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<title>Active Damping applied on the Simscape Model</title> <title>Active Damping applied on the Simscape Model</title>
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<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org9342dde">1. Undamped System</a> <li><a href="#org5d89cdc">1. Undamped System</a>
<ul> <ul>
<li><a href="#org8d4b4f6">1.1. Identification of the dynamics for Active Damping</a> <li><a href="#org75c59b5">1.1. Identification of the dynamics for Active Damping</a>
<ul> <ul>
<li><a href="#orgb855cd6">1.1.1. Initialize the Simulation</a></li> <li><a href="#org13c1b35">1.1.1. Initialize the Simulation</a></li>
<li><a href="#orgb12b84c">1.1.2. Identification</a></li> <li><a href="#org93e7893">1.1.2. Identification</a></li>
<li><a href="#org34365e1">1.1.3. Obtained Plants for Active Damping</a></li> <li><a href="#orgc283023">1.1.3. Obtained Plants for Active Damping</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgdb2efe9">1.2. Tomography Experiment</a> <li><a href="#org05ea47a">1.2. Tomography Experiment</a>
<ul> <ul>
<li><a href="#orgfb2c922">1.2.1. Simulation</a></li> <li><a href="#org22b92db">1.2.1. Simulation</a></li>
<li><a href="#org264103d">1.2.2. Results</a></li> <li><a href="#org2572ae7">1.2.2. Results</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</li> </li>
<li><a href="#org67089f2">2. Integral Force Feedback</a> <li><a href="#org7838397">2. Integral Force Feedback</a>
<ul> <ul>
<li><a href="#orgf44db18">2.1. Control Design</a> <li><a href="#org089ca66">2.1. Control Design</a>
<ul> <ul>
<li><a href="#orgf1f220a">2.1.1. Plant</a></li> <li><a href="#orgdfb8417">2.1.1. Plant</a></li>
<li><a href="#org9e39d4f">2.1.2. Control Design</a></li> <li><a href="#org87cd8ab">2.1.2. Control Design</a></li>
<li><a href="#org220ad45">2.1.3. Diagonal Controller</a></li> <li><a href="#org82f3b2f">2.1.3. Diagonal Controller</a></li>
<li><a href="#org6f43c28">2.1.4. IFF with High Pass Filter</a></li> <li><a href="#orgb93ab25">2.1.4. IFF with High Pass Filter</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgbd702ce">2.2. Tomography Experiment</a> <li><a href="#org64d8b6e">2.2. Tomography Experiment</a>
<ul> <ul>
<li><a href="#org6c6f2d1">2.2.1. Simulation with IFF Controller</a></li> <li><a href="#orga0d2c49">2.2.1. Simulation with IFF Controller</a></li>
<li><a href="#orgad8bea8">2.2.2. Simulation with IFF Controller with added High Pass Filter</a></li> <li><a href="#org73d7e8e">2.2.2. Simulation with IFF Controller with added High Pass Filter</a></li>
<li><a href="#orgedf02f4">2.2.3. Compare with Undamped system</a></li> <li><a href="#orgf00d1e2">2.2.3. Compare with Undamped system</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgc5f3f9b">2.3. Conclusion</a></li> <li><a href="#org1be894d">2.3. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org685023c">3. Direct Velocity Feedback</a> <li><a href="#orge87f2c6">3. Direct Velocity Feedback</a>
<ul> <ul>
<li><a href="#org60b5b30">3.1. Control Design</a> <li><a href="#org63708a2">3.1. Control Design</a>
<ul> <ul>
<li><a href="#orgf848412">3.1.1. Plant</a></li> <li><a href="#orge75a80d">3.1.1. Plant</a></li>
<li><a href="#org42b7fca">3.1.2. Control Design</a></li> <li><a href="#org93e6a45">3.1.2. Control Design</a></li>
<li><a href="#org2b8ee35">3.1.3. Diagonal Controller</a></li> <li><a href="#orgfe022fd">3.1.3. Diagonal Controller</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org508cd3e">3.2. Tomography Experiment</a> <li><a href="#orgfbc2c6e">3.2. Tomography Experiment</a>
