Analysis of FRF data (DVF + IFF)
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@article{souleille18_concep_activ_mount_space_applic,
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author = {Souleille, Adrien and Lampert, Thibault and Lafarga, V and
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Hellegouarch, Sylvain and Rondineau, Alan and Rodrigues,
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Gon{\c{c}}alo and Collette, Christophe},
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title = {A Concept of Active Mount for Space Applications},
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journal = {CEAS Space Journal},
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volume = 10,
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number = 2,
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pages = {157--165},
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year = 2018,
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publisher = {Springer},
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}
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@phdthesis{poel10_explor_activ_hard_mount_vibrat,
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author = {van der Poel, Gerrit Wijnand},
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doi = {10.3990/1.9789036530163},
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isbn = {978-90-365-3016-3},
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keywords = {parallel robot},
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school = {University of Twente},
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title = {An Exploration of Active Hard Mount Vibration Isolation for
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Precision Equipment},
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url = {https://doi.org/10.3990/1.9789036530163},
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year = 2010,
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}
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<head>
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<!-- 2021-06-07 lun. 19:00 -->
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<!-- 2021-06-08 mar. 21:51 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Nano-Hexapod - Test Bench</title>
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<title>Nano-Hexapod - Test Bench</title>
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<meta name="author" content="Dehaeze Thomas" />
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<meta name="author" content="Dehaeze Thomas" />
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@ -22,7 +22,17 @@
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<h2>Table of Contents</h2>
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<div id="text-table-of-contents">
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<ul>
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<ul>
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<li><a href="#orgc63308d">1. Test-Bench Description</a></li>
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<li><a href="#org401a850">1. Test-Bench Description</a></li>
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<li><a href="#org32d67fc">2. Encoders fixed to the Struts</a>
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<ul>
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<li><a href="#org332ecf2">2.1. Introduction</a></li>
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<li><a href="#orgf904215">2.2. Load Data</a></li>
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<li><a href="#org3689d6b">2.3. Spectral Analysis - Setup</a></li>
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<li><a href="#org9ac5c69">2.4. DVF Plant</a></li>
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<li><a href="#org4f1737c">2.5. IFF Plant</a></li>
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<li><a href="#org4238e67">2.6. Jacobian</a></li>
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</ul>
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</li>
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</ul>
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</ul>
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</div>
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</div>
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</div>
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</div>
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@ -30,10 +40,10 @@
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<p>This report is also available as a <a href="./test-bench-nano-hexapod.pdf">pdf</a>.</p>
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<p>This report is also available as a <a href="./test-bench-nano-hexapod.pdf">pdf</a>.</p>
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<hr>
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<hr>
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<div id="outline-container-orgc63308d" class="outline-2">
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<div id="outline-container-org401a850" class="outline-2">
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<h2 id="orgc63308d"><span class="section-number-2">1</span> Test-Bench Description</h2>
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<h2 id="org401a850"><span class="section-number-2">1</span> Test-Bench Description</h2>
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<div class="outline-text-2" id="text-1">
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<div class="outline-text-2" id="text-1">
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<div class="note" id="org060848e">
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<div class="note" id="orgdb43d80">
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<p>
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<p>
