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Update with last measured encoder

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Thomas Dehaeze 2021-02-04 20:23:22 +01:00
parent 006cb20df1
commit 30177e4809
10 changed files with 83 additions and 105 deletions
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@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <head>
<!-- 2021-02-03 mer. 11:20 --> <!-- 2021-02-04 jeu. 20:23 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Encoder Renishaw Vionic - Test Bench</title> <title>Encoder Renishaw Vionic - Test Bench</title>
<meta name="generator" content="Org mode" /> <meta name="generator" content="Org mode" />
@ -39,23 +39,23 @@
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org691fd8d">1. Encoder Model</a></li> <li><a href="#org5cfc524">1. Encoder Model</a></li>
<li><a href="#org6d49234">2. Noise Measurement</a> <li><a href="#orgdb597d2">2. Noise Measurement</a>
<ul> <ul>
<li><a href="#orga5ff56c">2.1. Test Bench</a></li> <li><a href="#orgcf20f40">2.1. Test Bench</a></li>
<li><a href="#org14877fe">2.2. Results</a></li> <li><a href="#orga00ea74">2.2. Results</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org2b0bcde">3. Linearity Measurement</a> <li><a href="#orgf37b64f">3. Linearity Measurement</a>
<ul> <ul>
<li><a href="#org175ba6f">3.1. Test Bench</a></li> <li><a href="#orgd7d0144">3.1. Test Bench</a></li>
<li><a href="#org69056ec">3.2. Results</a></li> <li><a href="#org664af52">3.2. Results</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org5ca0c03">4. Dynamical Measurement</a> <li><a href="#orgf3c325a">4. Dynamical Measurement</a>
<ul> <ul>
<li><a href="#orgde9a37d">4.1. Test Bench</a></li> <li><a href="#org5deba50">4.1. Test Bench</a></li>
<li><a href="#org8bc51db">4.2. Results</a></li> <li><a href="#org4eec56e">4.2. Results</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -65,7 +65,7 @@
<p>This report is also available as a <a href="./test-bench-vionic.pdf">pdf</a>.</p> <p>This report is also available as a <a href="./test-bench-vionic.pdf">pdf</a>.</p>
<hr> <hr>
<div class="note" id="org978e8ad"> <div class="note" id="org3ece63c">
<p> <p>
You can find below the document of: You can find below the document of:
</p> </p>
@ -90,7 +90,7 @@ In particular, we would like to measure:
</ul> </ul>
<div id="orgf372152" class="figure"> <div id="orga8ce6e5" class="figure">
<p><img src="figs/encoder_vionic.png" alt="encoder_vionic.png" /> <p><img src="figs/encoder_vionic.png" alt="encoder_vionic.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Picture of the Vionic Encoder</p> <p><span class="figure-number">Figure 1: </span>Picture of the Vionic Encoder</p>
@ -106,8 +106,8 @@ In particular, we would like to measure:
<li>7: 2YJ313</li> <li>7: 2YJ313</li>
</ul> </ul>
<div id="outline-container-org691fd8d" class="outline-2"> <div id="outline-container-org5cfc524" class="outline-2">
<h2 id="org691fd8d"><span class="section-number-2">1</span> Encoder Model</h2> <h2 id="org5cfc524"><span class="section-number-2">1</span> Encoder Model</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
The Encoder is characterized by its dynamics \(G_m(s)\) from the &ldquo;true&rdquo; displacement \(y\) to measured displacement \(y_m\). The Encoder is characterized by its dynamics \(G_m(s)\) from the &ldquo;true&rdquo; displacement \(y\) to measured displacement \(y_m\).
@ -119,27 +119,27 @@ It is also characterized by its measurement noise \(n\) that can be described by
</p> </p>
<p> <p>
The model of the encoder is shown in Figure <a href="#orgb6cf5b4">2</a>. The model of the encoder is shown in Figure <a href="#org3722c48">2</a>.
</p> </p>
<div id="orgb6cf5b4" class="figure"> <div id="org3722c48" class="figure">
<p><img src="figs/encoder-model-schematic.png" alt="encoder-model-schematic.png" /> <p><img src="figs/encoder-model-schematic.png" alt="encoder-model-schematic.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Model of the Encoder</p> <p><span class="figure-number">Figure 2: </span>Model of the Encoder</p>
</div> </div>
<p> <p>
We can also use a transfer function \(G_n(s)\) to shape a noise \(\tilde{n}\) with unity ASD as shown in Figure <a href="#orgd00343b">4</a>. We can also use a transfer function \(G_n(s)\) to shape a noise \(\tilde{n}\) with unity ASD as shown in Figure <a href="#org1f28b48">4</a>.
