Add analysis of disturbance: extract PSD
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<div id="org-div-home-and-up">
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<a accesskey="h" href="../index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Simscape Uniaxial Model</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#orga9da337">1. Identification</a></li>
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<li><a href="#org0c4c66f">2. Sensitivity to Disturbances</a></li>
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<li><a href="#orge0b60ba">3. Power Spectral Density of the effect of the disturbances</a></li>
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<li><a href="#orgf444bc6">4. Compute the Power Spectral Density of the disturbance force</a></li>
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<li><a href="#org9df3e1a">5. Noise Budget</a></li>
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<li><a href="#orgb1f811d">6. Save</a></li>
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</ul>
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</div>
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</div>
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<p>
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The goal here is to extract the Power Spectral Density of the sources of perturbation.
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</p>
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<p>
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The sources of perturbations are:
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</p>
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<ul class="org-ul">
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<li>Ground Motion</li>
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<li>Parasitic forces applied in the system when scanning with the Translation Stage and the Spindle.
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These forces can be due to imperfect guiding for instance.</li>
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</ul>
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<p>
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Because we cannot measure directly the perturbation forces, we have the measure the effect of those perturbations on the system (in terms of velocity for instance using geophones) and then, using a model, compute the forces that induced such velocity.
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</p>
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<ul class="org-ul">
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<li>Section <a href="#orge6f61b6">1</a>: transfer functions from the disturbance forces to the relative velocity of the hexapod with respect to the granite are computed using the Simscape Model representing the experimental setup</li>
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</ul>
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<div id="outline-container-orga9da337" class="outline-2">
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<h2 id="orga9da337"><span class="section-number-2">1</span> Identification</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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<a id="orge6f61b6"></a>
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
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options = linearizeOptions;
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options.SampleTime = <span class="org-highlight-numbers-number">0</span>;
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
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mdl = <span class="org-string">'sim_micro_station_disturbances'</span>;
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Micro-Hexapod</span></span>
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<span class="org-comment">% Input/Output definition</span>
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io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dw'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Ground Motion</span>
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io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fty'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Parasitic force Ty</span>
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io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Frz'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Parasitic force Rz</span>
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io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dgm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Absolute motion - Granite</span>
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io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dhm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Absolute Motion - Hexapod</span>
|
||||
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Vm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Relative Velocity hexapod/granite</span>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-comment">% Run the linearization</span>
|
||||
G = linearize<span class="org-rainbow-delimiters-depth-1">(</span>mdl, io, <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
|
||||
<span class="org-comment">% Input/Output names</span>
|
||||
G.InputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class="org-string">'Dw'</span>, <span class="org-string">'Fty'</span>, <span class="org-string">'Frz'</span><span class="org-rainbow-delimiters-depth-1">}</span>;
|
||||
G.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class="org-string">'Dgm'</span>, <span class="org-string">'Dhm'</span>, <span class="org-string">'Vm'</span><span class="org-rainbow-delimiters-depth-1">}</span>;
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0c4c66f" class="outline-2">
|
||||
<h2 id="org0c4c66f"><span class="section-number-2">2</span> Sensitivity to Disturbances</h2>
|
||||
<div class="outline-text-2" id="text-2">
|
||||
<p>
|
||||
<a id="org04b950a"></a>
|
||||
</p>
|
||||
|
||||
<div id="org3e3443b" class="figure">
|
||||
<p><img src="figs/sensitivity_dist_gm.png" alt="sensitivity_dist_gm.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 1: </span>Sensitivity to Ground Motion (<a href="./figs/sensitivity_dist_gm.png">png</a>, <a href="./figs/sensitivity_dist_gm.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
<div id="orgd9fb712" class="figure">
|
||||