<ul> <ul>
<li><a href="#org8f01b99">3.2.1. Initialize the Simulation</a></li> <li><a href="#org06c8b9d">3.2.1. Initialize the Simulation</a></li>
<li><a href="#org57c8573">3.2.2. Simulation</a></li> <li><a href="#org1172467">3.2.2. Simulation</a></li>
<li><a href="#org3b80a89">3.2.3. Compare with Undamped system</a></li> <li><a href="#org712bc79">3.2.3. Compare with Undamped system</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgbfc0305">3.3. Conclusion</a></li> <li><a href="#orgb7038fc">3.3. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org97c7099">4. Inertial Control</a> <li><a href="#org189c37a">4. Inertial Control</a>
<ul> <ul>
<li><a href="#org3d0c40e">4.1. Control Design</a> <li><a href="#org0b527cf">4.1. Control Design</a>
<ul> <ul>
<li><a href="#org7d50913">4.1.1. Plant</a></li> <li><a href="#org8f10824">4.1.1. Plant</a></li>
<li><a href="#org3bd6be5">4.1.2. Control Design</a></li> <li><a href="#orgbf5fc59">4.1.2. Control Design</a></li>
<li><a href="#orgb77c3b3">4.1.3. Diagonal Controller</a></li> <li><a href="#org26c423f">4.1.3. Diagonal Controller</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgfa1ca32">4.2. Tomography Experiment</a> <li><a href="#org4354127">4.2. Tomography Experiment</a>
<ul> <ul>
<li><a href="#orgf686c33">4.2.1. Initialize the Simulation</a></li> <li><a href="#org7a7d0fe">4.2.1. Initialize the Simulation</a></li>
<li><a href="#org1a7fe63">4.2.2. Simulation</a></li> <li><a href="#org4e1a6ec">4.2.2. Simulation</a></li>
<li><a href="#orge8b8bf8">4.2.3. Compare with Undamped system</a></li> <li><a href="#org43213af">4.2.3. Compare with Undamped system</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgde615df">4.3. Conclusion</a></li> <li><a href="#org1583f6b">4.3. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgada4654">5. Comparison</a> <li><a href="#org60a7861">5. Comparison</a>
<ul> <ul>
<li><a href="#org2976576">5.1. Load the plants</a></li> <li><a href="#orgcfb94b6">5.1. Load the plants</a></li>
<li><a href="#org835d9db">5.2. Sensitivity to Disturbance</a></li> <li><a href="#org478cd23">5.2. Sensitivity to Disturbance</a></li>
<li><a href="#orga94123d">5.3. Damped Plant</a></li> <li><a href="#org0c15520">5.3. Damped Plant</a></li>
<li><a href="#org75eccc0">5.4. Tomography Experiment</a> <li><a href="#org7cec242">5.4. Tomography Experiment</a>
<ul> <ul>
<li><a href="#org341a139">5.4.1. Load the Simulation Data</a></li> <li><a href="#org9cc6c6a">5.4.1. Load the Simulation Data</a></li>
<li><a href="#org267c98c">5.4.2. Frequency Domain Analysis</a></li> <li><a href="#org68b07c1">5.4.2. Frequency Domain Analysis</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</li> </li>
<li><a href="#org5f0f434">6. Useful Functions</a> <li><a href="#orgd1af630">6. Useful Functions</a>
<ul> <ul>
<li><a href="#org6ecc4dc">6.1. prepareTomographyExperiment</a> <li><a href="#org4da4ec2">6.1. prepareTomographyExperiment</a>
<ul> <ul>
<li><a href="#org435d4b8">Function Description</a></li> <li><a href="#orgd77a897">Function Description</a></li>
<li><a href="#org45dbf99">Optional Parameters</a></li> <li><a href="#org8bc4916">Optional Parameters</a></li>
<li><a href="#org80d47ea">Initialize the Simulation</a></li> <li><a href="#org2b62851">Initialize the Simulation</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -388,16 +388,16 @@ for the JavaScript code in this tag.
</div> </div>
<p> <p>
First, in section <a href="#org02231b3">1</a>, we will looked at the undamped system. First, in section <a href="#org977860d">1</a>, we will looked at the undamped system.
