957 lines
28 KiB
Org Mode
957 lines
28 KiB
Org Mode
#+TITLE: Test Bench APA95ML
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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/custom.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/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:matlab+ :tangle no
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#+PROPERTY: header-args:matlab+ :mkdirp yes
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#+PROPERTY: header-args:shell :eval no-export
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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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:END:
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* Introduction :ignore:
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#+name: fig:setup_picture
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#+caption: Picture of the Setup
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[[file:figs/setup_picture.png]]
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#+name: fig:setup_zoom
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#+caption: Zoom on the APA
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[[file:figs/setup_zoom.png]]
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* Setup
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:PROPERTIES:
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:header-args:matlab+: :tangle matlab/setup_experiment.m
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:header-args:matlab+: :comments org :mkdirp yes
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:END:
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** Parameters
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#+begin_src matlab
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Ts = 1e-4;
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#+end_src
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** Filter White Noise
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#+begin_src matlab
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Glpf = 1/(1 + s/2/pi/500);
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Gz = c2d(Glpf, Ts, 'tustin');
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#+end_src
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* Run Experiment and Save Data
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:PROPERTIES:
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:header-args:matlab+: :tangle matlab/run_experiment.m
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:header-args:matlab+: :comments org :mkdirp yes
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:END:
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** Load Data
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#+begin_src matlab
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data = SimulinkRealTime.utils.getFileScopeData('data/apa95ml.dat').data;
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#+end_src
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** Save Data
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#+begin_src matlab
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u = data(:, 1); % Input Voltage [V]
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y = data(:, 2); % Output Displacement [m]
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t = data(:, 3); % Time [s]
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#+end_src
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#+begin_src matlab
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save('./mat/huddle_test.mat', 't', 'u', 'y', 'Glpf');
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#+end_src
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* Huddle Test
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:PROPERTIES:
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:header-args:matlab+: :tangle matlab/huddle_test.m
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:header-args:matlab+: :comments org :mkdirp yes
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:END:
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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 :noexport:
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#+begin_src matlab
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load('./mat/huddle_test.mat', 't', 'y');
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#+end_src
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#+begin_src matlab
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y = y - mean(y(1000:end));
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#+end_src
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** Time Domain Data
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#+begin_src matlab :exports none
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figure;
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plot(t(1000:end), y(1000:end))
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ylabel('Output Displacement [m]'); xlabel('Time [s]');
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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: Measurement of the Mass displacement during Huddle Test
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#+RESULTS:
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[[file:figs/huddle_test_time_domain.png]]
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** PSD of Measurement Noise
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#+begin_src matlab
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Ts = t(end)/(length(t)-1);
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Fs = 1/Ts;
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win = hanning(ceil(1*Fs));
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#+end_src
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#+begin_src matlab
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[pxx, f] = pwelch(y(1000:end), win, [], [], Fs);
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#+end_src
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#+begin_src matlab :exports none
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figure;
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plot(f, sqrt(pxx));
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
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xlim([1, Fs/2]);
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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_pdf.pdf', 'width', 'wide', 'height', 'tall');
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#+end_src
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#+name: fig:huddle_test_pdf
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#+caption: Amplitude Spectral Density of the Displacement during Huddle Test
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#+RESULTS:
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[[file:figs/huddle_test_pdf.png]]
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* Transfer Function Estimation using the DAC as the driver :noexport:
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:PROPERTIES:
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:header-args:matlab+: :tangle matlab/tf_estimation.m
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:header-args:matlab+: :comments org :mkdirp yes
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:END:
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** Introduction :ignore:
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#+begin_important
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Results presented in this sections are wrong as the ADC cannot deliver enought current to the piezoelectric actuator.
