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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">Cedrat Actuator</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="#orgd28b4dd">1. Documentation</a></li>
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<li><a href="#org2594c75">2. Parameters</a></li>
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<li><a href="#org5b8504e">3. Identification</a></li>
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<li><a href="#org919f71c">4. Integral Force Feedback</a></li>
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<li><a href="#org7ec0c4b">5. Damped System</a></li>
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</ul>
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</div>
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</div>
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<div id="outline-container-orgd28b4dd" class="outline-2">
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<h2 id="orgd28b4dd"><span class="section-number-2">1</span> Documentation</h2>
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<div class="outline-text-2" id="text-1">
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<ul class="org-ul">
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<li>Blocked force: \(1400\ N\)</li>
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<li>Stiffness: \(10.8\ N/\mu m\)</li>
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<li>Resonance (free-free): \(6450\ Hz\)</li>
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<li>Resonance (blocked-free): \(1750\ Hz\)</li>
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<li>Height: \(H = 45\ mm\)</li>
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<li>Length: \(L = 80\ mm\)</li>
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<li>Width: \(22\ mm\)</li>
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<li>Mass: \(160\ g\)</li>
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</ul>
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<div class="figure">
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<p><img src="figs/cedrat_geometry.png" alt="cedrat_geometry.png" />
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</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org2594c75" class="outline-2">
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<h2 id="org2594c75"><span class="section-number-2">2</span> Parameters</h2>
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<div class="outline-text-2" id="text-2">
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<div class="org-src-container">
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<pre class="src src-matlab">cedrat.L = <span class="org-highlight-numbers-number">80</span>; <span class="org-comment">% Total Width of the Actuator[mm]</span>
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cedrat.H = <span class="org-highlight-numbers-number">45</span>; <span class="org-comment">% Total Height of the Actuator [mm]</span>
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cedrat.L2 = sqrt<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">(</span>cedrat.L<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">^</span><span class="org-highlight-numbers-number">2</span> <span class="org-type">+</span> <span class="org-rainbow-delimiters-depth-2">(</span>cedrat.H<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Length of the elipsoidal sections [mm]</span>
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cedrat.alpha = <span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>atan2<span class="org-rainbow-delimiters-depth-1">(</span>cedrat.L<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span>, cedrat.H<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% [deg]</span>
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cedrat.mtot = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">160</span>; <span class="org-comment">% Total mass of the Actuator [kg]</span>
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cedrat.m = cedrat.mtot<span class="org-type">/</span><span class="org-highlight-numbers-number">6</span>; <span class="org-comment">% Mass of each single element [kg]</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">cedrat.k = <span class="org-highlight-numbers-number">1e9</span>; <span class="org-comment">% Linear Stiffness of each "blade" [N/m]</span>
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cedrat.c = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>sqrt<span class="org-rainbow-delimiters-depth-1">(</span>cedrat.mtot<span class="org-type">*</span>cedrat.k<span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% [N/(m/s)]</span>
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cedrat.ka = <span class="org-highlight-numbers-number">5e7</span>; <span class="org-comment">% Linear Stiffness of the stack [N/m]</span>
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cedrat.ca = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>sqrt<span class="org-rainbow-delimiters-depth-1">(</span>cedrat.mtot<span class="org-type">*</span>cedrat.ka<span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% [N/(m/s)]</span>