</p> </p>
<p> <p>
Then, we will compare three active damping techniques: Then, we will compare three active damping techniques:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>In section <a href="#orgd1ce2e4">2</a>: the integral force feedback is used</li> <li>In section <a href="#org50f479b">2</a>: the integral force feedback is used</li>
<li>In section <a href="#orgafbde82">3</a>: the direct velocity feedback is used</li> <li>In section <a href="#org41f3a46">3</a>: the direct velocity feedback is used</li>
<li>In section <a href="#org431eadf">4</a>: inertial control is used</li> <li>In section <a href="#org79aba2e">4</a>: inertial control is used</li>
</ul> </ul>
<p> <p>
@ -417,11 +417,11 @@ The disturbances are:
<li>Motion errors of all the stages</li> <li>Motion errors of all the stages</li>
</ul> </ul>
<div id="outline-container-org9342dde" class="outline-2"> <div id="outline-container-org5d89cdc" class="outline-2">
<h2 id="org9342dde"><span class="section-number-2">1</span> Undamped System</h2> <h2 id="org5d89cdc"><span class="section-number-2">1</span> Undamped System</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
<a id="org02231b3"></a> <a id="org977860d"></a>
</p> </p>
<div class="note"> <div class="note">
<p> <p>
@ -435,12 +435,12 @@ The performance of this undamped system will be compared with the damped system
</p> </p>
</div> </div>
<div id="outline-container-org8d4b4f6" class="outline-3"> <div id="outline-container-org75c59b5" class="outline-3">
<h3 id="org8d4b4f6"><span class="section-number-3">1.1</span> Identification of the dynamics for Active Damping</h3> <h3 id="org75c59b5"><span class="section-number-3">1.1</span> Identification of the dynamics for Active Damping</h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-1-1">
</div> </div>
<div id="outline-container-orgb855cd6" class="outline-4"> <div id="outline-container-org13c1b35" class="outline-4">
<h4 id="orgb855cd6"><span class="section-number-4">1.1.1</span> Initialize the Simulation</h4> <h4 id="org13c1b35"><span class="section-number-4">1.1.1</span> Initialize the Simulation</h4>
<div class="outline-text-4" id="text-1-1-1"> <div class="outline-text-4" id="text-1-1-1">
<p> <p>
We initialize all the stages with the default parameters. We initialize all the stages with the default parameters.
@ -491,8 +491,8 @@ save(<span class="org-string">'./mat/controllers.mat'</span>, <span class="org-s
</div> </div>
</div> </div>
<div id="outline-container-orgb12b84c" class="outline-4"> <div id="outline-container-org93e7893" class="outline-4">
<h4 id="orgb12b84c"><span class="section-number-4">1.1.2</span> Identification</h4> <h4 id="org93e7893"><span class="section-number-4">1.1.2</span> Identification</h4>
<div class="outline-text-4" id="text-1-1-2"> <div class="outline-text-4" id="text-1-1-2">
<p> <p>
First, we identify the dynamics of the system using the <code>linearize</code> function. First, we identify the dynamics of the system using the <code>linearize</code> function.
@ -541,25 +541,25 @@ And we save them for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-org34365e1" class="outline-4"> <div id="outline-container-orgc283023" class="outline-4">
<h4 id="org34365e1"><span class="section-number-4">1.1.3</span> Obtained Plants for Active Damping</h4> <h4 id="orgc283023"><span class="section-number-4">1.1.3</span> Obtained Plants for Active Damping</h4>
<div class="outline-text-4" id="text-1-1-3"> <div class="outline-text-4" id="text-1-1-3">
<div id="orgac91a7a" class="figure"> <div id="orgb06c0f1" class="figure">
