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Add micro-station compliance measurement/analysis
2020-08-18 12:59:32 +02:00
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<title>Compliance Measurement of the Micro Station</title>
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<h1 class="title">Compliance Measurement of the Micro Station</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org0f99e70">1. Setup</a>
<ul>
<li><a href="#org3071865">1.1. Position of inertial sensors on top of the micro-hexapod</a></li>
<li><a href="#org93c276c">1.2. Hammer blow position/orientation</a></li>
</ul>
</li>
<li><a href="#org945c638">2. Results</a>
<ul>
<li><a href="#org36b19fa">2.1. Load Data</a></li>
<li><a href="#orgb64ed09">2.2. Compute Transfer Functions</a></li>
<li><a href="#orgc4d6849">2.3. Diagonal Dynamics</a></li>
<li><a href="#org87be1fb">2.4. Compare with Model</a></li>
<li><a href="#orgaa2c58a">2.5. Coupling Dynamics</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-org0f99e70" class="outline-2">
<h2 id="org0f99e70"><span class="section-number-2">1</span> Setup</h2>
<div class="outline-text-2" id="text-1">
</div>
<div id="outline-container-org3071865" class="outline-3">
<h3 id="org3071865"><span class="section-number-3">1.1</span> Position of inertial sensors on top of the micro-hexapod</h3>
<div class="outline-text-3" id="text-1-1">
<p>
Orientation is relative to the frame determined by the X-ray
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-right" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right"><b>Num</b></th>
<th scope="col" class="org-left"><b>Position</b></th>
<th scope="col" class="org-left"><b>Orientation</b></th>
<th scope="col" class="org-left"><b>Sensibility</b></th>
<th scope="col" class="org-right"><b>Channels</b></th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">1</td>
<td class="org-left">[0, +A, 0]</td>
<td class="org-left">[x, y, z]</td>
<td class="org-left">1V/g</td>
<td class="org-right">1-3</td>
</tr>
<tr>
<td class="org-right">2</td>
<td class="org-left">[-B, 0, 0]</td>
<td class="org-left">[x, y, z]</td>
<td class="org-left">1V/g</td>
<td class="org-right">4-6</td>
</tr>
<tr>
<td class="org-right">3</td>
<td class="org-left">[0, -A, 0]</td>
<td class="org-left">[x, y, z]</td>
<td class="org-left">0.1V/g</td>
<td class="org-right">7-9</td>
</tr>
<tr>
<td class="org-right">4</td>
<td class="org-left">[+B, 0, 0]</td>
<td class="org-left">[x, y, z]</td>
<td class="org-left">1V/g</td>
<td class="org-right">10-12</td>
</tr>
</tbody>
</table>
<p>
Instrumented Hammer:
</p>
<ul class="org-ul">
<li>Channel 13</li>
<li>Sensibility: 230 uV/N</li>
</ul>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-right" />
<col class="org-left" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right">Acc Number</th>
<th scope="col" class="org-left">Dir</th>
<th scope="col" class="org-right">Channel Number</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">1</td>
<td class="org-left">x</td>
<td class="org-right">1</td>
</tr>
<tr>
<td class="org-right">1</td>
<td class="org-left">y</td>
<td class="org-right">2</td>
</tr>
<tr>
<td class="org-right">1</td>
<td class="org-left">z</td>
<td class="org-right">3</td>
</tr>
<tr>
<td class="org-right">2</td>
<td class="org-left">x</td>
<td class="org-right">4</td>
</tr>
<tr>
<td class="org-right">2</td>
<td class="org-left">y</td>
<td class="org-right">5</td>
</tr>
<tr>
<td class="org-right">2</td>
<td class="org-left">z</td>
<td class="org-right">6</td>
</tr>
<tr>
<td class="org-right">3</td>
