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<title>Matlab Functions used for the NASS Project</title>
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<h1 class="title">Matlab Functions used for the NASS Project</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org3fa0f20">1. describeNassSetup</a>
<ul>
<li><a href="#org3615302">Function description</a></li>
<li><a href="#org3b8c4f7">Simscape Configuration</a></li>
<li><a href="#org5b65749">Disturbances</a></li>
<li><a href="#org59f7825">References</a></li>
<li><a href="#org90b1ac8">Controller</a></li>
<li><a href="#orgdd5b7a5">Micro-Station</a></li>
<li><a href="#org1687c05">Metrology</a></li>
<li><a href="#orgee5944e">Nano Hexapod</a></li>
<li><a href="#orga499c17">Sample</a></li>
</ul>
</li>
<li><a href="#orgdc168b9">2. computeReferencePose</a></li>
<li><a href="#org493ab7f">3. Compute the Sample Position Error w.r.t. the NASS</a></li>
</ul>
</div>
</div>
<div id="outline-container-org3fa0f20" class="outline-2">
<h2 id="org3fa0f20"><span class="section-number-2">1</span> describeNassSetup</h2>
<div class="outline-text-2" id="text-1">
<p>
<a id="org0b9cc9d"></a>
</p>
</div>
<div id="outline-container-org3615302" class="outline-3">
<h3 id="org3615302">Function description</h3>
<div class="outline-text-3" id="text-org3615302">
<div class="org-src-container">
<pre class="src src-matlab">function [] = describeNassSetup()
% describeNassSetup -
%
% Syntax: [] = describeNassSetup()
%
% Inputs:
% - -
%
% Outputs:
% - -
</pre>
</div>
</div>
</div>
<div id="outline-container-org3b8c4f7" class="outline-3">
<h3 id="org3b8c4f7">Simscape Configuration</h3>
<div class="outline-text-3" id="text-org3b8c4f7">
<div class="org-src-container">
<pre class="src src-matlab">load('./mat/conf_simscape.mat', 'conf_simscape');
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">fprintf('Simscape Configuration:\n');
if conf_simscape.type == 1
fprintf('- Gravity is included\n');
else
fprintf('- Gravity is not included\n');
end
fprintf('\n');
</pre>
</div>
</div>
</div>
<div id="outline-container-org5b65749" class="outline-3">
<h3 id="org5b65749">Disturbances</h3>
<div class="outline-text-3" id="text-org5b65749">
<div class="org-src-container">
<pre class="src src-matlab">load('./mat/nass_disturbances.mat', 'args');
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">fprintf('Disturbances:\n');
if ~args.enable
fprintf('- No disturbance is included\n');
else
if args.Dwx &amp;&amp; args.Dwy &amp;&amp; args.Dwz
fprintf('- Ground motion\n');
end
if args.Fty_x &amp;&amp; args.Fty_z
fprintf('- Vibrations of the Translation Stage\n');
end
if args.Frz_z
fprintf('- Vibrations of the Spindle\n');
end
end
fprintf('\n');
</pre>
</div>
</div>
</div>
<div id="outline-container-org59f7825" class="outline-3">
<h3 id="org59f7825">References</h3>
<div class="outline-text-3" id="text-org59f7825">