<p><img src="figs/sensitivity_dist_fty.png" alt="sensitivity_dist_fty.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 2: </span>Sensitivity to vertical forces applied by the Ty stage (<a href="./figs/sensitivity_dist_fty.png">png</a>, <a href="./figs/sensitivity_dist_fty.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
<div id="orgf7d4761" class="figure">
|
||||
<p><img src="figs/sensitivity_dist_frz.png" alt="sensitivity_dist_frz.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 3: </span>Sensitivity to vertical forces applied by the Rz stage (<a href="./figs/sensitivity_dist_frz.png">png</a>, <a href="./figs/sensitivity_dist_frz.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orge0b60ba" class="outline-2">
|
||||
<h2 id="orge0b60ba"><span class="section-number-2">3</span> Power Spectral Density of the effect of the disturbances</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
<p>
|
||||
<a id="org7ab0a1d"></a>
|
||||
The PSD of the relative velocity between the hexapod and the marble in \([(m/s)^2/Hz]\) are loaded for the following sources of disturbance:
|
||||
</p>
|
||||
<ul class="org-ul">
|
||||
<li>Slip Ring Rotation</li>
|
||||
<li>Scan of the translation stage (effect in the vertical direction and in the horizontal direction)</li>
|
||||
</ul>
|
||||
|
||||
<p>
|
||||
Also, the Ground Motion is measured.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">gm = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./disturbances/mat/psd_gm.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'psd_gm'</span>, <span class="org-string">'psd_gv'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
rz = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./disturbances/mat/pxsp_r.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'pxsp_r'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
tyz = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./disturbances/mat/pxz_ty_r.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'pxz_ty_r'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
tyx = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./disturbances/mat/pxe_ty_r.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'pxe_ty_r'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
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<span class="org-rainbow-delimiters-depth-1">(</span>squeeze<span class="org-rainbow-delimiters-depth-2">(</span>freqresp<span class="org-rainbow-delimiters-depth-3">(</span>G<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-string">'Vm'</span>, <span class="org-string">'Dw'</span><span class="org-rainbow-delimiters-depth-4">)</span>, gm.f, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The Power Spectral Density of the relative motion/velocity of the hexapod with respect to the granite are shown in figures <a href="#org048378a">4</a> and <a href="#orge887351">5</a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The Cumulative Amplitude Spectrum of the relative motion is shown in figure <a href="#orge3e2cf9">6</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org048378a" class="figure">
|
||||
<p><img src="figs/dist_effect_relative_velocity.png" alt="dist_effect_relative_velocity.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 4: </span>Amplitude Spectral Density of the relative velocity of the hexapod with respect to the granite due to different sources of perturbation (<a href="./figs/dist_effect_relative_velocity.png">png</a>, <a href="./figs/dist_effect_relative_velocity.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
<div id="orge887351" class="figure">
|
||||
<p><img src="figs/dist_effect_relative_motion.png" alt="dist_effect_relative_motion.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the relative displacement of the hexapod with respect to the granite due to different sources of perturbation (<a href="./figs/dist_effect_relative_motion.png">png</a>, <a href="./figs/dist_effect_relative_motion.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orge3e2cf9" class="figure">
|
||||
<p><img src="figs/dist_effect_relative_motion_cas.png" alt="dist_effect_relative_motion_cas.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 6: </span>Cumulative Amplitude Spectrum of the relative motion due to different sources of perturbation (<a href="./figs/dist_effect_relative_motion_cas.png">png</a>, <a href="./figs/dist_effect_relative_motion_cas.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf444bc6" class="outline-2">
|
||||
<h2 id="orgf444bc6"><span class="section-number-2">4</span> Compute the Power Spectral Density of the disturbance force</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
<p>
|
||||
<a id="orgf3934b5"></a>
|
||||
</p>
|
||||
|
||||
<p>
|
||||
Now, from the extracted transfer functions from the disturbance force to the relative motion of the hexapod with respect to the granite (section <a href="#org04b950a">2</a>) and from the measured PSD of the relative motion (section <a href="#org7ab0a1d">3</a>), we can compute the PSD of the disturbance force.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">rz.psd_f = rz.pxsp_r<span class="org-type">./</span>abs<span class="org-rainbow-delimiters-depth-1">(</span>squeeze<span class="org-rainbow-delimiters-depth-2">(</span>freqresp<span class="org-rainbow-delimiters-depth-3">(</span>G<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-string">'Vm'</span>, <span class="org-string">'Frz'</span><span class="org-rainbow-delimiters-depth-4">)</span>, rz.f, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span>;
|
||||
tyz.psd_f = tyz.pxz_ty_r<span class="org-type">./</span>abs<span class="org-rainbow-delimiters-depth-1">(</span>squeeze<span class="org-rainbow-delimiters-depth-2">(</span>freqresp<span class="org-rainbow-delimiters-depth-3">(</span>G<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-string">'Vm'</span>, <span class="org-string">'Fty'</span><span class="org-rainbow-delimiters-depth-4">)</span>, tyz.f, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgfc0e496" class="figure">
|
||||
<p><img src="figs/dist_force_psd.png" alt="dist_force_psd.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </span>Amplitude Spectral Density of the disturbance force (<a href="./figs/dist_force_psd.png">png</a>, <a href="./figs/dist_force_psd.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org9df3e1a" class="outline-2">
|
||||
<h2 id="org9df3e1a"><span class="section-number-2">5</span> Noise Budget</h2>
|
||||
<div class="outline-text-2" id="text-5">
|
||||
<p>
|
||||
Now, from the compute spectral density of the disturbance sources, we can compute the resulting relative motion of the Hexapod with respect to the granite using the model.
