutside');
|
|
#+end_src
|
|
|
|
#+NAME: fig:time_domain_hexa_driver
|
|
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
|
#+begin_src matlab :var filepath="figs/time_domain_hexa_driver.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
|
<<plt-matlab>>
|
|
#+end_src
|
|
|
|
#+NAME: fig:time_domain_hexa_driver
|
|
#+CAPTION: Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location
|
|
#+RESULTS: fig:time_domain_hexa_driver
|
|
[[file:figs/time_domain_hexa_driver.png]]
|
|
|
|
** Analysis - Frequency Domain
|
|
#+begin_src matlab :results none
|
|
dt = d_18(2, 3) - d_18(1, 3);
|
|
|
|
Fs = 1/dt;
|
|
win = hanning(ceil(10*Fs));
|
|
#+end_src
|
|
|
|
*** Vibrations at the sample location
|
|
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
|
|
#+begin_src matlab :results none
|
|
[px_18, f] = pwelch(d_18(:, 1), win, [], [], Fs);
|
|
[px_19, ~] = pwelch(d_19(:, 1), win, [], [], Fs);
|
|
#+end_src
|
|
|
|
#+begin_src matlab :results none
|
|
figure;
|
|
hold on;
|
|
plot(f, sqrt(px_19), 'DisplayName', 'Driver - Ground');
|
|
plot(f, sqrt(px_18), 'DisplayName', 'Driver - Granite');
|
|
hold off;
|
|
set(gca, 'xscale', 'log');
|
|
set(gca, 'yscale', 'log');
|
|
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
|
|
xlim([0.1, 500]);
|
|
legend('Location', 'southwest');
|
|
#+end_src
|
|
|
|
#+NAME: fig:psd_hexa_driver
|
|
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
|
#+begin_src matlab :var filepath="figs/psd_hexa_driver.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
|
<<plt-matlab>>
|
|
#+end_src
|
|
|
|
#+NAME: fig:psd_hexa_driver
|
|
#+CAPTION: Amplitude Spectral Density of the signal coming from the top geophone
|
|
#+RESULTS: fig:psd_hexa_driver
|
|
[[file:figs/psd_hexa_driver.png]]
|
|
|
|
|
|
#+begin_src matlab :results none :tangle no :exports none
|
|
xlim([80, 500]);
|
|
#+end_src
|
|
|
|
#+NAME: fig:psd_hexa_driver_high_freq
|
|
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
|
#+begin_src matlab :var filepath="figs/psd_hexa_driver_high_freq.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
|
<<plt-matlab>>
|
|
#+end_src
|
|
|
|
#+NAME: fig:psd_hexa_driver_high_freq
|
|
#+CAPTION: Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)
|
|
#+RESULTS: fig:psd_hexa_driver_high_freq
|
|
[[file:figs/psd_hexa_driver_high_freq.png]]
|
|
|
|
** Conclusion
|
|
#+begin_important
|
|
Even tough the Hexapod's driver vibrates quite a lot, it does not generate significant vibrations of the granite when either placed on the granite or on the ground.
|
|
#+end_important
|