<p><img src="figs/nass_active_damping_iff_plant.png" alt="nass_active_damping_iff_plant.png" /> <p><img src="figs/nass_active_damping_iff_plant.png" alt="nass_active_damping_iff_plant.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span><code>G_iff</code>: IFF Plant (<a href="./figs/nass_active_damping_iff_plant.png">png</a>, <a href="./figs/nass_active_damping_iff_plant.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 1: </span><code>G_iff</code>: IFF Plant (<a href="./figs/nass_active_damping_iff_plant.png">png</a>, <a href="./figs/nass_active_damping_iff_plant.pdf">pdf</a>)</p>
</div> </div>
<div id="org97d6cca" class="figure"> <div id="org90aa5ef" class="figure">
<p><img src="figs/nass_active_damping_ine_plant.png" alt="nass_active_damping_ine_plant.png" /> <p><img src="figs/nass_active_damping_ine_plant.png" alt="nass_active_damping_ine_plant.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span><code>G_dvf</code>: Plant for Direct Velocity Feedback (<a href="./figs/nass_active_damping_dvf_plant.png">png</a>, <a href="./figs/nass_active_damping_dvf_plant.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 2: </span><code>G_dvf</code>: Plant for Direct Velocity Feedback (<a href="./figs/nass_active_damping_dvf_plant.png">png</a>, <a href="./figs/nass_active_damping_dvf_plant.pdf">pdf</a>)</p>
</div> </div>
<div id="orgbb6a16f" class="figure"> <div id="orgcbf8f5e" class="figure">
<p><img src="figs/nass_active_damping_inertial_plant.png" alt="nass_active_damping_inertial_plant.png" /> <p><img src="figs/nass_active_damping_inertial_plant.png" alt="nass_active_damping_inertial_plant.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Inertial Feedback Plant (<a href="./figs/nass_active_damping_inertial_plant.png">png</a>, <a href="./figs/nass_active_damping_inertial_plant.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 3: </span>Inertial Feedback Plant (<a href="./figs/nass_active_damping_inertial_plant.png">png</a>, <a href="./figs/nass_active_damping_inertial_plant.pdf">pdf</a>)</p>
@ -568,12 +568,12 @@ And we save them for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-orgdb2efe9" class="outline-3"> <div id="outline-container-org05ea47a" class="outline-3">
<h3 id="orgdb2efe9"><span class="section-number-3">1.2</span> Tomography Experiment</h3> <h3 id="org05ea47a"><span class="section-number-3">1.2</span> Tomography Experiment</h3>
<div class="outline-text-3" id="text-1-2"> <div class="outline-text-3" id="text-1-2">
</div> </div>
<div id="outline-container-orgfb2c922" class="outline-4"> <div id="outline-container-org22b92db" class="outline-4">
<h4 id="orgfb2c922"><span class="section-number-4">1.2.1</span> Simulation</h4> <h4 id="org22b92db"><span class="section-number-4">1.2.1</span> Simulation</h4>
<div class="outline-text-4" id="text-1-2-1"> <div class="outline-text-4" id="text-1-2-1">
<p> <p>
We initialize elements for the tomography experiment. We initialize elements for the tomography experiment.
@ -610,8 +610,8 @@ Finally, we save the simulation results for further analysis
</div> </div>
</div> </div>
<div id="outline-container-org264103d" class="outline-4"> <div id="outline-container-org2572ae7" class="outline-4">
<h4 id="org264103d"><span class="section-number-4">1.2.2</span> Results</h4> <h4 id="org2572ae7"><span class="section-number-4">1.2.2</span> Results</h4>
<div class="outline-text-4" id="text-1-2-2"> <div class="outline-text-4" id="text-1-2-2">
<p> <p>
We load the results of tomography experiments. We load the results of tomography experiments.