</p> </p>
<div id="org2725c4b" class="figure"> <div id="org1ffb004" class="figure">
<p><img src="figs/encoder-model-schematic-with-asd.png" alt="encoder-model-schematic-with-asd.png" /> <p><img src="figs/encoder-model-schematic-with-asd.png" alt="encoder-model-schematic-with-asd.png" />
</p> </p>
</div> </div>
<table id="org20632fc" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org6be868a" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Characteristics of the Vionic Encoder</caption> <caption class="t-above"><span class="table-number">Table 1:</span> Characteristics of the Vionic Encoder</caption>
<colgroup> <colgroup>
@ -184,7 +184,7 @@ We can also use a transfer function \(G_n(s)\) to shape a noise \(\tilde{n}\) wi
</table> </table>
<div id="orgd00343b" class="figure"> <div id="org1f28b48" class="figure">
<p><img src="./figs/vionic_expected_noise.png" alt="vionic_expected_noise.png" /> <p><img src="./figs/vionic_expected_noise.png" alt="vionic_expected_noise.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Expected interpolation errors for the Vionic Encoder</p> <p><span class="figure-number">Figure 4: </span>Expected interpolation errors for the Vionic Encoder</p>
@ -193,15 +193,15 @@ We can also use a transfer function \(G_n(s)\) to shape a noise \(\tilde{n}\) wi
</div> </div>
<div id="outline-container-org6d49234" class="outline-2"> <div id="outline-container-orgdb597d2" class="outline-2">
<h2 id="org6d49234"><span class="section-number-2">2</span> Noise Measurement</h2> <h2 id="orgdb597d2"><span class="section-number-2">2</span> Noise Measurement</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<a id="org4cb96c9"></a> <a id="org4a8cf7a"></a>
</p> </p>
</div> </div>
<div id="outline-container-orga5ff56c" class="outline-3"> <div id="outline-container-orgcf20f40" class="outline-3">
<h3 id="orga5ff56c"><span class="section-number-3">2.1</span> Test Bench</h3> <h3 id="orgcf20f40"><span class="section-number-3">2.1</span> Test Bench</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<p> <p>
To measure the noise \(n\) of the encoder, one can rigidly fix the head and the ruler together such that no motion should be measured. To measure the noise \(n\) of the encoder, one can rigidly fix the head and the ruler together such that no motion should be measured.
@ -210,48 +210,35 @@ Then, the measured signal \(y_m\) corresponds to the noise \(n\).
</div> </div>
</div> </div>
<div id="outline-container-org14877fe" class="outline-3"> <div id="outline-container-orga00ea74" class="outline-3">
<h3 id="org14877fe"><span class="section-number-3">2.2</span> Results</h3> <h3 id="orga00ea74"><span class="section-number-3">2.2</span> Results</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<p> <p>
First we load the data. First we load the data.
</p> The raw measured data as well as the low pass filtered data (using a first order low pass filter with a cut-off at 10Hz) are shown in Figure <a href="#orgafb2d71">5</a>.
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Load Data</span></span>
enc1 = load(<span class="org-string">'noise_meas_100s_20kHz_1.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x'</span>);
enc2 = load(<span class="org-string">'noise_meas_100s_20kHz_2.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x'</span>);
enc3 = load(<span class="org-string">'noise_meas_100s_20kHz_3.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x'</span>);
enc4 = load(<span class="org-string">'noise_meas_100s_20kHz_4.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x'</span>);
enc6 = load(<span class="org-string">'noise_meas_100s_20kHz_6.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x'</span>);
enc7 = load(<span class="org-string">'noise_meas_100s_20kHz_7.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x'</span>);
</pre>
</div>
<p>
The raw measured data as well as the low pass filtered data (using a first order low pass filter with a cut-off at 10Hz) are shown in Figure <a href="#org72fd239">5</a>.
</p> </p>
<div id="org72fd239" class="figure"> <div id="orgafb2d71" class="figure">
<p><img src="figs/vionic_noise_raw_lpf.png" alt="vionic_noise_raw_lpf.png" /> <p><img src="figs/vionic_noise_raw_lpf.png" alt="vionic_noise_raw_lpf.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Time domain measurement (raw data and low pass filtered data with first order 10Hz LPF)</p> <p><span class="figure-number">Figure 5: </span>Time domain measurement (raw data and low pass filtered data with first order 10Hz LPF)</p>
</div> </div>
<p> <p>
The time domain data for all the encoders are compared in Figure <a href="#orgf7f2fda">6</a>. The time domain data for all the encoders are compared in Figure <a href="#org6fcc332">6</a>.
