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<title>Active Damping with an uni-axial model</title>
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</style>
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@@ -261,9 +260,9 @@ for the JavaScript code in this tag.
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</head>
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<body>
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<div id="org-div-home-and-up">
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<a accesskey="h" href="../index.html"> UP </a>
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<a accesskey="h" href="./index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </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">Active Damping with an uni-axial model</h1>
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<div id="table-of-contents">
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||||
@@ -274,63 +273,63 @@ for the JavaScript code in this tag.
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<ul>
|
||||
<li><a href="#org7409841">1.1. Init</a></li>
|
||||
<li><a href="#org7514f31">1.2. Identification</a></li>
|
||||
<li><a href="#org30a5b37">1.3. Sensitivity to disturbances</a></li>
|
||||
<li><a href="#orgbc3b2d2">1.3. Sensitivity to disturbances</a></li>
|
||||
<li><a href="#orgdda82c0">1.4. Undamped Plant</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org5a3389e">2. Integral Force Feedback</a>
|
||||
<ul>
|
||||
<li><a href="#orgf3a80f4">2.1. One degree-of-freedom example</a>
|
||||
<li><a href="#org8fee25f">2.1. One degree-of-freedom example</a>
|
||||
<ul>
|
||||
<li><a href="#orgfba4e95">2.1.1. Equations</a></li>
|
||||
<li><a href="#org8487491">2.1.2. Matlab Example</a></li>
|
||||
<li><a href="#orge4d9f41">2.1.1. Equations</a></li>
|
||||
<li><a href="#org3305ce8">2.1.2. Matlab Example</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#orgf884e9a">2.2. Control Design</a></li>
|
||||
<li><a href="#org55e3bff">2.3. Identification of the damped plant</a></li>
|
||||
<li><a href="#org340a3d7">2.4. Sensitivity to disturbances</a></li>
|
||||
<li><a href="#orgba948f4">2.5. Damped Plant</a></li>
|
||||
<li><a href="#org8b5a4f4">2.6. Conclusion</a></li>
|
||||
<li><a href="#orgc2ae0be">2.2. Control Design</a></li>
|
||||
<li><a href="#org6eda033">2.3. Identification of the damped plant</a></li>
|
||||
<li><a href="#orgae8bf4a">2.4. Sensitivity to disturbances</a></li>
|
||||
<li><a href="#orgf8558bc">2.5. Damped Plant</a></li>
|
||||
<li><a href="#org7146202">2.6. Conclusion</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#orgc4ca1b5">3. Relative Motion Control</a>
|
||||
<ul>
|
||||
<li><a href="#org3a4a38f">3.1. One degree-of-freedom example</a>
|
||||
<li><a href="#orgff968f4">3.1. One degree-of-freedom example</a>
|
||||
<ul>
|
||||
<li><a href="#orgc75e93d">3.1.1. Equations</a></li>
|
||||
<li><a href="#org6772235">3.1.2. Matlab Example</a></li>
|
||||
<li><a href="#orgd5a2de5">3.1.1. Equations</a></li>
|
||||
<li><a href="#orgfebe737">3.1.2. Matlab Example</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#orgf74b07b">3.2. Control Design</a></li>
|
||||
<li><a href="#org2b50744">3.3. Identification of the damped plant</a></li>
|
||||
<li><a href="#orgfe16b4e">3.4. Sensitivity to disturbances</a></li>
|
||||
<li><a href="#org1d28b24">3.5. Damped Plant</a></li>
|
||||
<li><a href="#org69267d0">3.6. Conclusion</a></li>
|
||||
<li><a href="#orgf3a1477">3.2. Control Design</a></li>
|
||||
<li><a href="#org0c94d61">3.3. Identification of the damped plant</a></li>
|
||||
<li><a href="#orgae7a685">3.4. Sensitivity to disturbances</a></li>
|
||||
<li><a href="#orgb0045d5">3.5. Damped Plant</a></li>
|
||||
<li><a href="#orgeacd46f">3.6. Conclusion</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org3cc03b0">4. Direct Velocity Feedback</a>
|
||||
<ul>
|
||||
