Update figures and tangle matlab code

Tangle piezo_parameters.m
Add new APA95ML model
2020-11-24 18:28:16 +01:00 · 2020-11-24 13:57:47 +01:00 · 2020-11-24 13:57:15 +01:00 · 2020-11-24 13:56:38 +01:00 · 2020-11-24 09:25:05 +01:00 · 2020-11-24 09:24:51 +01:00
108 changed files with 17994 additions and 1605 deletions
--- a/.gitignore
+++ b/.gitignore
@@ -0,0 +1,38 @@
+# Windows default autosave extension
+*.asv
+*rtw/
+test_at**.m
+data/
+
+# OSX / *nix default autosave extension
+*.m~
+
+# Compiled MEX binaries (all platforms)
+*.mex*
+
+# Packaged app and toolbox files
+*.mlappinstall
+*.slxc
+*.mldatx
+*.mltbx
+*.xml
+piezoapa_slrt_rtw/
+
+# Generated helpsearch folders
+helpsearch*/
+
+# Simulink code generation folders
+slprj/
+sccprj/
+
+# Matlab code generation folders
+codegen/
+
+# Simulink autosave extension
+*.autosave
+
+# Simulink cache files
+*.slxc
+
+# Octave session info
+octave-workspace
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--- a/css/readtheorg.css
+++ b/css/readtheorg.css
--- a/doc/APA95ML.pdf
+++ b/doc/APA95ML.pdf
--- a/doc/IDS3010.pdf
+++ b/doc/IDS3010.pdf
--- a/Datasheet.pdf
+++ b/Datasheet.pdf
--- a/doc/LA75B.pdf
+++ b/doc/LA75B.pdf
--- a/doc/model_5113.pdf
+++ b/doc/model_5113.pdf
--- a/figs/APA95ML_FEM.png
+++ b/figs/APA95ML_FEM.png
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--- a/figs/IMG_20200716_174810.jpg
+++ b/figs/IMG_20200716_174810.jpg
--- a/figs/IMG_20200720_091821.jpg
+++ b/figs/IMG_20200720_091821.jpg
--- a/figs/PI_E505_coh.pdf
+++ b/figs/PI_E505_coh.pdf
--- a/figs/PI_E505_coh.png
+++ b/figs/PI_E505_coh.png
--- a/figs/PI_E505_tf.pdf
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--- a/figs/PI_E505_tf.png
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--- a/figs/apa95ml_5kg_PI_coh.pdf
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--- a/figs/apa95ml_5kg_PI_coh.png
+++ b/figs/apa95ml_5kg_PI_coh.png
--- a/figs/apa95ml_5kg_PI_pdf_comp_huddle.pdf
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--- a/figs/apa95ml_5kg_PI_pdf_comp_huddle.png
+++ b/figs/apa95ml_5kg_PI_pdf_comp_huddle.png
--- a/figs/apa95ml_5kg_PI_tf.pdf
+++ b/figs/apa95ml_5kg_PI_tf.pdf
--- a/figs/apa95ml_5kg_PI_tf.png
+++ b/figs/apa95ml_5kg_PI_tf.png
--- a/figs/apa95ml_5kg_cedrat_coh.pdf
+++ b/figs/apa95ml_5kg_cedrat_coh.pdf
--- a/figs/apa95ml_5kg_cedrat_coh.png
+++ b/figs/apa95ml_5kg_cedrat_coh.png
--- a/figs/apa95ml_5kg_pi_comp_fem.pdf
+++ b/figs/apa95ml_5kg_pi_comp_fem.pdf
--- a/figs/apa95ml_5kg_pi_comp_fem.png
+++ b/figs/apa95ml_5kg_pi_comp_fem.png
--- a/figs/bode_plot_force_sensor_voltage_comp_fem.pdf
+++ b/figs/bode_plot_force_sensor_voltage_comp_fem.pdf
--- a/figs/bode_plot_force_sensor_voltage_comp_fem.png
+++ b/figs/bode_plot_force_sensor_voltage_comp_fem.png
--- a/figs/compare_Gd_id_simscape.pdf
+++ b/figs/compare_Gd_id_simscape.pdf
--- a/figs/compare_Gd_id_simscape.png
+++ b/figs/compare_Gd_id_simscape.png
--- a/figs/compare_Gf_id_simscape.pdf
+++ b/figs/compare_Gf_id_simscape.pdf
--- a/figs/compare_Gf_id_simscape.png
+++ b/figs/compare_Gf_id_simscape.png
--- a/figs/dynamics_act_disp_comp_mass.pdf
+++ b/figs/dynamics_act_disp_comp_mass.pdf
--- a/figs/dynamics_act_disp_comp_mass.png
+++ b/figs/dynamics_act_disp_comp_mass.png
--- a/figs/dynamics_force_force_sensor_comp_mass.pdf
+++ b/figs/dynamics_force_force_sensor_comp_mass.pdf
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+++ b/figs/dynamics_force_force_sensor_comp_mass.png
--- a/figs/exp_frf_identified_tf.pdf
+++ b/figs/exp_frf_identified_tf.pdf
--- a/figs/exp_frf_identified_tf.png
+++ b/figs/exp_frf_identified_tf.png
--- a/figs/gain_Va_to_Vs.pdf
+++ b/figs/gain_Va_to_Vs.pdf
