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Thomas Dehaeze
2022-06-02 18:23:48 +02:00
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@@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2022-02-15 mar. 14:18 -->
<!-- 2022-02-20 dim. 23:36 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>ESRF Double Crystal Monochromator - Feedback Controller</title>
<meta name="author" content="Dehaeze Thomas" />
@@ -22,40 +22,40 @@
<h2>Table of Contents</h2>
<div id="text-table-of-contents" role="doc-toc">
<ul>
<li><a href="#orga1bae1c">1. Estimation of Sensitivity Function</a>
<li><a href="#org8576b4a">1. Estimation of Sensitivity Function</a>
<ul>
<li><a href="#org735dcc9">1.1. Load Data</a></li>
<li><a href="#org3fc079f">1.2. Controller</a></li>
<li><a href="#org5af2b76">1.3. Test</a></li>
<li><a href="#orgdf402a0">1.1. Load Data</a></li>
<li><a href="#org8107511">1.2. Controller</a></li>
<li><a href="#org0a01799">1.3. Test</a></li>
</ul>
</li>
<li><a href="#orgbb0d924">2. System Identification</a>
<li><a href="#org9a5bd10">2. System Identification</a>
<ul>
<li><a href="#org6c48b35">2.1. Identification</a></li>
<li><a href="#org0b292a4">2.2. Identification - New</a></li>
<li><a href="#org2e5fa20">2.3. Identification - White noise</a></li>
<li><a href="#org71bfb62">2.4. Test</a></li>
<li><a href="#orge135bfd">2.5. New controller - Higher bandwidth</a></li>
<li><a href="#orgced05bb">2.6. Added gain</a></li>
<li><a href="#orgaafe900">2.1. Identification</a></li>
<li><a href="#orga4b6967">2.2. Identification - New</a></li>
<li><a href="#org3ea3501">2.3. Identification - White noise</a></li>
<li><a href="#org2f67dfc">2.4. Test</a></li>
<li><a href="#org675289a">2.5. New controller - Higher bandwidth</a></li>
<li><a href="#org2f12e07">2.6. Added gain</a></li>
</ul>
</li>
<li><a href="#org42b6fad">3. Noise Budgeting</a>
<li><a href="#orge30c950">3. Noise Budgeting</a>
<ul>
<li><a href="#orgfab07e0">3.1. No Displacement</a></li>
<li><a href="#org2959e07">3.2. Scans</a></li>
<li><a href="#orge57ff9f">3.3. Noise budgeting - No rotation</a></li>
<li><a href="#org5c8bbce">3.4. Noise budgeting - Bragg rotation</a></li>
<li><a href="#org8aeec43">3.1. No Displacement</a></li>
<li><a href="#org2e15aa7">3.2. Scans</a></li>
<li><a href="#org26d025b">3.3. Noise budgeting - No rotation</a></li>
<li><a href="#org8945ee2">3.4. Noise budgeting - Bragg rotation</a></li>
</ul>
</li>
<li><a href="#org84729e1">4. Test Mode C</a>
<li><a href="#orgc0ab5d1">4. Test Mode C</a>
<ul>
<li><a href="#org8cc30f1">4.1. Mode B and Mode C</a></li>
<li><a href="#org9996dc6">4.1. Mode B and Mode C</a></li>
</ul>
</li>
<li><a href="#org0d833d1">5. Export numerator and denominator</a>
<li><a href="#org1c0791b">5. Export numerator and denominator</a>
<ul>
<li><a href="#org4532b44">5.1. Export</a></li>
<li><a href="#org78d8a99">5.2. Verify</a></li>
<li><a href="#org22487de">5.1. Export</a></li>
<li><a href="#org2b8461a">5.2. Verify</a></li>
</ul>
</li>
</ul>
@@ -65,12 +65,12 @@
<p>This report is also available as a <a href="./dcm-feedback-control.pdf">pdf</a>.</p>
<hr>
<div id="outline-container-orga1bae1c" class="outline-2">
<h2 id="orga1bae1c"><span class="section-number-2">1.</span> Estimation of Sensitivity Function</h2>
<div id="outline-container-org8576b4a" class="outline-2">
<h2 id="org8576b4a"><span class="section-number-2">1.</span> Estimation of Sensitivity Function</h2>
<div class="outline-text-2" id="text-1">
</div>
<div id="outline-container-org735dcc9" class="outline-3">
<h3 id="org735dcc9"><span class="section-number-3">1.1.</span> Load Data</h3>
<div id="outline-container-orgdf402a0" class="outline-3">
<h3 id="orgdf402a0"><span class="section-number-3">1.1.</span> Load Data</h3>
<div class="outline-text-3" id="text-1-1">
<p>
Two scans are performed:
@@ -99,7 +99,7 @@ t = linspace(Ts, Ts<span class="org-builtin">*</span>length(ol_drx), length(ol_d
</div>
<p>
By comparison the frequency content of the crystal orientation errors between mode B and mode C, it is possible to estimate the Sensitivity transfer function (Figure <a href="#org5bf52a1">1</a>).