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Here are the documentation of the equipment used for this test bench:
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Here are the documentation of the equipment used for this test bench:
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</p>
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</p>
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@ -46,12 +56,202 @@ Here are the documentation of the equipment used for this test bench:
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</ul>
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</ul>
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</div>
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</div>
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<div id="org00dd2c1" class="figure">
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<p><img src="figs/IMG_20210608_152917.jpg" alt="IMG_20210608_152917.jpg" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Nano-Hexapod</p>
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</div>
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<div id="org0f5d79a" class="figure">
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<p><img src="figs/IMG_20210608_154722.jpg" alt="IMG_20210608_154722.jpg" />
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</p>
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<p><span class="figure-number">Figure 2: </span>Nano-Hexapod and the control electronics</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org32d67fc" class="outline-2">
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<h2 id="org32d67fc"><span class="section-number-2">2</span> Encoders fixed to the Struts</h2>
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<div class="outline-text-2" id="text-2">
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</div>
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<div id="outline-container-org332ecf2" class="outline-3">
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<h3 id="org332ecf2"><span class="section-number-3">2.1</span> Introduction</h3>
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</div>
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<div id="outline-container-orgf904215" class="outline-3">
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<h3 id="orgf904215"><span class="section-number-3">2.2</span> Load Data</h3>
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<div class="outline-text-3" id="text-2-2">
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<div class="org-src-container">
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<pre class="src src-matlab">meas_data_lf = {};
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<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:6</span>
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meas_data_lf(<span class="org-constant">i</span>) = {load(sprintf(<span class="org-string">'mat/frf_data_exc_strut_%i_noise_lf.mat'</span>, <span class="org-constant">i</span>), <span class="org-string">'t'</span>, <span class="org-string">'Va'</span>, <span class="org-string">'Vs'</span>, <span class="org-string">'de'</span>)};
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meas_data_hf(<span class="org-constant">i</span>) = {load(sprintf(<span class="org-string">'mat/frf_data_exc_strut_%i_noise_hf.mat'</span>, <span class="org-constant">i</span>), <span class="org-string">'t'</span>, <span class="org-string">'Va'</span>, <span class="org-string">'Vs'</span>, <span class="org-string">'de'</span>)};
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<span class="org-keyword">end</span>
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-org3689d6b" class="outline-3">
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<h3 id="org3689d6b"><span class="section-number-3">2.3</span> Spectral Analysis - Setup</h3>
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<div class="outline-text-3" id="text-2-3">
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-comment">% Sampling Time [s]</span>
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Ts = (meas_data_lf{1}.t(end) <span class="org-type">-</span> (meas_data_lf{1}.t(1)))<span class="org-type">/</span>(length(meas_data_lf{1}.t)<span class="org-type">-</span>1);
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<span class="org-comment">% Sampling Frequency [Hz]</span>
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Fs = 1<span class="org-type">/</span>Ts;
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<span class="org-comment">% Hannning Windows</span>
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win = hanning(ceil(1<span class="org-type">*</span>Fs));
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</pre>
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</div>
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<p>
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And we get the frequency vector.
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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-type">~</span>, f] = tfestimate(meas_data_lf{1}.Va, meas_data_lf{1}.de, win, [], [], 1<span class="org-type">/</span>Ts);
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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">i_lf = f <span class="org-type"><</span> 250; <span class="org-comment">% Points for low frequency excitation</span>
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i_hf = f <span class="org-type">></span> 250; <span class="org-comment">% Points for high frequency excitation</span>
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-org9ac5c69" class="outline-3">
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<h3 id="org9ac5c69"><span class="section-number-3">2.4</span> DVF Plant</h3>
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<div class="outline-text-3" id="text-2-4">