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#+end_important
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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 :noexport:
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#+begin_src matlab
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ht = load('./mat/huddle_test.mat', 't', 'u', 'y');
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load('./mat/apa95ml_5kg_10V.mat', 't', 'u', 'y');
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#+end_src
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** Time Domain Data
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#+begin_src matlab :exports none
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figure;
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subplot(1,2,1);
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plot(t, u)
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ylabel('Input Voltage [V]'); xlabel('Time [s]');
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subplot(1,2,2);
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plot(t, y)
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ylabel('Output Displacement [m]'); xlabel('Time [s]');
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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/apa95ml_5kg_10V_time_domain.pdf', 'width', 'full', 'height', 'tall');
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#+end_src
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#+name: fig:apa95ml_5kg_10V_time_domain
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#+caption: Time domain signals during the test
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#+RESULTS:
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[[file:figs/apa95ml_5kg_10V_time_domain.png]]
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** Comparison of the PSD with Huddle Test
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#+begin_src matlab
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Ts = t(end)/(length(t)-1);
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Fs = 1/Ts;
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win = hanning(ceil(1*Fs));
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#+end_src
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#+begin_src matlab
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[pxx, f] = pwelch(y, win, [], [], Fs);
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[pht, ~] = pwelch(ht.y, win, [], [], Fs);
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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(pxx), 'DisplayName', '5kg');
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plot(f, sqrt(pht), 'DisplayName', 'Huddle Test');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
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legend('location', 'northeast');
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xlim([1, Fs/2]);
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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/apa95ml_5kg_10V_pdf_comp_huddle.pdf', 'width', 'wide', 'height', 'tall');
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#+end_src
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#+name: fig:apa95ml_5kg_10V_pdf_comp_huddle
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#+caption: Comparison of the ASD for the identification test and the huddle test
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#+RESULTS:
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[[file:figs/apa95ml_5kg_10V_pdf_comp_huddle.png]]
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** Compute TF estimate and Coherence
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#+begin_src matlab
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Ts = t(end)/(length(t)-1);
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Fs = 1/Ts;
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#+end_src
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#+begin_src matlab
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win = hann(ceil(1/Ts));
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[tf_est, f] = tfestimate(u, -y, win, [], [], 1/Ts);
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[co_est, ~] = mscohere( u, -y, 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, co_est, 'k-')
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
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ylabel('Coherence'); xlabel('Frequency [Hz]');
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hold off;
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xlim([10, 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/apa95ml_5kg_10V_coh.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:apa95ml_5kg_10V_coh
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#+caption: Coherence
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#+RESULTS:
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[[file:figs/apa95ml_5kg_10V_coh.png]]
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#+begin_src matlab :exports 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(tf_est), 'k-')
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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ylabel('Amplitude'); xlabel('Frequency [Hz]');
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hold off;
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ax2 = subplot(2, 1, 2);
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hold on;
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plot(f, 180/pi*angle(tf_est), 'k-')
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
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ylabel('Phase'); xlabel('Frequency [Hz]');
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hold off;
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linkaxes([ax1,ax2], 'x');
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xlim([10, 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/apa95ml_5kg_10V_tf.pdf', 'width', 'full', 'height', 'full');
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#+end_src
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#+name: fig:apa95ml_5kg_10V_tf
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#+caption: Estimation of the transfer function from input voltage to displacement
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#+RESULTS:
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[[file:figs/apa95ml_5kg_10V_tf.png]]
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** Comparison with the FEM model
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#+begin_src matlab
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load('mat/fem_model_5kg.mat', 'Ghm');
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#+end_src
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#+begin_src matlab :exports 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(tf_est), 'DisplayName', 'Identification')
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plot(f, abs(squeeze(freqresp(Ghm, f, 'Hz'))), 'DisplayName', 'FEM')
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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ylabel('Amplitude'); xlabel('Frequency [Hz]');
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legend('location', 'northeast')
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hold off;
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ax2 = subplot(2, 1, 2);
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hold on;
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plot(f, 180/pi*angle(tf_est))
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plot(f, 180/pi*angle(squeeze(freqresp(Ghm, f, 'Hz'))))
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
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ylabel('Phase'); xlabel('Frequency [Hz]');
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hold off;
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linkaxes([ax1,ax2], 'x');
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xlim([10, 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/apa95ml_5kg_comp_fem.pdf', 'width', 'full', 'height', 'full');
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#+end_src
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#+name: fig:apa95ml_5kg_comp_fem
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#+caption: Comparison of the identified transfer function and the one estimated from the FE model
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#+RESULTS:
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[[file:figs/apa95ml_5kg_comp_fem.png]]
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** Conclusion :ignore:
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#+begin_important
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The problem comes from the fact that the piezo is driven directly by the DAC that cannot deliver enought current.
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In the next section, a current amplifier is used.
