.gitignore

@@ -1,38 +0,0 @@
-# Windows default autosave extension
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-data/
-
-# OSX / *nix default autosave extension
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-
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-
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-
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-slprj/
-sccprj/
-
-# Matlab code generation folders
-codegen/
-
-# Simulink autosave extension
-*.autosave
-
-# Simulink cache files
-*.slxc
-
-# Octave session info
-octave-workspace

figs/iff_plant_identification_apa95ml.pdf

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matlab/force_sensor_identification.m

@@ -1,95 +0,0 @@
-%% 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]);

matlab/huddle_test.m

@@ -1,34 +0,0 @@
-%% 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]);

matlab/integral_force_feedback.m

@@ -1,307 +0,0 @@
-%% 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');

matlab/mat/APA95ML_K.CSV

@@ -1,48 +0,0 @@
-2.8006425939072037e+08,-1.1121063492149115e+03,-2.7040964416936040e+04,-3.5940302362199873e+01,6.7202605779747944e+04,2.6563254029862583e+02,2.1550991792595461e+07,-2.7820061825215816e+01,-4.8864206375679933e+03,5.3746878486444984e+00,6.4147340757886577e+03,-6.9103225309070694e+01,-1.4902141053418255e+08,3.1993703876761720e+02,-8.4307353501717746e+07,-2.9571954231443669e+01,-9.7299097071200621e+05,-1.3674596425725031e+02,-1.8070558000868903e+06,-1.0795929480872983e+03,5.1952510213221348e+05,-4.5224368059107145e-01,2.6079383186555438e+03,5.4511244925179270e+00,4.8873270218593927e+04,9.4489019778934278e+00,-5.8397983819284718e+03,-3.2531085247855203e-02,-6.2918471367302182e+01,-1.2496202936659717e-01,-1.7731842407893836e+06,8.1375478259346767e+02,-5.1123347039108997e+05,1.2194408523968672e+01,2.5877380652997472e+03,-2.1293177717594958e+00,-1.4906247387838435e+08,1.0763786171675904e+03,8.4336829053448841e+07,1.5902058186794040e+01,-9.7339666199497378e+05,-1.1780862216647753e+02,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
--1.1121063492149115e+03,4.7730491508132935e+07,-6.6712862017229199e+03,7.6611869018770568e+05,-2.2771732319903094e+01,2.5697771680240112e+02,2.5046584590885905e+03,4.9188556552530117e+06,4.3537172244398971e+02,-4.0336240754204293e+04,1.0093903297611590e+01,-3.0040895701007685e+01,4.9300484376984259e+03,-2.6140658176972844e+07,4.3238956244327128e+03,2.7932991710742051e+05,5.3587293253229063e+01,-2.4962615235390115e+05,-1.5144639385201069e+03,-1.8045282502142349e+05,9.8273337770375747e+01,-2.1546155354311458e+02,-7.5845909022538160e-01,8.5867340366937083e+02,3.4168095517973164e+01,2.5982732568041661e+03,-1.6493997707717423e+00,3.0988036167784601e+00,1.7060148682097653e-02,-1.3164371203339355e+01,-3.0609109350055309e+02,-1.7730866244405447e+05,3.6248454679682692e+02,-2.1529494980833633e+02,-2.5450031839204650e+00,-8.5081622668093712e+02,-4.5362136668659678e+03,-2.6153525772239737e+07,1.4529103942845400e+03,2.7955733765678713e+05,-2.5642230276673335e+01,2.4982071748983007e+05,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
--2.7040964416936040e+04,-6.6712862017229199e+03,1.2285548521789551e+08,-2.1165449136868119e+02,-6.2570167329860851e+01,6.7610884573776275e+01,3.2760318125416525e+03,3.0241590192632284e+03,-8.0840469515924184e+06,-2.5543578307431289e+01,-9.9786997637811510e+00,-5.8094784265199451e+00,-9.7450985416590065e+07,3.4163202649923041e+03,-5.7704681259731278e+07,-4.4226277942335855e+01,-6.0824426082686370e+05,-6.7494805811660626e+01,-1.1211463549626507e+06,-9.1784517743146898e+02,3.3411300143844931e+05,3.7826403407554160e-01,1.6994404247450832e+03,4.4279894957496069e+00,1.7618134762291978e+04,1.3700935157684157e+01,-4.9017247278778896e+03,1.8230649515918174e-02,-2.6240776999055463e+01,-7.9805635581162049e-02,1.0998453798814712e+06,-3.2196924935058286e+02,3.2857684766166483e+05,-7.3159230152941390e+00,-1.6851640274102917e+03,1.8349500161920587e+00,9.7478433189517021e+07,1.4569204121141984e+03,-5.7724545130837284e+07,-2.4953418697151459e+00,6.0848443899733317e+05,5.9219626385886436e+01,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
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matlab/mat/APA95ML_M.CSV