--- a/figs/gain_Va_to_Vs.png
+++ b/figs/gain_Va_to_Vs.png
--- a/figs/gain_Va_to_d.pdf
+++ b/figs/gain_Va_to_d.pdf
--- a/figs/gain_Va_to_d.png
+++ b/figs/gain_Va_to_d.png
--- a/figs/huddle_test_pdf.pdf
+++ b/figs/huddle_test_pdf.pdf
--- a/figs/huddle_test_pdf.png
+++ b/figs/huddle_test_pdf.png
--- a/figs/huddle_test_time_domain.pdf
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--- a/figs/huddle_test_time_domain.png
+++ b/figs/huddle_test_time_domain.png
--- a/figs/iff_first_test_bode_plot.pdf
+++ b/figs/iff_first_test_bode_plot.pdf
--- a/figs/iff_first_test_bode_plot.png
+++ b/figs/iff_first_test_bode_plot.png
--- a/figs/iff_first_test_coherence.pdf
+++ b/figs/iff_first_test_coherence.pdf
--- a/figs/iff_first_test_coherence.png
+++ b/figs/iff_first_test_coherence.png
--- a/figs/iff_plant_identification_apa95ml.pdf
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+++ b/figs/iff_plant_identification_apa95ml.png
--- a/figs/iff_results_bode_plots.pdf
+++ b/figs/iff_results_bode_plots.pdf
--- a/figs/iff_results_bode_plots.png
+++ b/figs/iff_results_bode_plots.png
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+++ b/figs/iff_results_bode_plots_identification.png
--- a/figs/iff_results_root_locus.pdf
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--- a/figs/iff_results_root_locus.png
+++ b/figs/iff_results_root_locus.png
--- a/figs/root_locus_iff_apa95ml_identification.pdf
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+++ b/figs/test_bench_apa_schematic_iff.pdf
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+++ b/figs/test_bench_apa_schematic_iff.png
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@@ -1 +0,0 @@
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--- a/js/readtheorg.js
+++ b/js/readtheorg.js
@@ -1,85 +0,0 @@
-$(function() {
-    $('.note').before("<p class='admonition-title note'>Note</p>");
-    $('.seealso').before("<p class='admonition-title seealso'>See also</p>");
-    $('.warning').before("<p class='admonition-title warning'>Warning</p>");
-    $('.caution').before("<p class='admonition-title caution'>Caution</p>");
-    $('.attention').before("<p class='admonition-title attention'>Attention</p>");
-    $('.tip').before("<p class='admonition-title tip'>Tip</p>");
-    $('.important').before("<p class='admonition-title important'>Important</p>");
-    $('.hint').before("<p class='admonition-title hint'>Hint</p>");
-    $('.error').before("<p class='admonition-title error'>Error</p>");
-    $('.danger').before("<p class='admonition-title danger'>Danger</p>");
-});
-
-$( document ).ready(function() {
-
-    // Shift nav in mobile when clicking the menu.
-    $(document).on('click', "[data-toggle='wy-nav-top']", function() {
-      $("[data-toggle='wy-nav-shift']").toggleClass("shift");
-      $("[data-toggle='rst-versions']").toggleClass("shift");
-    });
-    // Close menu when you click a link.
-    $(document).on('click', ".wy-menu-vertical .current ul li a", function() {
-      $("[data-toggle='wy-nav-shift']").removeClass("shift");
-      $("[data-toggle='rst-versions']").toggleClass("shift");
-    });
-    $(document).on('click', "[data-toggle='rst-current-version']", function() {
-      $("[data-toggle='rst-versions']").toggleClass("shift-up");
-    });
-    // Make tables responsive
-    $("table.docutils:not(.field-list)").wrap("<div class='wy-table-responsive'></div>");
-});
-
-$( document ).ready(function() {
-    $('#text-table-of-contents ul').first().addClass('nav');
-                                        // ScrollSpy also requires that we use
-                                        // a Bootstrap nav component.