@ -623,14 +623,14 @@ t = linspace(0, 3, length(En(<span class="org-type">:</span>,1)));
</div> </div>
<div id="org625b4f8" class="figure"> <div id="org603a0d4" class="figure">
<p><img src="figs/nass_act_damp_undamped_sim_tomo_trans.png" alt="nass_act_damp_undamped_sim_tomo_trans.png" /> <p><img src="figs/nass_act_damp_undamped_sim_tomo_trans.png" alt="nass_act_damp_undamped_sim_tomo_trans.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Position Error during tomography experiment - Translations (<a href="./figs/nass_act_damp_undamped_sim_tomo_trans.png">png</a>, <a href="./figs/nass_act_damp_undamped_sim_tomo_trans.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 4: </span>Position Error during tomography experiment - Translations (<a href="./figs/nass_act_damp_undamped_sim_tomo_trans.png">png</a>, <a href="./figs/nass_act_damp_undamped_sim_tomo_trans.pdf">pdf</a>)</p>
</div> </div>
<div id="orgd213d43" class="figure"> <div id="orgdb366a5" class="figure">
<p><img src="figs/nass_act_damp_undamped_sim_tomo_rot.png" alt="nass_act_damp_undamped_sim_tomo_rot.png" /> <p><img src="figs/nass_act_damp_undamped_sim_tomo_rot.png" alt="nass_act_damp_undamped_sim_tomo_rot.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Position Error during tomography experiment - Rotations (<a href="./figs/nass_act_damp_undamped_sim_tomo_rot.png">png</a>, <a href="./figs/nass_act_damp_undamped_sim_tomo_rot.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 5: </span>Position Error during tomography experiment - Rotations (<a href="./figs/nass_act_damp_undamped_sim_tomo_rot.png">png</a>, <a href="./figs/nass_act_damp_undamped_sim_tomo_rot.pdf">pdf</a>)</p>
@ -640,11 +640,11 @@ t = linspace(0, 3, length(En(<span class="org-type">:</span>,1)));
</div> </div>
</div> </div>
<div id="outline-container-org67089f2" class="outline-2"> <div id="outline-container-org7838397" class="outline-2">
<h2 id="org67089f2"><span class="section-number-2">2</span> Integral Force Feedback</h2> <h2 id="org7838397"><span class="section-number-2">2</span> Integral Force Feedback</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<a id="orgd1ce2e4"></a> <a id="org50f479b"></a>
</p> </p>
<div class="note"> <div class="note">
<p> <p>
@ -657,12 +657,12 @@ Integral Force Feedback is applied on the simscape model.
</p> </p>
</div> </div>
<div id="outline-container-orgf44db18" class="outline-3"> <div id="outline-container-org089ca66" class="outline-3">
<h3 id="orgf44db18"><span class="section-number-3">2.1</span> Control Design</h3> <h3 id="org089ca66"><span class="section-number-3">2.1</span> Control Design</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
</div> </div>
<div id="outline-container-orgf1f220a" class="outline-4"> <div id="outline-container-orgdfb8417" class="outline-4">
<h4 id="orgf1f220a"><span class="section-number-4">2.1.1</span> Plant</h4> <h4 id="orgdfb8417"><span class="section-number-4">2.1.1</span> Plant</h4>
<div class="outline-text-4" id="text-2-1-1"> <div class="outline-text-4" id="text-2-1-1">
<p> <p>
Let&rsquo;s load the previously indentified undamped plant: Let&rsquo;s load the previously indentified undamped plant:
@ -673,11 +673,11 @@ Let&rsquo;s load the previously indentified undamped plant:
</div> </div>
<p> <p>
Let&rsquo;s look at the transfer function from actuator forces in the nano-hexapod to the force sensor in the nano-hexapod legs for all 6 pairs of actuator/sensor (figure <a href="#orgac31951">6</a>). Let&rsquo;s look at the transfer function from actuator forces in the nano-hexapod to the force sensor in the nano-hexapod legs for all 6 pairs of actuator/sensor (figure <a href="#org709c442">6</a>).
</p> </p>
<div id="orgac31951" class="figure"> <div id="org709c442" class="figure">
<p><img src="figs/iff_plant.png" alt="iff_plant.png" /> <p><img src="figs/iff_plant.png" alt="iff_plant.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Transfer function from forces applied in the legs to force sensor (<a href="./figs/iff_plant.png">png</a>, <a href="./figs/iff_plant.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 6: </span>Transfer function from forces applied in the legs to force sensor (<a href="./figs/iff_plant.png">png</a>, <a href="./figs/iff_plant.pdf">pdf</a>)</p>
@ -685,8 +685,8 @@ Let&rsquo;s look at the transfer function from actuator forces in the nano-hexap
</div> </div>
</div> </div>
<div id="outline-container-org9e39d4f" class="outline-4"> <div id="outline-container-org87cd8ab" class="outline-4">
<h4 id="org9e39d4f"><span class="section-number-4">2.1.2</span> Control Design</h4> <h4 id="org87cd8ab"><span class="section-number-4">2.1.2</span> Control Design</h4>
<div class="outline-text-4" id="text-2-1-2"> <div class="outline-text-4" id="text-2-1-2">
<p> <p>
The controller for each pair of actuator/sensor is: The controller for each pair of actuator/sensor is:
@ -697,11 +697,11 @@ The controller for each pair of actuator/sensor is:
</div> </div>
<p> <p>
The corresponding loop gains are shown in figure <a href="#org4d8791f">7</a>. The corresponding loop gains are shown in figure <a href="#org86c2154">7</a>.