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#+end_important
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* Transfer Function Estimation using the PI Amplifier
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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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ht = load('./mat/huddle_test.mat', 't', 'u', 'y');
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load('./mat/apa95ml_5kg_Amp_E505.mat', 't', 'u', 'um', 'y');
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#+end_src
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#+begin_src matlab
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u = 10*(u - mean(u)); % Input Voltage of Piezo [V]
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um = 10*(um - mean(um)); % Monitor [V]
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y = y - mean(y); % Mass displacement [m]
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ht.u = 10*(ht.u - mean(ht.u));
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ht.y = ht.y - mean(ht.y);
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#+end_src
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** Comparison of the PSD with Huddle Test
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#+begin_src matlab
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Ts = t(end)/(length(t)-1);
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Fs = 1/Ts;
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win = hanning(ceil(1*Fs));
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#+end_src
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#+begin_src matlab
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[pxx, f] = pwelch(y, win, [], [], Fs);
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[pht, ~] = pwelch(ht.y, win, [], [], Fs);
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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(pxx), 'DisplayName', '5kg');
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plot(f, sqrt(pht), 'DisplayName', 'Huddle Test');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
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legend('location', 'southwest');
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xlim([1, Fs/2]);
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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/apa95ml_5kg_PI_pdf_comp_huddle.pdf', 'width', 'wide', 'height', 'tall');
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#+end_src
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#+name: fig:apa95ml_5kg_PI_pdf_comp_huddle
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#+caption: Comparison of the ASD for the identification test and the huddle test
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#+RESULTS:
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[[file:figs/apa95ml_5kg_PI_pdf_comp_huddle.png]]
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** Compute TF estimate and Coherence
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#+begin_src matlab
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Ts = t(end)/(length(t)-1);
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Fs = 1/Ts;
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#+end_src
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#+begin_src matlab
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win = hann(ceil(1/Ts));
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[tf_est, f] = tfestimate(u, -y, win, [], [], 1/Ts);
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[tf_um , ~] = tfestimate(um, -y, win, [], [], 1/Ts);
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[co_est, ~] = mscohere( um, -y, 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, co_est, 'k-')
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
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ylabel('Coherence'); xlabel('Frequency [Hz]');
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hold off;
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xlim([10, 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/apa95ml_5kg_PI_coh.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:apa95ml_5kg_PI_coh
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#+caption: Coherence
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#+RESULTS:
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[[file:figs/apa95ml_5kg_PI_coh.png]]
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#+begin_src matlab :exports 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(tf_est), 'DisplayName', 'Input Voltage')