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cedrat.kr = <span class="org-highlight-numbers-number">10</span>; <span class="org-comment">% Rotation Stiffness [N*m/(deg)]</span>
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cedrat.cr = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">0001</span>; <span class="org-comment">% Rotation Damping [N*m/(deg/s)]</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">K_iff = tf<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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</pre>
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|
||||
<pre class="src src-matlab">% dummy_mass = <span class="org-highlight-numbers-number">140</span>; % [kg]
|
||||
dummy_mass = <span class="org-highlight-numbers-number">1</span>; <span class="org-comment">% [kg]</span>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org5b8504e" class="outline-2">
|
||||
<h2 id="org5b8504e"><span class="section-number-2">3</span> Identification</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = <span class="org-highlight-numbers-number">0</span>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||
mdl = <span class="org-string">'cedrat_piezo'</span>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/F'</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>;
|
||||
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">'/Fz'</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>;
|
||||
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">'/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>;
|
||||
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">'/Dz'</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>;
|
||||
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">'/Fm'</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-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
G = linearize<span class="org-rainbow-delimiters-depth-1">(</span>mdl, io, options<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
G.InputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class="org-string">'F'</span>, <span class="org-string">'Fz'</span>, <span class="org-string">'Dw'</span><span class="org-rainbow-delimiters-depth-1">}</span>;
|
||||
G.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class="org-string">'Dz'</span>, <span class="org-string">'Fm'</span><span class="org-rainbow-delimiters-depth-1">}</span>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org6ebf8c8" class="figure">
|
||||
<p><img src="figs/cedrat_piezo_identified_tf.png" alt="cedrat_piezo_identified_tf.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 2: </span>Identified Transfer function (<a href="./figs/cedrat_piezo_identified_tf.png">png</a>, <a href="./figs/cedrat_piezo_identified_tf.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org919f71c" class="outline-2">
|
||||
<h2 id="org919f71c"><span class="section-number-2">4</span> Integral Force Feedback</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
|
||||
<div id="org964c2d0" class="figure">
|
||||
<p><img src="figs/iff_plant_cedrat.png" alt="iff_plant_cedrat.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 3: </span>Transfer function from \(F\) to \(F_m\) (<a href="./figs/iff_plant_cedrat.png">png</a>, <a href="./figs/iff_plant_cedrat.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">K_iff = <span class="org-type">-</span><span class="org-highlight-numbers-number">100000</span><span class="org-type">/</span>s<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span>s<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span> <span class="org-type">+</span> s<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span>s<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span> <span class="org-type">+</span> s<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org090ce7f" class="figure">
|
||||
<p><img src="figs/iff_open_loop_cedrat.png" alt="iff_open_loop_cedrat.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 4: </span>Open Loop Gain Transfer Function - Cedrat (<a href="./figs/iff_open_loop_cedrat.png">png</a>, <a href="./figs/iff_open_loop_cedrat.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org7ec0c4b" class="outline-2">
|
||||
<h2 id="org7ec0c4b"><span class="section-number-2">5</span> Damped System</h2>
|
||||
<div class="outline-text-2" id="text-5">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = <span class="org-highlight-numbers-number">0</span>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||
mdl = <span class="org-string">'cedrat_piezo'</span>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
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">'/F'</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>;
|
||||
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">'/Fz'</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>;
|
||||
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">'/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>;
|
||||