</p> </p>
<div id="org4d8791f" class="figure"> <div id="org86c2154" class="figure">
<p><img src="figs/iff_open_loop.png" alt="iff_open_loop.png" /> <p><img src="figs/iff_open_loop.png" alt="iff_open_loop.png" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/iff_open_loop.png">png</a>, <a href="./figs/iff_open_loop.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 7: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/iff_open_loop.png">png</a>, <a href="./figs/iff_open_loop.pdf">pdf</a>)</p>
@ -709,8 +709,8 @@ The corresponding loop gains are shown in figure <a href="#org4d8791f">7</a>.
</div> </div>
</div> </div>
<div id="outline-container-org220ad45" class="outline-4"> <div id="outline-container-org82f3b2f" class="outline-4">
<h4 id="org220ad45"><span class="section-number-4">2.1.3</span> Diagonal Controller</h4> <h4 id="org82f3b2f"><span class="section-number-4">2.1.3</span> Diagonal Controller</h4>
<div class="outline-text-4" id="text-2-1-3"> <div class="outline-text-4" id="text-2-1-3">
<p> <p>
We create the diagonal controller and we add a minus sign as we have a positive We create the diagonal controller and we add a minus sign as we have a positive
@ -731,8 +731,8 @@ We save the controller for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-org6f43c28" class="outline-4"> <div id="outline-container-orgb93ab25" class="outline-4">
<h4 id="org6f43c28"><span class="section-number-4">2.1.4</span> IFF with High Pass Filter</h4> <h4 id="orgb93ab25"><span class="section-number-4">2.1.4</span> IFF with High Pass Filter</h4>
<div class="outline-text-4" id="text-2-1-4"> <div class="outline-text-4" id="text-2-1-4">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">w_hpf = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>10; <span class="org-comment">% Cut-off frequency for the high pass filter [rad/s]</span> <pre class="src src-matlab">w_hpf = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>10; <span class="org-comment">% Cut-off frequency for the high pass filter [rad/s]</span>
@ -743,10 +743,10 @@ K_iff = 2<span class="org-type">*</span><span class="org-constant">pi</span><spa
</div> </div>
<p> <p>
The corresponding loop gains are shown in figure <a href="#orgee0b506">8</a>. The corresponding loop gains are shown in figure <a href="#org483db09">8</a>.
</p> </p>
<div id="orgee0b506" class="figure"> <div id="org483db09" class="figure">
<p><img src="figs/iff_hpf_open_loop.png" alt="iff_hpf_open_loop.png" /> <p><img src="figs/iff_hpf_open_loop.png" alt="iff_hpf_open_loop.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>Loop Gain for the Integral Force Feedback with an High pass filter (<a href="./figs/iff_hpf_open_loop.png">png</a>, <a href="./figs/iff_hpf_open_loop.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 8: </span>Loop Gain for the Integral Force Feedback with an High pass filter (<a href="./figs/iff_hpf_open_loop.png">png</a>, <a href="./figs/iff_hpf_open_loop.pdf">pdf</a>)</p>
@ -772,12 +772,12 @@ We save the controller for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-orgbd702ce" class="outline-3"> <div id="outline-container-org64d8b6e" class="outline-3">
<h3 id="orgbd702ce"><span class="section-number-3">2.2</span> Tomography Experiment</h3> <h3 id="org64d8b6e"><span class="section-number-3">2.2</span> Tomography Experiment</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
</div> </div>
<div id="outline-container-org6c6f2d1" class="outline-4"> <div id="outline-container-orga0d2c49" class="outline-4">
<h4 id="org6c6f2d1"><span class="section-number-4">2.2.1</span> Simulation with IFF Controller</h4> <h4 id="orga0d2c49"><span class="section-number-4">2.2.1</span> Simulation with IFF Controller</h4>
<div class="outline-text-4" id="text-2-2-1"> <div class="outline-text-4" id="text-2-2-1">
<p> <p>
We initialize elements for the tomography experiment. We initialize elements for the tomography experiment.