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<p>
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First, let’s compute the coherence from the excitation voltage and the displacement as measured by the encoders (Figure <a href="#orga941078">3</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">%% Coherence</span></span>
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coh_dvf_lf = zeros(length(f), 6, 6);
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coh_dvf_hf = zeros(length(f), 6, 6);
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<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:6</span>
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coh_dvf_lf(<span class="org-type">:</span>, <span class="org-type">:</span>, <span class="org-constant">i</span>) = mscohere(meas_data_lf{<span class="org-constant">i</span>}.Va, meas_data_lf{<span class="org-constant">i</span>}.de, win, [], [], 1<span class="org-type">/</span>Ts);
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coh_dvf_hf(<span class="org-type">:</span>, <span class="org-type">:</span>, <span class="org-constant">i</span>) = mscohere(meas_data_hf{<span class="org-constant">i</span>}.Va, meas_data_hf{<span class="org-constant">i</span>}.de, win, [], [], 1<span class="org-type">/</span>Ts);
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<span class="org-keyword">end</span>
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</pre>
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</div>
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<div id="orga941078" class="figure">
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<p><img src="figs/enc_struts_dvf_coh.png" alt="enc_struts_dvf_coh.png" />
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</p>
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<p><span class="figure-number">Figure 3: </span>Obtained coherence for the DVF plant</p>
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</div>
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<p>
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Then the 6x6 transfer function matrix is estimated (Figure <a href="#org9c350f6">4</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">%% DVF Plant</span></span>
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G_dvf_lf = zeros(length(f), 6, 6);
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G_dvf_hf = zeros(length(f), 6, 6);
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<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:6</span>
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G_dvf_lf(<span class="org-type">:</span>, <span class="org-type">:</span>, <span class="org-constant">i</span>) = tfestimate(meas_data_lf{<span class="org-constant">i</span>}.Va, meas_data_lf{<span class="org-constant">i</span>}.de, win, [], [], 1<span class="org-type">/</span>Ts);
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G_dvf_hf(<span class="org-type">:</span>, <span class="org-type">:</span>, <span class="org-constant">i</span>) = tfestimate(meas_data_hf{<span class="org-constant">i</span>}.Va, meas_data_hf{<span class="org-constant">i</span>}.de, win, [], [], 1<span class="org-type">/</span>Ts);
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<span class="org-keyword">end</span>
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</pre>
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</div>
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<div id="org9c350f6" class="figure">
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<p><img src="figs/enc_struts_dvf_frf.png" alt="enc_struts_dvf_frf.png" />
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</p>
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<p><span class="figure-number">Figure 4: </span>Measured FRF for the DVF plant</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org4f1737c" class="outline-3">
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<h3 id="org4f1737c"><span class="section-number-3">2.5</span> IFF Plant</h3>
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<div class="outline-text-3" id="text-2-5">
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<p>
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First, let’s compute the coherence from the excitation voltage and the displacement as measured by the encoders (Figure <a href="#org2a3d572">5</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">%% Coherence</span></span>
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coh_iff_lf = zeros(length(f), 6, 6);
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coh_iff_hf = zeros(length(f), 6, 6);
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<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:6</span>
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coh_iff_lf(<span class="org-type">:</span>, <span class="org-type">:</span>, <span class="org-constant">i</span>) = mscohere(meas_data_lf{<span class="org-constant">i</span>}.Va, meas_data_lf{<span class="org-constant">i</span>}.Vs, win, [], [], 1<span class="org-type">/</span>Ts);
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coh_iff_hf(<span class="org-type">:</span>, <span class="org-type">:</span>, <span class="org-constant">i</span>) = mscohere(meas_data_hf{<span class="org-constant">i</span>}.Va, meas_data_hf{<span class="org-constant">i</span>}.Vs, win, [], [], 1<span class="org-type">/</span>Ts);
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<span class="org-keyword">end</span>
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</pre>
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</div>
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<div id="org2a3d572" class="figure">
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<p><img src="figs/enc_struts_iff_coh.png" alt="enc_struts_iff_coh.png" />
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</p>