<td class="org-left">x</td>
<td class="org-right">7</td>
</tr>
<tr>
<td class="org-right">3</td>
<td class="org-left">y</td>
<td class="org-right">8</td>
</tr>
<tr>
<td class="org-right">3</td>
<td class="org-left">z</td>
<td class="org-right">9</td>
</tr>
<tr>
<td class="org-right">4</td>
<td class="org-left">x</td>
<td class="org-right">10</td>
</tr>
<tr>
<td class="org-right">4</td>
<td class="org-left">y</td>
<td class="org-right">11</td>
</tr>
<tr>
<td class="org-right">4</td>
<td class="org-left">z</td>
<td class="org-right">12</td>
</tr>
<tr>
<td class="org-right">Hammer</td>
<td class="org-left">&#xa0;</td>
<td class="org-right">13</td>
</tr>
</tbody>
</table>
<p>
From the acceleration measurement of the 4 accelerometers, we can compute the translations and rotations:
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">&#xa0;</th>
<th scope="col" class="org-left"><b>Formula</b></th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">\(D_x\)</td>
<td class="org-left">(1x + 2x + 3x + 4x)/4</td>
</tr>
<tr>
<td class="org-left">\(D_y\)</td>
<td class="org-left">(1y + 2y + 3y + 4y)/4</td>
</tr>
<tr>
<td class="org-left">\(D_z\)</td>
<td class="org-left">(1z + 2z + 3z + 4z)/4</td>
</tr>
<tr>
<td class="org-left">\(R_x\)</td>
<td class="org-left">(1z - 3z)/A</td>
</tr>
<tr>
<td class="org-left">\(R_y\)</td>
<td class="org-left">(2z - 4z)/B</td>
</tr>
<tr>
<td class="org-left">\(R_z\)</td>
<td class="org-left">(3x - 1x)/A, (4y - 2y)/B</td>
</tr>
</tbody>
</table>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">&#xa0;</th>
<th scope="col" class="org-left"><b>Formula</b></th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">\(D_x\)</td>
<td class="org-left">(1 + 4 + 7 + 10)/4</td>
</tr>
<tr>
<td class="org-left">\(D_y\)</td>
<td class="org-left">(2 + 5 + 8 + 11)/4</td>
</tr>
<tr>
<td class="org-left">\(D_z\)</td>
<td class="org-left">(3 + 6 + 9 + 12)/4</td>
</tr>
<tr>
<td class="org-left">\(R_x\)</td>
<td class="org-left">(1 - 9)/A</td>
</tr>
<tr>
<td class="org-left">\(R_y\)</td>
<td class="org-left">(6 - 12)/B</td>
</tr>
<tr>
<td class="org-left">\(R_z\)</td>
<td class="org-left">(7 - 1)/A, (11 - 5)/B</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org93c276c" class="outline-3">
<h3 id="org93c276c"><span class="section-number-3">1.2</span> Hammer blow position/orientation</h3>
<div class="outline-text-3" id="text-1-2">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-right" />
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right"><b>Num</b></th>
<th scope="col" class="org-left"><b>Direction</b></th>
<th scope="col" class="org-left"><b>Position</b></th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">1</td>
<td class="org-left">-Y</td>
<td class="org-left">[0, +A, 0]</td>
</tr>
<tr>
<td class="org-right">2</td>
<td class="org-left">-Z</td>
<td class="org-left">[0, +A, 0]</td>
</tr>
<tr>
<td class="org-right">3</td>
<td class="org-left">X</td>
<td class="org-left">[-B, 0, 0]</td>
</tr>
<tr>
<td class="org-right">4</td>
<td class="org-left">-Z</td>
<td class="org-left">[-B, 0, 0]</td>
</tr>
<tr>
<td class="org-right">5</td>
<td class="org-left">Y</td>
<td class="org-left">[0, -A, 0]</td>
</tr>
<tr>
<td class="org-right">6</td>
<td class="org-left">-Z</td>
<td class="org-left">[0, -A, 0]</td>
</tr>
<tr>
<td class="org-right">7</td>
<td class="org-left">-X</td>
<td class="org-left">[+B, 0, 0]</td>
</tr>
<tr>
<td class="org-right">8</td>
<td class="org-left">-Z</td>
<td class="org-left">[+B, 0, 0]</td>
</tr>
<tr>
<td class="org-right">9</td>
<td class="org-left">-X</td>