<li><a href="#org8fee25f">4.1. One degree-of-freedom example</a>
|
||||
<li><a href="#orgb2d2757">4.1. One degree-of-freedom example</a>
|
||||
<ul>
|
||||
<li><a href="#orge4d9f41">4.1.1. Equations</a></li>
|
||||
<li><a href="#org3305ce8">4.1.2. Matlab Example</a></li>
|
||||
<li><a href="#org0d13907">4.1.1. Equations</a></li>
|
||||
<li><a href="#org5d7b09d">4.1.2. Matlab Example</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#orgc2ae0be">4.2. Control Design</a></li>
|
||||
<li><a href="#org6eda033">4.3. Identification of the damped plant</a></li>
|
||||
<li><a href="#orgbc3b2d2">4.4. Sensitivity to disturbances</a></li>
|
||||
<li><a href="#org69d8b1b">4.5. Damped Plant</a></li>
|
||||
<li><a href="#org0fffc79">4.6. Conclusion</a></li>
|
||||
<li><a href="#org1fe076f">4.2. Control Design</a></li>
|
||||
<li><a href="#orgee6ab5a">4.3. Identification of the damped plant</a></li>
|
||||
<li><a href="#org455bb51">4.4. Sensitivity to disturbances</a></li>
|
||||
<li><a href="#org6d852f5">4.5. Damped Plant</a></li>
|
||||
<li><a href="#org5d33a43">4.6. Conclusion</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org21441bc">5. Comparison</a>
|
||||
<ul>
|
||||
<li><a href="#orgbe907b4">5.1. Load the plants</a></li>
|
||||
<li><a href="#orgde6308d">5.2. Sensitivity to Disturbance</a></li>
|
||||
<li><a href="#orgf8558bc">5.3. Damped Plant</a></li>
|
||||
<li><a href="#orgb849304">5.3. Damped Plant</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org7146202">6. Conclusion</a></li>
|
||||
<li><a href="#org333697a">6. Conclusion</a></li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
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||||
@@ -444,8 +443,8 @@ And we save it for further analysis.
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||||
</div>
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||||
</div>
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||||
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||||
<div id="outline-container-org30a5b37" class="outline-3">
|
||||
<h3 id="org30a5b37"><span class="section-number-3">1.3</span> Sensitivity to disturbances</h3>
|
||||
<div id="outline-container-orgbc3b2d2" class="outline-3">
|
||||
<h3 id="orgbc3b2d2"><span class="section-number-3">1.3</span> Sensitivity to disturbances</h3>
|
||||
<div class="outline-text-3" id="text-1-3">
|
||||
<p>
|
||||
The sensitivity to disturbances are shown on figure <a href="#orgcf7fa15">1</a>.
|
||||
@@ -503,15 +502,15 @@ Then, it is applied on the simscape model.
|
||||
</p>
|
||||
</div>
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||||
|
||||
<div id="outline-container-orgf3a80f4" class="outline-3">
|
||||
<h3 id="orgf3a80f4"><span class="section-number-3">2.1</span> One degree-of-freedom example</h3>
|
||||
<div id="outline-container-org8fee25f" class="outline-3">
|
||||
<h3 id="org8fee25f"><span class="section-number-3">2.1</span> One degree-of-freedom example</h3>
|
||||
<div class="outline-text-3" id="text-2-1">
|
||||
<p>
|
||||
<a id="org7f37ded"></a>
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-orgfba4e95" class="outline-4">
|
||||
<h4 id="orgfba4e95"><span class="section-number-4">2.1.1</span> Equations</h4>
|
||||
<div id="outline-container-orge4d9f41" class="outline-4">
|
||||
<h4 id="orge4d9f41"><span class="section-number-4">2.1.1</span> Equations</h4>
|
||||
<div class="outline-text-4" id="text-2-1-1">
|
||||
|
||||
<div id="org1acdc30" class="figure">
|
||||
@@ -577,8 +576,8 @@ This is attainable if we have:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org8487491" class="outline-4">
|
||||
<h4 id="org8487491"><span class="section-number-4">2.1.2</span> Matlab Example</h4>
|
||||
<div id="outline-container-org3305ce8" class="outline-4">
|
||||
<h4 id="org3305ce8"><span class="section-number-4">2.1.2</span> Matlab Example</h4>
|
||||
<div class="outline-text-4" id="text-2-1-2">
|
||||
<p>
|
||||
Let define the system parameters.