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plot(f, abs(tf_um), 'DisplayName', 'Monitor Voltage')
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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ylabel('Amplitude [m/V]'); xlabel('Frequency [Hz]');
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hold off;
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legend('location', 'southwest')
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ax2 = subplot(2, 1, 2);
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hold on;
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plot(f, 180/pi*unwrap(angle(tf_est)))
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plot(f, 180/pi*unwrap(angle(tf_um)))
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
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ylabel('Phase'); xlabel('Frequency [Hz]');
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hold off;
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ylim([-540, 0]);
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yticks(-540:90:0);
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linkaxes([ax1,ax2], 'x');
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xlim([10, 5e3]);
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
|
|
exportFig('figs/apa95ml_5kg_PI_tf.pdf', 'width', 'full', 'height', 'full');
|
|
#+end_src
|
|
|
|
#+name: fig:apa95ml_5kg_PI_tf
|
|
#+caption: Estimation of the transfer function from input voltage to displacement
|
|
#+RESULTS:
|
|
[[file:figs/apa95ml_5kg_PI_tf.png]]
|
|
|
|
** Comparison with the FEM model
|
|
#+begin_src matlab
|
|
load('mat/fem_model_5kg.mat', 'G');
|
|
#+end_src
|
|
|
|
#+begin_src matlab :exports none
|
|
freqs = logspace(0, 4, 1000);
|
|
figure;
|
|
ax1 = subplot(2, 1, 1);
|
|
hold on;
|
|
plot(f, abs(tf_um), 'DisplayName', 'Identification')
|
|
plot(freqs, abs(squeeze(freqresp(G, freqs, 'Hz'))), 'DisplayName', 'FEM')
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
|
ylabel('Amplitude [m/V]'); xlabel('Frequency [Hz]');
|
|
legend('location', 'northeast')
|
|
hold off;
|
|
|
|
ax2 = subplot(2, 1, 2);
|
|
hold on;
|
|
plot(f, 180/pi*unwrap(angle(tf_um)))
|
|
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G, freqs, 'Hz')))))
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
|
|
ylabel('Phase'); xlabel('Frequency [Hz]');
|
|
hold off;
|
|
ylim([-540, 0]);
|
|
yticks(-540:90:0);
|
|
|
|
linkaxes([ax1,ax2], 'x');
|
|
xlim([10, 5e3]);
|
|
#+end_src
|
|
|
|
#+begin_src matlab :tangle no :exports results :results file replace
|
|
exportFig('figs/apa95ml_5kg_pi_comp_fem.pdf', 'width', 'full', 'height', 'full');
|
|
#+end_src
|
|
|
|
#+name: fig:apa95ml_5kg_pi_comp_fem
|
|
#+caption: Comparison of the identified transfer function and the one estimated from the FE model
|
|
#+RESULTS:
|
|
[[file:figs/apa95ml_5kg_pi_comp_fem.png]]
|
|
|
|
* Transfer function from force actuator to force sensor
|
|
** Introduction :ignore:
|
|
Two measurements are performed:
|
|
- Speedgoat DAC => Voltage Amplifier (x20) => 1 Piezo Stack => ... => 2 Stacks as Force Sensor (parallel) => Speedgoat ADC
|
|
- Speedgoat DAC => Voltage Amplifier (x20) => 2 Piezo Stacks (parallel) => ... => 1 Stack as Force Sensor => Speedgoat ADC
|
|
|
|
The obtained dynamics from force actuator to force sensor are compare with the FEM model.
|
|
|
|
** 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 :ignore:
|
|
The data are loaded:
|
|
#+begin_src matlab
|
|
a_ss = load('mat/apa95ml_5kg_1a_2s.mat', 't', 'u', 'y', 'v');
|
|
aa_s = load('mat/apa95ml_5kg_2a_1s.mat', 't', 'u', 'y', 'v');
|
|
load('mat/G_force_sensor_5kg.mat', 'G');
|
|
#+end_src
|
|
|
|
** Adjust gain :ignore:
|
|
Let's use the amplifier gain to obtain the true voltage applied to the actuator stack(s)
|
|
|
|
The parameters of the piezoelectric stacks are defined below:
|
|
#+begin_src matlab
|
|
d33 = 3e-10; % Strain constant [m/V]
|
|
n = 80; % Number of layers per stack
|
|
eT = 1.6e-8; % Permittivity under constant stress [F/m]
|
|
sD = 2e-11; % Elastic compliance under constant electric displacement [m2/N]
|
|
ka = 235e6; % Stack stiffness [N/m]
|
|
#+end_src
|
|
|
|
From the FEM, we construct the transfer function from DAC voltage to ADC voltage.
|
|
#+begin_src matlab
|
|
Gfem_aa_s = exp(-s/1e4)*20*(2*d33*n*ka)*(G(3,1)+G(3,2))*d33/(eT*sD*n);
|
|
Gfem_a_ss = exp(-s/1e4)*20*( d33*n*ka)*(G(3,1)+G(2,1))*d33/(eT*sD*n);
|
|
#+end_src
|
|
|
|
** Compute TF estimate and Coherence :ignore:
|
|
The transfer function from input voltage to output voltage are computed and shown in Figure [[fig:bode_plot_force_sensor_voltage_comp_fem]].