By comparison the frequency content of the crystal orientation errors between mode B and mode C, it is possible to estimate the Sensitivity transfer function (Figure <a href="#orgb0c8317">1</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab">win = hanning(ceil(1<span class="org-builtin">/</span>Ts));
@@ -113,7 +113,7 @@ By comparison the frequency content of the crystal orientation errors between mo
</div>
<div id="org5bf52a1" class="figure">
<div id="orgb0c8317" class="figure">
<p><img src="figs/sensitivity_function_drx_est.png" alt="sensitivity_function_drx_est.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Estimation of the sensitivity transfer function magnitude</p>
@@ -122,8 +122,8 @@ By comparison the frequency content of the crystal orientation errors between mo
</div>
<div id="outline-container-org3fc079f" class="outline-3">
<h3 id="org3fc079f"><span class="section-number-3">1.2.</span> Controller</h3>
<div id="outline-container-org8107511" class="outline-3">
<h3 id="org8107511"><span class="section-number-3">1.2.</span> Controller</h3>
<div class="outline-text-3" id="text-1-2">
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'X_tal_cage_PID.mat'</span>, <span class="org-string">'K'</span>);
@@ -131,7 +131,7 @@ By comparison the frequency content of the crystal orientation errors between mo
</div>
<div id="org2e1f293" class="figure">
<div id="orgabcb99b" class="figure">
<p><img src="figs/bode_plot_cur_controller.png" alt="bode_plot_cur_controller.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Bode Plot of the Controller</p>
@@ -139,8 +139,8 @@ By comparison the frequency content of the crystal orientation errors between mo
</div>
</div>
<div id="outline-container-org5af2b76" class="outline-3">
<h3 id="org5af2b76"><span class="section-number-3">1.3.</span> Test</h3>
<div id="outline-container-org0a01799" class="outline-3">
<h3 id="org0a01799"><span class="section-number-3">1.3.</span> Test</h3>
<div class="outline-text-3" id="text-1-3">
<div class="org-src-container">
<pre class="src src-matlab">Ts = 5e<span class="org-builtin">-</span>3;
@@ -170,12 +170,12 @@ t = linspace(Ts, Ts<span class="org-builtin">*</span>length(ol_drx), length(ol_d
</div>
</div>
<div id="outline-container-orgbb0d924" class="outline-2">
<h2 id="orgbb0d924"><span class="section-number-2">2.</span> System Identification</h2>
<div id="outline-container-org9a5bd10" class="outline-2">
<h2 id="org9a5bd10"><span class="section-number-2">2.</span> System Identification</h2>
<div class="outline-text-2" id="text-2">
</div>
<div id="outline-container-org6c48b35" class="outline-3">
<h3 id="org6c48b35"><span class="section-number-3">2.1.</span> Identification</h3>
<div id="outline-container-orgaafe900" class="outline-3">
<h3 id="orgaafe900"><span class="section-number-3">2.1.</span> Identification</h3>
<div class="outline-text-3" id="text-2-1">
<div class="org-src-container">
<pre class="src src-matlab">ur = load(<span class="org-string">'FJPUR_step.mat'</span>);
@@ -321,7 +321,7 @@ win = hanning(ceil(5<span class="org-builtin">*</span>Fs));
</div>
<div id="orgb5ed826" class="figure">
<div id="org9466993" class="figure">
<p><img src="figs/coherence_id_dcm_dyn.png" alt="coherence_id_dcm_dyn.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Coherence</p>
@@ -329,7 +329,7 @@ win = hanning(ceil(5<span class="org-builtin">*</span>Fs));