|
||||
We should verify that this is coherent with the measurements.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org8995b51" class="figure">
|
||||
<p><img src="figs/psd_effect_dist_verif.png" alt="psd_effect_dist_verif.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 8: </span>Computed Effect of the disturbances on the relative displacement hexapod/granite (<a href="./figs/psd_effect_dist_verif.png">png</a>, <a href="./figs/psd_effect_dist_verif.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
<div id="org4921ccd" class="figure">
|
||||
<p><img src="figs/cas_computed_relative_displacement.png" alt="cas_computed_relative_displacement.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 9: </span>CAS of the total Relative Displacement due to all considered sources of perturbation (<a href="./figs/cas_computed_relative_displacement.png">png</a>, <a href="./figs/cas_computed_relative_displacement.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb1f811d" class="outline-2">
|
||||
<h2 id="orgb1f811d"><span class="section-number-2">6</span> Save</h2>
|
||||
<div class="outline-text-2" id="text-6">
|
||||
<p>
|
||||
The PSD of the disturbance force are now saved for further noise budgeting when control is applied.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">dist_f = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
|
||||
dist_f.f = gm.f; <span class="org-comment">% Frequency Vector [Hz]</span>
|
||||
dist_f.psd_gm = gm.psd_gm; % Power Spectral Density of the Ground Motion [m<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span>Hz]
|
||||
dist_f.psd_ty = tyz.psd_f; % Power Spectral Density of the force induced by the Ty stage in the Z direction [N<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span>Hz]
|
||||
dist_f.psd_rz = rz.psd_f; % Power Spectral Density of the force induced by the Rz stage in the Z direction [N<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span>Hz]
|
||||
|
||||
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./disturbances/mat/disturbance-forces.mat'</span>, <span class="org-string">'dist_f'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2019-11-04 lun. 15:46</p>
|
||||
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
379
disturbances/index.org
Normal file
379
disturbances/index.org
Normal file
@ -0,0 +1,379 @@
|
||||
#+TITLE: Simscape Uniaxial Model
|
||||
:DRAWER:
|
||||
#+STARTUP: overview
|
||||
|
||||
#+LANGUAGE: en
|
||||
#+EMAIL: dehaeze.thomas@gmail.com
|
||||
#+AUTHOR: Dehaeze Thomas
|
||||
|
||||
#+HTML_LINK_HOME: ../index.html
|
||||
#+HTML_LINK_UP: ../index.html
|
||||
|
||||
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/>
|
||||
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/>
|
||||
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/zenburn.css"/>
|
||||
#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.min.js"></script>
|
||||
#+HTML_HEAD: <script type="text/javascript" src="../js/bootstrap.min.js"></script>
|
||||
#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.stickytableheaders.min.js"></script>
|
||||
#+HTML_HEAD: <script type="text/javascript" src="../js/readtheorg.js"></script>
|
||||
|
||||
#+HTML_MATHJAX: align: center tagside: right font: TeX
|
||||
|
||||
#+PROPERTY: header-args:matlab :session *MATLAB*
|
||||
#+PROPERTY: header-args:matlab+ :comments org
|
||||
#+PROPERTY: header-args:matlab+ :results none
|
||||
#+PROPERTY: header-args:matlab+ :exports both
|
||||
#+PROPERTY: header-args:matlab+ :eval no-export
|
||||
#+PROPERTY: header-args:matlab+ :output-dir figs
|
||||
#+PROPERTY: header-args:matlab+ :tangle matlab/modal_frf_coh.m
|
||||
#+PROPERTY: header-args:matlab+ :mkdirp yes
|
||||
|
||||
#+PROPERTY: header-args:shell :eval no-export
|
||||
|
||||
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/}{config.tex}")
|
||||
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
|
||||
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
|
||||
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
|
||||
#+PROPERTY: header-args:latex+ :results raw replace :buffer no
|
||||
#+PROPERTY: header-args:latex+ :eval no-export
|
||||
#+PROPERTY: header-args:latex+ :exports both
|
||||
#+PROPERTY: header-args:latex+ :mkdirp yes
|
||||
#+PROPERTY: header-args:latex+ :output-dir figs
|
||||
:END:
|
||||
|
||||
* Introduction :ignore:
|
||||
The goal here is to extract the Power Spectral Density of the sources of perturbation.