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<p><span class="figure-number">Figure 5: </span>Obtained coherence for the IFF plant</p>
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</div>
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<p>
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Then the 6x6 transfer function matrix is estimated (Figure <a href="#orgaacf7b8">6</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">%% IFF Plant</span></span>
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G_iff_lf = zeros(length(f), 6, 6);
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G_iff_hf = zeros(length(f), 6, 6);
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<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:6</span>
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G_iff_lf(<span class="org-type">:</span>, <span class="org-type">:</span>, <span class="org-constant">i</span>) = tfestimate(meas_data_lf{<span class="org-constant">i</span>}.Va, meas_data_lf{<span class="org-constant">i</span>}.Vs, win, [], [], 1<span class="org-type">/</span>Ts);
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G_iff_hf(<span class="org-type">:</span>, <span class="org-type">:</span>, <span class="org-constant">i</span>) = tfestimate(meas_data_hf{<span class="org-constant">i</span>}.Va, meas_data_hf{<span class="org-constant">i</span>}.Vs, win, [], [], 1<span class="org-type">/</span>Ts);
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<span class="org-keyword">end</span>
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</pre>
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</div>
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<div id="orgaacf7b8" class="figure">
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<p><img src="figs/enc_struts_iff_frf.png" alt="enc_struts_iff_frf.png" />
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||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 6: </span>Measured FRF for the IFF plant</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org4238e67" class="outline-3">
|
||||||
|
<h3 id="org4238e67"><span class="section-number-3">2.6</span> Jacobian</h3>
|
||||||
|
<div class="outline-text-3" id="text-2-6">
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">load(<span class="org-string">'jacobian.mat'</span>, <span class="org-string">'J'</span>);
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div class="org-src-container">
|
||||||
|
<pre class="src src-matlab">G_dvf_J_lf = G_dvf_lf(i_lf, <span class="org-constant">i</span>, <span class="org-constant">j</span>)
|
||||||
|
</pre>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
#+end_src</p>
|
||||||
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Dehaeze Thomas</p>
|
<p class="author">Author: Dehaeze Thomas</p>
|
||||||
<p class="date">Created: 2021-06-07 lun. 19:00</p>
|
<p class="date">Created: 2021-06-08 mar. 21:51</p>
|
||||||
</div>
|
</div>
|
||||||
</body>
|
</body>
|
||||||
</html>
|
</html>
|
||||||
|
|||||||
@ -46,6 +46,7 @@
|
|||||||
<hr>
|
<hr>
|
||||||
#+end_export
|
#+end_export
|
||||||
|
|
||||||
|
* Introduction :ignore:
|
||||||
* Test-Bench Description
|
* Test-Bench Description
|
||||||
|
|
||||||
#+begin_note
|
#+begin_note
|
||||||
@ -56,3 +57,425 @@ Here are the documentation of the equipment used for this test bench:
|
|||||||
- Encoder: Renishaw [[file:doc/L-9517-9678-05-A_Data_sheet_VIONiC_series_en.pdf][Vionic]] and used [[file:doc/L-9517-9862-01-C_Data_sheet_RKLC_EN.pdf][Ruler]]
|
- Encoder: Renishaw [[file:doc/L-9517-9678-05-A_Data_sheet_VIONiC_series_en.pdf][Vionic]] and used [[file:doc/L-9517-9862-01-C_Data_sheet_RKLC_EN.pdf][Ruler]]
|
||||||
- Interferometers: Attocube
|
- Interferometers: Attocube
|
||||||
#+end_note
|
#+end_note
|
||||||
|
|
||||||
|
#+name: fig:picture_bench_granite_nano_hexapod
|
||||||
|
#+caption: Nano-Hexapod
|
||||||
|
[[file:figs/IMG_20210608_152917.jpg]]
|
||||||
|
|
||||||
|
#+name: fig:picture_bench_granite_overview
|
||||||
|
#+caption: Nano-Hexapod and the control electronics
|
||||||
|
[[file:figs/IMG_20210608_154722.jpg]]
|
||||||
|
|
||||||
|
* Encoders fixed to the Struts
|
||||||
|
** Introduction
|
||||||
|
|
||||||
|
** 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
|
||||||
|
addpath('./matlab/mat/');
|
||||||
|
addpath('./matlab/src/');
|
||||||
|
addpath('./matlab/');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :eval no
|
||||||
|
addpath('./mat/');
|
||||||
|
addpath('./src/');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
** Load Data
|
||||||
|
#+begin_src matlab
|
||||||
|
meas_data_lf = {};
|
||||||
|
|
||||||
|
for i = 1:6
|
||||||
|
meas_data_lf(i) = {load(sprintf('mat/frf_data_exc_strut_%i_noise_lf.mat', i), 't', 'Va', 'Vs', 'de')};
|
||||||
|
meas_data_hf(i) = {load(sprintf('mat/frf_data_exc_strut_%i_noise_hf.mat', i), 't', 'Va', 'Vs', 'de')};
|
||||||
|
end
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
** Spectral Analysis - Setup
|
||||||
|
#+begin_src matlab
|
||||||
|
% Sampling Time [s]
|
||||||
|
Ts = (meas_data_lf{1}.t(end) - (meas_data_lf{1}.t(1)))/(length(meas_data_lf{1}.t)-1);
|
||||||
|
|
||||||
|
% Sampling Frequency [Hz]
|
||||||
|
Fs = 1/Ts;
|
||||||
|
|
||||||
|
% Hannning Windows
|
||||||
|
win = hanning(ceil(1*Fs));
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
And we get the frequency vector.
|
||||||
|
#+begin_src matlab
|
||||||
|
[~, f] = tfestimate(meas_data_lf{1}.Va, meas_data_lf{1}.de, win, [], [], 1/Ts);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab
|
||||||
|
i_lf = f < 250; % Points for low frequency excitation
|
||||||
|
i_hf = f > 250; % Points for high frequency excitation
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
** DVF Plant
|
||||||
|
First, let's compute the coherence from the excitation voltage and the displacement as measured by the encoders (Figure [[fig:enc_struts_dvf_coh]]).