|
||||
@@ -641,8 +640,8 @@ And the closed loop system is computed below.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf884e9a" class="outline-3">
|
||||
<h3 id="orgf884e9a"><span class="section-number-3">2.2</span> Control Design</h3>
|
||||
<div id="outline-container-orgc2ae0be" class="outline-3">
|
||||
<h3 id="orgc2ae0be"><span class="section-number-3">2.2</span> Control Design</h3>
|
||||
<div class="outline-text-3" id="text-2-2">
|
||||
<p>
|
||||
Let’s load the undamped plant:
|
||||
@@ -684,8 +683,8 @@ The corresponding loop gains are shown in figure <a href="#org36e3a94">7</a>.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org55e3bff" class="outline-3">
|
||||
<h3 id="org55e3bff"><span class="section-number-3">2.3</span> Identification of the damped plant</h3>
|
||||
<div id="outline-container-org6eda033" class="outline-3">
|
||||
<h3 id="org6eda033"><span class="section-number-3">2.3</span> Identification of the damped plant</h3>
|
||||
<div class="outline-text-3" id="text-2-3">
|
||||
<p>
|
||||
Let’s initialize the system prior to identification.
|
||||
@@ -738,8 +737,8 @@ And we save the damped plant for further analysis
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org340a3d7" class="outline-3">
|
||||
<h3 id="org340a3d7"><span class="section-number-3">2.4</span> Sensitivity to disturbances</h3>
|
||||
<div id="outline-container-orgae8bf4a" class="outline-3">
|
||||
<h3 id="orgae8bf4a"><span class="section-number-3">2.4</span> Sensitivity to disturbances</h3>
|
||||
<div class="outline-text-3" id="text-2-4">
|
||||
<p>
|
||||
As shown on figure <a href="#org38217ee">8</a>:
|
||||
@@ -775,8 +774,8 @@ For instance, the plots are not the same when using <code>minreal</code>.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgba948f4" class="outline-3">
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||||
<h3 id="orgba948f4"><span class="section-number-3">2.5</span> Damped Plant</h3>
|
||||
<div id="outline-container-orgf8558bc" class="outline-3">
|
||||
<h3 id="orgf8558bc"><span class="section-number-3">2.5</span> Damped Plant</h3>
|
||||
<div class="outline-text-3" id="text-2-5">
|
||||
<p>
|
||||
Now, look at the new damped plant to control.
|
||||
@@ -805,8 +804,8 @@ However, it increases coupling at low frequency (figure <a href="#org8017b2f">11
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org8b5a4f4" class="outline-3">
|
||||
<h3 id="org8b5a4f4"><span class="section-number-3">2.6</span> Conclusion</h3>
|
||||
<div id="outline-container-org7146202" class="outline-3">
|
||||
<h3 id="org7146202"><span class="section-number-3">2.6</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-2-6">
|
||||
<div class="important">
|
||||
<p>
|
||||
@@ -840,15 +839,15 @@ In the Relative Motion Control (RMC), a derivative feedback is applied between t
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org3a4a38f" class="outline-3">
|
||||
<h3 id="org3a4a38f"><span class="section-number-3">3.1</span> One degree-of-freedom example</h3>
|
||||
<div id="outline-container-orgff968f4" class="outline-3">
|
||||
<h3 id="orgff968f4"><span class="section-number-3">3.1</span> One degree-of-freedom example</h3>
|
||||
<div class="outline-text-3" id="text-3-1">
|
||||
<p>
|
||||
<a id="org6f16e09"></a>
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-orgc75e93d" class="outline-4">
|
||||
<h4 id="orgc75e93d"><span class="section-number-4">3.1.1</span> Equations</h4>
|
||||
<div id="outline-container-orgd5a2de5" class="outline-4">
|
||||
<h4 id="orgd5a2de5"><span class="section-number-4">3.1.1</span> Equations</h4>
|
||||
<div class="outline-text-4" id="text-3-1-1">
|
||||
|
||||
<div id="org64900ec" class="figure">
|
||||
@@ -907,8 +906,8 @@ This corresponds to a gain:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org6772235" class="outline-4">
|
||||
<h4 id="org6772235"><span class="section-number-4">3.1.2</span> Matlab Example</h4>
|
||||
<div id="outline-container-orgfebe737" class="outline-4">
|
||||
<h4 id="orgfebe737"><span class="section-number-4">3.1.2</span> Matlab Example</h4>
|
||||
<div class="outline-text-4" id="text-3-1-2">
|
||||
<p>
|
||||
Let define the system parameters.