|
||||
|
||||
The sources of perturbations are:
|
||||
- Ground Motion
|
||||
- Parasitic forces applied in the system when scanning with the Translation Stage and the Spindle.
|
||||
These forces can be due to imperfect guiding for instance.
|
||||
|
||||
Because we cannot measure directly the perturbation forces, we have the measure the effect of those perturbations on the system (in terms of velocity for instance using geophones) and then, using a model, compute the forces that induced such velocity.
|
||||
|
||||
- Section [[sec:identification]]: transfer functions from the disturbance forces to the relative velocity of the hexapod with respect to the granite are computed using the Simscape Model representing the experimental setup
|
||||
|
||||
* Matlab Init :noexport:ignore:
|
||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||
<<matlab-dir>>
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none :results silent :noweb yes
|
||||
<<matlab-init>>
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no
|
||||
simulinkproject('../');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
open 'simscape/sim_micro_station_disturbances.slx'
|
||||
#+end_src
|
||||
|
||||
* Identification
|
||||
<<sec:identification>>
|
||||
|
||||
#+begin_src matlab
|
||||
%% Options for Linearized
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
%% Name of the Simulink File
|
||||
mdl = 'sim_micro_station_disturbances';
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
%% Micro-Hexapod
|
||||
% Input/Output definition
|
||||
io(1) = linio([mdl, '/Dw'], 1, 'input'); % Ground Motion
|
||||
io(2) = linio([mdl, '/Fty'], 1, 'input'); % Parasitic force Ty
|
||||
io(3) = linio([mdl, '/Frz'], 1, 'input'); % Parasitic force Rz
|
||||
io(4) = linio([mdl, '/Dgm'], 1, 'output'); % Absolute motion - Granite
|
||||
io(5) = linio([mdl, '/Dhm'], 1, 'output'); % Absolute Motion - Hexapod
|
||||
io(6) = linio([mdl, '/Vm'], 1, 'output'); % Relative Velocity hexapod/granite
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
% Run the linearization
|
||||
G = linearize(mdl, io, 0);
|
||||
|
||||
% Input/Output names
|
||||
G.InputName = {'Dw', 'Fty', 'Frz'};
|
||||
G.OutputName = {'Dgm', 'Dhm', 'Vm'};
|
||||
#+end_src
|
||||
|
||||
* Sensitivity to Disturbances
|
||||
<<sec:sensitivity_disturbances>>
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
title('$D_w$ to $D$');
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G('Vm', 'Dw')/s, freqs, 'Hz'))), 'k-');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]');
|
||||
#+end_src
|
||||
|
||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/sensitivity_dist_gm.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:sensitivity_dist_gm
|
||||
#+CAPTION: Sensitivity to Ground Motion ([[./figs/sensitivity_dist_gm.png][png]], [[./figs/sensitivity_dist_gm.pdf][pdf]])
|
||||
[[file:figs/sensitivity_dist_gm.png]]
|
||||
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
title('$F_{ty}$ to $D$');
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G('Vm', 'Fty')/s, freqs, 'Hz'))), 'k-');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||
#+end_src
|
||||
|
||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/sensitivity_dist_fty.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:sensitivity_dist_fty
|
||||
#+CAPTION: Sensitivity to vertical forces applied by the Ty stage ([[./figs/sensitivity_dist_fty.png][png]], [[./figs/sensitivity_dist_fty.pdf][pdf]])
|
||||
[[file:figs/sensitivity_dist_fty.png]]
|
||||
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
title('$F_{rz}$ to $D$');
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G('Vm', 'Frz')/s, freqs, 'Hz'))), 'k-');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||
#+end_src
|
||||
|
||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/sensitivity_dist_frz.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:sensitivity_dist_frz
|
||||
#+CAPTION: Sensitivity to vertical forces applied by the Rz stage ([[./figs/sensitivity_dist_frz.png][png]], [[./figs/sensitivity_dist_frz.pdf][pdf]])
|
||||
[[file:figs/sensitivity_dist_frz.png]]
|
||||
|
||||
* Power Spectral Density of the effect of the disturbances
|
||||
<<sec:psd_dist>>
|
||||
The PSD of the relative velocity between the hexapod and the marble in $[(m/s)^2/Hz]$ are loaded for the following sources of disturbance:
|
||||
- Slip Ring Rotation
|
||||
- Scan of the translation stage (effect in the vertical direction and in the horizontal direction)
|
||||
|
||||
Also, the Ground Motion is measured.
