453 lines
16 KiB
Org Mode
453 lines
16 KiB
Org Mode
#+TITLE:Vibrations induced by simultaneous scans of the translation stage and of the slip-ring
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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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* Measurement description
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** Setup :ignore:
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*Setup*:
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All the stages are OFF except the translation stage and the Slip-Ring.
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Each of the signal is amplified by voltage amplifiers with the following settings:
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- Gain: 40dB
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- AC/DC option: AC
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- Low pass filter: 1kHz
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The slip-ring is rotating at 60rpm. At the same time, scans with the translation stage are done at 1Hz with an amplitude of 600000cnt (= 3mm).
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Two geophones are used to measure the motion in the vertical direction of the marble and of the sample.
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** Goal :ignore:
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*Goal*:
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- The goal is to estimate the vibrations induced by the simultaneous scans of the spindle (here the slip-ring is used as the spindle is not fully functional yet) and of the translation stage
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** Measurements :ignore:
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*Measurements*:
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Three measurements are done:
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| Measurement File | Description |
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|--------------------+------------------------------------------------------------------------------|
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| =mat/data_050.mat= | Slip-Ring at 1Hz, Ty OFF |
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| =mat/data_051.mat= | Slip-Ring at 1Hz, Ty ON (The current and cnt error of Ty is also registered) |
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| =mat/data_052.mat= | Slip-Ring at 1Hz, Ty 1Hz 600000cnt |
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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 on the marble |
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| 2 | Geophone at the sample location |
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| 3 | Time |
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* Data Analysis
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:PROPERTIES:
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:header-args:matlab+: :tangle matlab/disturbance_ty_sr.m
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:header-args:matlab+: :comments org :mkdirp yes
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:END:
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<<sec:disturbance_ty_sr>>
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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/disturbance_ty_sr.m -nt data/disturbance_ty_sr.zip ]; then
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cp matlab/disturbance_ty_sr.m disturbance_ty_sr.m;
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zip data/disturbance_ty_sr \
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mat/data_050.mat \
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mat/data_051.mat \
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mat/data_052.mat \
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mat/Ty-when-Rz-1Hz-and-Ty-1Hz.csv \
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mat/Ty-when-Rz-1Hz.csv \
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disturbance_ty_sr.m
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rm disturbance_ty_sr.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/disturbance_ty_sr.zip][here]].
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#+end_note
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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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addpath('../src');
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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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#+begin_src matlab
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ty_of = load('mat/data_050.mat', 'data'); ty_of = ty_of.data;
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ty_on = load('mat/data_051.mat', 'data'); ty_on = ty_on.data;
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ty_1h = load('mat/data_052.mat', 'data'); ty_1h = ty_1h.data;
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#+end_src
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** Voltage to Velocity
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We convert the measured voltage to velocity using the function =voltageToVelocityL22= (accessible [[file:~/MEGA/These/meas/src/index.org][here]]).
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#+begin_src matlab
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gain = 40; % [dB]
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ty_of(:, 1) = voltageToVelocityL22(ty_of(:, 1), ty_of(:, 3), gain);
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ty_on(:, 1) = voltageToVelocityL22(ty_on(:, 1), ty_on(:, 3), gain);
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ty_1h(:, 1) = voltageToVelocityL22(ty_1h(:, 1), ty_1h(:, 3), gain);
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ty_of(:, 2) = voltageToVelocityL22(ty_of(:, 2), ty_of(:, 3), gain);
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ty_on(:, 2) = voltageToVelocityL22(ty_on(:, 2), ty_on(:, 3), gain);
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ty_1h(:, 2) = voltageToVelocityL22(ty_1h(:, 2), ty_1h(:, 3), gain);
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#+end_src
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** Time domain plots
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We plot the measured velocity of the marble (figure [[fig:ty_marble_time]]), sample (figure [[fig:ty_sample_time]]) and the relative velocity of the sample with respect to the marble (figure [[fig:ty_relative_time]]).