|
||||||
|
|
||||||
|
#+begin_src matlab
|
||||||
|
%% Coherence
|
||||||
|
coh_dvf_lf = zeros(length(f), 6, 6);
|
||||||
|
coh_dvf_hf = zeros(length(f), 6, 6);
|
||||||
|
|
||||||
|
for i = 1:6
|
||||||
|
coh_dvf_lf(:, :, i) = mscohere(meas_data_lf{i}.Va, meas_data_lf{i}.de, win, [], [], 1/Ts);
|
||||||
|
coh_dvf_hf(:, :, i) = mscohere(meas_data_hf{i}.Va, meas_data_hf{i}.de, win, [], [], 1/Ts);
|
||||||
|
end
|
||||||
|
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
for i = 1:5
|
||||||
|
for j = i+1:6
|
||||||
|
plot(f(i_lf), coh_dvf_lf(i_lf, i, j), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
plot(f(i_hf), coh_dvf_hf(i_hf, i, j), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
end
|
||||||
|
for i =1:6
|
||||||
|
set(gca,'ColorOrderIndex',i)
|
||||||
|
plot(f(i_lf), coh_dvf_lf(i_lf,i, i), ...
|
||||||
|
'DisplayName', sprintf('$G_{dvf}(%i,%i)$', i, i));
|
||||||
|
set(gca,'ColorOrderIndex',i)
|
||||||
|
plot(f(i_hf), coh_dvf_hf(i_hf,i, i), ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
plot(f(i_lf), coh_dvf_lf(i_lf, 1, 2), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'DisplayName', '$G_{dvf}(i,j)$');
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
xlabel('Frequency [Hz]'); ylabel('Coherence [-]');
|
||||||
|
xlim([20, 2e3]); ylim([0, 1]);
|
||||||
|
legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 3);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :tangle no :exports results :results file replace
|
||||||
|
exportFig('figs/enc_struts_dvf_coh.pdf', 'width', 'wide', 'height', 'normal');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+name: fig:enc_struts_dvf_coh
|
||||||
|
#+caption: Obtained coherence for the DVF plant
|
||||||
|
#+RESULTS:
|
||||||
|
[[file:figs/enc_struts_dvf_coh.png]]
|
||||||
|
|
||||||
|
Then the 6x6 transfer function matrix is estimated (Figure [[fig:enc_struts_dvf_frf]]).
|
||||||
|
#+begin_src matlab
|
||||||
|
%% DVF Plant
|
||||||
|
G_dvf_lf = zeros(length(f), 6, 6);
|
||||||
|
G_dvf_hf = zeros(length(f), 6, 6);
|
||||||
|
|
||||||
|
for i = 1:6
|
||||||
|
G_dvf_lf(:, :, i) = tfestimate(meas_data_lf{i}.Va, meas_data_lf{i}.de, win, [], [], 1/Ts);
|
||||||
|
G_dvf_hf(:, :, i) = tfestimate(meas_data_hf{i}.Va, meas_data_hf{i}.de, win, [], [], 1/Ts);
|
||||||
|
end
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
figure;
|
||||||
|
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||||
|
|
||||||
|
ax1 = nexttile([2,1]);
|
||||||
|
hold on;
|
||||||
|
for i = 1:5
|
||||||
|
for j = i+1:6
|
||||||
|
plot(f(i_lf), abs(G_dvf_lf(i_lf, i, j)), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
plot(f(i_hf), abs(G_dvf_hf(i_hf, i, j)), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
end
|
||||||
|
for i =1:6
|
||||||
|
set(gca,'ColorOrderIndex',i)
|
||||||
|
plot(f(i_lf), abs(G_dvf_lf(i_lf,i, i)), ...