|
||||
|
||||
#+begin_src matlab
|
||||
gm = load('./disturbances/mat/psd_gm.mat', 'f', 'psd_gm', 'psd_gv');
|
||||
rz = load('./disturbances/mat/pxsp_r.mat', 'f', 'pxsp_r');
|
||||
tyz = load('./disturbances/mat/pxz_ty_r.mat', 'f', 'pxz_ty_r');
|
||||
tyx = load('./disturbances/mat/pxe_ty_r.mat', 'f', 'pxe_ty_r');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
gm.f = gm.f(2:end);
|
||||
rz.f = rz.f(2:end);
|
||||
tyz.f = tyz.f(2:end);
|
||||
tyx.f = tyx.f(2:end);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
gm.psd_gm = gm.psd_gm(2:end); % PSD of Ground Motion [m^2/Hz]
|
||||
gm.psd_gv = gm.psd_gv(2:end); % PSD of Ground Velocity [(m/s)^2/Hz]
|
||||
rz.pxsp_r = rz.pxsp_r(2:end); % PSD of Relative Velocity [(m/s)^2/Hz]
|
||||
tyz.pxz_ty_r = tyz.pxz_ty_r(2:end); % PSD of Relative Velocity [(m/s)^2/Hz]
|
||||
tyx.pxe_ty_r = tyx.pxe_ty_r(2:end); % PSD of Relative Velocity [(m/s)^2/Hz]
|
||||
#+end_src
|
||||
|
||||
We now compute the relative velocity between the hexapod and the granite due to ground motion.
|
||||
#+begin_src matlab
|
||||
gm.psd_rv = gm.psd_gm.*abs(squeeze(freqresp(G('Vm', 'Dw'), gm.f, 'Hz'))).^2;
|
||||
#+end_src
|
||||
|
||||
The Power Spectral Density of the relative motion/velocity of the hexapod with respect to the granite are shown in figures [[fig:dist_effect_relative_velocity]] and [[fig:dist_effect_relative_motion]].
|
||||
|
||||
The Cumulative Amplitude Spectrum of the relative motion is shown in figure [[fig:dist_effect_relative_motion_cas]].