-    $('body').scrollspy({target: '#text-table-of-contents'});
-
-    // add sticky table headers
-    $('table').stickyTableHeaders();
-
-    // set the height of tableOfContents
-    var $postamble = $('#postamble');
-    var $tableOfContents = $('#table-of-contents');
-    $tableOfContents.css({paddingBottom: $postamble.outerHeight()});
-
-    // add TOC button
-    var toggleSidebar = $('<div id="toggle-sidebar"><a href="#table-of-contents"><h2>Table of Contents</h2></a></div>');
-    $('#content').prepend(toggleSidebar);
-
-    // add close button when sidebar showed in mobile screen
-    var closeBtn = $('<a class="close-sidebar" href="#">Close</a>');
-    var tocTitle = $('#table-of-contents').find('h2');
-    tocTitle.append(closeBtn);
-});
-
-window.SphinxRtdTheme = (function (jquery) {
-    var stickyNav = (function () {
-        var navBar,
-            win,
-            stickyNavCssClass = 'stickynav',
-            applyStickNav = function () {
-                if (navBar.height() <= win.height()) {
-                    navBar.addClass(stickyNavCssClass);
-                } else {
-                    navBar.removeClass(stickyNavCssClass);
-                }
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-            enable = function () {
-                applyStickNav();
-                win.on('resize', applyStickNav);
-            },
-            init = function () {
-                navBar = jquery('nav.wy-nav-side:first');
-                win    = jquery(window);
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-        jquery(init);
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-    return {
-        StickyNav : stickyNav
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-}($));
--- a/matlab/force_sensor_identification.m
+++ b/matlab/force_sensor_identification.m
@@ -0,0 +1,95 @@
+%% Clear Workspace and Close figures
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+addpath('./mat/');
+
+% Load Data                                                         :ignore:
+% The data are loaded:
+
+load('apa95ml_5kg_2a_1s.mat', 't', 'u', 'v');
+
+
+
+% Any offset is removed.
+
+u = detrend(u, 0); % Speedgoat DAC output Voltage [V]
+v = detrend(v, 0); % Speedgoat ADC input Voltage (sensor stack) [V]
+
+
+
+% Here, the amplifier gain is 20.
+
+u = 20*u; % Actuator Stack Voltage [V]
+
+% Compute TF estimate and Coherence                                 :ignore:
+% The transfer function from the actuator voltage $V_a$ to the force sensor stack voltage $V_s$ is computed.
+
+
+Ts = t(end)/(length(t)-1);
+Fs = 1/Ts;
+
+win = hann(ceil(5/Ts));
+
+[tf_est,  f] = tfestimate(u, v, win, [], [], 1/Ts);
+[coh,     ~] = mscohere(  u, v, win, [], [], 1/Ts);
+
+
+
+% The coherence is shown in Figure [[fig:apa95ml_5kg_cedrat_coh]].
+
+
+figure;
+
+hold on;
+plot(f, coh, 'k-')
+set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
+ylabel('Coherence'); xlabel('Frequency [Hz]');
+hold off;
+xlim([10, 5e3]);
+
+
+
+% #+name: fig:apa95ml_5kg_cedrat_coh
+% #+caption: Coherence
+% #+RESULTS:
+% [[file:figs/apa95ml_5kg_cedrat_coh.png]]
+
+% The Simscape model is loaded and compared with the identified dynamics in Figure [[fig:bode_plot_force_sensor_voltage_comp_fem]].
+% The non-minimum phase zero is just a side effect of the not so great identification.
+% Taking longer measurements would results in a minimum phase zero.
+
+
+load('mat/fem_simscape_models.mat', 'Gfm');
+
+freqs = logspace(1, 4, 1000);
+
+figure;
+tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
+
+ax1 = nexttile([2,1]);
+hold on;
+plot(f, abs(tf_est))
+plot(freqs, abs(squeeze(freqresp(Gfm, freqs, 'Hz'))))
+set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
+ylabel('Amplitude [V/V]'); set(gca, 'XTickLabel',[]);
+hold off;
+ylim([1e-3, 1e1]);
+
+ax2 = nexttile;
+hold on;
+plot(f, 180/pi*angle(tf_est), ...