<td class="org-left">[0, -A, 0]</td>
</tr>
<tr>
<td class="org-right">10</td>
<td class="org-left">-X</td>
<td class="org-left">[0, +A, 0]</td>
</tr>
</tbody>
</table>
<p>
From hammer blows to pure forces / torques:
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">&#xa0;</th>
<th scope="col" class="org-left"><b>Formula</b></th>
<th scope="col" class="org-left">Alternative</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">\(F_x\)</td>
<td class="org-left">+3</td>
<td class="org-left">-7</td>
</tr>
<tr>
<td class="org-left">\(F_y\)</td>
<td class="org-left">-1</td>
<td class="org-left">+5</td>
</tr>
<tr>
<td class="org-left">\(F_z\)</td>
<td class="org-left">-(2 + 6)/2</td>
<td class="org-left">-(4 + 8)/2</td>
</tr>
<tr>
<td class="org-left">\(M_x\)</td>
<td class="org-left">A/2*(2 - 6)</td>
<td class="org-left">&#xa0;</td>
</tr>
<tr>
<td class="org-left">\(M_y\)</td>
<td class="org-left">B/2*(8 - 4)</td>
<td class="org-left">&#xa0;</td>
</tr>
<tr>
<td class="org-left">\(M_z\)</td>
<td class="org-left">A/2*(10 - 9)</td>
<td class="org-left">&#xa0;</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
<div id="outline-container-org945c638" class="outline-2">
<h2 id="org945c638"><span class="section-number-2">2</span> Results</h2>
<div class="outline-text-2" id="text-2">
</div>
<div id="outline-container-org36b19fa" class="outline-3">
<h3 id="org36b19fa"><span class="section-number-3">2.1</span> Load Data</h3>
<div class="outline-text-3" id="text-2-1">
<div class="org-src-container">
<pre class="src src-matlab">m1 = load('data/Measurement1.mat');
m2 = load('data/Measurement2.mat');
m3 = load('data/Measurement3.mat');
m4 = load('data/Measurement4.mat');
m5 = load('data/Measurement5.mat');
m6 = load('data/Measurement6.mat');
m7 = load('data/Measurement7.mat');
m8 = load('data/Measurement8.mat');
m9 = load('data/Measurement9.mat');
m10 = load('data/Measurement10.mat');
</pre>
</div>
</div>
</div>
<div id="outline-container-orgb64ed09" class="outline-3">
<h3 id="orgb64ed09"><span class="section-number-3">2.2</span> Compute Transfer Functions</h3>
<div class="outline-text-3" id="text-2-2">
<div class="org-src-container">
<pre class="src src-matlab">freqs = m3.FFT1_H1_1_13_X_Val;
w = 2*pi*freqs';
A = 0.14;
B = 0.14;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">G = zeros(6,6,length(freqs));
% Fx
G(1,1,:) = (m3.FFT1_H1_1_13_Y_ReIm + m3.FFT1_H1_4_13_Y_ReIm + m3.FFT1_H1_7_13_Y_ReIm + m3.FFT1_H1_10_13_Y_ReIm)./4;
G(2,1,:) = (m3.FFT1_H1_2_13_Y_ReIm + m3.FFT1_H1_5_13_Y_ReIm + m3.FFT1_H1_8_13_Y_ReIm + m3.FFT1_H1_11_13_Y_ReIm)./4;
G(3,1,:) = (m3.FFT1_H1_3_13_Y_ReIm + m3.FFT1_H1_6_13_Y_ReIm + m3.FFT1_H1_9_13_Y_ReIm + m3.FFT1_H1_12_13_Y_ReIm)./4;
G(4,1,:) = (m3.FFT1_H1_1_13_Y_ReIm - m3.FFT1_H1_9_13_Y_ReIm )./A;
G(5,1,:) = (m3.FFT1_H1_6_13_Y_ReIm - m3.FFT1_H1_12_13_Y_ReIm)./B;
G(6,1,:) = (m3.FFT1_H1_7_13_Y_ReIm - m3.FFT1_H1_1_13_Y_ReIm )./A;
% Fy
G(1,2,:) = -(m1.FFT1_H1_2_13_Y_ReIm + m1.FFT1_H1_5_13_Y_ReIm + m1.FFT1_H1_8_13_Y_ReIm + m1.FFT1_H1_11_13_Y_ReIm)./4;
G(2,2,:) = -(m1.FFT1_H1_2_13_Y_ReIm + m1.FFT1_H1_5_13_Y_ReIm + m1.FFT1_H1_8_13_Y_ReIm + m1.FFT1_H1_11_13_Y_ReIm)./4;
G(3,2,:) = -(m1.FFT1_H1_3_13_Y_ReIm + m1.FFT1_H1_6_13_Y_ReIm + m1.FFT1_H1_9_13_Y_ReIm + m1.FFT1_H1_12_13_Y_ReIm)./4;
G(4,2,:) = -(m1.FFT1_H1_1_13_Y_ReIm - m1.FFT1_H1_9_13_Y_ReIm )./A;
G(5,2,:) = -(m1.FFT1_H1_6_13_Y_ReIm - m1.FFT1_H1_12_13_Y_ReIm)./B;
G(6,2,:) = -(m1.FFT1_H1_7_13_Y_ReIm - m1.FFT1_H1_1_13_Y_ReIm )./A;
% Fz
G(1,3,:) = -1/2./(1./(m2.FFT1_H1_1_13_Y_ReIm + m2.FFT1_H1_4_13_Y_ReIm + m2.FFT1_H1_7_13_Y_ReIm + m2.FFT1_H1_10_13_Y_ReIm) + ...
