404 lines
13 KiB
Org Mode
404 lines
13 KiB
Org Mode
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#+TITLE: Encoder - Test Bench
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:DRAWER:
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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_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:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/tikz/org/}{config.tex}")
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#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
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#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
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#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
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#+PROPERTY: header-args:latex+ :results raw replace :buffer no
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#+PROPERTY: header-args:latex+ :eval no-export
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#+PROPERTY: header-args:latex+ :exports both
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#+PROPERTY: header-args:latex+ :mkdirp yes
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#+PROPERTY: header-args:latex+ :output-dir figs
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#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
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#+PROPERTY: header-args:matlab :session *MATLAB*
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#+PROPERTY: header-args:matlab+ :tangle script.m
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#+PROPERTY: header-args:matlab+ :comments org
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#+PROPERTY: header-args:matlab+ :exports both
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#+PROPERTY: header-args:matlab+ :results none
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#+PROPERTY: header-args:matlab+ :eval no-export
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#+PROPERTY: header-args:matlab+ :noweb yes
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#+PROPERTY: header-args:matlab+ :mkdirp yes
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#+PROPERTY: header-args:matlab+ :output-dir figs
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:END:
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* Experimental Setup
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The experimental Setup is schematically represented in Figure [[fig:exp_setup_schematic]].
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The mass can be vertically moved using the amplified piezoelectric actuator.
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The displacement of the mass (relative to the mechanical frame) is measured both by the interferometer and by the encoder.
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#+name: fig:exp_setup_schematic
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#+caption: Schematic of the Experiment
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[[file:figs/exp_setup_schematic.png]]
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#+name: fig:encoder_side_view
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#+caption: Side View of the encoder
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[[file:figs/IMG_20201023_153905.jpg]]
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#+name: fig:encoder_front_view
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#+caption: Front View of the encoder
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[[file:figs/IMG_20201023_153914.jpg]]
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* Huddle Test
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** Introduction :ignore:
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The goal in this section is the estimate the noise of both the encoder and the intereferometer.
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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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#+begin_src matlab
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load('mat/int_enc_huddle_test.mat', 'interferometer', 'encoder', 't');
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#+end_src
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#+begin_src matlab
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interferometer = detrend(interferometer, 0);
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encoder = detrend(encoder, 0);
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#+end_src
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** Time Domain Results
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#+begin_src matlab :exports none
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figure;
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hold on;
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plot(t, encoder, 'DisplayName', 'Encoder')
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plot(t, interferometer, 'DisplayName', 'Interferometer')
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hold off;
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xlabel('Time [s]'); ylabel('Displacement [m]');
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legend('location', 'northeast');
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/huddle_test_time_domain.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:huddle_test_time_domain
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#+caption: Huddle test - Time domain signals
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#+RESULTS:
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[[file:figs/huddle_test_time_domain.png]]
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#+begin_src matlab
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G_lpf = 1/(1 + s/2/pi/10);
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#+end_src
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#+begin_src matlab :exports none
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figure;
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hold on;
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plot(t, lsim(G_lpf, encoder, t), 'DisplayName', 'Encoder')
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plot(t, lsim(G_lpf, interferometer, t), 'DisplayName', 'Interferometer')
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hold off;
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xlabel('Time [s]'); ylabel('Displacement [m]');
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legend('location', 'northeast');
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/huddle_test_time_domain_filtered.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:huddle_test_time_domain_filtered
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#+caption: Huddle test - Time domain signals filtered with a LPF at 10Hz
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#+RESULTS:
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[[file:figs/huddle_test_time_domain_filtered.png]]
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** Frequency Domain Noise
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#+begin_src matlab
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Ts = 1e-4;
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win = hann(ceil(10/Ts));
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[p_i, f] = pwelch(interferometer, win, [], [], 1/Ts);
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[p_e, ~] = pwelch(encoder, win, [], [], 1/Ts);
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#+end_src
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#+begin_src matlab :exports none
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figure;
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hold on;
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plot(f, sqrt(p_i), 'DisplayName', 'Interferometer');
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plot(f, sqrt(p_e), 'DisplayName', 'Encoder');
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hold off;
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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ylabel('ASD [$m/\sqrt{Hz}$]'); xlabel('Frequency [Hz]');
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legend();
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xlim([1e-1, 5e3]);
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/huddle_test_asd.pdf', 'width', 'wide', 'height', 'tall');
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#+end_src
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#+name: fig:huddle_test_asd
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#+caption: Amplitude Spectral Density of the signals during the Huddle test
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#+RESULTS:
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[[file:figs/huddle_test_asd.png]]
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* Comparison Interferometer / Encoder
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** Introduction :ignore:
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The goal here is to make sure that the interferometer and encoder measurements are coherent.