</p> </p>
<div id="orgf7f2fda" class="figure"> <div id="org6fcc332" class="figure">
<p><img src="figs/vionic_noise_time.png" alt="vionic_noise_time.png" /> <p><img src="figs/vionic_noise_time.png" alt="vionic_noise_time.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Comparison of the time domain measurement</p> <p><span class="figure-number">Figure 6: </span>Comparison of the time domain measurement</p>
</div> </div>
<p> <p>
The amplitude spectral density is computed and shown in Figure <a href="#orgf3c083c">7</a>. The amplitude spectral density is computed and shown in Figure <a href="#org0596231">7</a>.
</p> </p>
<div id="orgf3c083c" class="figure"> <div id="org0596231" class="figure">
<p><img src="figs/vionic_noise_asd.png" alt="vionic_noise_asd.png" /> <p><img src="figs/vionic_noise_asd.png" alt="vionic_noise_asd.png" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>Amplitude Spectral Density of the measured signal</p> <p><span class="figure-number">Figure 7: </span>Amplitude Spectral Density of the measured signal</p>
@ -266,11 +253,11 @@ Let&rsquo;s create a transfer function that approximate the measured noise of th
</div> </div>
<p> <p>
The amplitude of the transfer function and the measured ASD are shown in Figure <a href="#org8714af7">8</a>. The amplitude of the transfer function and the measured ASD are shown in Figure <a href="#org2802608">8</a>.
</p> </p>
<div id="org8714af7" class="figure"> <div id="org2802608" class="figure">
<p><img src="figs/vionic_noise_asd_model.png" alt="vionic_noise_asd_model.png" /> <p><img src="figs/vionic_noise_asd_model.png" alt="vionic_noise_asd_model.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>Measured ASD of the noise and modelled one</p> <p><span class="figure-number">Figure 8: </span>Measured ASD of the noise and modelled one</p>
@ -279,15 +266,15 @@ The amplitude of the transfer function and the measured ASD are shown in Figure
</div> </div>
</div> </div>
<div id="outline-container-org2b0bcde" class="outline-2"> <div id="outline-container-orgf37b64f" class="outline-2">
<h2 id="org2b0bcde"><span class="section-number-2">3</span> Linearity Measurement</h2> <h2 id="orgf37b64f"><span class="section-number-2">3</span> Linearity Measurement</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<p> <p>
<a id="orgc339bfd"></a> <a id="org55aba7f"></a>
</p> </p>
</div> </div>
<div id="outline-container-org175ba6f" class="outline-3"> <div id="outline-container-orgd7d0144" class="outline-3">
<h3 id="org175ba6f"><span class="section-number-3">3.1</span> Test Bench</h3> <h3 id="orgd7d0144"><span class="section-number-3">3.1</span> Test Bench</h3>
<div class="outline-text-3" id="text-3-1"> <div class="outline-text-3" id="text-3-1">
<p> <p>
In order to measure the linearity, we have to compare the measured displacement with a reference sensor with a known linearity. In order to measure the linearity, we have to compare the measured displacement with a reference sensor with a known linearity.
@ -296,7 +283,7 @@ An actuator should also be there so impose a displacement.
</p> </p>
<p> <p>
One idea is to use the test-bench shown in Figure <a href="#org30ec1c0">9</a>. One idea is to use the test-bench shown in Figure <a href="#orgd759dea">9</a>.