@@ -1,48 +0,0 @@
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--7.9777071278578457e-02,4.7956717518138041e-06,6.6421434037352574e-05,6.1909083196197981e-09,7.9021985008522388e-04,2.7445921375687554e-07,-7.7387397421131057e-02,-2.2921163837503677e-06,-8.8440333316480292e-05,-4.7461520105455249e-08,-7.6834254700137170e-04,-3.0523910613528989e-07,1.1219152737909712e-02,-1.0129828730097952e-05,1.1406693219195212e-03,-8.2272948829386070e-08,-2.0596980593299636e-06,-1.9015521824711558e-07,-6.7372582698069434e-04,5.3733609906283185e-07,-3.2109057159520681e-06,1.2223707979128812e-10,-2.2607563601444972e-08,-4.5620287725375530e-09,1.8201731320476220e-05,-1.0016063303645008e-08,3.6924610901191410e-08,-2.8203606444204103e-11,4.9036674112997472e-10,5.0421284288298962e-11,-6.5946792211396988e-04,1.2511252048145841e-06,2.8916342548818845e-06,7.7399061354200012e-09,-1.8437588960879804e-08,4.9339540557165012e-09,1.1012960637114129e-02,4.8705598891685342e-06,-1.1536165462402326e-03,-2.4823897830424456e-08,-2.1225441452107405e-06,-4.8211101543752413e-08,1.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
--8.1256077086162670e-02,-6.7272098201318146e-06,7.5771457821461653e-05,-7.7709489701395768e-08,7.6390655602689517e-04,3.9243186558967079e-07,8.3411402346350888e-02,-1.0303188618379029e-05,9.7185193603567353e-05,1.5593413540609805e-07,7.8580803193457329e-04,2.0047273910764479e-07,-1.4352940644354729e-04,1.5240641488740904e-05,8.0446216462971995e-02,7.3074689694699413e-08,-1.6621235360125423e-04,2.0699949835743692e-08,1.2249695867239195e-05,2.6081359946877276e-06,-7.5323545999567929e-05,-9.5230602640564974e-09,-6.5627717002762233e-07,-8.5023924694583477e-09,-3.4179421907823598e-07,-4.0018003432193134e-08,9.4225525774726048e-07,1.0727578731882579e-10,1.3446152959872664e-08,1.4953568702017696e-10,1.3756544526853177e-05,1.5393418288057589e-06,7.0273514652427875e-05,2.8985908002077392e-10,-6.2722271433620583e-07,1.4897571687958023e-09,-1.3937424135569246e-04,-2.9335108265574481e-06,-7.9429976096105998e-02,-9.1935137527123019e-08,-1.6534188875036679e-04,-1.2128195040244157e-07,0.0000000000000000e+00,1.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
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matlab/mat/APA95ML_out_nodes_3D.txt

@@ -1,75 +0,0 @@
-
- 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

matlab/motion_identification.m

@@ -1,100 +0,0 @@
-%% 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]);