+     'DisplayName', 'Identification')
+plot(freqs, 180/pi*angle(squeeze(freqresp(Gfm, freqs, 'Hz'))), ...
+     'DisplayName', '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]);
--- a/matlab/huddle_test.m
+++ b/matlab/huddle_test.m
@@ -0,0 +1,34 @@
+%% Clear Workspace and Close figures
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+addpath('./mat/');
+
+% Load Data                                                       :noexport:
+
+load('huddle_test.mat', 't', 'y');
+
+y = y - mean(y(1000:end));
+
+% Time Domain Data
+
+figure;
+plot(t(1000:end), y(1000:end))
+ylabel('Output Displacement [m]'); xlabel('Time [s]');
+
+% PSD of Measurement Noise
+
+Ts = t(end)/(length(t)-1);
+Fs = 1/Ts;
+
+win = hanning(ceil(1*Fs));
+
+[pxx, f] = pwelch(y(1000:end), win, [], [], Fs);
+
+figure;
+plot(f, sqrt(pxx));
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
+xlim([1, Fs/2]);
--- a/matlab/integral_force_feedback.m
+++ b/matlab/integral_force_feedback.m
@@ -0,0 +1,307 @@
+%% Clear Workspace and Close figures
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+addpath('./mat/');
+
+% IFF Plant
+% From the identified plant, a model of the transfer function from the actuator stack voltage to the force sensor generated voltage is developed.
+
+
+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 = 0.1;
+
+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);
+
+
+
+% Its bode plot is shown in Figure [[fig:iff_plant_identification_apa95ml]].
+
+
+freqs = logspace(1, 4, 1000);
+
+figure;
+tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
+
+ax1 = nexttile([2,1]);
+hold on;
+plot(freqs, abs(squeeze(freqresp(Gi, freqs, 'Hz'))), 'k-')
+set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
+ylabel('Amplitude'); set(gca, 'XTickLabel', []);
+hold off;
+ylim([1e-3, 1e1]);
+
+ax2 = nexttile;
+hold on;
+plot(freqs, 180/pi*angle(squeeze(freqresp(Gi, freqs, 'Hz'))), 'k-')
+set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
+ylabel('Phase'); xlabel('Frequency [Hz]');
+hold off;
+ylim([-180, 180]);
+yticks(-180:90:180);
+
+linkaxes([ax1,ax2], 'x');
+xlim([10, 5e3]);
+
+
+
+% #+name: fig:iff_plant_identification_apa95ml
+% #+caption: Bode plot of the IFF plant
+% #+RESULTS:
+% [[file:figs/iff_plant_identification_apa95ml.png]]
+
+% The controller used in the Integral Force Feedback Architecture is:
+% \begin{equation}
+%   K_{\text{IFF}}(s) = \frac{g}{s + 2\cdot 2\pi} \cdot \frac{s}{s + 0.5 \cdot 2\pi}
+% \end{equation}
+% where $g$ is a gain that can be tuned.
+
+% Above 2 Hz the controller is basically an integrator, whereas an high pass filter is added at 0.5Hz to further reduce the low frequency gain.
+
+% In the frequency band of interest, this controller should mostly act as a pure integrator.
+
+% The Root Locus corresponding to this controller is shown in Figure [[fig:root_locus_iff_apa95ml_identification]].
+
+
+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
+
+% First tests with few gains
+% The controller is now implemented in practice, and few controller gains are tested: $g = 0$, $g = 10$ and $g = 100$.
+
+% For each controller gain, the identification shown in Figure [[fig:test_bench_apa_schematic_iff]] is performed.
+
+iff_g10  = load('apa95ml_iff_g10_res.mat',  'u', 't', 'y', 'v');
+iff_g100 = load('apa95ml_iff_g100_res.mat', 'u', 't', 'y', 'v');
+iff_of   = load('apa95ml_iff_off_res.mat',  'u', 't', 'y', 'v');
+
+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, ~] = 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);
+
+
+
+% The coherence between the excitation signal and the mass displacement as measured by the interferometer is shown in Figure [[fig:iff_first_test_coherence]].
+
+
+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])
+
+
+
+% #+name: fig:iff_first_test_coherence
+% #+caption: Coherence
+% #+RESULTS:
+% [[file:figs/iff_first_test_coherence.png]]
+
+% The obtained transfer functions are shown in Figure [[fig:iff_first_test_bode_plot]].
+% It is clear that the IFF architecture can actively damp the main resonance of the system.