<div class="org-src-container">
<pre class="src src-matlab">load('./mat/nass_references.mat', 'args');
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">fprintf('Reference Tracking:\n');
fprintf('- Translation Stage:\n');
switch args.Dy_type
case 'constant'
fprintf(' - Constant Position\n');
fprintf(' - Dy = %.0f [mm]\n', args.Dy_amplitude*1e3);
case 'triangular'
fprintf(' - Triangular Path\n');
fprintf(' - Amplitude = %.0f [mm]\n', args.Dy_amplitude*1e3);
fprintf(' - Period = %.0f [s]\n', args.Dy_period);
case 'sinusoidal'
fprintf(' - Sinusoidal Path\n');
fprintf(' - Amplitude = %.0f [mm]\n', args.Dy_amplitude*1e3);
fprintf(' - Period = %.0f [s]\n', args.Dy_period);
end
fprintf('- Tilt Stage:\n');
switch args.Ry_type
case 'constant'
fprintf(' - Constant Position\n');
fprintf(' - Ry = %.0f [mm]\n', args.Ry_amplitude*1e3);
case 'triangular'
fprintf(' - Triangular Path\n');
fprintf(' - Amplitude = %.0f [mm]\n', args.Ry_amplitude*1e3);
fprintf(' - Period = %.0f [s]\n', args.Ry_period);
case 'sinusoidal'
fprintf(' - Sinusoidal Path\n');
fprintf(' - Amplitude = %.0f [mm]\n', args.Ry_amplitude*1e3);
fprintf(' - Period = %.0f [s]\n', args.Ry_period);
end
fprintf('- Spindle:\n');
switch args.Rz_type
case 'constant'
fprintf(' - Constant Position\n');
fprintf(' - Rz = %.0f [deg]\n', 180/pi*args.Rz_amplitude);
case { 'rotating', 'rotating-not-filtered' }
fprintf(' - Rotating\n');
fprintf(' - Speed = %.0f [rpm]\n', 60/args.Rz_period);
end
fprintf('- Micro Hexapod:\n');
switch args.Dh_type
case 'constant'
fprintf(' - Constant Position\n');
fprintf(' - Dh = %.0f, %.0f, %.0f [mm]\n', args.Dh_pos(1), args.Dh_pos(2), args.Dh_pos(3));
fprintf(' - Rh = %.0f, %.0f, %.0f [deg]\n', args.Dh_pos(4), args.Dh_pos(5), args.Dh_pos(6));
end
fprintf('\n');
</pre>
</div>
</div>
</div>
<div id="outline-container-org90b1ac8" class="outline-3">
<h3 id="org90b1ac8">Controller</h3>
<div class="outline-text-3" id="text-org90b1ac8">
<div class="org-src-container">
<pre class="src src-matlab">load('./mat/controller.mat', 'controller');
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">fprintf('Controller:\n');
fprintf('- %s\n', controller.name);
fprintf('\n');
</pre>
</div>
</div>
</div>
<div id="outline-container-orgdd5b7a5" class="outline-3">
<h3 id="orgdd5b7a5">Micro-Station</h3>
<div class="outline-text-3" id="text-orgdd5b7a5">
<div class="org-src-container">
<pre class="src src-matlab">load('./mat/stages.mat', 'ground', 'granite', 'ty', 'ry', 'rz', 'micro_hexapod', 'axisc');
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">fprintf('Micro Station:\n');
if granite.type == 1 &amp;&amp; ...
ty.type == 1 &amp;&amp; ...
ry.type == 1 &amp;&amp; ...
rz.type == 1 &amp;&amp; ...
micro_hexapod.type == 1;
fprintf('- All stages are rigid\n');
elseif granite.type == 2 &amp;&amp; ...
ty.type == 2 &amp;&amp; ...
ry.type == 2 &amp;&amp; ...
rz.type == 2 &amp;&amp; ...