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We may see non-linearity in the interferometric measurement.
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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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#+begin_src matlab
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load('mat/int_enc_comp.mat', 'interferometer', 'encoder', 'u', 't');
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#+end_src
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#+begin_src matlab
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interferometer = detrend(interferometer, 0);
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encoder = detrend(encoder, 0);
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u = detrend(u, 0);
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#+end_src
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** Time Domain Results
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#+begin_src matlab :exports none
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figure;
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hold on;
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plot(t, encoder, '-', 'DisplayName', 'Encoder')
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plot(t, interferometer, '--', 'DisplayName', 'Interferometer')
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hold off;
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xlabel('Time [s]'); ylabel('Displacement [m]');
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legend('location', 'northeast');
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xlim([50, 52])
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/int_enc_one_cycle.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:int_enc_one_cycle
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#+caption: One cycle measurement
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#+RESULTS:
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[[file:figs/int_enc_one_cycle.png]]
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#+begin_src matlab :exports none
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figure;
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hold on;
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plot(t, encoder - interferometer, 'DisplayName', 'Difference')
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hold off;
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xlabel('Time [s]'); ylabel('Displacement [m]');
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legend('location', 'northeast');
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xlim([50, 52])
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/int_enc_one_cycle_error.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:int_enc_one_cycle_error
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#+caption: Difference between the Encoder and the interferometer during one cycle
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#+RESULTS:
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[[file:figs/int_enc_one_cycle_error.png]]
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** Difference between Encoder and Interferometer as a function of time
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#+begin_src matlab
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Ts = 1e-4;
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d_i_mean = reshape(interferometer, [2/Ts floor(Ts/2*length(interferometer))]);
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d_e_mean = reshape(encoder, [2/Ts floor(Ts/2*length(encoder))]);
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#+end_src
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#+begin_src matlab
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w0 = 2*pi*5; % [rad/s]
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xi = 0.7;
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G_lpf = 1/(1 + 2*xi/w0*s + s^2/w0^2);
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d_err_mean = reshape(lsim(G_lpf, encoder - interferometer, t), [2/Ts floor(Ts/2*length(encoder))]);
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d_err_mean = d_err_mean - mean(d_err_mean);
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#+end_src
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#+begin_src matlab :exports none
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figure;
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hold on;
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for i_i = 1:size(d_err_mean, 2)
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plot(t(1:size(d_err_mean, 1)), d_err_mean(:, i_i), 'k-')
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end
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plot(t(1:size(d_err_mean, 1)), mean(d_err_mean, 2), 'r-')
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hold off;
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xlabel('Time [s]'); ylabel('Displacement [m]');
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/int_enc_error_mean_time.pdf', 'width', 'wide', 'height', 'normal', 'pdf', false);
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#+end_src
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#+name: fig:int_enc_error_mean_time
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#+caption: Difference between the two measurement in the time domain, averaged for all the cycles
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#+RESULTS:
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[[file:figs/int_enc_error_mean_time.png]]
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** Difference between Encoder and Interferometer as a function of position
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Compute the mean of the interferometer measurement corresponding to each of the encoder measurement.
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#+begin_src matlab
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[e_sorted, ~, e_ind] = unique(encoder);
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i_mean = zeros(length(e_sorted), 1);
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for i = 1:length(e_sorted)
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i_mean(i) = mean(interferometer(e_ind == i));
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end
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i_mean_error = (i_mean - e_sorted);
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#+end_src
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#+begin_src matlab :exports none
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figure;
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hold on;
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% plot(encoder, interferometer - encoder, 'k.', 'DisplayName', 'Difference')
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plot(1e6*(e_sorted), 1e9*(i_mean_error))
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hold off;
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xlabel('Encoder Measurement [$\mu m$]'); ylabel('Measrement Error [nm]');
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/int_enc_error_mean_position.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:int_enc_error_mean_position
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#+caption: Difference between the two measurement as a function of the measured position by the encoder, averaged for all the cycles
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#+RESULTS:
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[[file:figs/int_enc_error_mean_position.png]]
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The period of the non-linearity seems to be $1.53 \mu m$ which corresponds to the wavelength of the Laser.