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
hold on;
|
||||
plot(gm.f, sqrt(gm.psd_rv), 'DisplayName', 'Ground Motion');
|
||||
plot(tyz.f, sqrt(tyz.pxz_ty_r), 'DisplayName', 'Ty');
|
||||
plot(rz.f, sqrt(rz.pxsp_r), 'DisplayName', 'Rz');
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
|
||||
legend('Location', 'southwest');
|
||||
xlim([2, 500]);
|
||||
#+end_src
|
||||
|
||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/dist_effect_relative_velocity.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:dist_effect_relative_velocity
|
||||
#+CAPTION: Amplitude Spectral Density of the relative velocity of the hexapod with respect to the granite due to different sources of perturbation ([[./figs/dist_effect_relative_velocity.png][png]], [[./figs/dist_effect_relative_velocity.pdf][pdf]])
|
||||
[[file:figs/dist_effect_relative_velocity.png]]
|
||||
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
hold on;
|
||||
plot(gm.f, sqrt(gm.psd_rv)./(2*pi*gm.f), 'DisplayName', 'Ground Motion');
|
||||
plot(tyz.f, sqrt(tyz.pxz_ty_r)./(2*pi*tyz.f), 'DisplayName', 'Ty');
|
||||
plot(rz.f, sqrt(rz.pxsp_r)./(2*pi*rz.f), 'DisplayName', 'Rz');
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('ASD of the displacement $\left[\frac{m}{\sqrt{Hz}}\right]$')
|
||||
legend('Location', 'southwest');
|
||||
xlim([2, 500]);
|
||||
#+end_src
|
||||
|
||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/dist_effect_relative_motion.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:dist_effect_relative_motion
|
||||
#+CAPTION: Amplitude Spectral Density of the relative displacement of the hexapod with respect to the granite due to different sources of perturbation ([[./figs/dist_effect_relative_motion.png][png]], [[./figs/dist_effect_relative_motion.pdf][pdf]])
|
||||
[[file:figs/dist_effect_relative_motion.png]]
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
hold on;
|
||||
plot(gm.f, flip(sqrt(-cumtrapz(flip(gm.f), flip(gm.psd_rv./((2*pi*gm.f).^2))))), 'DisplayName', 'Ground Motion');
|
||||
plot(tyz.f, flip(sqrt(-cumtrapz(flip(tyz.f), flip(tyz.pxz_ty_r./((2*pi*tyz.f).^2))))), 'DisplayName', 'Ty');
|
||||
plot(rz.f, flip(sqrt(-cumtrapz(flip(rz.f), flip(rz.pxsp_r./((2*pi*rz.f).^2))))), 'DisplayName', 'Rz');
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('CAS of the relative displacement $[m]$')
|
||||
legend('Location', 'southwest');
|
||||
xlim([2, 500]); ylim([1e-11, 1e-6]);
|
||||
#+end_src
|
||||
|
||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/dist_effect_relative_motion_cas.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:dist_effect_relative_motion_cas
|
||||
#+CAPTION: Cumulative Amplitude Spectrum of the relative motion due to different sources of perturbation ([[./figs/dist_effect_relative_motion_cas.png][png]], [[./figs/dist_effect_relative_motion_cas.pdf][pdf]])
|
||||
[[file:figs/dist_effect_relative_motion_cas.png]]
|
||||
|
||||
* Compute the Power Spectral Density of the disturbance force
|
||||
<<sec:psd_force_dist>>
|
||||
|
||||
Now, from the extracted transfer functions from the disturbance force to the relative motion of the hexapod with respect to the granite (section [[sec:sensitivity_disturbances]]) and from the measured PSD of the relative motion (section [[sec:psd_dist]]), we can compute the PSD of the disturbance force.
|
||||
|
||||
#+begin_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;
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
hold on;
|
||||
set(gca,'ColorOrderIndex',2);
|
||||
plot(tyz.f, sqrt(tyz.psd_f), 'DisplayName', 'F - Ty');
|
||||
plot(rz.f, sqrt(rz.psd_f), 'DisplayName', 'F - Rz');
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('ASD of the disturbance force $\left[\frac{F}{\sqrt{Hz}}\right]$')
|
||||
legend('Location', 'southwest');
|
||||
xlim([2, 500]);
|
||||
#+end_src
|
||||
|
||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/dist_force_psd.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:dist_force_psd
|
||||
#+CAPTION: Amplitude Spectral Density of the disturbance force ([[./figs/dist_force_psd.png][png]], [[./figs/dist_force_psd.pdf][pdf]])
|
||||
[[file:figs/dist_force_psd.png]]
|
||||
|
||||
* Noise Budget
|
||||
Now, from the compute spectral density of the disturbance sources, we can compute the resulting relative motion of the Hexapod with respect to the granite using the model.
|
||||
We should verify that this is coherent with the measurements.
