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Thomas Dehaeze
2020-09-01 13:51:37 +02:00
parent 2389e6ba8e
commit 184c755fb8
15 changed files with 1326 additions and 872 deletions
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docs/disturbances.html
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@@ -1,10 +1,9 @@
<?xml version="1.0" encoding="utf-8"?>
<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2020-04-17 ven. 09:35 -->
<!-- 2020-09-01 mar. 13:48 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Identification of the disturbances</title>
<meta name="generator" content="Org mode" />
@@ -112,8 +111,8 @@ Also, we measure the absolute displacement of the granite and of the top platfor
We load the configuration and we set a small <code>StopTime</code>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'mat/conf_simulink.mat'</span>);
<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'0.5'</span>);
<pre class="src src-matlab">load('mat/conf_simulink.mat');
set_param(conf_simulink, 'StopTime', '0.5');
</pre>
</div>
@@ -123,15 +122,15 @@ The obtained system corresponds to the status micro-station when the vibration m
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeGround();
initializeGranite(<span class="org-string">'type'</span>, <span class="org-string">'modal-analysis'</span>);
initializeGranite('type', 'modal-analysis');
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod(<span class="org-string">'type'</span>, <span class="org-string">'modal-analysis'</span>);
initializeAxisc(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
initializeMirror(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
initializeNanoHexapod(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
initializeSample(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
initializeMicroHexapod('type', 'modal-analysis');
initializeAxisc('type', 'none');
initializeMirror('type', 'none');
initializeNanoHexapod('type', 'none');
initializeSample('type', 'none');
</pre>
</div>
@@ -139,7 +138,7 @@ initializeSample(<span class="org-string">'type'</span>, <span class="org-string
Open Loop Control.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
<pre class="src src-matlab">initializeController('type', 'open-loop');
</pre>
</div>
@@ -147,7 +146,7 @@ Open Loop Control.
We don&rsquo;t need gravity here.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">false</span>);
<pre class="src src-matlab">initializeSimscapeConfiguration('gravity', false);
</pre>
</div>
@@ -155,7 +154,7 @@ We don&rsquo;t need gravity here.
We log the signals.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'all'</span>);
<pre class="src src-matlab">initializeLoggingConfiguration('log', 'all');
</pre>
</div>
</div>
@@ -170,19 +169,19 @@ The transfer functions from the disturbance forces to the relative velocity of t
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
mdl = <span class="org-string">'nass_model'</span>;
<pre class="src src-matlab">%% Name of the Simulink File
mdl = 'nass_model';
<span class="org-matlab-cellbreak"><span class="org-comment">%% Micro-Hexapod</span></span>
%% Micro-Hexapod
clear io; io_i = 1;
io(io_i) = linio([mdl, <span class="org-string">'/Disturbances'</span>], 1, <span class="org-string">'openinput'</span>, [], <span class="org-string">'Dwz'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Vertical Ground Motion</span>
io(io_i) = linio([mdl, <span class="org-string">'/Disturbances'</span>], 1, <span class="org-string">'openinput'</span>, [], <span class="org-string">'Fty_z'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Parasitic force Ty</span>
io(io_i) = linio([mdl, <span class="org-string">'/Disturbances'</span>], 1, <span class="org-string">'openinput'</span>, [], <span class="org-string">'Frz_z'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Parasitic force Rz</span>
io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Dwz'); io_i = io_i + 1; % Vertical Ground Motion
io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Fty_z'); io_i = io_i + 1; % Parasitic force Ty
io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Frz_z'); io_i = io_i + 1; % Parasitic force Rz
io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station/Granite/Modal Analysis/accelerometer'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute motion - Granite</span>
io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station/Micro Hexapod/Modal Analysis/accelerometer'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute Motion - Hexapod</span>
io(io_i) = linio([mdl, '/Micro-Station/Granite/Modal Analysis/accelerometer'], 1, 'openoutput'); io_i = io_i + 1; % Absolute motion - Granite
io(io_i) = linio([mdl, '/Micro-Station/Micro Hexapod/Modal Analysis/accelerometer'], 1, 'openoutput'); io_i = io_i + 1; % Absolute Motion - Hexapod
<span class="org-comment">% Run the linearization</span>
% Run the linearization
G = linearize(mdl, io, 0);
</pre>
</div>
@@ -191,11 +190,11 @@ G = linearize(mdl, io, 0);
We Take only the outputs corresponding to the vertical acceleration.