+
+
+figure;
+tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
+
+ax1 = nexttile([2, 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'); set(gca, 'XTickLabel',[]);
+hold off;
+legend();
+
+ax2 = nexttile;
+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;
+yticks(-360:90:360);
+
+linkaxes([ax1,ax2], 'x');
+xlim([60, 600]);
+
+% Second test with many Gains
+% Then, the same identification test is performed for many more gains.
+
+load('apa95ml_iff_test.mat', 'results');
+
+Ts = 1e-4;
+win = hann(ceil(10/Ts));
+
+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
+
+
+
+% The obtained dynamics are shown in Figure [[fig:iff_results_bode_plots]].
+
+
+figure;
+tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
+
+ax1 = nexttile([2, 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'); set(gca, 'XTickLabel',[]);
+hold off;
+legend();
+
+ax2 = nexttile;
+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]');
+yticks(-360:90:360);
+axis padded 'auto x'
+
+linkaxes([ax1,ax2], 'x');
+xlim([60, 600]);
+
+
+
+% #+name: fig:iff_results_bode_plots
+% #+caption: Identified dynamics from excitation voltage to the mass displacement
+% #+RESULTS:
+% [[file:figs/iff_results_bode_plots.png]]
+
+% For each gain, the parameters of a second order resonant system that best fits the data are estimated and are compared with the data in Figure [[fig:iff_results_bode_plots_identification]].
+
+
+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
+
+figure;
+tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
+
+ax1 = nexttile([2, 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'); set(gca, 'XTickLabel',[]);
+hold off;
+legend();
+
+ax2 = nexttile;
+hold on;
+for i = 1:length(results)
+  set(gca,'ColorOrderIndex',i)
+  plot(f, 180/pi*angle(tf_iff{i}), '-')
+  set(gca,'ColorOrderIndex',i)
+  plot(f, 180/pi*angle(squeeze(freqresp(G_id{i}, f, 'Hz'))), '--')
+end
+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([60, 600]);
+
+
+
+% #+name: fig:iff_results_bode_plots_identification
+% #+caption: Comparison of the measured dynamic and the identified 2nd order resonant systems that best fits the data
+% #+RESULTS:
+% [[file:figs/iff_results_bode_plots_identification.png]]
+
+% Finally, we can represent the position of the poles of the 2nd order systems on the Root Locus plot (Figure [[fig:iff_results_root_locus]]).
+
+
+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');
--- a/matlab/mat/APA95ML_K.CSV
+++ b/matlab/mat/APA95ML_K.CSV
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+++ b/matlab/mat/APA95ML_M.CSV
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+3.6700089328994298e-06,2.1007419070983017e-06,-2.2507614142865459e-06,-1.1462974253298323e-06,2.3194359654359551e-07,-2.5095534857133388e-04,1.8036219703654935e-05,2.5545484696192206e-05,1.1871946297445109e-05,-1.6381252890882443e-06,2.1810598507161741e-07,2.5177251691959474e-04,-1.7578159271992778e-05,-1.6998768321436073e-06,5.0911161449586316e-06,-4.8703199072597480e-04,-1.9165620633813443e-07,1.9139117282718920e-09,2.7012543385631668e-06,-5.5791770435657260e-09,3.1880812736881621e-07,6.5918824320239989e-07,3.3913962270503795e-09,5.0829572341789608e-10,-4.1164191882921470e-08,4.6417288010822681e-09,-2.3586505657443102e-09,-4.9069695022575735e-09,-7.3526181970332634e-11,2.8189473468022100e-11,-2.6338255260384415e-06,-1.1967338289737897e-06,-4.6722249982480806e-07,-6.4303711148784267e-07,1.7915568247723615e-09,-4.5480182279923772e-09,-1.0341089437166899e-05,-1.0212703971756771e-05,-1.2999262224332882e-05,4.8182243776653436e-04,-1.2035752233129000e-07,1.5971162742113723e-07,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,1.0000000000000000e+00,0.0000000000000000e+00