matlab/piezo_parameters.m

@@ -1,317 +0,0 @@
-%% Clear Workspace and Close figures
-clear; close all; clc;
-
-%% Intialize Laplace variable
-s = zpk('s');
-
-addpath('./mat/');
-
-% Estimation from Data-sheet
-% <<sec:estimation_datasheet>>
-
-% The stack parameters taken from the data-sheet are shown in Table [[tab:stack_parameters]].
-
-% #+name: tab:stack_parameters
-% #+caption: Stack Parameters
-% | Parameter      | Unit      |    Value |
-% |----------------+-----------+----------|
-% | Nominal Stroke | $\mu m$   |       20 |
-% | Blocked force  | $N$       |     4700 |
-% | Stiffness      | $N/\mu m$ |      235 |
-% | Voltage Range  | $V$       | -20..150 |
-% | Capacitance    | $\mu F$   |      4.4 |
-% | Length         | $mm$      |       20 |
-% | Stack Area     | $mm^2$    |    10x10 |
-
-% Let's compute the generated force
-
-% The stroke is $L_{\max} = 20\mu m$ for a voltage range of $V_{\max} = 170 V$.
-% Furthermore, the stiffness is $k_a = 235 \cdot 10^6 N/m$.
-
-% The relation between the applied voltage and the generated force can be estimated as follows:
-% \begin{equation}
-%   g_a = k_a \frac{L_{\max}}{V_{\max}}
-% \end{equation}
-
-
-ka = 235e6; % [N/m]
-Lmax = 20e-6; % [m]
-Vmax = 170; % [V]
-
-ga = ka*Lmax/Vmax; % [N/V]
-
-% Estimation from Piezoelectric parameters
-% <<sec:estimation_piezo_params>>
-
-% In order to make the conversion from applied voltage to generated force or from the strain to the generated voltage, we need to defined some parameters corresponding to the piezoelectric material:
-
-d33 = 300e-12; % Strain constant [m/V]
-n   = 80;      % Number of layers per stack
-ka  = 235e6;   % Stack stiffness [N/m]
-
-
-
-% The ratio of the developed force to applied voltage is:
-% #+name: eq:piezo_voltage_to_force
-% \begin{equation}
-%   F_a = g_a V_a, \quad g_a = d_{33} n k_a
-% \end{equation}
-% where:
-% - $F_a$: developed force in [N]
-% - $n$: number of layers of the actuator stack
-% - $d_{33}$: strain constant in [m/V]
-% - $k_a$: actuator stack stiffness in [N/m]
-% - $V_a$: applied voltage in [V]
-
-% If we take the numerical values, we obtain:
-
-ga = d33*n*ka; % [N/V]
-
-
-
-% #+RESULTS:
-% : ga = 5.6 [N/V]
-
-
-% From cite:fleming14_desig_model_contr_nanop_system (page 123), the relation between relative displacement of the sensor stack and generated voltage is:
-% #+name: eq:piezo_strain_to_voltage
-% \begin{equation}
-%   V_s = \frac{d_{33}}{\epsilon^T s^D n} \Delta h
-% \end{equation}
-% where:
-% - $V_s$: measured voltage in [V]
-% - $d_{33}$: strain constant in [m/V]
-% - $\epsilon^T$: permittivity under constant stress in [F/m]
-% - $s^D$: elastic compliance under constant electric displacement in [m^2/N]
-% - $n$: number of layers of the sensor stack
-% - $\Delta h$: relative displacement in [m]
-
-% If we take the numerical values, we obtain:
-
-d33 = 300e-12; % Strain constant [m/V]
-n   = 80;      % Number of layers per stack
-eT  = 5.3e-9;  % Permittivity under constant stress [F/m]
-sD  = 2e-11;   % Compliance under constant electric displacement [m2/N]
-
-gs = d33/(eT*sD*n); % [V/m]
-
-% From actuator voltage $V_a$ to actuator force $F_a$