<div id="orgeff963e" class="figure">
<div id="org6e09695" class="figure">
<p><img src="figs/bode_plot_dcm_dynamics.png" alt="bode_plot_dcm_dynamics.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Bode Plot of the DCM dynamics in the frame of the fast jack.</p>
@@ -359,7 +359,7 @@ Kb = eye(3)<span class="org-builtin">*</span>(2<span class="org-builtin">*</span
</div>
<div id="orgb03f205" class="figure">
<div id="org4f0fbea" class="figure">
<p><img src="figs/loop_gain_dcm_contr_simple.png" alt="loop_gain_dcm_contr_simple.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Loop gain</p>
@@ -367,7 +367,7 @@ Kb = eye(3)<span class="org-builtin">*</span>(2<span class="org-builtin">*</span
<div id="orgc507071" class="figure">
<div id="orgf361fc7" class="figure">
<p><img src="figs/loop_gain_diag_old_new_contr.png" alt="loop_gain_diag_old_new_contr.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Loop gain</p>
@@ -377,7 +377,7 @@ Kb = eye(3)<span class="org-builtin">*</span>(2<span class="org-builtin">*</span
Compare Sensitivity functions
</p>
<div id="orgd925333" class="figure">
<div id="orgb76f72d" class="figure">
<p><img src="figs/sensitivity_comp.png" alt="sensitivity_comp.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Comparison of sensitivity functions</p>
@@ -396,7 +396,7 @@ Lb = zeros(3, 3, length(f));
</div>
<div id="org18dbc34" class="figure">
<div id="orgb0888a7" class="figure">
<p><img src="figs/loci_loop_gain_comp_controllers.png" alt="loci_loop_gain_comp_controllers.png" />
</p>
<p><span class="figure-number">Figure 8: </span>Root Locus</p>
@@ -405,8 +405,8 @@ Lb = zeros(3, 3, length(f));
</div>
<div id="outline-container-org0b292a4" class="outline-3">
<h3 id="org0b292a4"><span class="section-number-3">2.2.</span> Identification - New</h3>
<div id="outline-container-orga4b6967" class="outline-3">
<h3 id="orga4b6967"><span class="section-number-3">2.2.</span> Identification - New</h3>
<div class="outline-text-3" id="text-2-2">
<div class="org-src-container">
<pre class="src src-matlab">ur = load(<span class="org-string">'FJPUR_step_new.mat'</span>);
@@ -577,7 +577,7 @@ Kb = eye(3)<span class="org-builtin">*</span>(2<span class="org-builtin">*</span
Compare Sensitivity functions
</p>
<div id="orga50e1b0" class="figure">
<div id="org61be61a" class="figure">
<p><img src="figs/sensitivity_comp.png" alt="sensitivity_comp.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Comparison of sensitivity functions</p>
@@ -596,7 +596,7 @@ Lb = zeros(3, 3, length(f));
</div>
<div id="org8eb0924" class="figure">
<div id="org400e20f" class="figure">
<p><img src="figs/loci_loop_gain_comp_controllers.png" alt="loci_loop_gain_comp_controllers.png" />
</p>
<p><span class="figure-number">Figure 10: </span>Root Locus</p>
@@ -605,8 +605,8 @@ Lb = zeros(3, 3, length(f));
</div>
<div id="outline-container-org2e5fa20" class="outline-3">
<h3 id="org2e5fa20"><span class="section-number-3">2.3.</span> Identification - White noise</h3>
<div id="outline-container-org3ea3501" class="outline-3">
<h3 id="org3ea3501"><span class="section-number-3">2.3.</span> Identification - White noise</h3>
<div class="outline-text-3" id="text-2-3">
<div class="org-src-container">
<pre class="src src-matlab">ur = load(<span class="org-string">'fjpur_white_noise.mat'</span>);
@@ -725,14 +725,14 @@ win = hanning(ceil(0.5<span class="org-builtin">*</span>Fs));
</div>