+1.3106492228986189e-05,-3.5723349268193733e-03,1.6572383417626479e-05,-2.4524528394658456e-04,-1.2883784457938332e-07,1.3929093978201961e-06,-2.0053507774652502e-06,3.5728283551551688e-03,1.1824141280798525e-05,-2.4569778440730589e-04,8.1551244794981474e-08,-1.3764616335374010e-06,-1.5481986761443345e-05,-1.9044813141402933e-06,7.4544369185691846e-06,-4.4752055263868424e-04,-1.8068106002131866e-07,2.4370502902649210e-08,2.5687112618053921e-06,4.1655314389244600e-08,3.4122220147010140e-07,6.2083014580506038e-07,3.3940992746034015e-09,3.0044442082434653e-10,-7.1708411131971589e-08,-5.1027076387319601e-09,-6.2175221737627398e-09,-9.7248995910835063e-09,-4.6159749121076536e-11,-3.9694148835885484e-11,2.6170179656636316e-06,1.1901652322187288e-06,4.4732338266589198e-07,6.1967397606540059e-07,-1.7074057077706677e-09,4.5938289091603020e-09,8.6144457711177801e-06,1.7922379514314945e-05,1.6394035147424517e-05,-4.5310817532855151e-04,1.0946019552401556e-07,-1.6079171905942081e-07,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,1.0000000000000000e+00
--- a/matlab/mat/APA95ML_out_nodes_3D.txt
+++ b/matlab/mat/APA95ML_out_nodes_3D.txt
@@ -0,0 +1,75 @@
+
+ LIST ALL SELECTED NODES.   DSYS=      0
+
+ *** ANSYS - ENGINEERING ANALYSIS SYSTEM  RELEASE 2020 R2          20.2     ***
+ DISTRIBUTED ANSYS Academic Research                           
+
+ 00208316  VERSION=WINDOWS x64   15:24:46  NOV 18, 2020 CP=      2.031
+
+ Piezo-APA95ML-3DElm--Modal (A5)                                               
+
+
+
+    NODE        X             Y             Z           THXY     THYZ     THZX
+    40467   0.0000        0.0000       0.29997E-001     0.00     0.00     0.00
+    40469   0.0000        0.0000      -0.29997E-001     0.00     0.00     0.00
+    40470 -0.35000E-001   0.0000        0.0000          0.00     0.00     0.00
+    40475 -0.15000E-001   0.0000        0.0000          0.00     0.00     0.00
+    40476 -0.50000E-002   0.0000        0.0000          0.00     0.00     0.00
+    40477  0.15000E-001   0.0000        0.0000          0.00     0.00     0.00
+    40478  0.35000E-001   0.0000        0.0000          0.00     0.00     0.00
+
+ LIST MASTERS ON ALL SELECTED NODES.
+ CURRENT DOF SET= UX   UY   UZ   ROTX ROTY ROTZ
+
+ *** ANSYS - ENGINEERING ANALYSIS SYSTEM  RELEASE 2020 R2          20.2     ***
+ DISTRIBUTED ANSYS Academic Research                           
+
+ 00208316  VERSION=WINDOWS x64   15:24:46  NOV 18, 2020 CP=      2.156
+
+ Piezo-APA95ML-3DElm--Modal (A5)                                               
+
+
+     NODE  LABEL     SUPPORT
+     40467  UX  
+     40467  UY  
+     40467  UZ  
+     40467  ROTX
+     40467  ROTY
+     40467  ROTZ
+     40469  UX  
+     40469  UY  
+     40469  UZ  
+     40469  ROTX
+     40469  ROTY
+     40469  ROTZ
+     40470  UX  
+     40470  UY  
+     40470  UZ  
+     40470  ROTX
+     40470  ROTY
+     40470  ROTZ
+     40475  UX  
+     40475  UY  
+     40475  UZ  
+     40475  ROTX
+     40475  ROTY
+     40475  ROTZ
+     40476  UX  
+     40476  UY  
+     40476  UZ  
+     40476  ROTX
+     40476  ROTY
+     40476  ROTZ
+     40477  UX  
+     40477  UY  