-% The data from the identification test is loaded.
-
-load('apa95ml_5kg_Amp_E505.mat', 't', 'um', 'y');
-
-% Any offset value is removed:
-um = detrend(um, 0); % Amplifier Input Voltage [V]
-y  = detrend(y , 0); % Mass displacement [m]
-
-
-
-% Now we add a factor 10 to take into account the gain of the voltage amplifier and thus obtain the voltage across the piezoelectric stack.
-
-um = 10*um; % Stack Actuator Input Voltage [V]
-
-
-
-% Then, the transfer function from the stack voltage to the vertical displacement is computed.
-
-Ts = t(end)/(length(t)-1);
-Fs = 1/Ts;
-
-win = hanning(ceil(1*Fs));
-
-[tf_est, f] = tfestimate(um, y, win, [], [], 1/Ts);
-
-
-
-% The gain from input voltage of the stack to the vertical displacement is determined:
-
-g_d_Va = 4e-7; % [m/V]
-
-freqs = logspace(0, 4, 1000);
-
-figure;
-hold on;
-plot(f, abs(tf_est), 'DisplayName', 'Identification')
-plot([f(2) f(end)], [g_d_Va g_d_Va], '--', 'DisplayName', sprintf('$d/V_a \\approx %.0g\\ m/V$', g_d_Va))
-hold off;
-set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
-xlabel('Frequency [Hz]'); ylabel('Amplitude $d/V_a$ [m/V]');
-xlim([10, 5e3]); ylim([1e-8, 1e-5]);
-legend('location', 'southwest');
-
-
-
-% #+name: fig:gain_Va_to_d
-% #+caption: Transfer function from actuator stack voltage $V_a$ to vertical displacement of the mass $d$
-% #+RESULTS:
-% [[file:figs/gain_Va_to_d.png]]
-
-% Then, the transfer function from forces applied by the stack actuator to the vertical displacement of the mass is identified from the Simscape model.
-
-% Load Parameters
-K = readmatrix('APA95ML_K.CSV');
-M = readmatrix('APA95ML_M.CSV');
-[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('APA95ML_out_nodes_3D.txt');
-
-% Define parameters just for the simulation
-ga = 1; % [N/V]
-gs = 1; % [V/m]
-
-m = 5.5;
-
-%% Name of the Simulink File
-mdl = 'piezo_amplified_3d';
-
-%% Input/Output definition
-clear io; io_i = 1;
-io(io_i) = linio([mdl, '/Fa'], 1, 'openinput');  io_i = io_i + 1; % Actuator Force [N]
-io(io_i) = linio([mdl, '/y'],  1, 'openoutput'); io_i = io_i + 1; % Vertical Displacement [m]
-
-Gd = linearize(mdl, io);
-
-
-
-% The DC gain the the identified dynamics
-
-g_d_Fa = abs(dcgain(Gd)); % [m/N]
-
-
-
-% #+RESULTS:
-% : G_d_Fa = 1.2e-08 [m/N]
-
-
-% And finally, the gain $g_a$ from the the actuator voltage $V_a$ to the generated force $F_a$ can be computed:
-% \begin{equation}
-%   g_a = \frac{F_a}{V_a} = \frac{F_a}{d} \frac{d}{V_a}
-% \end{equation}
-
-
-ga = g_d_Va/g_d_Fa;
-
-
-
-% #+RESULTS:
-% : ga = 33.7 [N/V]
-
-% The obtained comparison between the Simscape model and the identified dynamics is shown in Figure [[fig:compare_Gd_id_simscape]].
-
-
-freqs = logspace(1, 4, 1000);
-
-figure;
-hold on;
-plot(f, abs(tf_est), 'DisplayName', 'Identification')
-plot(f, ga*abs(squeeze(freqresp(Gd, f, 'Hz'))), 'DisplayName', 'Simscape Model')
-set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
-ylabel('Amplitude $d/V_a$ [m/V]'); xlabel('Frequency [Hz]');
-hold off;
-xlim([1, 5e3]); ylim([1e-9, 1e-5]);
-legend('location', 'southwest');
-
-% From stack strain $\Delta h$ to generated voltage $V_s$