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We also integrate the relative velocity to obtain the relative displacement (figure [[fig:ty_relative_disp_time]]).
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#+begin_src matlab
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figure;
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hold on;
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plot(ty_1h(:, 3), ty_1h(:, 1), 'DisplayName', 'Marble - Ty 1Hz');
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plot(ty_on(:, 3), ty_on(:, 1), 'DisplayName', 'Marble - Ty ON');
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plot(ty_of(:, 3), ty_of(:, 1), 'DisplayName', 'Marble - Ty OFF');
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hold off;
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xlabel('Time [s]'); ylabel('Velocity [m/s]');
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xlim([0, 2]);
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legend('Location', 'southwest');
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#+end_src
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#+NAME: fig:ty_marble_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/ty_marble_time.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:ty_marble_time
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#+CAPTION: Velocity of the marble in the vertical direction
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#+RESULTS: fig:ty_marble_time
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[[file:figs/ty_marble_time.png]]
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#+begin_src matlab
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figure;
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hold on;
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plot(ty_1h(:, 3), ty_1h(:, 2), 'DisplayName', 'Sample - Ty - 1Hz');
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plot(ty_on(:, 3), ty_on(:, 2), 'DisplayName', 'Sample - Ty - ON');
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plot(ty_of(:, 3), ty_of(:, 2), 'DisplayName', 'Sample - Ty - OFF');
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hold off;
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xlabel('Time [s]'); ylabel('Velocity [m/s]');
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xlim([0, 2]);
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legend('Location', 'southwest');
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#+end_src
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#+NAME: fig:ty_sample_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/ty_sample_time.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:ty_sample_time
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#+CAPTION: Velocity of the sample in the vertical direction
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#+RESULTS: fig:ty_sample_time
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[[file:figs/ty_sample_time.png]]
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#+begin_src matlab
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figure;
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hold on;
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plot(ty_1h(:, 3), ty_1h(:, 2)-ty_1h(:, 1), 'DisplayName', 'Relative Velocity - Ty - 1Hz');
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plot(ty_on(:, 3), ty_on(:, 2)-ty_on(:, 1), 'DisplayName', 'Relative Velocity - Ty - ON');
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plot(ty_of(:, 3), ty_of(:, 2)-ty_of(:, 1), 'DisplayName', 'Relative Velocity - Ty - OFF');
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hold off;
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xlabel('Time [s]'); ylabel('Velocity [m/s]');
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xlim([0, 2]);
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legend('Location', 'southwest');
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#+end_src
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#+NAME: fig:ty_relative_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/ty_relative_time.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:ty_relative_time
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#+CAPTION: Relative velocity of the sample with respect to the marble
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#+RESULTS: fig:ty_relative_time
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[[file:figs/ty_relative_time.png]]
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#+begin_src matlab
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figure;
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hold on;
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plot(ty_1h(:, 3), lsim(1/s, ty_1h(:, 2)-ty_1h(:, 1), ty_1h(:, 3)), 'DisplayName', 'Relative Displacement- Ty - 1Hz');
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plot(ty_on(:, 3), lsim(1/s, ty_on(:, 2)-ty_on(:, 1), ty_on(:, 3)), 'DisplayName', 'Relative Displacement- Ty - ON');
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plot(ty_of(:, 3), lsim(1/s, ty_of(:, 2)-ty_of(:, 1), ty_of(:, 3)), 'DisplayName', 'Relative Displacement- Ty - OFF');
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hold off;
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xlabel('Time [s]'); ylabel('Displacement [m]');
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xlim([0, 2]);
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legend('Location', 'southwest');
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#+end_src
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#+NAME: fig:ty_relative_disp_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/ty_relative_disp_time.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:ty_relative_disp_time
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#+CAPTION: Relative Displacement of the sample with respect to the marble
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#+RESULTS: fig:ty_relative_disp_time
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[[file:figs/ty_relative_disp_time.png]]
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** Frequency Domain
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We first compute some parameters that will be used for the PSD computation.