1./(m6.FFT1_H1_1_13_Y_ReIm + m6.FFT1_H1_4_13_Y_ReIm + m6.FFT1_H1_7_13_Y_ReIm + m6.FFT1_H1_10_13_Y_ReIm));
G(2,3,:) = -1/2./(1./(m2.FFT1_H1_2_13_Y_ReIm + m2.FFT1_H1_5_13_Y_ReIm + m2.FFT1_H1_8_13_Y_ReIm + m2.FFT1_H1_11_13_Y_ReIm) + ...
1./(m6.FFT1_H1_2_13_Y_ReIm + m6.FFT1_H1_5_13_Y_ReIm + m6.FFT1_H1_8_13_Y_ReIm + m6.FFT1_H1_11_13_Y_ReIm));
G(3,3,:) = -1/2./(1./(m2.FFT1_H1_3_13_Y_ReIm + m2.FFT1_H1_6_13_Y_ReIm + m2.FFT1_H1_9_13_Y_ReIm + m2.FFT1_H1_12_13_Y_ReIm) + ...
1./(m6.FFT1_H1_3_13_Y_ReIm + m6.FFT1_H1_6_13_Y_ReIm + m6.FFT1_H1_9_13_Y_ReIm + m6.FFT1_H1_12_13_Y_ReIm));
G(4,3,:) = -2/A./(1./(m2.FFT1_H1_1_13_Y_ReIm - m2.FFT1_H1_9_13_Y_ReIm) + ...
1./(m6.FFT1_H1_1_13_Y_ReIm - m6.FFT1_H1_9_13_Y_ReIm));
G(5,3,:) = -2/B./(1./(m2.FFT1_H1_6_13_Y_ReIm - m2.FFT1_H1_12_13_Y_ReIm) + ...
1./(m6.FFT1_H1_6_13_Y_ReIm - m6.FFT1_H1_12_13_Y_ReIm));
G(6,3,:) = -2/A./(1./(m2.FFT1_H1_7_13_Y_ReIm - m2.FFT1_H1_1_13_Y_ReIm) + ...
1./(m6.FFT1_H1_7_13_Y_ReIm - m6.FFT1_H1_1_13_Y_ReIm));
% Mx
G(1,4,:) = 1/A/2./(1./(m2.FFT1_H1_1_13_Y_ReIm + m2.FFT1_H1_4_13_Y_ReIm + m2.FFT1_H1_7_13_Y_ReIm + m2.FFT1_H1_10_13_Y_ReIm) - ...
1./(m6.FFT1_H1_1_13_Y_ReIm + m6.FFT1_H1_4_13_Y_ReIm + m6.FFT1_H1_7_13_Y_ReIm + m6.FFT1_H1_10_13_Y_ReIm));
G(2,4,:) = 1/A/2./(1./(m2.FFT1_H1_2_13_Y_ReIm + m2.FFT1_H1_5_13_Y_ReIm + m2.FFT1_H1_8_13_Y_ReIm + m2.FFT1_H1_11_13_Y_ReIm) - ...
1./(m6.FFT1_H1_2_13_Y_ReIm + m6.FFT1_H1_5_13_Y_ReIm + m6.FFT1_H1_8_13_Y_ReIm + m6.FFT1_H1_11_13_Y_ReIm));
G(3,4,:) = 1/A/2./(1./(m2.FFT1_H1_3_13_Y_ReIm + m2.FFT1_H1_6_13_Y_ReIm + m2.FFT1_H1_9_13_Y_ReIm + m2.FFT1_H1_12_13_Y_ReIm) - ...
1./(m6.FFT1_H1_3_13_Y_ReIm + m6.FFT1_H1_6_13_Y_ReIm + m6.FFT1_H1_9_13_Y_ReIm + m6.FFT1_H1_12_13_Y_ReIm));
G(4,4,:) = 1/A^2*2./(1./(m2.FFT1_H1_1_13_Y_ReIm - m2.FFT1_H1_9_13_Y_ReIm) - ...
1./(m6.FFT1_H1_1_13_Y_ReIm - m6.FFT1_H1_9_13_Y_ReIm));
G(5,4,:) = 2/A/B./(1./(m2.FFT1_H1_6_13_Y_ReIm - m2.FFT1_H1_12_13_Y_ReIm) - ...