-% Now, the gain from the stack strain $\Delta h$ to the generated voltage $V_s$ is estimated.
-
-% We can determine the gain from actuator voltage $V_a$ to sensor voltage $V_s$ thanks to the identification.
-% Using the simscape model, we can have the transfer function from the actuator voltage $V_a$ (using the previously estimated gain $g_a$) to the sensor stack strain $\Delta h$.
-
-% Finally, using these two values, we can compute the gain $g_s$ from the stack strain $\Delta h$ to the generated Voltage $V_s$.
-
-% Identification data is loaded.
-
-load('apa95ml_5kg_2a_1s.mat', 't', 'u', 'v');
-
-u = detrend(u, 0); % Input Voltage of the Amplifier [V]
-v = detrend(v, 0); % Voltage accross the stack sensor [V]
-
-
-
-% Here, an amplifier with a gain of 20 is used.
-
-u = 20*u; % Input Voltage of the Amplifier [V]
-
-
-
-% Then, the transfer function from $V_a$ to $V_s$ is identified and its DC gain is estimated (Figure [[fig:gain_Va_to_Vs]]).
-
-Ts = t(end)/(length(t)-1);
-Fs = 1/Ts;
-
-win = hann(ceil(10/Ts));
-
-[tf_est, f] = tfestimate(u, v, win, [], [], 1/Ts);
-
-g_Vs_Va = 0.022; % [V/V]
-
-freqs = logspace(1, 4, 1000);
-
-figure;
-hold on;
-plot(f, abs(tf_est), 'DisplayName', 'Identification')
-plot([f(2); f(end)], [g_Vs_Va; g_Vs_Va], '--', 'DisplayName', sprintf('$V_s/V_a \\approx %.0g\\ m/V$', g_Vs_Va))
-hold off;
-set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
-ylabel('Amplitude $V_s/V_a$ [V/V]'); xlabel('Frequency [Hz]');
-xlim([5e-1 5e3]); ylim([1e-3, 1e1]);
-legend('location', 'northwest');
-
-
-
-% #+name: fig:gain_Va_to_Vs
-% #+caption: Transfer function from actuator stack voltage $V_a$ to sensor stack voltage $V_s$
-% #+RESULTS:
-% [[file:figs/gain_Va_to_Vs.png]]
-
-
-% Now the transfer function from the actuator stack voltage to the sensor stack strain is estimated using the Simscape model.
-
-m = 5.5;
-
-%% Name of the Simulink File
-mdl = 'piezo_amplified_3d';
-
-%% Input/Output definition
-clear io; io_i = 1;
-io(io_i) = linio([mdl, '/Va'], 1, 'openinput');  io_i = io_i + 1; % Actuator Voltage [V]
-io(io_i) = linio([mdl, '/dL'], 1, 'openoutput'); io_i = io_i + 1; % Sensor Stack displacement [m]
-
-Gf = linearize(mdl, io);
-
-
-
-% The gain from the actuator stack voltage to the sensor stack strain is estimated below.
-
-G_dh_Va = abs(dcgain(Gf));
-
-
-
-% #+RESULTS:
-% : G_dh_Va = 6.2e-09 [m/V]
-
-% And finally, the gain $g_s$ from the sensor stack strain to the generated voltage can be estimated:
-% \begin{equation}
-%   g_s = \frac{V_s}{\Delta h} = \frac{V_s}{V_a} \frac{V_a}{\Delta h}
-% \end{equation}
-
-
-gs = g_Vs_Va/G_dh_Va; % [V/m]
-
-
-
-% #+RESULTS:
-% : gs = 3.5 [V/um]
-
-
-freqs = logspace(1, 4, 1000);
-
-figure;
-hold on;
-plot(f, abs(tf_est), 'DisplayName', 'Identification')
-plot(f, gs*abs(squeeze(freqresp(Gf, f, 'Hz'))), 'DisplayName', 'Simscape Model')
-set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
-ylabel('Amplitude $V_s/V_a$ [V/V]'); xlabel('Frequency [Hz]');
-hold off;
-xlim([1, 5e3]); ylim([1e-3, 1e1]);
-legend('location', 'southwest');
-
-save('./mat/apa95ml_params.mat', 'ga', 'gs');