+     40477  UZ  
+     40477  ROTX
+     40477  ROTY
+     40477  ROTZ
+     40478  UX  
+     40478  UY  
+     40478  UZ  
+     40478  ROTX
+     40478  ROTY
+     40478  ROTZ
--- a/matlab/mat/apa95ml_5kg_10V.mat
+++ b/matlab/mat/apa95ml_5kg_10V.mat
--- a/matlab/mat/apa95ml_5kg_1a_2s.mat
+++ b/matlab/mat/apa95ml_5kg_1a_2s.mat
--- a/matlab/mat/apa95ml_5kg_2a_1s.mat
+++ b/matlab/mat/apa95ml_5kg_2a_1s.mat
--- a/matlab/mat/apa95ml_5kg_2s_1a.mat
+++ b/matlab/mat/apa95ml_5kg_2s_1a.mat
--- a/matlab/mat/apa95ml_5kg_Amp_E503.mat
+++ b/matlab/mat/apa95ml_5kg_Amp_E503.mat
--- a/matlab/mat/apa95ml_5kg_Amp_E505.mat
+++ b/matlab/mat/apa95ml_5kg_Amp_E505.mat
--- a/matlab/mat/apa95ml_5kg_Amp_E505_no_lpf.mat
+++ b/matlab/mat/apa95ml_5kg_Amp_E505_no_lpf.mat
--- a/matlab/mat/apa95ml_iff_g100_res.mat
+++ b/matlab/mat/apa95ml_iff_g100_res.mat
--- a/matlab/mat/apa95ml_iff_g10_res.mat
+++ b/matlab/mat/apa95ml_iff_g10_res.mat
--- a/matlab/mat/apa95ml_iff_off_res.mat
+++ b/matlab/mat/apa95ml_iff_off_res.mat
--- a/matlab/mat/apa95ml_iff_test.mat
+++ b/matlab/mat/apa95ml_iff_test.mat
--- a/matlab/mat/apa95ml_params.mat
+++ b/matlab/mat/apa95ml_params.mat
--- a/matlab/mat/fem_simscape_models.mat
+++ b/matlab/mat/fem_simscape_models.mat
--- a/matlab/mat/huddle_test.mat
+++ b/matlab/mat/huddle_test.mat
--- a/matlab/motion_identification.m
+++ b/matlab/motion_identification.m
@@ -0,0 +1,100 @@
+%% Clear Workspace and Close figures
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+addpath('./mat/');
+
+% Load Data
+% The data from the "noise test" and the identification test are loaded.
+
+ht = load('huddle_test.mat', 't', 'y');
+load('apa95ml_5kg_Amp_E505.mat', 't', 'um', 'y');
+
+
+
+% Any offset value is removed:
+
+um = detrend(um, 0); % Generated DAC Voltage [V]
+y  = detrend(y , 0); % Mass displacement [m]
+
+ht.y  = detrend(ht.y, 0);
+
+
+
+% Now we add a factor 10 to take into account the gain of the voltage amplifier.
+
+Va = 10*um;
+
+% Comparison of the PSD with Huddle Test
+
+Ts = t(end)/(length(t)-1);
+Fs = 1/Ts;
+
+win = hanning(ceil(1*Fs));
+
+[pxx, f] = pwelch(y, win, [], [], Fs);
+[pht, ~] = pwelch(ht.y, win, [], [], Fs);
+
+figure;
+hold on;
+plot(f, sqrt(pxx), 'DisplayName', '5kg');
+plot(f, sqrt(pht), 'DisplayName', 'Huddle Test');
+hold off;
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
+xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
+legend('location', 'northeast');
+xlim([1, Fs/2]);
+
+% Compute TF estimate and Coherence
+
+[tf_est, f] = tfestimate(Va, -y, win, [], [], 1/Ts);
+[co_est, ~] = mscohere(  Va, -y, win, [], [], 1/Ts);
+
+figure;
+
+hold on;
+plot(f, co_est, 'k-')
+set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
+ylabel('Coherence'); xlabel('Frequency [Hz]');
+hold off;
+xlim([10, 5e3]);
+
+
+
+% #+name: fig:apa95ml_5kg_PI_coh
+% #+caption: Coherence
+% #+RESULTS:
+% [[file:figs/apa95ml_5kg_PI_coh.png]]
+
+% Comparison with the FEM model
+
+load('mat/fem_simscape_models.mat', 'Ghm');
+
+freqs = logspace(0, 4, 1000);
+
+figure;
+tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
+
+ax1 = nexttile([2,1]);
+hold on;
+plot(f, abs(tf_est), 'DisplayName', 'Identification')
+plot(freqs, abs(squeeze(freqresp(Ghm, freqs, 'Hz'))), 'DisplayName', 'FEM')
+set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
+ylabel('Amplitude [m/V]'); set(gca, 'XTickLabel', []);
+legend('location', 'northeast')
+hold off;
+
+ax2 = nexttile;
+hold on;