1./(m6.FFT1_H1_6_13_Y_ReIm - m6.FFT1_H1_12_13_Y_ReIm));
G(6,4,:) = 1/A^2*2./(1./(m2.FFT1_H1_7_13_Y_ReIm - m2.FFT1_H1_1_13_Y_ReIm) - ...
1./(m6.FFT1_H1_7_13_Y_ReIm - m6.FFT1_H1_1_13_Y_ReIm));
% My
G(1,5,:) = 1/B/2./(1./(m8.FFT1_H1_1_13_Y_ReIm + m8.FFT1_H1_4_13_Y_ReIm + m8.FFT1_H1_7_13_Y_ReIm + m8.FFT1_H1_10_13_Y_ReIm) - ...
1./(m4.FFT1_H1_1_13_Y_ReIm + m4.FFT1_H1_4_13_Y_ReIm + m4.FFT1_H1_7_13_Y_ReIm + m4.FFT1_H1_10_13_Y_ReIm));
G(2,5,:) = 1/B/2./(1./(m8.FFT1_H1_2_13_Y_ReIm + m8.FFT1_H1_5_13_Y_ReIm + m8.FFT1_H1_8_13_Y_ReIm + m8.FFT1_H1_11_13_Y_ReIm) - ...
1./(m4.FFT1_H1_2_13_Y_ReIm + m4.FFT1_H1_5_13_Y_ReIm + m4.FFT1_H1_8_13_Y_ReIm + m4.FFT1_H1_11_13_Y_ReIm));
G(3,5,:) = 1/B/2./(1./(m8.FFT1_H1_3_13_Y_ReIm + m8.FFT1_H1_6_13_Y_ReIm + m8.FFT1_H1_9_13_Y_ReIm + m8.FFT1_H1_12_13_Y_ReIm) - ...
1./(m4.FFT1_H1_3_13_Y_ReIm + m4.FFT1_H1_6_13_Y_ReIm + m4.FFT1_H1_9_13_Y_ReIm + m4.FFT1_H1_12_13_Y_ReIm));
G(4,5,:) = 2/B/A./(1./(m8.FFT1_H1_1_13_Y_ReIm - m8.FFT1_H1_9_13_Y_ReIm) - ...
1./(m4.FFT1_H1_1_13_Y_ReIm - m4.FFT1_H1_9_13_Y_ReIm));
G(5,5,:) = 1/B^2*2./(1./(m8.FFT1_H1_6_13_Y_ReIm - m8.FFT1_H1_12_13_Y_ReIm) - ...
1./(m4.FFT1_H1_6_13_Y_ReIm - m4.FFT1_H1_12_13_Y_ReIm));
G(6,5,:) = 2/B/A./(1./(m8.FFT1_H1_7_13_Y_ReIm - m8.FFT1_H1_1_13_Y_ReIm) - ...
1./(m4.FFT1_H1_7_13_Y_ReIm - m4.FFT1_H1_1_13_Y_ReIm));
% Mz
G(1,6,:) = 1/A/2./(1./(m10.FFT1_H1_1_13_Y_ReIm + m10.FFT1_H1_4_13_Y_ReIm + m10.FFT1_H1_7_13_Y_ReIm + m10.FFT1_H1_10_13_Y_ReIm) - ...
1./(m9.FFT1_H1_1_13_Y_ReIm + m9.FFT1_H1_4_13_Y_ReIm + m9.FFT1_H1_7_13_Y_ReIm + m9.FFT1_H1_10_13_Y_ReIm));
G(2,6,:) = 1/A/2./(1./(m10.FFT1_H1_2_13_Y_ReIm + m10.FFT1_H1_5_13_Y_ReIm + m10.FFT1_H1_8_13_Y_ReIm + m10.FFT1_H1_11_13_Y_ReIm) - ...
1./(m9.FFT1_H1_2_13_Y_ReIm + m9.FFT1_H1_5_13_Y_ReIm + m9.FFT1_H1_8_13_Y_ReIm + m9.FFT1_H1_11_13_Y_ReIm));
G(3,6,:) = 1/A/2./(1./(m10.FFT1_H1_3_13_Y_ReIm + m10.FFT1_H1_6_13_Y_ReIm + m10.FFT1_H1_9_13_Y_ReIm + m10.FFT1_H1_12_13_Y_ReIm) - ...