|
|
#+begin_src matlab
|
|
Ts = a_ss.t(end)/(length(a_ss.t)-1);
|
|
Fs = 1/Ts;
|
|
|
|
win = hann(ceil(10/Ts));
|
|
|
|
[tf_a_ss, f] = tfestimate(a_ss.u, a_ss.v, win, [], [], 1/Ts);
|
|
[coh_a_ss, ~] = mscohere( a_ss.u, a_ss.v, win, [], [], 1/Ts);
|
|
|
|
[tf_aa_s, f] = tfestimate(aa_s.u, aa_s.v, win, [], [], 1/Ts);
|
|
[coh_aa_s, ~] = mscohere( aa_s.u, aa_s.v, win, [], [], 1/Ts);
|
|
#+end_src
|
|
|
|
#+begin_src matlab :exports none
|
|
freqs = logspace(1, 4, 1000);
|
|
|
|
figure;
|
|
ax1 = subplot(2, 1, 1);
|
|
hold on;
|
|
set(gca,'ColorOrderIndex',1)
|
|
plot(f, abs(tf_aa_s), '-')
|
|
set(gca,'ColorOrderIndex',1)
|
|
plot(freqs, abs(squeeze(freqresp(Gfem_aa_s, freqs, 'Hz'))), '--')
|
|
set(gca,'ColorOrderIndex',2)
|
|
plot(f, abs(tf_a_ss), '-')
|
|
set(gca,'ColorOrderIndex',2)
|
|
plot(freqs, abs(squeeze(freqresp(Gfem_a_ss, freqs, 'Hz'))), '--')
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
|
ylabel('Amplitude'); xlabel('Frequency [Hz]');
|
|
hold off;
|
|
ylim([1e-2, 1e2]);
|
|
|
|
ax2 = subplot(2, 1, 2);
|
|
hold on;
|
|
set(gca,'ColorOrderIndex',1)
|
|
plot(f, 180/pi*angle(tf_aa_s), '-', 'DisplayName', '2 Act - 1 Sen')
|
|
set(gca,'ColorOrderIndex',1)
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gfem_aa_s, freqs, 'Hz'))), '--', 'DisplayName', '2 Act - 1 Sen, - FEM')
|
|
set(gca,'ColorOrderIndex',2)
|
|
plot(f, 180/pi*angle(tf_a_ss), '-', 'DisplayName', '1 Act - 2 Sen')
|
|
set(gca,'ColorOrderIndex',2)
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gfem_a_ss, freqs, 'Hz'))), '--', 'DisplayName', '1 Act - 2 Sen, - FEM')
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
|
|
ylabel('Phase'); xlabel('Frequency [Hz]');
|
|
hold off;
|
|
ylim([-180, 180]);
|
|
yticks(-180:90:180);
|
|
legend('location', 'northeast')
|
|
|
|
linkaxes([ax1,ax2], 'x');
|
|
xlim([10, 5e3]);
|
|
#+end_src
|
|
|
|
#+begin_src matlab :tangle no :exports results :results file replace
|
|
exportFig('figs/bode_plot_force_sensor_voltage_comp_fem.pdf', 'width', 'full', 'height', 'full');
|
|
#+end_src
|
|
|
|
#+name: fig:bode_plot_force_sensor_voltage_comp_fem
|
|
#+caption: Comparison of the identified dynamics from voltage output to voltage input and the FEM
|
|
#+RESULTS:
|
|
[[file:figs/bode_plot_force_sensor_voltage_comp_fem.png]]
|
|
|
|
** System Identification
|
|
#+begin_src matlab
|
|
w_z = 2*pi*111; % Zeros frequency [rad/s]
|
|
w_p = 2*pi*255; % Pole frequency [rad/s]
|
|
xi_z = 0.05;
|
|
xi_p = 0.015;
|
|
G_inf = 2;
|
|
|
|
Gi = G_inf*(s^2 - 2*xi_z*w_z*s + w_z^2)/(s^2 + 2*xi_p*w_p*s + w_p^2);
|
|
#+end_src
|
|
|
|
#+begin_src matlab :exports none
|
|
freqs = logspace(1, 4, 1000);
|
|
|
|
figure;
|
|
ax1 = subplot(2, 1, 1);
|
|
hold on;
|
|
plot(f, abs(tf_aa_s), '-')
|
|
plot(freqs, abs(squeeze(freqresp(Gi, freqs, 'Hz'))), '--')
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
|
ylabel('Amplitude'); xlabel('Frequency [Hz]');
|
|
hold off;
|
|
ylim([1e-2, 1e2]);
|
|
|
|
ax2 = subplot(2, 1, 2);
|
|
hold on;
|
|
plot(f, 180/pi*angle(tf_aa_s), '-', 'DisplayName', '2 Act - 1 Sen')
|
|
plot(freqs, 180/pi*angle(squeeze(freqresp(Gi, freqs, 'Hz'))), '--', 'DisplayName', '2 Act - 1 Sen, - FEM')