micro_hexapod.type == 2;
fprintf('- All stages are flexible\n');
else
if granite.type == 1 || granite.type == 4
fprintf('- Granite is rigid\n');
else
fprintf('- Granite is flexible\n');
end
if ty.type == 1 || ty.type == 4
fprintf('- Translation Stage is rigid\n');
else
fprintf('- Translation Stage is flexible\n');
end
if ry.type == 1 || ry.type == 4
fprintf('- Tilt Stage is rigid\n');
else
fprintf('- Tilt Stage is flexible\n');
end
if rz.type == 1 || rz.type == 4
fprintf('- Spindle is rigid\n');
else
fprintf('- Spindle is flexible\n');
end
if micro_hexapod.type == 1 || micro_hexapod.type == 4
fprintf('- Micro Hexapod is rigid\n');
else
fprintf('- Micro Hexapod is flexible\n');
end
end
fprintf('\n');
</pre>
</div>
</div>
</div>
<div id="outline-container-org1687c05" class="outline-3">
<h3 id="org1687c05">Metrology</h3>
<div class="outline-text-3" id="text-org1687c05">
<div class="org-src-container">
<pre class="src src-matlab">load('./mat/stages.mat', 'mirror');
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">fprintf('Reference Mirror:\n');
if mirror.type == 2;
fprintf('- flexible fixation\n');
fprintf('- w = %.0f [Hz]\n', mirror.freq(1));
else
fprintf('- rigidly attached to the nano-hexapod\n');
end
fprintf('- m = %.0f [kg]\n', mirror.mass);
fprintf('\n');
</pre>
</div>
</div>
</div>
<div id="outline-container-orgee5944e" class="outline-3">
<h3 id="orgee5944e">Nano Hexapod</h3>
<div class="outline-text-3" id="text-orgee5944e">
<div class="org-src-container">
<pre class="src src-matlab">load('./mat/stages.mat', 'nano_hexapod');
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">fprintf('Nano Hexapod:\n');
if nano_hexapod.type == 0;
fprintf('- no included\n');
elseif nano_hexapod.type == 1 || nano_hexapod.type == 3;
fprintf('- rigid\n');
elseif nano_hexapod.type == 2;
fprintf('- flexible\n');
fprintf('- Ki = %.0g [N/m]\n', nano_hexapod.actuators.K(1));
end
fprintf('\n');
</pre>
</div>
</div>
</div>
<div id="outline-container-orga499c17" class="outline-3">
<h3 id="orga499c17">Sample</h3>
<div class="outline-text-3" id="text-orga499c17">
<div class="org-src-container">
<pre class="src src-matlab">load('./mat/stages.mat', 'sample');
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">fprintf('Sample:\n');
if sample.type == 0;
fprintf('- no included\n');
elseif sample.type == 1 || sample.type == 3;
fprintf('- rigid\n');
fprintf('- mass = %.0f [kg]\n', sample.mass);
fprintf('- moment of inertia = %.2f, %.2f, %.2f [kg m2]\n', sample.inertia(1), sample.inertia(2), sample.inertia(3));
elseif sample.type == 2;
fprintf('- flexible\n');
fprintf('- mass = %.0f [kg]\n', sample.mass);
fprintf('- moment of inertia = %.2f, %.2f, %.2f [kg m2]\n', sample.inertia(1), sample.inertia(2), sample.inertia(3));
% fprintf('- Kt = %.0g, %.0g, %.0g [N/m]\n', sample.K(1), sample.K(2), sample.K(3));
% fprintf('- Kr = %.0g, %.0g, %.0g [Nm/rad]\n', sample.K(4), sample.K(5), sample.K(6));
fprintf('- wt(x,y,z) = %.0f, %.0f, %.0f [Hz]\n', 1/2/pi*sqrt(sample.K(1)/sample.mass), 1/2/pi*sqrt(sample.K(1)/sample.mass), 1/2/pi*sqrt(sample.K(1)/sample.mass));
fprintf('- wr(x,y,z) = %.0f, %.0f, %.0f [Hz]\n', 1/2/pi*sqrt(sample.K(4)/sample.inertia(1)), 1/2/pi*sqrt(sample.K(5)/sample.inertia(2)), 1/2/pi*sqrt(sample.K(6)/sample.inertia(3)));