</p> </p>
<p> <p>
@ -309,7 +296,7 @@ As the interferometer has a very large bandwidth, we should be able to estimate
</p> </p>
<div id="org30ec1c0" class="figure"> <div id="orgd759dea" class="figure">
<p><img src="figs/test_bench_encoder_calibration.png" alt="test_bench_encoder_calibration.png" /> <p><img src="figs/test_bench_encoder_calibration.png" alt="test_bench_encoder_calibration.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>Schematic of the test bench</p> <p><span class="figure-number">Figure 9: </span>Schematic of the test bench</p>
@ -317,30 +304,30 @@ As the interferometer has a very large bandwidth, we should be able to estimate
</div> </div>
</div> </div>
<div id="outline-container-org69056ec" class="outline-3"> <div id="outline-container-org664af52" class="outline-3">
<h3 id="org69056ec"><span class="section-number-3">3.2</span> Results</h3> <h3 id="org664af52"><span class="section-number-3">3.2</span> Results</h3>
</div> </div>
</div> </div>
<div id="outline-container-org5ca0c03" class="outline-2"> <div id="outline-container-orgf3c325a" class="outline-2">
<h2 id="org5ca0c03"><span class="section-number-2">4</span> Dynamical Measurement</h2> <h2 id="orgf3c325a"><span class="section-number-2">4</span> Dynamical Measurement</h2>
<div class="outline-text-2" id="text-4"> <div class="outline-text-2" id="text-4">
<p> <p>
<a id="org71dc40b"></a> <a id="org7abf850"></a>
</p> </p>
</div> </div>
<div id="outline-container-orgde9a37d" class="outline-3"> <div id="outline-container-org5deba50" class="outline-3">
<h3 id="orgde9a37d"><span class="section-number-3">4.1</span> Test Bench</h3> <h3 id="org5deba50"><span class="section-number-3">4.1</span> Test Bench</h3>
</div> </div>
<div id="outline-container-org8bc51db" class="outline-3"> <div id="outline-container-org4eec56e" class="outline-3">
<h3 id="org8bc51db"><span class="section-number-3">4.2</span> Results</h3> <h3 id="org4eec56e"><span class="section-number-3">4.2</span> Results</h3>
</div> </div>
</div> </div>
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2021-02-03 mer. 11:20</p> <p class="date">Created: 2021-02-04 jeu. 20:23</p>
</div> </div>
</body> </body>
</html> </html>

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test-bench-vionic.org
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@ -173,32 +173,27 @@ addpath('./mat/');
** Results ** Results
First we load the data. First we load the data.
#+begin_src matlab #+begin_src matlab :exports none
%% Load Data %% Load all the measurements
enc1 = load('noise_meas_100s_20kHz_1.mat', 't', 'x'); enc = {};
enc2 = load('noise_meas_100s_20kHz_2.mat', 't', 'x'); for i = 1:7
enc3 = load('noise_meas_100s_20kHz_3.mat', 't', 'x'); enc(i) = {load(['mat/noise_meas_100s_20kHz_' num2str(i) '.mat'], 't', 'x')};
enc4 = load('noise_meas_100s_20kHz_4.mat', 't', 'x'); end
enc6 = load('noise_meas_100s_20kHz_6.mat', 't', 'x');
enc7 = load('noise_meas_100s_20kHz_7.mat', 't', 'x');
#+end_src #+end_src
#+begin_src matlab :exports none #+begin_src matlab :exports none
%% Remove initial offset %% Remove initial offset
enc1.x = enc1.x - mean(enc1.x(1:1000)); for i = 1:7
enc2.x = enc2.x - mean(enc2.x(1:1000)); enc{i}.x = enc{i}.x - mean(enc{i}.x(1:1000));
enc3.x = enc3.x - mean(enc3.x(1:1000)); end
enc4.x = enc4.x - mean(enc4.x(1:1000));
enc6.x = enc6.x - mean(enc6.x(1:1000));
enc7.x = enc7.x - mean(enc7.x(1:1000));
#+end_src #+end_src
The raw measured data as well as the low pass filtered data (using a first order low pass filter with a cut-off at 10Hz) are shown in Figure [[fig:vionic_noise_raw_lpf]]. The raw measured data as well as the low pass filtered data (using a first order low pass filter with a cut-off at 10Hz) are shown in Figure [[fig:vionic_noise_raw_lpf]].
#+begin_src matlab :exports none #+begin_src matlab :exports none
figure; figure;
hold on; hold on;
plot(enc1.t, 1e9*enc1.x, '.', 'DisplayName', 'Enc 1 - Raw'); plot(enc{1}.t, 1e9*enc{1}.x, '.', 'DisplayName', 'Enc 1 - Raw');
plot(enc1.t, 1e9*lsim(1/(1 + s/2/pi/10), enc1.x, enc1.t), '-', 'DisplayName', 'Enc 1 - LPF'); plot(enc{1}.t, 1e9*lsim(1/(1 + s/2/pi/10), enc{1}.x, enc{1}.t), '-', 'DisplayName', 'Enc 1 - LPF');
hold off; hold off;
xlabel('Time [s]'); xlabel('Time [s]');
ylabel('Displacement [nm]'); ylabel('Displacement [nm]');
@ -218,12 +213,10 @@ The time domain data for all the encoders are compared in Figure [[fig:vionic_no
#+begin_src matlab :exports none #+begin_src matlab :exports none
figure; figure;
hold on; hold on;
plot(enc1.t, 1e9*lsim(1/(1 + s/2/pi/10), enc1.x, enc1.t), '.', 'DisplayName', 'Enc 1'); for i=1:7
plot(enc2.t, 1e9*lsim(1/(1 + s/2/pi/10), enc2.x, enc2.t), '.', 'DisplayName', 'Enc 2'); plot(enc{i}.t, 1e9*lsim(1/(1 + s/2/pi/10), enc{i}.x, enc{i}.t), '.', ...