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">'/Dz'</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>;
|
||||
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">'/Fm'</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-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
G_iff = linearize<span class="org-rainbow-delimiters-depth-1">(</span>mdl, io, options<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
G_iff.InputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class="org-string">'F'</span>, <span class="org-string">'Fz'</span>, <span class="org-string">'Dw'</span><span class="org-rainbow-delimiters-depth-1">}</span>;
|
||||
G_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class="org-string">'Dz'</span>, <span class="org-string">'Fm'</span><span class="org-rainbow-delimiters-depth-1">}</span>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org2e7eff5" class="figure">
|
||||
<p><img src="figs/cedrat_iff_piezo_identified_tf.png" alt="cedrat_iff_piezo_identified_tf.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 5: </span>Identified Transfer function (<a href="./figs/cedrat_iff_piezo_identified_tf.png">png</a>, <a href="./figs/cedrat_iff_piezo_identified_tf.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2019-10-29 mar. 11:06</p>
|
||||
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
@ -1,330 +0,0 @@
|
||||
#+TITLE: Cedrat Actuator
|
||||
: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:
|
||||
|
||||
* Documentation
|
||||
- Blocked force: $1400\ N$
|
||||
- Stiffness: $10.8\ N/\mu m$
|
||||
- Resonance (free-free): $6450\ Hz$
|
||||
- Resonance (blocked-free): $1750\ Hz$
|
||||
- Height: $H = 45\ mm$
|
||||
- Length: $L = 80\ mm$
|
||||
- Width: $22\ mm$
|
||||
- Mass: $160\ g$
|
||||
|
||||
#+begin_src latex :file cedrat_geometry.pdf :post pdf2svg(file=*this*, ext="png") :exports results
|
||||
\begin{tikzpicture}
|
||||
\node[branch] (O) at ( 0, 0){};
|
||||
\node[branch] (A) at (-3, 1.5){};
|
||||
\node[branch] (C) at ( 0, 1.5){};
|
||||
\node[branch] (B) at ( 3, 1.5){};
|
||||
\node[branch] (T) at ( 0, 3){};
|
||||
|
||||
\draw[] (O) -- (A);
|
||||
\draw[] (O) -- node[midway, below]{$L_2$} (B);
|
||||
\draw[] (A) -- (C);
|
||||
\draw[] (C) -- (B);
|
||||
\draw[] (A) -- (T);
|
||||
\draw[] (B) -- (T);
|
||||
|
||||
\draw[dashed] (O) -- (T);
|
||||
\draw[dashed] (0, 0.5) arc (90:26:0.5) node[midway, above]{$\alpha$};
|
||||
|
||||
\draw[dashed, <->] ($(O) + (3.5, 0)$) -- node[right]{$H$} ($(T) + (3.5, 0)$);
|
||||
\draw[dashed, <->] ($(A) + (0, -2)$) -- node[below]{$L$} ($(B) + (0, -2)$);
|
||||
\end{tikzpicture}
|
||||
#+end_src
|
||||
|
||||
#+RESULTS:
|
||||
[[file:figs/cedrat_geometry.png]]
|
||||
|
||||
|
||||
* 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/cedrat_piezo.slx'
|
||||
#+end_src
|
||||
|
||||
* Parameters
|
||||
#+begin_src matlab
|
||||
cedrat.L = 80; % Total Width of the Actuator[mm]
|
||||
cedrat.H = 45; % Total Height of the Actuator [mm]
|
||||
cedrat.L2 = sqrt((cedrat.L/2)^2 + (cedrat.H/2)^2); % Length of the elipsoidal sections [mm]
|
||||
cedrat.alpha = 180/pi*atan2(cedrat.L/2, cedrat.H/2); % [deg]
|
||||
cedrat.mtot = 0.160; % Total mass of the Actuator [kg]
|
||||
cedrat.m = cedrat.mtot/6; % Mass of each single element [kg]
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
cedrat.k = 1e9; % Linear Stiffness of each "blade" [N/m]
|
||||
cedrat.c = 0.1*sqrt(cedrat.mtot*cedrat.k); % [N/(m/s)]
|
||||
|
||||
cedrat.ka = 5e7; % Linear Stiffness of the stack [N/m]
|
||||
cedrat.ca = 0.1*sqrt(cedrat.mtot*cedrat.ka); % [N/(m/s)]
|
||||
|
||||
cedrat.kr = 10; % Rotation Stiffness [N*m/(deg)]
|
||||
cedrat.cr = 0.0001; % Rotation Damping [N*m/(deg/s)]
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
K_iff = tf(0);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
% dummy_mass = 140; % [kg]
|
||||
dummy_mass = 1; % [kg]
|
||||
#+end_src
|
||||
|
||||
* Identification
|
||||
#+begin_src matlab
|
||||
%% Options for Linearized
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
%% Name of the Simulink File
|
||||
mdl = 'cedrat_piezo';
|
||||
|
||||
%% Input/Output definition
|
||||
io(1) = linio([mdl, '/F'], 1, 'input');
|
||||
io(2) = linio([mdl, '/Fz'], 1, 'input');
|
||||
io(3) = linio([mdl, '/Dw'], 1, 'input');
|
||||
io(4) = linio([mdl, '/Dz'], 1, 'output');
|
||||
io(5) = linio([mdl, '/Fm'], 1, 'output');
|
||||
|
||||
%% Run the linearization
|
||||
G = linearize(mdl, io, options);
|
||||
G.InputName = {'F', 'Fz', 'Dw'};
|
||||
G.OutputName = {'Dz', 'Fm'};
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(0, 5, 1000);
|
||||
|
||||
figure;
|
||||
subplot(2, 2, 1);
|
||||
title('From $F_z$ to $D_z$ - Compliance');
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G('Dz', 'Fz'), freqs, 'Hz'))), 'k-');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||
|
||||
subplot(2, 2, 2);
|
||||
title('From $D_w$ to $D_z$ - Transmissibility');
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G('Dz', 'Dw'), freqs, 'Hz'))), 'k-');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [V/N]'); xlabel('Frequency [Hz]');
|
||||
|
||||
subplot(2, 2, 3);
|