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
|
|
ylabel('Phase'); xlabel('Frequency [Hz]');
|
|
hold off;
|
|
ylim([-180, 180]);
|
|
yticks(-180:90:180);
|
|
legend('location', 'northeast')
|
|
|
|
linkaxes([ax1,ax2], 'x');
|
|
xlim([10, 5e3]);
|
|
#+end_src
|
|
|
|
#+begin_src matlab :tangle no :exports results :results file replace
|
|
exportFig('figs/iff_plant_identification_apa95ml.pdf', 'width', 'full', 'height', 'full');
|
|
#+end_src
|
|
|
|
#+name: fig:iff_plant_identification_apa95ml
|
|
#+caption: Identification of the IFF plant
|
|
#+RESULTS:
|
|
[[file:figs/iff_plant_identification_apa95ml.png]]
|
|
|
|
|
|
** Integral Force Feedback
|
|
#+begin_src matlab :exports none
|
|
gains = logspace(0, 5, 1000);
|
|
|
|
figure;
|
|
hold on;
|
|
plot(real(pole(Gi)), imag(pole(Gi)), 'kx');
|
|
plot(real(tzero(Gi)), imag(tzero(Gi)), 'ko');
|
|
for i = 1:length(gains)
|
|
cl_poles = pole(feedback(Gi, (gains(i)/(s + 2*2*pi)*s/(s + 0.5*2*pi))));
|
|
plot(real(cl_poles), imag(cl_poles), 'k.');
|
|
end
|
|
ylim([0, 1800]);
|
|
xlim([-1600,200]);
|
|
xlabel('Real Part')
|
|
ylabel('Imaginary Part')
|
|
axis square
|
|
#+end_src
|
|
|
|
#+begin_src matlab :tangle no :exports results :results file replace
|
|
exportFig('figs/root_locus_iff_apa95ml_identification.pdf', 'width', 'wide', 'height', 'tall');
|
|
#+end_src
|
|
|
|
#+name: fig:root_locus_iff_apa95ml_identification
|
|
#+caption: Root Locus for IFF
|
|
#+RESULTS:
|
|
[[file:figs/root_locus_iff_apa95ml_identification.png]]
|
|
|
|
* IFF Tests
|
|
** 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
|
|
|
|
** First tests with few gains
|
|
#+begin_src matlab
|
|
iff_g10 = load('./mat/apa95ml_iff_g10_res.mat', 'u', 't', 'y', 'v');
|
|
iff_g100 = load('./mat/apa95ml_iff_g100_res.mat', 'u', 't', 'y', 'v');
|
|
iff_of = load('./mat/apa95ml_iff_off_res.mat', 'u', 't', 'y', 'v');
|
|
#+end_src
|
|
|
|
#+begin_src matlab
|
|
Ts = 1e-4;
|
|
win = hann(ceil(10/Ts));
|
|
|
|
[tf_iff_g10, f] = tfestimate(iff_g10.u, iff_g10.y, win, [], [], 1/Ts);
|
|
[co_iff_g10, ~] = mscohere(iff_g10.u, iff_g10.y, win, [], [], 1/Ts);
|
|
|
|
[tf_iff_g100, f] = tfestimate(iff_g100.u, iff_g100.y, win, [], [], 1/Ts);
|
|
[co_iff_g100, ~] = mscohere(iff_g100.u, iff_g100.y, win, [], [], 1/Ts);
|
|
|
|
[tf_iff_of, ~] = tfestimate(iff_of.u, iff_of.y, win, [], [], 1/Ts);
|
|
[co_iff_of, ~] = mscohere(iff_of.u, iff_of.y, win, [], [], 1/Ts);
|
|
#+end_src
|
|
|
|
#+begin_src matlab :exports none
|
|
figure;
|
|
|
|
hold on;
|
|
plot(f, co_iff_of, '-', 'DisplayName', 'g=0')
|
|
plot(f, co_iff_g10, '-', 'DisplayName', 'g=10')
|
|
plot(f, co_iff_g100, '-', 'DisplayName', 'g=100')
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
|
|
ylabel('Coherence'); xlabel('Frequency [Hz]');
|
|
hold off;
|
|
legend();
|
|
xlim([60, 600])
|
|
#+end_src
|
|
|
|
#+begin_src matlab :tangle no :exports results :results file replace
|
|
exportFig('figs/iff_first_test_coherence.pdf', 'width', 'wide', 'height', 'normal');
|
|
#+end_src
|
|
|
|
#+name: fig:iff_first_test_coherence
|
|
#+caption: Coherence
|
|
#+RESULTS:
|
|
[[file:figs/iff_first_test_coherence.png]]