</p>
<div class="org-src-container">
<pre class="src src-matlab">G = G([3,9], <span class="org-type">:</span>);
<pre class="src src-matlab">G = G([3,9], :);
<span class="org-comment">% Input/Output names</span>
G.InputName = {<span class="org-string">'Dw'</span>, <span class="org-string">'Fty'</span>, <span class="org-string">'Frz'</span>};
G.OutputName = {<span class="org-string">'Agm'</span>, <span class="org-string">'Ahm'</span>};
% Input/Output names
G.InputName = {'Dw', 'Fty', 'Frz'};
G.OutputName = {'Agm', 'Ahm'};
</pre>
</div>
@@ -203,11 +202,11 @@ G.OutputName = {<span class="org-string">'Agm'</span>, <span class="org-string">
We integrate 1 time the output to have the velocity and we substract the absolute velocities to have the relative velocity.
</p>
<div class="org-src-container">
<pre class="src src-matlab">G = (1<span class="org-type">/</span>s)<span class="org-type">*</span>tf([<span class="org-type">-</span>1, 1])<span class="org-type">*</span>G;
<pre class="src src-matlab">G = (1/s)*tf([-1, 1])*G;
<span class="org-comment">% Input/Output names</span>
G.InputName = {<span class="org-string">'Dw'</span>, <span class="org-string">'Fty'</span>, <span class="org-string">'Frz'</span>};
G.OutputName = {<span class="org-string">'Vm'</span>};
% Input/Output names
G.InputName = {'Dw', 'Fty', 'Frz'};
G.OutputName = {'Vm'};
</pre>
</div>
</div>
@@ -273,10 +272,10 @@ Also, the Ground Motion is measured.
</p>
<div class="org-src-container">
<pre class="src src-matlab">gm = load(<span class="org-string">'./mat/psd_gm.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'psd_gm'</span>);
rz = load(<span class="org-string">'./mat/pxsp_r.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'pxsp_r'</span>);
tyz = load(<span class="org-string">'./mat/pxz_ty_r.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'pxz_ty_r'</span>);
tyx = load(<span class="org-string">'./mat/pxe_ty_r.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'pxe_ty_r'</span>);
<pre class="src src-matlab">gm = load('./mat/psd_gm.mat', 'f', 'psd_gm');
rz = load('./mat/pxsp_r.mat', 'f', 'pxsp_r');
tyz = load('./mat/pxz_ty_r.mat', 'f', 'pxz_ty_r');
tyx = load('./mat/pxe_ty_r.mat', 'f', 'pxe_ty_r');
</pre>
</div>
@@ -285,10 +284,10 @@ Because some 50Hz and harmonics were present in the ground motion measurement, w
</p>
<div class="org-src-container">
<pre class="src src-matlab">f0s = [50, 100, 150, 200, 250, 350, 450];
<span class="org-keyword">for</span> <span class="org-variable-name">f0</span> = <span class="org-constant">f0s</span>
<span class="org-constant">i</span> = find(gm.f <span class="org-type">&gt;</span> f0<span class="org-type">-</span>0.5 <span class="org-type">&amp;</span> gm.f <span class="org-type">&lt;</span> f0<span class="org-type">+</span>0.5);
gm.psd_gm(<span class="org-constant">i</span>) = linspace(gm.psd_gm(<span class="org-constant">i</span>(1)), gm.psd_gm(<span class="org-constant">i</span>(end)), length(<span class="org-constant">i</span>));
<span class="org-keyword">end</span>
for f0 = f0s
i = find(gm.f &gt; f0-0.5 &amp; gm.f &lt; f0+0.5);
gm.psd_gm(i) = linspace(gm.psd_gm(i(1)), gm.psd_gm(i(end)), length(i));
end
</pre>
</div>
@@ -296,7 +295,7 @@ Because some 50Hz and harmonics were present in the ground motion measurement, w
We now compute the relative velocity between the hexapod and the granite due to ground motion.