|
||||
@@ -971,8 +970,8 @@ And the closed loop system is computed below.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf74b07b" class="outline-3">
|
||||
<h3 id="orgf74b07b"><span class="section-number-3">3.2</span> Control Design</h3>
|
||||
<div id="outline-container-orgf3a1477" class="outline-3">
|
||||
<h3 id="orgf3a1477"><span class="section-number-3">3.2</span> Control Design</h3>
|
||||
<div class="outline-text-3" id="text-3-2">
|
||||
<p>
|
||||
Let’s load the undamped plant:
|
||||
@@ -1015,8 +1014,8 @@ The obtained loop gains are shown in figure <a href="#orga5b8f12">15</a>.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org2b50744" class="outline-3">
|
||||
<h3 id="org2b50744"><span class="section-number-3">3.3</span> Identification of the damped plant</h3>
|
||||
<div id="outline-container-org0c94d61" class="outline-3">
|
||||
<h3 id="org0c94d61"><span class="section-number-3">3.3</span> Identification of the damped plant</h3>
|
||||
<div class="outline-text-3" id="text-3-3">
|
||||
<p>
|
||||
Let’s initialize the system prior to identification.
|
||||
@@ -1069,8 +1068,8 @@ And we save the damped plant for further analysis.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgfe16b4e" class="outline-3">
|
||||
<h3 id="orgfe16b4e"><span class="section-number-3">3.4</span> Sensitivity to disturbances</h3>
|
||||
<div id="outline-container-orgae7a685" class="outline-3">
|
||||
<h3 id="orgae7a685"><span class="section-number-3">3.4</span> Sensitivity to disturbances</h3>
|
||||
<div class="outline-text-3" id="text-3-4">
|
||||
<p>
|
||||
As shown in figure <a href="#org58aec78">16</a>, RMC control succeed in lowering the sensitivity to disturbances near resonance of the system.
|
||||
@@ -1092,8 +1091,8 @@ As shown in figure <a href="#org58aec78">16</a>, RMC control succeed in lowering
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org1d28b24" class="outline-3">
|
||||
<h3 id="org1d28b24"><span class="section-number-3">3.5</span> Damped Plant</h3>
|
||||
<div id="outline-container-orgb0045d5" class="outline-3">
|
||||
<h3 id="orgb0045d5"><span class="section-number-3">3.5</span> Damped Plant</h3>
|
||||
<div class="outline-text-3" id="text-3-5">
|
||||
|
||||
<div id="org2267bd4" class="figure">
|
||||
@@ -1104,8 +1103,8 @@ As shown in figure <a href="#org58aec78">16</a>, RMC control succeed in lowering
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org69267d0" class="outline-3">
|
||||
<h3 id="org69267d0"><span class="section-number-3">3.6</span> Conclusion</h3>
|
||||
<div id="outline-container-orgeacd46f" class="outline-3">
|
||||
<h3 id="orgeacd46f"><span class="section-number-3">3.6</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-3-6">
|
||||
<div class="important">
|
||||
<p>
|
||||
@@ -1137,15 +1136,15 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org8fee25f" class="outline-3">
|
||||
<h3 id="org8fee25f"><span class="section-number-3">4.1</span> One degree-of-freedom example</h3>
|
||||
<div id="outline-container-orgb2d2757" class="outline-3">
|
||||
<h3 id="orgb2d2757"><span class="section-number-3">4.1</span> One degree-of-freedom example</h3>
|
||||
<div class="outline-text-3" id="text-4-1">
|
||||
<p>
|
||||
<a id="org3a699cb"></a>
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-orge4d9f41" class="outline-4">
|
||||
<h4 id="orge4d9f41"><span class="section-number-4">4.1.1</span> Equations</h4>
|
||||
<div id="outline-container-org0d13907" class="outline-4">
|
||||
<h4 id="org0d13907"><span class="section-number-4">4.1.1</span> Equations</h4>
|
||||
<div class="outline-text-4" id="text-4-1-1">
|
||||
|
||||
<div id="org93ae6e4" class="figure">
|
||||
@@ -1204,8 +1203,8 @@ This corresponds to a gain:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org3305ce8" class="outline-4">
|
||||
<h4 id="org3305ce8"><span class="section-number-4">4.1.2</span> Matlab Example</h4>
|
||||
<div id="outline-container-org5d7b09d" class="outline-4">
|
||||
<h4 id="org5d7b09d"><span class="section-number-4">4.1.2</span> Matlab Example</h4>
|
||||
<div class="outline-text-4" id="text-4-1-2">
|
||||
<p>
|
||||
Let define the system parameters.