matlab/simscape_model.m

@@ -1,120 +0,0 @@
-%% Clear Workspace and Close figures
-clear; close all; clc;
-
-%% Intialize Laplace variable
-s = zpk('s');
-
-addpath('./mat/');
-
-% Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates
-% We first extract the stiffness and mass matrices.
-
-K = readmatrix('APA95ML_K.CSV');
-M = readmatrix('APA95ML_M.CSV');
-
-
-
-% #+caption: First 10x10 elements of the Mass matrix
-% #+RESULTS:
-% |    0.03 |   7e-08 |  2e-06 | -3e-09 | -0.0002 | -6e-08 | -0.001 |   8e-07 |  6e-07 | -8e-09 |
-% |   7e-08 |    0.02 | -1e-06 |  9e-05 |  -3e-09 | -4e-09 | -1e-06 | -0.0006 | -4e-08 |  5e-06 |
-% |   2e-06 |  -1e-06 |   0.02 | -3e-08 |  -4e-08 |  1e-08 |  1e-07 |  -2e-07 | 0.0003 |  1e-09 |
-% |  -3e-09 |   9e-05 | -3e-08 |  1e-06 |  -3e-11 | -3e-13 | -7e-09 |  -5e-06 | -3e-10 |  3e-08 |
-% | -0.0002 |  -3e-09 | -4e-08 | -3e-11 |   2e-06 |  6e-10 |  2e-06 |  -7e-09 | -2e-09 |  7e-11 |
-% |  -6e-08 |  -4e-09 |  1e-08 | -3e-13 |   6e-10 |  1e-06 |  1e-08 |   3e-09 | -2e-09 |  2e-13 |
-% |  -0.001 |  -1e-06 |  1e-07 | -7e-09 |   2e-06 |  1e-08 |   0.03 |   4e-08 | -2e-06 |  8e-09 |
-% |   8e-07 | -0.0006 | -2e-07 | -5e-06 |  -7e-09 |  3e-09 |  4e-08 |    0.02 | -9e-07 | -9e-05 |
-% |   6e-07 |  -4e-08 | 0.0003 | -3e-10 |  -2e-09 | -2e-09 | -2e-06 |  -9e-07 |   0.02 |  2e-08 |
-% |  -8e-09 |   5e-06 |  1e-09 |  3e-08 |   7e-11 |  2e-13 |  8e-09 |  -9e-05 |  2e-08 |  1e-06 |
-
-% Then, we extract the coordinates of the interface nodes.
-
-[int_xyz, int_i, n_xyz, n_i, nodes] = extractNodes('APA95ML_out_nodes_3D.txt');
-
-% Simscape Model
-% The flexible element is imported using the =Reduced Order Flexible Solid= Simscape block.
-
-% To model the actuator, an =Internal Force= block is added between the nodes 3 and 12.
-% A =Relative Motion Sensor= block is added between the nodes 1 and 2 to measure the displacement and the amplified piezo.
-
-% One mass is fixed at one end of the piezo-electric stack actuator, the other end is fixed to the world frame.
-
-m = 5.5;
-
-load('apa95ml_params.mat', 'ga', 'gs');
-
-% Dynamics from Actuator Voltage to Vertical Mass Displacement
-% The identified dynamics is shown in Figure [[fig:dynamics_act_disp_comp_mass]].
-
-
-%% Name of the Simulink File
-mdl = 'piezo_amplified_3d';
-
-%% Input/Output definition
-clear io; io_i = 1;
-io(io_i) = linio([mdl, '/Va'], 1, 'openinput');  io_i = io_i + 1; % Actuator Voltage [V]
-io(io_i) = linio([mdl, '/y'],  1, 'openoutput'); io_i = io_i + 1; % Vertical Displacement [m]
-
-Ghm = linearize(mdl, io);
-
-freqs = logspace(0, 4, 5000);
-
-figure;
-tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
-
-ax1 = nexttile([2,1]);
-hold on;
-plot(freqs, abs(squeeze(freqresp(Ghm, freqs, 'Hz'))));
-hold off;
-set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
-ylabel('Amplitude $d/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
-hold off;
-
-ax2 = nexttile;
-hold on;
-plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Ghm, freqs, 'Hz')))));
-set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
-yticks(-360:90:360);
-xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
-hold off;
-linkaxes([ax1,ax2],'x');
-xlim([freqs(1), freqs(end)]);
-
-% Dynamics from Actuator Voltage to Force Sensor Voltage
-% The obtained dynamics is shown in Figure [[fig:dynamics_force_force_sensor_comp_mass]].
-
-
-%% Name of the Simulink File
-mdl = 'piezo_amplified_3d';
-
-%% Input/Output definition
-clear io; io_i = 1;
-io(io_i) = linio([mdl, '/Va'], 1, 'openinput');  io_i = io_i + 1; % Voltage Actuator [V]
-io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; % Sensor Voltage [V]
-
-Gfm = linearize(mdl, io);
-
-freqs = logspace(1, 5, 1000);
-
-figure;
-tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
-
-ax1 = nexttile([2,1]);
-hold on;
-plot(freqs, abs(squeeze(freqresp(Gfm, freqs, 'Hz'))));
-hold off;
-set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
-ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]);
-hold off;
-
-ax2 = nexttile;
-hold on;
-plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Gfm, freqs, 'Hz')))));
-set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
-yticks(-360:90:360); ylim([-360, 180]);
-xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
-hold off;
-linkaxes([ax1,ax2],'x');
-xlim([freqs(1), freqs(end)]);
-
-save('mat/fem_simscape_models.mat', 'Ghm', 'Gfm')