|
|
|
|
|
|
#+begin_src matlab :exports none
|
|
figure;
|
|
ax1 = subplot(2, 1, 1);
|
|
hold on;
|
|
plot(f, abs(tf_iff_of), '-', 'DisplayName', 'g=0')
|
|
plot(f, abs(tf_iff_g10), '-', 'DisplayName', 'g=10')
|
|
plot(f, abs(tf_iff_g100), '-', 'DisplayName', 'g=100')
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
|
ylabel('Amplitude'); xlabel('Frequency [Hz]');
|
|
hold off;
|
|
legend();
|
|
|
|
ax2 = subplot(2, 1, 2);
|
|
hold on;
|
|
plot(f, 180/pi*angle(-tf_iff_of), '-')
|
|
plot(f, 180/pi*angle(-tf_iff_g10), '-')
|
|
plot(f, 180/pi*angle(-tf_iff_g100), '-')
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
|
|
ylabel('Phase'); xlabel('Frequency [Hz]');
|
|
hold off;
|
|
|
|
linkaxes([ax1,ax2], 'x');
|
|
xlim([60, 600]);
|
|
#+end_src
|
|
|
|
#+begin_src matlab :tangle no :exports results :results file replace
|
|
exportFig('figs/iff_first_test_bode_plot.pdf', 'width', 'full', 'height', 'full');
|
|
#+end_src
|
|
|
|
#+name: fig:iff_first_test_bode_plot
|
|
#+caption: Bode plot for different values of IFF gain
|
|
#+RESULTS:
|
|
[[file:figs/iff_first_test_bode_plot.png]]
|
|
|
|
** Second test with many Gains
|
|
#+begin_src matlab
|
|
load('./mat/apa95ml_iff_test.mat', 'results');
|
|
#+end_src
|
|
|
|
#+begin_src matlab
|
|
Ts = 1e-4;
|
|
win = hann(ceil(10/Ts));
|
|
#+end_src
|
|
|
|
#+begin_src matlab
|
|
tf_iff = {zeros(1, length(results))};
|
|
co_iff = {zeros(1, length(results))};
|
|
g_iff = [0, 1, 5, 10, 50, 100];
|
|
|
|
for i=1:length(results)
|
|
[tf_est, f] = tfestimate(results{i}.u, results{i}.y, win, [], [], 1/Ts);
|
|
[co_est, ~] = mscohere(results{i}.u, results{i}.y, win, [], [], 1/Ts);
|
|
|
|
tf_iff(i) = {tf_est};
|
|
co_iff(i) = {co_est};
|
|
end
|
|
#+end_src
|
|
|
|
#+begin_src matlab :exports none
|
|
figure;
|
|
|
|
hold on;
|
|
for i = 1:length(results)
|
|
plot(f, co_iff{i}, '-', 'DisplayName', sprintf('g = %0.f', g_iff(i)))
|
|
end
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
|
|
ylabel('Coherence'); xlabel('Frequency [Hz]');
|
|
hold off;
|
|
legend();
|
|
xlim([60, 600])
|
|
#+end_src
|
|
|
|
#+begin_src matlab :exports none
|
|
figure;
|
|
ax1 = subplot(2, 1, 1);
|
|
hold on;
|
|
for i = 1:length(results)
|
|
plot(f, abs(tf_iff{i}), '-', 'DisplayName', sprintf('g = %0.f', g_iff(i)))
|
|
end
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
|
ylabel('Amplitude'); xlabel('Frequency [Hz]');
|
|
hold off;
|
|
legend();
|
|
|
|
ax2 = subplot(2, 1, 2);
|
|
hold on;
|
|
for i = 1:length(results)
|
|
plot(f, 180/pi*angle(-tf_iff{i}), '-')
|
|
end
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
|
|
ylabel('Phase'); xlabel('Frequency [Hz]');
|
|
hold off;
|
|
|
|
linkaxes([ax1,ax2], 'x');
|
|
xlim([60, 600]);
|
|
#+end_src
|
|
|
|
#+begin_src matlab :tangle no :exports results :results file replace
|
|
exportFig('figs/iff_results_bode_plots.pdf', 'width', 'full', 'height', 'full');
|
|
#+end_src
|
|
|
|
#+name: fig:iff_results_bode_plots
|
|
#+caption:
|
|
#+RESULTS:
|
|
[[file:figs/iff_results_bode_plots.png]]
|
|
|
|
#+begin_src matlab
|
|
G_id = {zeros(1,length(results))};
|
|
|
|
f_start = 70; % [Hz]
|
|