|
||||
@@ -1292,8 +1291,8 @@ The obtained sensitivity to disturbances is shown in figure <a href="#org1c3277a
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgc2ae0be" class="outline-3">
|
||||
<h3 id="orgc2ae0be"><span class="section-number-3">4.2</span> Control Design</h3>
|
||||
<div id="outline-container-org1fe076f" class="outline-3">
|
||||
<h3 id="org1fe076f"><span class="section-number-3">4.2</span> Control Design</h3>
|
||||
<div class="outline-text-3" id="text-4-2">
|
||||
<p>
|
||||
Let’s load the undamped plant:
|
||||
@@ -1332,8 +1331,8 @@ The controller is defined below and the obtained loop gain is shown in figure <a
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org6eda033" class="outline-3">
|
||||
<h3 id="org6eda033"><span class="section-number-3">4.3</span> Identification of the damped plant</h3>
|
||||
<div id="outline-container-orgee6ab5a" class="outline-3">
|
||||
<h3 id="orgee6ab5a"><span class="section-number-3">4.3</span> Identification of the damped plant</h3>
|
||||
<div class="outline-text-3" id="text-4-3">
|
||||
<p>
|
||||
Let’s initialize the system prior to identification.
|
||||
@@ -1386,8 +1385,8 @@ And we save the damped plant for further analysis.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgbc3b2d2" class="outline-3">
|
||||
<h3 id="orgbc3b2d2"><span class="section-number-3">4.4</span> Sensitivity to disturbances</h3>
|
||||
<div id="outline-container-org455bb51" class="outline-3">
|
||||
<h3 id="org455bb51"><span class="section-number-3">4.4</span> Sensitivity to disturbances</h3>
|
||||
<div class="outline-text-3" id="text-4-4">
|
||||
|
||||
<div id="org2558226" class="figure">
|
||||
@@ -1406,8 +1405,8 @@ And we save the damped plant for further analysis.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org69d8b1b" class="outline-3">
|
||||
<h3 id="org69d8b1b"><span class="section-number-3">4.5</span> Damped Plant</h3>
|
||||
<div id="outline-container-org6d852f5" class="outline-3">
|
||||
<h3 id="org6d852f5"><span class="section-number-3">4.5</span> Damped Plant</h3>
|
||||
<div class="outline-text-3" id="text-4-5">
|
||||
|
||||
<div id="org2fa3671" class="figure">
|
||||
@@ -1418,8 +1417,8 @@ And we save the damped plant for further analysis.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0fffc79" class="outline-3">
|
||||
<h3 id="org0fffc79"><span class="section-number-3">4.6</span> Conclusion</h3>
|
||||
<div id="outline-container-org5d33a43" class="outline-3">
|
||||
<h3 id="org5d33a43"><span class="section-number-3">4.6</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-4-6">
|
||||
<div class="important">
|
||||
<p>
|
||||
@@ -1490,8 +1489,8 @@ Direct Velocity Feedback:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf8558bc" class="outline-3">
|
||||
<h3 id="orgf8558bc"><span class="section-number-3">5.3</span> Damped Plant</h3>
|
||||
<div id="outline-container-orgb849304" class="outline-3">
|
||||
<h3 id="orgb849304"><span class="section-number-3">5.3</span> Damped Plant</h3>
|
||||
<div class="outline-text-3" id="text-5-3">
|
||||
|
||||
<div id="org043ecf3" class="figure">
|
||||
@@ -1517,8 +1516,8 @@ Direct Velocity Feedback:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org7146202" class="outline-2">
|
||||
<h2 id="org7146202"><span class="section-number-2">6</span> Conclusion</h2>
|
||||
<div id="outline-container-org333697a" class="outline-2">
|
||||
<h2 id="org333697a"><span class="section-number-2">6</span> Conclusion</h2>
|
||||
<div class="outline-text-2" id="text-6">
|
||||
<p>
|
||||
<a id="org58549a4"></a>
|
||||
@@ -1528,7 +1527,7 @@ Direct Velocity Feedback:
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2020-02-25 mar. 18:08</p>
|
||||
<p class="date">Created: 2020-02-25 mar. 18:21</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
Reference in New Issue
Block a user