plot(enc3.t, 1e9*lsim(1/(1 + s/2/pi/10), enc3.x, enc3.t), '.', 'DisplayName', 'Enc 3'); 'DisplayName', sprintf('Enc %i', i));
plot(enc4.t, 1e9*lsim(1/(1 + s/2/pi/10), enc4.x, enc4.t), '.', 'DisplayName', 'Enc 4'); end
plot(enc6.t, 1e9*lsim(1/(1 + s/2/pi/10), enc6.x, enc6.t), '.', 'DisplayName', 'Enc 6');
plot(enc7.t, 1e9*lsim(1/(1 + s/2/pi/10), enc7.x, enc7.t), '.', 'DisplayName', 'Enc 7');
hold off; hold off;
xlabel('Time [s]'); xlabel('Time [s]');
ylabel('Displacement [nm]'); ylabel('Displacement [nm]');
@ -248,23 +241,22 @@ Fs = 1/Ts;
% Hannning Windows % Hannning Windows
win = hanning(ceil(0.5/Ts)); win = hanning(ceil(0.5/Ts));
[p1, f] = pwelch(enc1.x, win, [], [], Fs); [pxx, f] = pwelch(enc{1}.x, win, [], [], Fs);
[p2, ~] = pwelch(enc2.x, win, [], [], Fs); enc{1}.pxx = pxx;
[p3, ~] = pwelch(enc3.x, win, [], [], Fs);
[p4, ~] = pwelch(enc4.x, win, [], [], Fs); for i=2:7
[p6, ~] = pwelch(enc6.x, win, [], [], Fs); [pxx, ~] = pwelch(enc{i}.x, win, [], [], Fs);
[p7, ~] = pwelch(enc7.x, win, [], [], Fs); enc{i}.pxx = pxx;
end
#+end_src #+end_src
#+begin_src matlab :exports none #+begin_src matlab :exports none
figure; figure;
hold on; hold on;
plot(f, sqrt(p1), 'DisplayName', 'Enc 1'); for i=1:7
plot(f, sqrt(p2), 'DisplayName', 'Enc 2'); plot(f, sqrt(enc{i}.pxx), ...
plot(f, sqrt(p3), 'DisplayName', 'Enc 3'); 'DisplayName', sprintf('Enc %i', i));
plot(f, sqrt(p4), 'DisplayName', 'Enc 4'); end
plot(f, sqrt(p6), 'DisplayName', 'Enc 6');
plot(f, sqrt(p7), 'DisplayName', 'Enc 7');
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]'); xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
xlim([10, Fs/2]); xlim([10, Fs/2]);
@ -292,11 +284,10 @@ The amplitude of the transfer function and the measured ASD are shown in Figure
figure; figure;
hold on; hold on;
plot(f, sqrt(p1), 'color', [0, 0, 0, 0.5], 'DisplayName', '$\Gamma_n(\omega)$'); plot(f, sqrt(p1), 'color', [0, 0, 0, 0.5], 'DisplayName', '$\Gamma_n(\omega)$');
plot(f, sqrt(p2), 'color', [0, 0, 0, 0.5], 'HandleVisibility', 'off'); for i=2:7
plot(f, sqrt(p3), 'color', [0, 0, 0, 0.5], 'HandleVisibility', 'off'); plot(f, sqrt(enc{i}.pxx), 'color', [0, 0, 0, 0.5], ...
plot(f, sqrt(p4), 'color', [0, 0, 0, 0.5], 'HandleVisibility', 'off'); 'HandleVisibility', 'off');
plot(f, sqrt(p6), 'color', [0, 0, 0, 0.5], 'HandleVisibility', 'off'); end
plot(f, sqrt(p7), 'color', [0, 0, 0, 0.5], 'HandleVisibility', 'off');
plot(f, abs(squeeze(freqresp(Gn_e, f, 'Hz'))), 'r-', 'DisplayName', '$|G_n(j\omega)|$'); plot(f, abs(squeeze(freqresp(Gn_e, f, 'Hz'))), 'r-', 'DisplayName', '$|G_n(j\omega)|$');
hold off; hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');

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test-bench-vionic.pdf
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