</p>
<div class="org-src-container">
<pre class="src src-matlab">gm.psd_rv = gm.psd_gm<span class="org-type">.*</span>abs(squeeze(freqresp(G(<span class="org-string">'Vm'</span>, <span class="org-string">'Dw'</span>), gm.f, <span class="org-string">'Hz'</span>)))<span class="org-type">.^</span>2;
<pre class="src src-matlab">gm.psd_rv = gm.psd_gm.*abs(squeeze(freqresp(G('Vm', 'Dw'), gm.f, 'Hz'))).^2;
</pre>
</div>
@@ -355,8 +354,8 @@ Using the extracted transfer functions from the disturbance force to the relativ
This is done below.
</p>
<div class="org-src-container">
<pre class="src src-matlab">rz.psd_f = rz.pxsp_r<span class="org-type">./</span>abs(squeeze(freqresp(G(<span class="org-string">'Vm'</span>, <span class="org-string">'Frz'</span>), rz.f, <span class="org-string">'Hz'</span>)))<span class="org-type">.^</span>2;
tyz.psd_f = tyz.pxz_ty_r<span class="org-type">./</span>abs(squeeze(freqresp(G(<span class="org-string">'Vm'</span>, <span class="org-string">'Fty'</span>), tyz.f, <span class="org-string">'Hz'</span>)))<span class="org-type">.^</span>2;
<pre class="src src-matlab">rz.psd_f = rz.pxsp_r./abs(squeeze(freqresp(G('Vm', 'Frz'), rz.f, 'Hz'))).^2;
tyz.psd_f = tyz.pxz_ty_r./abs(squeeze(freqresp(G('Vm', 'Fty'), tyz.f, 'Hz'))).^2;
</pre>
</div>
@@ -394,9 +393,9 @@ The power spectral density of the relative motion is computed below and the resu
We can see that this is exactly the same as the Figure <a href="#org4c2c215">6</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">psd_gm_d = gm.psd_gm<span class="org-type">.*</span>abs(squeeze(freqresp(G(<span class="org-string">'Vm'</span>, <span class="org-string">'Dw'</span>)<span class="org-type">/</span>s, gm.f, <span class="org-string">'Hz'</span>)))<span class="org-type">.^</span>2;
psd_ty_d = tyz.psd_f<span class="org-type">.*</span>abs(squeeze(freqresp(G(<span class="org-string">'Vm'</span>, <span class="org-string">'Fty'</span>)<span class="org-type">/</span>s, tyz.f, <span class="org-string">'Hz'</span>)))<span class="org-type">.^</span>2;
psd_rz_d = rz.psd_f<span class="org-type">.*</span>abs(squeeze(freqresp(G(<span class="org-string">'Vm'</span>, <span class="org-string">'Frz'</span>)<span class="org-type">/</span>s, rz.f, <span class="org-string">'Hz'</span>)))<span class="org-type">.^</span>2;
<pre class="src src-matlab">psd_gm_d = gm.psd_gm.*abs(squeeze(freqresp(G('Vm', 'Dw')/s, gm.f, 'Hz'))).^2;
psd_ty_d = tyz.psd_f.*abs(squeeze(freqresp(G('Vm', 'Fty')/s, tyz.f, 'Hz'))).^2;
psd_rz_d = rz.psd_f.*abs(squeeze(freqresp(G('Vm', 'Frz')/s, rz.f, 'Hz'))).^2;
</pre>
</div>
@@ -419,13 +418,13 @@ The PSD of the disturbance force are now saved for further analysis.