<div id="orgd142314" class="figure">
<div id="org2130cf9" class="figure">
<p><img src="figs/coherence_ident_noise.png" alt="coherence_ident_noise.png" />
</p>
<p><span class="figure-number">Figure 11: </span>description</p>
</div>
<div id="orgc5ce01c" class="figure">
<div id="org6275987" class="figure">
<p><img src="figs/bode_plot_ident_noise.png" alt="bode_plot_ident_noise.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Bode Plot of the DCM dynamics in the frame of the fast jack.</p>
@@ -762,14 +762,14 @@ Kb = eye(3)<span class="org-builtin">*</span>(2<span class="org-builtin">*</span
</div>
<div id="org5a9c5a7" class="figure">
<div id="orgde5672c" class="figure">
<p><img src="figs/loop_gain_dcm_contr_simple.png" alt="loop_gain_dcm_contr_simple.png" />
</p>
<p><span class="figure-number">Figure 13: </span>Loop gain</p>
</div>
<div id="org24e16fe" class="figure">
<div id="org816756f" class="figure">
<p><img src="figs/loop_gain_diag_old_new_contr.png" alt="loop_gain_diag_old_new_contr.png" />
</p>
<p><span class="figure-number">Figure 14: </span>Loop gain</p>
@@ -779,7 +779,7 @@ Kb = eye(3)<span class="org-builtin">*</span>(2<span class="org-builtin">*</span
Compare Sensitivity functions
</p>
<div id="orgffa2ebc" class="figure">
<div id="org9c6d15d" class="figure">
<p><img src="figs/sensitivity_comp.png" alt="sensitivity_comp.png" />
</p>
<p><span class="figure-number">Figure 15: </span>Comparison of sensitivity functions</p>
@@ -798,7 +798,7 @@ Lb = zeros(3, 3, length(f));
</div>
<div id="org7a84791" class="figure">
<div id="orgcf68c9d" class="figure">
<p><img src="figs/loci_loop_gain_comp_controllers.png" alt="loci_loop_gain_comp_controllers.png" />
</p>
<p><span class="figure-number">Figure 16: </span>Root Locus</p>
@@ -807,8 +807,8 @@ Lb = zeros(3, 3, length(f));
</div>
<div id="outline-container-org71bfb62" class="outline-3">
<h3 id="org71bfb62"><span class="section-number-3">2.4.</span> Test</h3>
<div id="outline-container-org2f67dfc" class="outline-3">
<h3 id="org2f67dfc"><span class="section-number-3">2.4.</span> Test</h3>
<div class="outline-text-3" id="text-2-4">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak">%% Notch</span>
@@ -851,8 +851,8 @@ Kb = 0.8<span class="org-builtin">*</span>eye(3)<span class="org-builtin">*</sp
</div>
</div>
</div>
<div id="outline-container-orge135bfd" class="outline-3">
<h3 id="orge135bfd"><span class="section-number-3">2.5.</span> New controller - Higher bandwidth</h3>
<div id="outline-container-org675289a" class="outline-3">
<h3 id="org675289a"><span class="section-number-3">2.5.</span> New controller - Higher bandwidth</h3>
<div class="outline-text-3" id="text-2-5">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak">%% Previously used controller</span>
@@ -916,7 +916,7 @@ Kb = 0.9<span class="org-builtin">*</span>eye(3)<span class="org-builtin">*</sp
</div>
<div id="org0c92a80" class="figure">
<div id="org729d6bc" class="figure">
<p><img src="figs/loop_gain_compare.png" alt="loop_gain_compare.png" />
</p>
<p><span class="figure-number">Figure 17: </span>description</p>
@@ -937,14 +937,14 @@ Lb_new = zeros(3, 3, length(f));
</div>
<div id="orgeff107d" class="figure">
<div id="org9b73c58" class="figure">
<p><img src="figs/nyquist_compare.png" alt="nyquist_compare.png" />
</p>
<p><span class="figure-number">Figure 18: </span>n</p>
</div>
<div id="orga2251e0" class="figure">