|
||||||
|
'DisplayName', sprintf('$G_{dvf}(%i,%i)$', i, i));
|
||||||
|
set(gca,'ColorOrderIndex',i)
|
||||||
|
plot(f(i_hf), abs(G_dvf_hf(i_hf,i, i)), ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
plot(f(i_lf), abs(G_dvf_lf(i_lf, 1, 2)), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'DisplayName', '$G_{dvf}(i,j)$');
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude $d_e/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
|
||||||
|
ylim([1e-9, 1e-3]);
|
||||||
|
legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 3);
|
||||||
|
|
||||||
|
ax2 = nexttile;
|
||||||
|
hold on;
|
||||||
|
for i =1:6
|
||||||
|
set(gca,'ColorOrderIndex',i)
|
||||||
|
plot(f(i_lf), 180/pi*angle(G_dvf_lf(i_lf,i, i)));
|
||||||
|
set(gca,'ColorOrderIndex',i)
|
||||||
|
plot(f(i_hf), 180/pi*angle(G_dvf_hf(i_hf,i, i)));
|
||||||
|
end
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||||
|
hold off;
|
||||||
|
yticks(-360:90:360);
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
xlim([20, 2e3]);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :tangle no :exports results :results file replace
|
||||||
|
exportFig('figs/enc_struts_dvf_frf.pdf', 'width', 'wide', 'height', 'tall');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+name: fig:enc_struts_dvf_frf
|
||||||
|
#+caption: Measured FRF for the DVF plant
|
||||||
|
#+RESULTS:
|
||||||
|
[[file:figs/enc_struts_dvf_frf.png]]
|
||||||
|
|
||||||
|
|
||||||
|
** IFF Plant
|
||||||
|
First, let's compute the coherence from the excitation voltage and the displacement as measured by the encoders (Figure [[fig:enc_struts_iff_coh]]).
|
||||||
|
|
||||||
|
#+begin_src matlab
|
||||||
|
%% Coherence
|
||||||
|
coh_iff_lf = zeros(length(f), 6, 6);
|
||||||
|
coh_iff_hf = zeros(length(f), 6, 6);
|
||||||
|
|
||||||
|
for i = 1:6
|
||||||
|
coh_iff_lf(:, :, i) = mscohere(meas_data_lf{i}.Va, meas_data_lf{i}.Vs, win, [], [], 1/Ts);
|
||||||
|
coh_iff_hf(:, :, i) = mscohere(meas_data_hf{i}.Va, meas_data_hf{i}.Vs, win, [], [], 1/Ts);
|
||||||
|
end
|
||||||
|
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
for i = 1:5
|
||||||
|
for j = i+1:6
|
||||||
|
plot(f(i_lf), coh_iff_lf(i_lf, i, j), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
plot(f(i_hf), coh_iff_hf(i_hf, i, j), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
end
|
||||||
|
for i =1:6
|
||||||
|
set(gca,'ColorOrderIndex',i)
|
||||||
|
plot(f(i_lf), coh_iff_lf(i_lf,i, i), ...
|
||||||
|
'DisplayName', sprintf('$G_{iff}(%i,%i)$', i, i));
|
||||||
|
set(gca,'ColorOrderIndex',i)
|
||||||
|
plot(f(i_hf), coh_iff_hf(i_hf,i, i), ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
plot(f(i_lf), coh_iff_lf(i_lf, 1, 2), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'DisplayName', '$G_{iff}(i,j)$');
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
xlabel('Frequency [Hz]'); ylabel('Coherence [-]');
|
||||||
|
xlim([20, 2e3]); ylim([0, 1]);
|
||||||
|
legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 3);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :tangle no :exports results :results file replace
|
||||||
|
exportFig('figs/enc_struts_iff_coh.pdf', 'width', 'wide', 'height', 'normal');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+name: fig:enc_struts_iff_coh
|
||||||
|
#+caption: Obtained coherence for the IFF plant
|
||||||
|
#+RESULTS:
|
||||||
|
[[file:figs/enc_struts_iff_coh.png]]
|
||||||
|
|
||||||
|
Then the 6x6 transfer function matrix is estimated (Figure [[fig:enc_struts_iff_frf]]).