@ -825,8 +825,8 @@ save(<span class="org-string">'./active_damping/mat/tomo_exp.mat'</span>, <span
</div> </div>
</div> </div>
<div id="outline-container-orgad8bea8" class="outline-4"> <div id="outline-container-org73d7e8e" class="outline-4">
<h4 id="orgad8bea8"><span class="section-number-4">2.2.2</span> Simulation with IFF Controller with added High Pass Filter</h4> <h4 id="org73d7e8e"><span class="section-number-4">2.2.2</span> Simulation with IFF Controller with added High Pass Filter</h4>
<div class="outline-text-4" id="text-2-2-2"> <div class="outline-text-4" id="text-2-2-2">
<p> <p>
We initialize elements for the tomography experiment. We initialize elements for the tomography experiment.
@ -874,8 +874,8 @@ save(<span class="org-string">'./active_damping/mat/tomo_exp.mat'</span>, <span
</div> </div>
</div> </div>
<div id="outline-container-orgedf02f4" class="outline-4"> <div id="outline-container-orgf00d1e2" class="outline-4">
<h4 id="orgedf02f4"><span class="section-number-4">2.2.3</span> Compare with Undamped system</h4> <h4 id="orgf00d1e2"><span class="section-number-4">2.2.3</span> Compare with Undamped system</h4>
<div class="outline-text-4" id="text-2-2-3"> <div class="outline-text-4" id="text-2-2-3">
<p> <p>
We load the results of tomography experiments. We load the results of tomography experiments.
@ -887,21 +887,21 @@ t = linspace(0, 3, length(En(<span class="org-type">:</span>,1)));
</div> </div>
<div id="orgbe947f0" class="figure"> <div id="org40817f4" class="figure">
<p><img src="figs/nass_act_damp_iff_sim_tomo_xy.png" alt="nass_act_damp_iff_sim_tomo_xy.png" /> <p><img src="figs/nass_act_damp_iff_sim_tomo_xy.png" alt="nass_act_damp_iff_sim_tomo_xy.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>Position Error during tomography experiment - XY Motion (<a href="./figs/nass_act_damp_iff_sim_tomo_xy.png">png</a>, <a href="./figs/nass_act_damp_iff_sim_tomo_xy.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 9: </span>Position Error during tomography experiment - XY Motion (<a href="./figs/nass_act_damp_iff_sim_tomo_xy.png">png</a>, <a href="./figs/nass_act_damp_iff_sim_tomo_xy.pdf">pdf</a>)</p>
</div> </div>
<div id="orgc275297" class="figure"> <div id="org59740ae" class="figure">
<p><img src="figs/nass_act_damp_iff_sim_tomo_trans.png" alt="nass_act_damp_iff_sim_tomo_trans.png" /> <p><img src="figs/nass_act_damp_iff_sim_tomo_trans.png" alt="nass_act_damp_iff_sim_tomo_trans.png" />
</p> </p>
<p><span class="figure-number">Figure 10: </span>Position Error during tomography experiment - Translations (<a href="./figs/nass_act_damp_iff_sim_tomo_trans.png">png</a>, <a href="./figs/nass_act_damp_iff_sim_tomo_trans.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 10: </span>Position Error during tomography experiment - Translations (<a href="./figs/nass_act_damp_iff_sim_tomo_trans.png">png</a>, <a href="./figs/nass_act_damp_iff_sim_tomo_trans.pdf">pdf</a>)</p>
</div> </div>
<div id="org03d0c7d" class="figure"> <div id="orgf2e1614" class="figure">
<p><img src="figs/nass_act_damp_iff_sim_tomo_rot.png" alt="nass_act_damp_iff_sim_tomo_rot.png" /> <p><img src="figs/nass_act_damp_iff_sim_tomo_rot.png" alt="nass_act_damp_iff_sim_tomo_rot.png" />
</p> </p>
<p><span class="figure-number">Figure 11: </span>Position Error during tomography experiment - Rotations (<a href="./figs/nass_act_damp_iff_sim_tomo_rot.png">png</a>, <a href="./figs/nass_act_damp_iff_sim_tomo_rot.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 11: </span>Position Error during tomography experiment - Rotations (<a href="./figs/nass_act_damp_iff_sim_tomo_rot.png">png</a>, <a href="./figs/nass_act_damp_iff_sim_tomo_rot.pdf">pdf</a>)</p>
@ -910,8 +910,8 @@ t = linspace(0, 3, length(En(<span class="org-type">:</span>,1)));
</div> </div>
</div> </div>
<div id="outline-container-orgc5f3f9b" class="outline-3"> <div id="outline-container-org1be894d" class="outline-3">
<h3 id="orgc5f3f9b"><span class="section-number-3">2.3</span> Conclusion</h3> <h3 id="org1be894d"><span class="section-number-3">2.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<div class="important"> <div class="important">
<p> <p>
@ -928,11 +928,11 @@ Integral Force Feedback:
</div> </div>
</div> </div>
<div id="outline-container-org685023c" class="outline-2"> <div id="outline-container-orge87f2c6" class="outline-2">
<h2 id="org685023c"><span class="section-number-2">3</span> Direct Velocity Feedback</h2> <h2 id="orge87f2c6"><span class="section-number-2">3</span> Direct Velocity Feedback</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<p> <p>
<a id="orgafbde82"></a> <a id="org41f3a46"></a>
</p> </p>
<div class="note"> <div class="note">
<p> <p>
@ -946,12 +946,12 @@ The actuator displacement can be measured with a capacitive sensor for instance.