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#+begin_src matlab :results none
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dt = ty_of(2, 3)-ty_of(1, 3);
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Fs = 1/dt; % [Hz]
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win = hanning(ceil(10*Fs));
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#+end_src
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Then we compute the Power Spectral Density using =pwelch= function.
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First for the geophone located on the marble
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#+begin_src matlab
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[pxof_m, f] = pwelch(ty_of(:, 1), win, [], [], Fs);
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[pxon_m, ~] = pwelch(ty_on(:, 1), win, [], [], Fs);
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[px1h_m, ~] = pwelch(ty_1h(:, 1), win, [], [], Fs);
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#+end_src
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And for the geophone located at the sample position.
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#+begin_src matlab
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[pxof_s, f] = pwelch(ty_of(:, 2), win, [], [], Fs);
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[pxon_s, ~] = pwelch(ty_on(:, 2), win, [], [], Fs);
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[px1h_s, ~] = pwelch(ty_1h(:, 2), win, [], [], Fs);
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#+end_src
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Finally, for the relative velocity.
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#+begin_src matlab
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[pxof_r, f] = pwelch(ty_of(:, 2)-ty_of(:, 1), win, [], [], Fs);
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[pxon_r, ~] = pwelch(ty_on(:, 2)-ty_on(:, 1), win, [], [], Fs);
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[px1h_r, ~] = pwelch(ty_1h(:, 2)-ty_1h(:, 1), win, [], [], Fs);
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#+end_src
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And we plot the ASD of the measured velocities:
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- figure [[fig:psd_marble_compare]] for the geophone located on the marble
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- figure [[fig:psd_sample_compare]] for the geophone at the sample position
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- figure [[fig:psd_relative_compare]] for the relative velocity
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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(px1h_m), 'DisplayName', 'Marble - Ty 1Hz');
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plot(f, sqrt(pxon_m), 'DisplayName', 'Marble - Ty ON');
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plot(f, sqrt(pxof_m), 'DisplayName', 'Marble - Ty 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 of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
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legend('Location', 'southwest');
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xlim([1, 500]);
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#+end_src
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#+NAME: fig:psd_marble_compare
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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_compare.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_compare
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#+CAPTION: Comparison of the ASD of the measured velocities from the Geophone on the marble
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#+RESULTS: fig:psd_marble_compare
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[[file:figs/psd_marble_compare.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(f, sqrt(px1h_s), 'DisplayName', 'Sample - Ty 1Hz');
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plot(f, sqrt(pxon_s), 'DisplayName', 'Sample - Ty ON');
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plot(f, sqrt(pxof_s), 'DisplayName', 'Sample - Ty 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 of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
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legend('Location', 'southwest');
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xlim([1, 500]);
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#+end_src
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#+NAME: fig:psd_sample_compare
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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_compare.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_compare
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#+CAPTION: Comparison of the ASD of the measured velocities from the Geophone at the sample location
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#+RESULTS: fig:psd_sample_compare
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[[file:figs/psd_sample_compare.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(f, sqrt(px1h_r), 'DisplayName', 'Relative - Ty 1Hz');
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plot(f, sqrt(pxon_r), 'DisplayName', 'Relative - Ty ON');
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plot(f, sqrt(pxof_r), 'DisplayName', 'Relative - Ty 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 of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
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legend('Location', 'southwest');
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xlim([1, 500]);
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#+end_src
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#+NAME: fig:psd_relative_compare
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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_relative_compare.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_relative_compare
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#+CAPTION: Comparison of the ASD of the relative velocity
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#+RESULTS: fig:psd_relative_compare
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[[file:figs/psd_relative_compare.png]]
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** Ty motion and current
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The position of the translation stage and current flowing in its actuator are measured using the elmo software and saved as an csv file.
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*** Data pre-processing
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Let's look at at the start of the csv file.