1./(m9.FFT1_H1_3_13_Y_ReIm + m9.FFT1_H1_6_13_Y_ReIm + m9.FFT1_H1_9_13_Y_ReIm + m9.FFT1_H1_12_13_Y_ReIm));
G(4,6,:) = 1/A^2*2./(1./(m10.FFT1_H1_1_13_Y_ReIm - m10.FFT1_H1_9_13_Y_ReIm) - ...
1./(m9.FFT1_H1_1_13_Y_ReIm - m9.FFT1_H1_9_13_Y_ReIm));
G(5,6,:) = 2*A/B./(1./(m10.FFT1_H1_6_13_Y_ReIm - m10.FFT1_H1_12_13_Y_ReIm) - ...
1./(m9.FFT1_H1_6_13_Y_ReIm - m9.FFT1_H1_12_13_Y_ReIm));
G(6,6,:) = 1/A^2*2./(1./(m10.FFT1_H1_7_13_Y_ReIm - m10.FFT1_H1_1_13_Y_ReIm) - ...
1./(m9.FFT1_H1_7_13_Y_ReIm - m9.FFT1_H1_1_13_Y_ReIm));
</pre>
</div>
</div>
</div>
<div id="outline-container-orgc4d6849" class="outline-3">
<h3 id="orgc4d6849"><span class="section-number-3">2.3</span> Diagonal Dynamics</h3>
<div class="outline-text-3" id="text-2-3">
<div class="org-src-container">
<pre class="src src-matlab">figure;
ax1 = subplot(2,1,1);
hold on;
plot(freqs, abs(squeeze(G(1,1,:))./(-w.^2)), '.')
plot(freqs, abs(squeeze(G(2,2,:))./(-w.^2)), '.')
plot(freqs, abs(squeeze(G(3,3,:))./(-w.^2)), '.')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Magnitude [m/N]'); set(gca, 'XTickLabel',[]);
ylim([1e-9, 2e-6]);
ax2 = subplot(2,1,2);
hold on;
plot(freqs, 180/pi*angle(squeeze(G(1,1,:))./(-w.^2)), '.', 'DisplayName', '$D_x/F_x$')
plot(freqs, 180/pi*angle(squeeze(G(2,2,:))./(-w.^2)), '.', 'DisplayName', '$D_y/F_y$')
plot(freqs, 180/pi*angle(squeeze(G(3,3,:))./(-w.^2)), '.', 'DisplayName', '$D_z/F_z$')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
xlabel('Freqency [Hz]'); ylabel('Phase [deg]');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
legend('location', 'southwest');
linkaxes([ax1,ax2],'x');
xlim([30, 300]);
</pre>
</div>
<div id="org7d6f1be" class="figure">
<p><img src="figs/compliance_diagonal_translations.png" alt="compliance_diagonal_translations.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Dynamics from Forces to Translations</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab">figure;
ax1 = subplot(2,1,1);
hold on;
plot(freqs, abs(squeeze(G(4,4,:))./(-w.^2)), '.')
plot(freqs, abs(squeeze(G(5,5,:))./(-w.^2)), '.')
plot(freqs, abs(squeeze(G(6,6,:))./(-w.^2)), '.')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Magnitude [rad/Nm]'); set(gca, 'XTickLabel',[]);
ylim([1e-9, 2e-6]);
ax2 = subplot(2,1,2);
hold on;
plot(freqs, 180/pi*angle(squeeze(G(4,4,:))./(-w.^2)), '.', 'DisplayName', '$R_x/M_x$')
plot(freqs, 180/pi*angle(squeeze(G(5,5,:))./(-w.^2)), '.', 'DisplayName', '$R_y/M_y$')
plot(freqs, 180/pi*angle(squeeze(G(6,6,:))./(-w.^2)), '.', 'DisplayName', '$R_z/M_z$')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
xlabel('Freqency [Hz]'); ylabel('Phase [deg]');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
legend('location', 'southwest');
linkaxes([ax1,ax2],'x');
xlim([30, 300]);
</pre>
</div>
<div id="org445a1e9" class="figure">
<p><img src="figs/compliance_diagonal_rotations.png" alt="compliance_diagonal_rotations.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Dynamics from Torques to Rotations</p>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-right" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">&#xa0;</th>
<th scope="col" class="org-right">Stiffness</th>
<th scope="col" class="org-left">Unit</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">\(K_x\)</td>
<td class="org-right">1e7</td>
<td class="org-left">[N/m]</td>
</tr>
<tr>
<td class="org-left">\(K_y\)</td>
<td class="org-right">1e7</td>
<td class="org-left">[N/m]</td>
</tr>
<tr>
<td class="org-left">\(K_z\)</td>
<td class="org-right">2e8</td>
<td class="org-left">[N/m]</td>
</tr>
<tr>
<td class="org-left">\(K_{R_x}\)</td>
<td class="org-right">?</td>
<td class="org-left">[Nm/rad]</td>
</tr>
<tr>
<td class="org-left">\(K_{R_y}\)</td>
<td class="org-right">1.8e7</td>
<td class="org-left">[Nm/rad]</td>
</tr>
<tr>
<td class="org-left">\(K_{R_z}\)</td>
<td class="org-right">1e7</td>
<td class="org-left">[Nm/rad]</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org87be1fb" class="outline-3">
<h3 id="org87be1fb"><span class="section-number-3">2.4</span> Compare with Model</h3>
<div class="outline-text-3" id="text-2-4">
<div class="org-src-container">
<pre class="src src-matlab">load('./mat/model.mat', 'Gm');
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">figure;
ax1 = subplot(2,1,1);
hold on;
plot(freqs, abs(squeeze(G(1,1,:))./(-w.^2)), '.')