|
||||||
|
#+begin_src matlab
|
||||||
|
%% IFF Plant
|
||||||
|
G_iff_lf = zeros(length(f), 6, 6);
|
||||||
|
G_iff_hf = zeros(length(f), 6, 6);
|
||||||
|
|
||||||
|
for i = 1:6
|
||||||
|
G_iff_lf(:, :, i) = tfestimate(meas_data_lf{i}.Va, meas_data_lf{i}.Vs, win, [], [], 1/Ts);
|
||||||
|
G_iff_hf(:, :, i) = tfestimate(meas_data_hf{i}.Va, meas_data_hf{i}.Vs, win, [], [], 1/Ts);
|
||||||
|
end
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
figure;
|
||||||
|
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||||
|
|
||||||
|
ax1 = nexttile([2,1]);
|
||||||
|
hold on;
|
||||||
|
for i = 1:5
|
||||||
|
for j = i+1:6
|
||||||
|
plot(f(i_lf), abs(G_iff_lf(i_lf, i, j)), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
plot(f(i_hf), abs(G_iff_hf(i_hf, i, j)), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
end
|
||||||
|
for i =1:6
|
||||||
|
set(gca,'ColorOrderIndex',i)
|
||||||
|
plot(f(i_lf), abs(G_iff_lf(i_lf,i, i)), ...
|
||||||
|
'DisplayName', sprintf('$G_{iff}(%i,%i)$', i, i));
|
||||||
|
set(gca,'ColorOrderIndex',i)
|
||||||
|
plot(f(i_hf), abs(G_iff_hf(i_hf,i, i)), ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
plot(f(i_lf), abs(G_iff_lf(i_lf, 1, 2)), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'DisplayName', '$G_{iff}(i,j)$');
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]);
|
||||||
|
legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 3);
|
||||||
|
ylim([1e-3, 1e2]);
|
||||||
|
|
||||||
|
ax2 = nexttile;
|
||||||
|
hold on;
|
||||||
|
for i =1:6
|
||||||
|
set(gca,'ColorOrderIndex',i)
|
||||||
|
plot(f(i_lf), 180/pi*angle(G_iff_lf(i_lf,i, i)));
|
||||||
|
set(gca,'ColorOrderIndex',i)
|
||||||
|
plot(f(i_hf), 180/pi*angle(G_iff_hf(i_hf,i, i)));
|
||||||
|
end
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||||
|
hold off;
|
||||||
|
yticks(-360:90:360);
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
xlim([20, 2e3]);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :tangle no :exports results :results file replace
|
||||||
|
exportFig('figs/enc_struts_iff_frf.pdf', 'width', 'wide', 'height', 'tall');
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+name: fig:enc_struts_iff_frf
|
||||||
|
#+caption: Measured FRF for the IFF plant
|
||||||
|
#+RESULTS:
|
||||||
|
[[file:figs/enc_struts_iff_frf.png]]
|
||||||
|
|
||||||
|
** Jacobian
|
||||||
|
#+begin_src matlab
|
||||||
|
load('jacobian.mat', 'J');
|
||||||
|
#+end_src
|
||||||
|
*** DVF Plant
|
||||||
|
#+begin_src matlab
|
||||||
|
G_dvf_J_lf = permute(pagemtimes(inv(J), pagemtimes(permute(G_dvf_lf, [2 3 1]), inv(J'))), [3 1 2]);
|
||||||
|
G_dvf_J_hf = permute(pagemtimes(inv(J), pagemtimes(permute(G_dvf_hf, [2 3 1]), inv(J'))), [3 1 2]);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
labels = {'$D_x/F_{x}$', '$D_y/F_{y}$', '$D_z/F_{z}$', '$R_{x}/M_{x}$', '$R_{y}/M_{y}$', '$R_{R}/M_{z}$'};
|
||||||
|
|
||||||
|
figure;
|
||||||
|
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||||
|
|
||||||
|
ax1 = nexttile([2,1]);
|
||||||
|
hold on;
|
||||||
|
for i = 1:5
|
||||||
|
for j = i+1:6
|
||||||
|
plot(f(i_lf), abs(G_dvf_J_lf(i_lf, i, j)), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
plot(f(i_hf), abs(G_dvf_J_hf(i_hf, i, j)), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
end
|
||||||
|
for i =1:6
|
||||||
|
set(gca,'ColorOrderIndex',i)
|
||||||
|
plot(f(i_lf), abs(G_dvf_J_lf(i_lf,i, i)), ...