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#+begin_src bash :results output
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sed -n 1,30p mat/Ty-when-Rz-1Hz-and-Ty-1Hz.csv | nl -ba -
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#+end_src
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#+RESULTS:
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#+begin_example
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1 Elmo txt chart ver 2.0
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2
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3 [File Properties]
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4 Creation Time,2019-05-13 05:33:43
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5 Last Updated,2019-05-13 05:33:43
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6 Resolution,0.001
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7 Sampling Time,5E-05
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8 Recording Time,5.461
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9
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10 [Chart Properties]
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11 No.,Name,X Linear,X No.
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12 1,Chart #1,True,0
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13 2,Chart #2,True,0
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14
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15 [Chart Data]
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16 Display No.,X No.,Y No.,X Unit,Y Unit,Color,Style,Width
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17 1,1,2,sec,N/A,ff0000ff,Solid,TwoPoint
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18 2,1,3,sec,N/A,ff0000ff,Solid,TwoPoint
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19 2,1,4,sec,N/A,ff007f00,Solid,TwoPoint
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20
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21 [Signal Names]
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22 1,Time (sec)
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23 2,Position [cnt]
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24 3,Current Command [A]
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25 4,Total Current Command [A]
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26
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27 [Signals Data Group 1]
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28 1,2,3,4,
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29 0,-141044,-0.537239575086517,-0.537239575086517,
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30 0.001,-143127,-0.530803752974691,-0.530803752974691,
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#+end_example
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The real data starts at line 29.
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We then load this =cvs= file starting at line 29.
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#+begin_src matlab
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tye_on = csvread("mat/Ty-when-Rz-1Hz.csv", 29, 0);
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tye_1h = csvread("mat/Ty-when-Rz-1Hz-and-Ty-1Hz.csv", 29, 0);
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#+end_src
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*** Time domain data
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We plot the position of the translation stage measured by the encoders.
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There is 200000 encoder count for each mm, we then divide by 200000 to obtain mm.
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The result is shown on figure [[fig:ty_position_time]].
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#+begin_src matlab
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figure;
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subplot(1, 2, 1);
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plot(tye_on(:, 1), (tye_on(:, 2)-mean(tye_on(:, 2)))/200000);
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xlim([0, 5]);
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xlabel('Time [s]'); ylabel('Position [mm]');
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legend({'Ty - ON'}, 'Location', 'northeast');
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subplot(1, 2, 2);
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plot(tye_1h(:, 1), (tye_1h(:, 2)-mean(tye_1h(:, 2)))/200000);
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xlim([0, 5]);
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xlabel('Time [s]'); ylabel('Position [mm]');
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legend({'Ty - 1Hz'}, 'Location', 'northeast');
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#+end_src
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#+NAME: fig:ty_position_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/ty_position_time.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:ty_position_time
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#+CAPTION: Y position of the translation stage measured by the encoders
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#+RESULTS: fig:ty_position_time
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[[file:figs/ty_position_time.png]]
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We also plot the current as function of the time on figure [[fig:ty_current_time]].
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#+begin_src matlab
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figure;
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subplot(1, 2, 1);
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plot(tye_on(:, 1), tye_on(:, 3)-mean(tye_on(:, 3)));
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xlim([0, 5]);
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xlabel('Time [s]'); ylabel('Current [A]');
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legend({'Ty - ON'}, 'Location', 'northeast');
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subplot(1, 2, 2);
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plot(tye_1h(:, 1), tye_1h(:, 3)-mean(tye_1h(:, 3)));
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xlim([0, 5]);
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xlabel('Time [s]'); ylabel('Current [A]');
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legend({'Ty - 1Hz'}, 'Location', 'northeast');
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#+end_src
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#+NAME: fig:ty_current_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/ty_current_time.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:ty_current_time
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#+CAPTION: Current going through the actuator of the translation stage
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#+RESULTS: fig:ty_current_time
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[[file:figs/ty_current_time.png]]
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** Conclusion
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#+begin_important
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-
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#+end_important
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