<div id="orgd808ef9" class="figure">
<p><img src="figs/sensitivity_function_compare.png" alt="sensitivity_function_compare.png" />
</p>
<p><span class="figure-number">Figure 19: </span>description</p>
@@ -954,8 +954,8 @@ Lb_new = zeros(3, 3, length(f));
<div id="outline-container-orgced05bb" class="outline-3">
<h3 id="orgced05bb"><span class="section-number-3">2.6.</span> Added gain</h3>
<div id="outline-container-org2f12e07" class="outline-3">
<h3 id="org2f12e07"><span class="section-number-3">2.6.</span> Added gain</h3>
<div class="outline-text-3" id="text-2-6">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak">%% Notch</span>
@@ -1017,21 +1017,21 @@ Kb_gain = 0.9<span class="org-builtin">*</span>eye(3)<span class="org-builtin">
</div>
<div id="org00ceb71" class="figure">
<div id="org97a53c6" class="figure">
<p><img src="figs/loop_gain_compare_added_gain.png" alt="loop_gain_compare_added_gain.png" />
</p>
<p><span class="figure-number">Figure 20: </span>description</p>
</div>
<div id="org83020b4" class="figure">
<div id="org63d3ae0" class="figure">
<p><img src="figs/sensitivity_new_gain_compare.png" alt="sensitivity_new_gain_compare.png" />
</p>
<p><span class="figure-number">Figure 21: </span>description</p>
</div>
<div id="org003317c" class="figure">
<div id="orgded1447" class="figure">
<p><img src="figs/nyquist_after_gain_frequency.png" alt="nyquist_after_gain_frequency.png" />
</p>
<p><span class="figure-number">Figure 22: </span>nyquist plot</p>
@@ -1041,12 +1041,12 @@ Kb_gain = 0.9<span class="org-builtin">*</span>eye(3)<span class="org-builtin">
</div>
<div id="outline-container-org42b6fad" class="outline-2">
<h2 id="org42b6fad"><span class="section-number-2">3.</span> Noise Budgeting</h2>
<div id="outline-container-orge30c950" class="outline-2">
<h2 id="orge30c950"><span class="section-number-2">3.</span> Noise Budgeting</h2>
<div class="outline-text-2" id="text-3">
</div>
<div id="outline-container-orgfab07e0" class="outline-3">
<h3 id="orgfab07e0"><span class="section-number-3">3.1.</span> No Displacement</h3>
<div id="outline-container-org8aeec43" class="outline-3">
<h3 id="org8aeec43"><span class="section-number-3">3.1.</span> No Displacement</h3>
<div class="outline-text-3" id="text-3-1">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
@@ -1275,8 +1275,8 @@ data_70_deg.drx = data_70_deg.allValues(<span class="org-builtin">:</span>,6) <s
<div id="outline-container-org2959e07" class="outline-3">
<h3 id="org2959e07"><span class="section-number-3">3.2.</span> Scans</h3>
<div id="outline-container-org2e15aa7" class="outline-3">
<h3 id="org2e15aa7"><span class="section-number-3">3.2.</span> Scans</h3>
<div class="outline-text-3" id="text-3-2">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
@@ -1437,8 +1437,8 @@ CPS_70_10_d = flip(<span class="org-builtin">-</span>cumtrapz(flip(f), flip(pxx
</div>
</div>
<div id="outline-container-orge57ff9f" class="outline-3">
<h3 id="orge57ff9f"><span class="section-number-3">3.3.</span> Noise budgeting - No rotation</h3>
<div id="outline-container-org26d025b" class="outline-3">
<h3 id="org26d025b"><span class="section-number-3">3.3.</span> Noise budgeting - No rotation</h3>
<div class="outline-text-3" id="text-3-3">
<p>
First, we look at the position errors when the bragg axis is not moving
@@ -1488,7 +1488,7 @@ win = hanning(ceil(1<span class="org-builtin">/</span>Ts));
</div>