||||
title('From $F$ to $D_z$ - Plant');
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G('Dz', 'F'), freqs, 'Hz'))), 'k-');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||
|
||||
subplot(2, 2, 4);
|
||||
title('From $F$ to $F_m$ - IFF Plant');
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G('Fm', 'F'), freqs, 'Hz'))), 'k-');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [V/N]'); xlabel('Frequency [Hz]');
|
||||
#+end_src
|
||||
|
||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/cedrat_piezo_identified_tf.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:cedrat_piezo_identified_tf
|
||||
#+CAPTION: Identified Transfer function ([[./figs/cedrat_piezo_identified_tf.png][png]], [[./figs/cedrat_piezo_identified_tf.pdf][pdf]])
|
||||
[[file:figs/cedrat_piezo_identified_tf.png]]
|
||||
|
||||
* Integral Force Feedback
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(1, 5, 1000);
|
||||
|
||||
figure;
|
||||
|
||||
ax1 = subplot(2, 1, 1);
|
||||
plot(freqs, abs(squeeze(freqresp(-G('Fm', 'F'), freqs, 'Hz'))), 'k-');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
|
||||
|
||||
ax2 = subplot(2, 1, 2);
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(-G('Fm', 'F'), freqs, 'Hz'))), 'k-');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
#+end_src
|
||||
|
||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/iff_plant_cedrat.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:iff_plant_cedrat
|
||||
#+CAPTION: Transfer function from $F$ to $F_m$ ([[./figs/iff_plant_cedrat.png][png]], [[./figs/iff_plant_cedrat.pdf][pdf]])
|
||||
[[file:figs/iff_plant_cedrat.png]]
|
||||
|
||||
|
||||
#+begin_src matlab
|
||||
K_iff = -100000/s*(s/2/pi/100)/(1 + s/2/pi/100)*(s/2/pi/100)/(1 + s/2/pi/100);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(0, 5, 1000);
|
||||
|
||||
figure;
|
||||
|
||||
ax1 = subplot(2, 1, 1);
|
||||
plot(freqs, abs(squeeze(freqresp(K_iff*G('Fm', 'F'), freqs, 'Hz'))), 'k-');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
|
||||
|
||||
ax2 = subplot(2, 1, 2);
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(K_iff*G('Fm', 'F'), freqs, 'Hz'))), 'k-');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
#+end_src
|
||||
|
||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/iff_open_loop_cedrat.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:iff_open_loop_cedrat
|
||||
#+CAPTION: Open Loop Gain Transfer Function - Cedrat ([[./figs/iff_open_loop_cedrat.png][png]], [[./figs/iff_open_loop_cedrat.pdf][pdf]])
|
||||
[[file:figs/iff_open_loop_cedrat.png]]
|
||||
|
||||
* Damped System
|
||||
#+begin_src matlab
|
||||
%% Options for Linearized
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
%% Name of the Simulink File
|
||||
mdl = 'cedrat_piezo';
|
||||
|
||||
%% Input/Output definition
|
||||
io(1) = linio([mdl, '/F'], 1, 'input');
|
||||
io(2) = linio([mdl, '/Fz'], 1, 'input');
|
||||
io(3) = linio([mdl, '/Dw'], 1, 'input');
|
||||
io(4) = linio([mdl, '/Dz'], 1, 'output');
|
||||
io(5) = linio([mdl, '/Fm'], 1, 'output');
|
||||
|
||||
%% Run the linearization
|
||||
G_iff = linearize(mdl, io, options);
|
||||
G_iff.InputName = {'F', 'Fz', 'Dw'};
|
||||
G_iff.OutputName = {'Dz', 'Fm'};
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(0, 5, 1000);
|
||||
|
||||
figure;
|
||||
subplot(2, 2, 1);
|
||||
title('From $F_z$ to $D_z$ - Compliance');
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G('Dz', 'Fz'), freqs, 'Hz'))), 'k-');
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff('Dz', 'Fz'), freqs, 'Hz'))), 'k--');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||
|
||||
subplot(2, 2, 2);
|
||||
title('From $D_w$ to $D_z$ - Transmissibility');
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G('Dz', 'Dw'), freqs, 'Hz'))), 'k-');
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff('Dz', 'Dw'), freqs, 'Hz'))), 'k--');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [V/N]'); xlabel('Frequency [Hz]');
|
||||
|
||||
subplot(2, 2, 3);
|
||||
title('From $F$ to $D_z$ - Plant');
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G('Dz', 'F'), freqs, 'Hz'))), 'k-');
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff('Dz', 'F'), freqs, 'Hz'))), 'k--');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||
|
||||
subplot(2, 2, 4);
|
||||
title('From $F$ to $F_m$ - IFF Plant');
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G('Fm', 'F'), freqs, 'Hz'))), 'k-');
|
||||
plot(freqs, abs(squeeze(freqresp(G_iff('Fm', 'F'), freqs, 'Hz'))), 'k--');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [V/N]'); xlabel('Frequency [Hz]');
|
||||
#+end_src
|
||||
|
||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/cedrat_iff_piezo_identified_tf.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:cedrat_iff_piezo_identified_tf
|
||||
#+CAPTION: Identified Transfer function ([[./figs/cedrat_iff_piezo_identified_tf.png][png]], [[./figs/cedrat_iff_piezo_identified_tf.pdf][pdf]])
|
||||
[[file:figs/cedrat_iff_piezo_identified_tf.png]]
|
||||
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Loading…
Reference in New Issue
Block a user