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
% Power Spectral Density of the relative Displacement
|
||||
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;
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
hold on;
|
||||
plot(gm.f, sqrt(psd_gm_d), 'DisplayName', 'Ground Motion');
|
||||
plot(tyz.f, sqrt(psd_ty_d), 'DisplayName', 'Ty');
|
||||
plot(rz.f, sqrt(psd_rz_d), 'DisplayName', 'Rz');
|
||||
plot(rz.f, sqrt(psd_gm_d + psd_ty_d + psd_rz_d), 'k--', 'DisplayName', 'tot');
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('ASD of the relative motion $\left[\frac{m}{\sqrt{Hz}}\right]$')
|
||||
legend('Location', 'southwest');
|
||||
xlim([2, 500]);
|
||||
#+end_src
|
||||
|
||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/psd_effect_dist_verif.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:psd_effect_dist_verif
|
||||
#+CAPTION: Computed Effect of the disturbances on the relative displacement hexapod/granite ([[./figs/psd_effect_dist_verif.png][png]], [[./figs/psd_effect_dist_verif.pdf][pdf]])
|
||||
[[file:figs/psd_effect_dist_verif.png]]
|
||||
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
hold on;
|
||||
plot(gm.f, flip(sqrt(-cumtrapz(flip(gm.f), flip(psd_gm_d)))), 'DisplayName', 'Ground Motion');
|
||||
plot(gm.f, flip(sqrt(-cumtrapz(flip(gm.f), flip(psd_ty_d)))), 'DisplayName', 'Ty');
|
||||
plot(gm.f, flip(sqrt(-cumtrapz(flip(gm.f), flip(psd_rz_d)))), 'DisplayName', 'Rz');
|
||||
plot(gm.f, flip(sqrt(-cumtrapz(flip(gm.f), flip(psd_gm_d + psd_ty_d + psd_rz_d)))), 'k-', 'DisplayName', 'tot');
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Cumulative Amplitude Spectrum [m]')
|
||||
legend('location', 'northeast');
|
||||
xlim([2, 500]); ylim([1e-11, 1e-6]);
|
||||
#+end_src
|
||||
|
||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/cas_computed_relative_displacement.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:cas_computed_relative_displacement
|
||||
#+CAPTION: CAS of the total Relative Displacement due to all considered sources of perturbation ([[./figs/cas_computed_relative_displacement.png][png]], [[./figs/cas_computed_relative_displacement.pdf][pdf]])
|
||||
[[file:figs/cas_computed_relative_displacement.png]]
|
||||
|
||||
* Save
|
||||
The PSD of the disturbance force are now saved for further noise budgeting when control is applied.
|
||||
|
||||
#+begin_src matlab
|
||||
dist_f = struct();
|
||||
dist_f.f = gm.f; % Frequency Vector [Hz]
|
||||
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('./disturbances/mat/disturbance-forces.mat', 'dist_f');
|
||||
#+end_src
|
||||
BIN
disturbances/mat/dist_psd.mat
Normal file
BIN
disturbances/mat/dist_psd.mat
Normal file
Binary file not shown.
BIN
disturbances/mat/psd_gm.mat
Normal file
BIN
disturbances/mat/psd_gm.mat
Normal file
Binary file not shown.
BIN
disturbances/mat/pxe_ty_r.mat
Normal file
BIN
disturbances/mat/pxe_ty_r.mat
Normal file
Binary file not shown.
BIN
disturbances/mat/pxsp_r.mat
Normal file
BIN
disturbances/mat/pxsp_r.mat
Normal file
Binary file not shown.
BIN
disturbances/mat/pxz_ty_r.mat
Normal file
BIN
disturbances/mat/pxz_ty_r.mat
Normal file
Binary file not shown.
BIN
disturbances/mat/tf_dist.mat
Normal file
BIN
disturbances/mat/tf_dist.mat
Normal file
Binary file not shown.
BIN
figs/cas_computed_relative_displacement.png
Normal file
BIN
figs/cas_computed_relative_displacement.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 118 KiB |
BIN
figs/dist_effect_relative_motion.png
Normal file
BIN
figs/dist_effect_relative_motion.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 178 KiB |
BIN
figs/dist_effect_relative_motion_cas.png
Normal file
BIN
figs/dist_effect_relative_motion_cas.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 109 KiB |
BIN
figs/dist_effect_relative_velocity.png
Normal file
BIN
figs/dist_effect_relative_velocity.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 174 KiB |
BIN
figs/dist_force_psd.png
Normal file
BIN
figs/dist_force_psd.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 155 KiB |
BIN
figs/identification_comp_bot_stages.png
Normal file
BIN
figs/identification_comp_bot_stages.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 159 KiB |
BIN
figs/identification_comp_mid_stages.png
Normal file
BIN
figs/identification_comp_mid_stages.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 156 KiB |
BIN
figs/identification_comp_top_stages.png
Normal file
BIN
figs/identification_comp_top_stages.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 73 KiB |
Loading…
Reference in New Issue
Block a user