+plot(f,     180/pi*angle(tf_est))
+plot(freqs, 180/pi*angle(squeeze(freqresp(Ghm, freqs, 'Hz'))))
+set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
+ylabel('Phase'); xlabel('Frequency [Hz]');
+hold off;
+ylim([-180, 180]);
+yticks(-180:90:180);
+
+linkaxes([ax1,ax2], 'x');
+xlim([10, 5e3]);
--- a/matlab/piezo_amplified_3d.slx
+++ b/matlab/piezo_amplified_3d.slx
--- a/Show More
+++ b/Show More
Author	SHA1	Message	Date
Thomas Dehaeze	805af508fd	Update figures and tangle matlab code	2020-11-24 18:28:16 +01:00
Thomas Dehaeze	0b0c5d14a9	Tangle piezo_parameters.m	2020-11-24 13:57:47 +01:00
Thomas Dehaeze	a7d6e3c509	Add new APA95ML model	2020-11-24 13:57:15 +01:00
Thomas Dehaeze	ff9a33f2c3	Identification of Piezo parameters	2020-11-24 13:56:38 +01:00
Thomas Dehaeze	09eea08de1	Update Figures	2020-11-24 09:25:05 +01:00
Thomas Dehaeze	6d744ddcaf	Add simscape model	2020-11-24 09:24:51 +01:00
Thomas Dehaeze	5734ae5d6b	Add documentation	2020-11-24 09:24:02 +01:00
Thomas Dehaeze	f9159c78c5	Use online CSS and JS	2020-11-12 10:36:40 +01:00
Thomas Dehaeze	c4584ed06e	Remove CSS/JS => use the one on the server	2020-11-12 09:30:03 +01:00
Thomas Dehaeze	acae193de0	Move data folder	2020-11-12 09:27:57 +01:00
Thomas Dehaeze	9677b4d3c4	Removed few scripts	2020-11-12 09:27:24 +01:00
Thomas Dehaeze	f32ff33474	Removed section about identification with DAC	2020-11-12 09:24:52 +01:00
Thomas Dehaeze	7b5a3c521f	Move mat files	2020-11-12 09:23:35 +01:00
Thomas Dehaeze	2a0b6be82f	Update CSS	2020-11-12 09:18:40 +01:00
Thomas Dehaeze	054ae6e094	Add few figures	2020-11-03 10:11:21 +01:00
Thomas Dehaeze	3859eca154	Add IFF Closed loop test figures	2020-08-21 15:27:24 +02:00
Thomas Dehaeze	a4f91c68e1	add script to test multiple iff gains	2020-08-21 14:12:22 +02:00
Thomas Dehaeze	040f2b42cc	add iff test for multiple gain	2020-08-21 11:27:42 +02:00
Thomas Dehaeze	8e95886e68	Add IFF identification / model comp	2020-08-20 23:09:03 +02:00
Thomas Dehaeze	610bc525be	Add IFF results figures	2020-08-20 23:08:38 +02:00
Thomas Dehaeze	21cd0b1471	IFF first CL tests	2020-08-20 18:00:00 +02:00
Thomas Dehaeze	f10d48cccf	force sensor measurements	2020-08-14 10:41:16 +02:00
Thomas Dehaeze	e4c52fa4db	Update few figures	2020-07-24 15:48:22 +02:00
Thomas Dehaeze	b6ad126460	Update figure adding the voltage monitor	2020-07-24 13:16:28 +02:00
Thomas Dehaeze	a4046ed618	Add time delay estimation	2020-07-24 13:06:02 +02:00
Thomas Dehaeze	16465e1f08	Add figure about the PI amplifier	2020-07-24 11:34:18 +02:00
Thomas Dehaeze	63bb2cf11b	Add data when not filtering the input noise	2020-07-24 11:20:17 +02:00
Thomas Dehaeze	eb68a99c13	add monitor voltage to data	2020-07-24 10:55:46 +02:00
Thomas Dehaeze	658346a0a1	Add figures for when using the PI amplifier	2020-07-23 09:43:42 +02:00
Thomas Dehaeze	c5ce3c182c	Identification with 2 PI amplifiers	2020-07-22 16:49:48 +02:00
Thomas Dehaeze	94bf676ddf	Add Comparison with the FEM	2020-07-20 13:29:36 +02:00
Thomas Dehaeze	af27d03c17	Remove unused block	2020-07-20 13:22:45 +02:00
Thomas Dehaeze	1347fd3559	Add Picture of the setup	2020-07-20 13:17:34 +02:00
Thomas Dehaeze	22afad9d07	Update title	2020-07-20 12:55:13 +02:00
Thomas Dehaeze	4e780d6b82	Add figures	2020-07-20 11:27:55 +02:00
Thomas Dehaeze	c2fec7b236	Tangle files	2020-07-20 10:55:38 +02:00
Thomas Dehaeze	89e0e13629	Add code to analyze experiments	2020-07-20 10:47:13 +02:00
				`@@ -1 +0,0 @@`
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