Analysis of FRF data (DVF + IFF)
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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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<title>Nano-Hexapod - Test Bench</title>
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<meta name="author" content="Dehaeze Thomas" />
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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="#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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</div>
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</div>
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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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<div id="outline-container-orgc63308d" 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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<div id="outline-container-org401a850" class="outline-2">
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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="note" id="org060848e">
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<div class="note" id="orgdb43d80">
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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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</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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</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>
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<p><span class="figure-number">Figure 6: </span>Measured FRF for the IFF 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-org4238e67" class="outline-3">
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<h3 id="org4238e67"><span class="section-number-3">2.6</span> Jacobian</h3>
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<div class="outline-text-3" id="text-2-6">
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<div class="org-src-container">
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<pre class="src src-matlab">load(<span class="org-string">'jacobian.mat'</span>, <span class="org-string">'J'</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">G_dvf_J_lf = G_dvf_lf(i_lf, <span class="org-constant">i</span>, <span class="org-constant">j</span>)
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</pre>
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</div>
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<p>
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#+end_src</p>
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</div>
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</div>
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</div>
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</div>
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<div id="postamble" class="status">
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<p class="author">Author: Dehaeze Thomas</p>
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<p class="date">Created: 2021-06-07 lun. 19:00</p>
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<p class="date">Created: 2021-06-08 mar. 21:51</p>
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</div>
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