f_end = 500; % [Hz]
|
|
|
|
for i = 1:length(results)
|
|
tf_id = tf_iff{i}(sum(f<f_start):length(f)-sum(f>f_end));
|
|
f_id = f(sum(f<f_start):length(f)-sum(f>f_end));
|
|
|
|
gfr = idfrd(tf_id, 2*pi*f_id, Ts);
|
|
G_id(i) = {procest(gfr,'P2UDZ')};
|
|
end
|
|
#+end_src
|
|
|
|
#+begin_src matlab :exports none
|
|
figure;
|
|
ax1 = subplot(2, 1, 1);
|
|
hold on;
|
|
for i = 1:length(results)
|
|
set(gca,'ColorOrderIndex',i)
|
|
plot(f, abs(tf_iff{i}), '-', 'DisplayName', sprintf('g = %0.f', g_iff(i)))
|
|
set(gca,'ColorOrderIndex',i)
|
|
plot(f, abs(squeeze(freqresp(G_id{i}, f, 'Hz'))), '--', 'HandleVisibility', 'off')
|
|
end
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
|
ylabel('Amplitude'); xlabel('Frequency [Hz]');
|
|
hold off;
|
|
legend();
|
|
|
|
ax2 = subplot(2, 1, 2);
|
|
hold on;
|
|
for i = 1:length(results)
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|
set(gca,'ColorOrderIndex',i)
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|
plot(f, 180/pi*angle(tf_iff{i}), '-')
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|
set(gca,'ColorOrderIndex',i)
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|
plot(f, 180/pi*angle(squeeze(freqresp(G_id{i}, f, 'Hz'))), '--')
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|
end
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|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
|
|
ylabel('Phase'); xlabel('Frequency [Hz]');
|
|
hold off;
|
|
|
|
linkaxes([ax1,ax2], 'x');
|
|
xlim([60, 600]);
|
|
#+end_src
|
|
|
|
#+begin_src matlab :tangle no :exports results :results file replace
|
|
exportFig('figs/iff_results_bode_plots_identification.pdf', 'width', 'full', 'height', 'full');
|
|
#+end_src
|
|
|
|
#+name: fig:iff_results_bode_plots_identification
|
|
#+caption:
|
|
#+RESULTS:
|
|
[[file:figs/iff_results_bode_plots_identification.png]]
|
|
|
|
#+begin_src matlab :exports none
|
|
w_z = 2*pi*111; % Zeros frequency [rad/s]
|
|
w_p = 2*pi*255; % Pole frequency [rad/s]
|
|
xi_z = 0.05;
|
|
xi_p = 0.015;
|
|
G_inf = 2;
|
|
|
|
Gi = G_inf*(s^2 - 2*xi_z*w_z*s + w_z^2)/(s^2 + 2*xi_p*w_p*s + w_p^2);
|
|
|
|
|
|
gains = logspace(0, 5, 1000);
|
|
|
|
figure;
|
|
hold on;
|
|
plot(real(pole(Gi)), imag(pole(Gi)), 'kx', 'HandleVisibility', 'off');
|
|
plot(real(tzero(Gi)), imag(tzero(Gi)), 'ko', 'HandleVisibility', 'off');
|
|
for i = 1:length(results)
|
|
set(gca,'ColorOrderIndex',i)
|
|
plot(real(pole(G_id{i})), imag(pole(G_id{i})), 'o', 'DisplayName', sprintf('g = %0.f', g_iff(i)));
|
|
end
|
|
for i = 1:length(gains)
|
|
cl_poles = pole(feedback(Gi, (gains(i)/(s + 2*pi*2))));
|
|
plot(real(cl_poles), imag(cl_poles), 'k.', 'HandleVisibility', 'off');
|
|
end
|
|
ylim([0, 1800]);
|
|
xlim([-1600,200]);
|
|
xlabel('Real Part')
|
|
ylabel('Imaginary Part')
|
|
axis square
|
|
legend('location', 'northwest');
|
|
#+end_src
|
|
|
|
#+begin_src matlab :tangle no :exports results :results file replace
|
|
exportFig('figs/iff_results_root_locus.pdf', 'width', 'wide', 'height', 'tall');
|
|
#+end_src
|
|
|
|
#+name: fig:iff_results_root_locus
|
|
#+caption:
|
|
#+RESULTS:
|
|
[[file:figs/iff_results_root_locus.png]]
|