|
||||||
|
'DisplayName', labels{i});
|
||||||
|
set(gca,'ColorOrderIndex',i)
|
||||||
|
plot(f(i_hf), abs(G_dvf_J_hf(i_hf,i, i)), ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
plot(f(i_lf), abs(G_dvf_J_lf(i_lf, 1, 2)), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'DisplayName', '$D_i/F_j$');
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude $d_e/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
|
||||||
|
ylim([1e-7, 1e-1]);
|
||||||
|
legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 3);
|
||||||
|
|
||||||
|
ax2 = nexttile;
|
||||||
|
hold on;
|
||||||
|
for i =1:6
|
||||||
|
set(gca,'ColorOrderIndex',i)
|
||||||
|
plot(f(i_lf), 180/pi*angle(G_dvf_J_lf(i_lf,i, i)));
|
||||||
|
set(gca,'ColorOrderIndex',i)
|
||||||
|
plot(f(i_hf), 180/pi*angle(G_dvf_J_hf(i_hf,i, i)));
|
||||||
|
end
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||||
|
hold off;
|
||||||
|
yticks(-360:90:360);
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
xlim([20, 2e3]);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
*** IFF Plant
|
||||||
|
#+begin_src matlab
|
||||||
|
G_iff_J_lf = permute(pagemtimes(inv(J), pagemtimes(permute(G_iff_lf, [2 3 1]), inv(J'))), [3 1 2]);
|
||||||
|
G_iff_J_hf = permute(pagemtimes(inv(J), pagemtimes(permute(G_iff_hf, [2 3 1]), inv(J'))), [3 1 2]);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab :exports none
|
||||||
|
labels = {'$F_{m,x}/F_{x}$', '$F_{m,y}/F_{y}$', '$F_{m,z}/F_{z}$', '$M_{m,x}/M_{x}$', '$M_{m,y}/M_{y}$', '$M_{m,z}/M_{z}$'};
|
||||||
|
|
||||||
|
figure;
|
||||||
|
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||||
|
|
||||||
|
ax1 = nexttile([2,1]);
|
||||||
|
hold on;
|
||||||
|
for i = 1:5
|
||||||
|
for j = i+1:6
|
||||||
|
plot(f(i_lf), abs(G_iff_J_lf(i_lf, i, j)), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
plot(f(i_hf), abs(G_iff_J_hf(i_hf, i, j)), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
end
|
||||||
|
for i =1:6
|
||||||
|
set(gca,'ColorOrderIndex',i)
|
||||||
|
plot(f(i_lf), abs(G_iff_J_lf(i_lf,i, i)), ...
|
||||||
|
'DisplayName', labels{i});
|
||||||
|
set(gca,'ColorOrderIndex',i)
|
||||||
|
plot(f(i_hf), abs(G_iff_J_hf(i_hf,i, i)), ...
|
||||||
|
'HandleVisibility', 'off');
|
||||||
|
end
|
||||||
|
plot(f(i_lf), abs(G_iff_J_lf(i_lf, 1, 2)), 'color', [0, 0, 0, 0.2], ...
|
||||||
|
'DisplayName', '$D_i/F_j$');
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||||
|
ylabel('Amplitude $d_e/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
|
||||||
|
ylim([1e-7, 1e-1]);
|
||||||
|
legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 3);
|
||||||
|
|
||||||
|
ax2 = nexttile;
|
||||||
|
hold on;
|
||||||
|
for i =1:6
|
||||||
|
set(gca,'ColorOrderIndex',i)
|
||||||
|
plot(f(i_lf), 180/pi*angle(G_iff_J_lf(i_lf,i, i)));
|
||||||
|
set(gca,'ColorOrderIndex',i)
|
||||||
|
plot(f(i_hf), 180/pi*angle(G_iff_J_hf(i_hf,i, i)));
|
||||||
|
end
|
||||||
|
hold off;
|
||||||
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
|
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||||
|
hold off;
|
||||||
|
yticks(-360:90:360);
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
xlim([20, 2e3]);
|
||||||
|
#+end_src
|
||||||
|
|||||||
BIN
test-bench-nano-hexapod.pdf
Normal file
BIN
test-bench-nano-hexapod.pdf
Normal file
Binary file not shown.
Loading…
Reference in New Issue
Block a user