plot(freqs, abs(squeeze(G(2,2,:))./(-w.^2)), '.')
plot(freqs, abs(squeeze(G(3,3,:))./(-w.^2)), '.')
set(gca,'ColorOrderIndex',1);
plot(freqs, abs(squeeze(freqresp(Gm(1,1,:), freqs, 'Hz'))), '-')
plot(freqs, abs(squeeze(freqresp(Gm(2,2,:), freqs, 'Hz'))), '-')
plot(freqs, abs(squeeze(freqresp(Gm(3,3,:), freqs, 'Hz'))), '-')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Magnitude [m/N]'); set(gca, 'XTickLabel',[]);
ylim([1e-9, 2e-6]);
ax2 = subplot(2,1,2);
hold on;
plot(freqs, 180/pi*angle(squeeze(G(1,1,:))./(-w.^2)), '.', 'DisplayName', '$D_x/F_x$')
plot(freqs, 180/pi*angle(squeeze(G(2,2,:))./(-w.^2)), '.', 'DisplayName', '$D_y/F_y$')
plot(freqs, 180/pi*angle(squeeze(G(3,3,:))./(-w.^2)), '.', 'DisplayName', '$D_z/F_z$')
set(gca,'ColorOrderIndex',1);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(1,1,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off')
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(2,2,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off')
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(3,3,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
xlabel('Freqency [Hz]'); ylabel('Phase [deg]');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
legend('location', 'southwest');
linkaxes([ax1,ax2],'x');
xlim([30, 300]);
</pre>
</div>
<div id="org40c0b41" class="figure">
<p><img src="figs/compliance_diagonal_translations_comp_model.png" alt="compliance_diagonal_translations_comp_model.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Dynamics from Forces to Translations</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab">figure;
ax1 = subplot(2,1,1);
hold on;
plot(freqs, abs(squeeze(G(4,4,:))./(-w.^2)), '.')
plot(freqs, abs(squeeze(G(5,5,:))./(-w.^2)), '.')
plot(freqs, abs(squeeze(G(6,6,:))./(-w.^2)), '.')
set(gca,'ColorOrderIndex',1);
plot(freqs, abs(squeeze(freqresp(Gm(4,4,:), freqs, 'Hz'))), '-')
plot(freqs, abs(squeeze(freqresp(Gm(5,5,:), freqs, 'Hz'))), '-')
plot(freqs, abs(squeeze(freqresp(Gm(6,6,:), freqs, 'Hz'))), '-')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Magnitude [rad/Nm]'); set(gca, 'XTickLabel',[]);
% ylim([1e-9, 2e-6]);
ax2 = subplot(2,1,2);
hold on;
plot(freqs, 180/pi*angle(squeeze(G(4,4,:))./(-w.^2)), '.', 'DisplayName', '$R_x/M_x$')
plot(freqs, 180/pi*angle(squeeze(G(5,5,:))./(-w.^2)), '.', 'DisplayName', '$R_y/M_y$')
plot(freqs, 180/pi*angle(squeeze(G(6,6,:))./(-w.^2)), '.', 'DisplayName', '$R_z/M_z$')
set(gca,'ColorOrderIndex',1);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(4,4,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off')
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(5,5,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off')
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(6,6,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
xlabel('Freqency [Hz]'); ylabel('Phase [deg]');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
legend('location', 'southwest');
linkaxes([ax1,ax2],'x');
xlim([30, 300]);
</pre>
</div>
<div id="org644f661" class="figure">
<p><img src="figs/compliance_diagonal_rotations_comp_model.png" alt="compliance_diagonal_rotations_comp_model.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Dynamics from Torques to Rotations</p>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-right" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">&#xa0;</th>
<th scope="col" class="org-right">Stiffness</th>
<th scope="col" class="org-left">Unit</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">\(K_x\)</td>