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#+begin_src matlab
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win_length = 1530; % length of the windows (corresponds to 1.53 um)
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num_avg = floor(length(e_sorted)/win_length); % number of averaging
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i_init = ceil((length(e_sorted) - win_length*num_avg)/2); % does not start at the extremity
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e_sorted_mean_over_period = mean(reshape(i_mean_error(i_init:i_init+win_length*num_avg-1), [win_length num_avg]), 2);
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#+end_src
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#+begin_src matlab :exports none
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figure;
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hold on;
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plot(1e-3*(0:win_length-1), e_sorted_mean_over_period)
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hold off;
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xlabel('Displacement [$\mu m$]'); ylabel('Measurement Non-Linearity [nm]');
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/int_non_linearity_period_wavelength.pdf', 'width', 'wide', 'height', 'tall');
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#+end_src
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#+name: fig:int_non_linearity_period_wavelength
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#+caption: Non-Linearity of the Interferometer over the period of the wavelength
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#+RESULTS:
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[[file:figs/int_non_linearity_period_wavelength.png]]
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* Identification
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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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#+begin_src matlab
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load('mat/int_enc_id_noise_bis.mat', 'interferometer', 'encoder', 'u', 't');
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#+end_src
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#+begin_src matlab
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interferometer = detrend(interferometer, 0);
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encoder = detrend(encoder, 0);
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u = detrend(u, 0);
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#+end_src
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** Identification
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#+begin_src matlab
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Ts = 1e-4; % Sampling Time [s]
|
||
|
|
win = hann(ceil(10/Ts));
|
||
|
|
#+end_src
|
||
|
|
|
||
|
|
#+begin_src matlab
|
||
|
|
[tf_i_est, f] = tfestimate(u, interferometer, win, [], [], 1/Ts);
|
||
|
|
[co_i_est, ~] = mscohere(u, interferometer, win, [], [], 1/Ts);
|
||
|
|
|
||
|
|
[tf_e_est, ~] = tfestimate(u, encoder, win, [], [], 1/Ts);
|
||
|
|
[co_e_est, ~] = mscohere(u, encoder, win, [], [], 1/Ts);
|
||
|
|
#+end_src
|
||
|
|
|
||
|
|
#+begin_src matlab :exports none
|
||
|
|
figure;
|
||
|
|
hold on;
|
||
|
|
plot(f, co_i_est, '-')
|
||
|
|
plot(f, co_e_est, '-')
|
||
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
|
||
|
|
ylabel('Coherence'); xlabel('Frequency [Hz]');
|
||
|
|
hold off;
|
||
|
|
xlim([0.5, 5e3]);
|
||
|
|
#+end_src
|
||
|
|
|
||
|
|
#+begin_src matlab :tangle no :exports results :results file replace
|
||
|
|
exportFig('figs/identification_dynamics_coherence.pdf', 'width', 'normal', 'height', 'normal');
|
||
|
|
#+end_src
|
||
|
|
|
||
|
|
#+name: fig:identification_dynamics_coherence
|
||
|
|
#+caption:
|
||
|
|
#+RESULTS:
|
||
|
|
[[file:figs/identification_dynamics_coherence.png]]
|
||
|
|
|
||
|
|
|
||
|
|
#+begin_src matlab :exports none
|
||
|
|
figure;
|
||
|
|
tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||
|
|
|
||
|
|
ax1 = nexttile;
|
||
|
|
hold on;
|
||
|
|
plot(f, abs(tf_i_est), '-', 'DisplayName', 'Int')
|
||
|
|
plot(f, abs(tf_e_est), '-', 'DisplayName', 'Enc')
|
||
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||
|
|
ylabel('Amplitude'); set(gca, 'XTickLabel',[]);
|
||
|
|
hold off;
|
||
|
|
ylim([1e-7, 3e-4]);
|
||
|
|
|
||
|
|
ax2 = nexttile;
|
||
|
|
hold on;
|
||
|
|
plot(f, 180/pi*angle(tf_i_est), '-')
|
||
|
|
plot(f, 180/pi*angle(tf_e_est), '-')
|
||
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
|
||
|
|
ylabel('Phase'); xlabel('Frequency [Hz]');
|
||
|
|
hold off;
|
||
|
|
yticks(-360:90:360);
|
||
|
|
axis padded 'auto x'
|
||
|
|
|
||
|
|
linkaxes([ax1,ax2], 'x');
|
||
|
|
xlim([0.5, 5e3]);
|
||
|
|
#+end_src
|
||
|
|
|
||
|
|
#+begin_src matlab :tangle no :exports results :results file replace
|
||
|
|
exportFig('figs/identification_dynamics_bode.pdf', 'width', 'wide', 'height', 'tall');
|
||
|
|
#+end_src
|
||
|
|
|
||
|
|
#+name: fig:identification_dynamics_bode
|
||
|
|
#+caption:
|
||
|
|
#+RESULTS:
|
||
|
|
[[file:figs/identification_dynamics_bode.png]]
|