<div class="org-src-container">
<pre class="src src-matlab">dist_f = struct();
dist_f.f = gm.f; <span class="org-comment">% Frequency Vector [Hz]</span>
dist_f.f = gm.f; % Frequency Vector [Hz]
dist_f.psd_gm = gm.psd_gm; <span class="org-comment">% Power Spectral Density of the Ground Motion [m^2/Hz]</span>
dist_f.psd_ty = tyz.psd_f; <span class="org-comment">% Power Spectral Density of the force induced by the Ty stage in the Z direction [N^2/Hz]</span>
dist_f.psd_rz = rz.psd_f; <span class="org-comment">% Power Spectral Density of the force induced by the Rz stage in the Z direction [N^2/Hz]</span>
dist_f.psd_gm = gm.psd_gm; % Power Spectral Density of the Ground Motion [m^2/Hz]
dist_f.psd_ty = tyz.psd_f; % Power Spectral Density of the force induced by the Ty stage in the Z direction [N^2/Hz]
dist_f.psd_rz = rz.psd_f; % Power Spectral Density of the force induced by the Rz stage in the Z direction [N^2/Hz]
save(<span class="org-string">'./mat/dist_psd.mat'</span>, <span class="org-string">'dist_f'</span>);
save('./mat/dist_psd.mat', 'dist_f');
</pre>
</div>
</div>
@@ -439,7 +438,7 @@ Let&rsquo;s initialize the time domain disturbances and load them.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeDisturbances();
dist = load(<span class="org-string">'nass_disturbances.mat'</span>);
dist = load('nass_disturbances.mat');
</pre>
</div>
@@ -482,22 +481,22 @@ initializeMirror();
The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeNanoHexapod(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>);
initializeSample(<span class="org-string">'mass'</span>, 1);
<pre class="src src-matlab">initializeNanoHexapod('type', 'rigid');
initializeSample('mass', 1);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">initializeReferences();
initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">false</span>);
initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'all'</span>);
initializeController('type', 'open-loop');
initializeSimscapeConfiguration('gravity', false);
initializeLoggingConfiguration('log', 'all');
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'mat/conf_simulink.mat'</span>);
<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'2'</span>);
<pre class="src src-matlab">load('mat/conf_simulink.mat');
set_param(conf_simulink, 'StopTime', '2');
</pre>
</div>
</div>
@@ -510,8 +509,8 @@ initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span clas
No disturbances:
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeDisturbances(<span class="org-string">'enable'</span>, <span class="org-constant">false</span>);
<span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
<pre class="src src-matlab">initializeDisturbances('enable', false);
sim('nass_model');
sim_no = simout;
</pre>
</div>
@@ -520,8 +519,8 @@ sim_no = simout;
Ground Motion:
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeDisturbances(<span class="org-string">'Fty_x'</span>, <span class="org-constant">false</span>, <span class="org-string">'Fty_z'</span>, <span class="org-constant">false</span>, <span class="org-string">'Frz_z'</span>, <span class="org-constant">false</span>);
<span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
<pre class="src src-matlab">initializeDisturbances('Fty_x', false, 'Fty_z', false, 'Frz_z', false);
sim('nass_model');
sim_gm = simout;
</pre>
</div>
@@ -530,8 +529,8 @@ sim_gm = simout;
Translation Stage Vibrations:
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeDisturbances(<span class="org-string">'Dwx'</span>, <span class="org-constant">false</span>, <span class="org-string">'Dwy'</span>, <span class="org-constant">false</span>, <span class="org-string">'Dwz'</span>, <span class="org-constant">false</span>, <span class="org-string">'Frz_z'</span>, <span class="org-constant">false</span>);
<span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
<pre class="src src-matlab">initializeDisturbances('Dwx', false, 'Dwy', false, 'Dwz', false, 'Frz_z', false);
sim('nass_model');
sim_ty = simout;
</pre>
</div>
@@ -540,8 +539,8 @@ sim_ty = simout;
Rotation Stage Vibrations:
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeDisturbances(<span class="org-string">'Dwx'</span>, <span class="org-constant">false</span>, <span class="org-string">'Dwy'</span>, <span class="org-constant">false</span>, <span class="org-string">'Dwz'</span>, <span class="org-constant">false</span>, <span class="org-string">'Fty_x'</span>, <span class="org-constant">false</span>, <span class="org-string">'Fty_z'</span>, <span class="org-constant">false</span>);
<span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
<pre class="src src-matlab">initializeDisturbances('Dwx', false, 'Dwy', false, 'Dwz', false, 'Fty_x', false, 'Fty_z', false);
sim('nass_model');
sim_rz = simout;
</pre>
</div>
@@ -567,7 +566,7 @@ Let&rsquo;s now compare the effect of those perturbations on the position error
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-04-17 ven. 09:35</p>
<p class="date">Created: 2020-09-01 mar. 13:48</p>
</div>
</body>
</html>