end
fprintf('\n');
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-orgdc168b9" class="outline-2">
<h2 id="orgdc168b9"><span class="section-number-2">2</span> computeReferencePose</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="org98cbe6e"></a>
</p>
<p>
This Matlab function is accessible <a href="..//src/computeReferencePose.m">here</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">function [WTr] = computeReferencePose(Dy, Ry, Rz, Dh, Dn)
% computeReferencePose - Compute the homogeneous transformation matrix corresponding to the wanted pose of the sample
%
% Syntax: [WTr] = computeReferencePose(Dy, Ry, Rz, Dh, Dn)
%
% Inputs:
% - Dy - Reference of the Translation Stage [m]
% - Ry - Reference of the Tilt Stage [rad]
% - Rz - Reference of the Spindle [rad]
% - Dh - Reference of the Micro Hexapod (Pitch, Roll, Yaw angles) [m, m, m, rad, rad, rad]
% - Dn - Reference of the Nano Hexapod [m, m, m, rad, rad, rad]
%
% Outputs:
% - WTr -
%% Translation Stage
Rty = [1 0 0 0;
0 1 0 Dy;
0 0 1 0;
0 0 0 1];
%% Tilt Stage - Pure rotating aligned with Ob
Rry = [ cos(Ry) 0 sin(Ry) 0;
0 1 0 0;
-sin(Ry) 0 cos(Ry) 0;
0 0 0 1];
%% Spindle - Rotation along the Z axis
Rrz = [cos(Rz) -sin(Rz) 0 0 ;
sin(Rz) cos(Rz) 0 0 ;
0 0 1 0 ;
0 0 0 1 ];
%% Micro-Hexapod
Rhx = [1 0 0;
0 cos(Dh(4)) -sin(Dh(4));
0 sin(Dh(4)) cos(Dh(4))];
Rhy = [ cos(Dh(5)) 0 sin(Dh(5));
0 1 0;
-sin(Dh(5)) 0 cos(Dh(5))];
Rhz = [cos(Dh(6)) -sin(Dh(6)) 0;
sin(Dh(6)) cos(Dh(6)) 0;
0 0 1];
Rh = [1 0 0 Dh(1) ;
0 1 0 Dh(2) ;
0 0 1 Dh(3) ;
0 0 0 1 ];
Rh(1:3, 1:3) = Rhz*Rhy*Rhx;
%% Nano-Hexapod
Rnx = [1 0 0;
0 cos(Dn(4)) -sin(Dn(4));
0 sin(Dn(4)) cos(Dn(4))];
Rny = [ cos(Dn(5)) 0 sin(Dn(5));
0 1 0;
-sin(Dn(5)) 0 cos(Dn(5))];
Rnz = [cos(Dn(6)) -sin(Dn(6)) 0;
sin(Dn(6)) cos(Dn(6)) 0;
0 0 1];
Rn = [1 0 0 Dn(1) ;
0 1 0 Dn(2) ;
0 0 1 Dn(3) ;
0 0 0 1 ];
Rn(1:3, 1:3) = Rnz*Rny*Rnx;
%% Total Homogeneous transformation
WTr = Rty*Rry*Rrz*Rh*Rn;
end
</pre>
</div>
</div>
</div>
<div id="outline-container-org493ab7f" class="outline-2">
<h2 id="org493ab7f"><span class="section-number-2">3</span> Compute the Sample Position Error w.r.t. the NASS</h2>
<div class="outline-text-2" id="text-3">
<p>
<a id="org6dcd4fb"></a>
</p>
<p>
This Matlab function is accessible <a href="..//src/computeSampleError.m">here</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">function [MTr] = computeSampleError(WTm, WTr)
% computeSampleError -
%
% Syntax: [MTr] = computeSampleError(WTm, WTr)
%
% Inputs:
% - WTm - Homoegeneous transformation that represent the
% wanted pose of the sample with respect to the granite
% - WTr - Homoegeneous transformation that represent the
% measured pose of the sample with respect to the granite
%
% Outputs:
% - MTr - Homoegeneous transformation that represent the
% wanted pose of the sample expressed in a frame
% attached to the top platform of the nano-hexapod
MTr = zeros(4,4);
MTr = [WTm(1:3,1:3)', -WTm(1:3,1:3)'*WTm(1:3,4) ; 0 0 0 1]*WTr;
end
</pre>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-05-05 mar. 10:33</p>
</div>
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