<td class="org-right">1e7</td>
<td class="org-left">[N/m]</td>
</tr>
<tr>
<td class="org-left">\(K_y\)</td>
<td class="org-right">1e7</td>
<td class="org-left">[N/m]</td>
</tr>
<tr>
<td class="org-left">\(K_z\)</td>
<td class="org-right">2e8</td>
<td class="org-left">[N/m]</td>
</tr>
<tr>
<td class="org-left">\(K_{R_x}\)</td>
<td class="org-right">5e7</td>
<td class="org-left">[Nm/rad]</td>
</tr>
<tr>
<td class="org-left">\(K_{R_y}\)</td>
<td class="org-right">3e7</td>
<td class="org-left">[Nm/rad]</td>
</tr>
<tr>
<td class="org-left">\(K_{R_z}\)</td>
<td class="org-right">2e7</td>
<td class="org-left">[Nm/rad]</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-orgaa2c58a" class="outline-3">
<h3 id="orgaa2c58a"><span class="section-number-3">2.5</span> Coupling Dynamics</h3>
<div class="outline-text-3" id="text-2-5">
<div class="org-src-container">
<pre class="src src-matlab">figure;
ax1 = subplot(2,1,1);
hold on;
plot(freqs, abs(squeeze(G(1,1,:))./(-w.^2)), '.')
plot(freqs, abs(squeeze(G(2,1,:))./(-w.^2)), '.')
plot(freqs, abs(squeeze(G(3,1,:))./(-w.^2)), '.')
set(gca,'ColorOrderIndex',1);
plot(freqs, abs(squeeze(freqresp(Gm(1,1,:), freqs, 'Hz'))), '-')
plot(freqs, abs(squeeze(freqresp(Gm(2,1,:), freqs, 'Hz'))), '-')
plot(freqs, abs(squeeze(freqresp(Gm(3,1,:), freqs, 'Hz'))), '-')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Magnitude [m/N]'); set(gca, 'XTickLabel',[]);
ylim([1e-9, 2e-6]);
ax2 = subplot(2,1,2);
hold on;
plot(freqs, 180/pi*angle(squeeze(G(1,1,:))./(-w.^2)), '.', 'DisplayName', '$D_x/F_x$')
plot(freqs, 180/pi*angle(squeeze(G(2,1,:))./(-w.^2)), '.', 'DisplayName', '$D_y/F_x$')
plot(freqs, 180/pi*angle(squeeze(G(3,1,:))./(-w.^2)), '.', 'DisplayName', '$D_z/F_x$')
set(gca,'ColorOrderIndex',1);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(1,1,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off')
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(2,1,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off')
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(3,1,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
xlabel('Freqency [Hz]'); ylabel('Phase [deg]');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
legend('location', 'southwest');
linkaxes([ax1,ax2],'x');
xlim([30, 300]);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">figure;
ax1 = subplot(2,1,1);
hold on;
plot(freqs, abs(squeeze(G(5,1,:))./(-w.^2)), '.')
plot(freqs, abs(squeeze(G(4,2,:))./(-w.^2)), '.')
set(gca,'ColorOrderIndex',1);
plot(freqs, abs(squeeze(freqresp(Gm(5,1,:), freqs, 'Hz'))), '-')
plot(freqs, abs(squeeze(freqresp(Gm(4,2,:), freqs, 'Hz'))), '-')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Magnitude [m/N]'); set(gca, 'XTickLabel',[]);
ylim([1e-9, 2e-6]);
ax2 = subplot(2,1,2);
hold on;
plot(freqs, 180/pi*angle(squeeze(G(5,1,:))./(-w.^2)), '.', 'DisplayName', '$R_y/F_x$')
plot(freqs, 180/pi*angle(squeeze(G(4,2,:))./(-w.^2)), '.', 'DisplayName', '$R_x/F_y$')
set(gca,'ColorOrderIndex',1);
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(5,1,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off')
plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(4,2,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
xlabel('Freqency [Hz]'); ylabel('Phase [deg]');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
legend('location', 'southwest');
linkaxes([ax1,ax2],'x');
xlim([30, 300]);
</pre>
</div>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-08-18 mar. 12:57</p>
</div>
</body>
</html>
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