<div id="org2f9ead0" class="figure">
<div id="org7fb6c81" class="figure">
<p><img src="figs/noise_budget_no_mov_asd.png" alt="noise_budget_no_mov_asd.png" />
</p>
<p><span class="figure-number">Figure 23: </span>Amplitude Spectral Density</p>
@@ -1511,7 +1511,7 @@ CPS_dz = cumtrapz(f, pxx_ol_dz);
</div>
<div id="orgda9f408" class="figure">
<div id="org2f67e0e" class="figure">
<p><img src="figs/noise_budget_no_mov_cas.png" alt="noise_budget_no_mov_cas.png" />
</p>
<p><span class="figure-number">Figure 24: </span>Cumulative Amplitude Spectrum</p>
@@ -1520,17 +1520,17 @@ CPS_dz = cumtrapz(f, pxx_ol_dz);
</div>
<div id="outline-container-org5c8bbce" class="outline-3">
<h3 id="org5c8bbce"><span class="section-number-3">3.4.</span> Noise budgeting - Bragg rotation</h3>
<div id="outline-container-org8945ee2" class="outline-3">
<h3 id="org8945ee2"><span class="section-number-3">3.4.</span> Noise budgeting - Bragg rotation</h3>
</div>
</div>
<div id="outline-container-org84729e1" class="outline-2">
<h2 id="org84729e1"><span class="section-number-2">4.</span> Test Mode C</h2>
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<h2 id="orgc0ab5d1"><span class="section-number-2">4.</span> Test Mode C</h2>
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<h3 id="org8cc30f1"><span class="section-number-3">4.1.</span> Mode B and Mode C</h3>
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<h3 id="org9996dc6"><span class="section-number-3">4.1.</span> Mode B and Mode C</h3>
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<pre class="src src-matlab">data_B = extractDatData(sprintf(<span class="org-string">"/home/thomas/mnt/data_id21/22Jan/blc13491/id21/test_regul_220119/%s"</span>,<span class="org-string">"lut_const_fj_vel_19012022_1450.dat"</span>), <span class="org-comment-delimiter">.</span><span class="org-comment">..</span>
@@ -1620,12 +1620,12 @@ win = hanning(ceil(1<span class="org-builtin">/</span>Ts));
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<h2 id="org0d833d1"><span class="section-number-2">5.</span> Export numerator and denominator</h2>
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<h2 id="org1c0791b"><span class="section-number-2">5.</span> Export numerator and denominator</h2>
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<h3 id="org4532b44"><span class="section-number-3">5.1.</span> Export</h3>
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<h3 id="org22487de"><span class="section-number-3">5.1.</span> Export</h3>
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<pre class="src src-matlab">K_order = 10;
@@ -1673,8 +1673,8 @@ fclose(fileID);
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<h3 id="org78d8a99"><span class="section-number-3">5.2.</span> Verify</h3>
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<h3 id="org2b8461a"><span class="section-number-3">5.2.</span> Verify</h3>
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<pre class="src src-matlab">K_data = importdata(<span class="org-string">'X_tal_cage_PID_20Hz.dat'</span>);
@@ -1687,7 +1687,7 @@ K = tf(K_data(1,<span class="org-builtin">:</span>), K_data(2,<span class="org-b
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<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2022-02-15 mar. 14:18</p>
<p class="date">Created: 2022-02-20 dim. 23:36</p>
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