</p> </p>
</div> </div>
<div id="outline-container-org60b5b30" class="outline-3"> <div id="outline-container-org63708a2" class="outline-3">
<h3 id="org60b5b30"><span class="section-number-3">3.1</span> Control Design</h3> <h3 id="org63708a2"><span class="section-number-3">3.1</span> Control Design</h3>
<div class="outline-text-3" id="text-3-1"> <div class="outline-text-3" id="text-3-1">
</div> </div>
<div id="outline-container-orgf848412" class="outline-4"> <div id="outline-container-orge75a80d" class="outline-4">
<h4 id="orgf848412"><span class="section-number-4">3.1.1</span> Plant</h4> <h4 id="orge75a80d"><span class="section-number-4">3.1.1</span> Plant</h4>
<div class="outline-text-4" id="text-3-1-1"> <div class="outline-text-4" id="text-3-1-1">
<p> <p>
Let&rsquo;s load the undamped plant: Let&rsquo;s load the undamped plant:
@ -962,11 +962,11 @@ Let&rsquo;s load the undamped plant:
</div> </div>
<p> <p>
Let&rsquo;s look at the transfer function from actuator forces in the nano-hexapod to the measured displacement of the actuator for all 6 pairs of actuator/sensor (figure <a href="#org8ead4ee">12</a>). Let&rsquo;s look at the transfer function from actuator forces in the nano-hexapod to the measured displacement of the actuator for all 6 pairs of actuator/sensor (figure <a href="#org1c4b9c5">12</a>).
</p> </p>
<div id="org8ead4ee" class="figure"> <div id="org1c4b9c5" class="figure">
<p><img src="figs/dvf_plant.png" alt="dvf_plant.png" /> <p><img src="figs/dvf_plant.png" alt="dvf_plant.png" />
</p> </p>
<p><span class="figure-number">Figure 12: </span>Transfer function from forces applied in the legs to leg displacement sensor (<a href="./figs/dvf_plant.png">png</a>, <a href="./figs/dvf_plant.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 12: </span>Transfer function from forces applied in the legs to leg displacement sensor (<a href="./figs/dvf_plant.png">png</a>, <a href="./figs/dvf_plant.pdf">pdf</a>)</p>
@ -974,8 +974,8 @@ Let&rsquo;s look at the transfer function from actuator forces in the nano-hexap
</div> </div>
</div> </div>
<div id="outline-container-org42b7fca" class="outline-4"> <div id="outline-container-org93e6a45" class="outline-4">
<h4 id="org42b7fca"><span class="section-number-4">3.1.2</span> Control Design</h4> <h4 id="org93e6a45"><span class="section-number-4">3.1.2</span> Control Design</h4>
<div class="outline-text-4" id="text-3-1-2"> <div class="outline-text-4" id="text-3-1-2">
<p> <p>
The Direct Velocity Feedback is defined below. The Direct Velocity Feedback is defined below.
@ -987,11 +987,11 @@ A Low pass Filter is added to make the controller transfer function proper.
</div> </div>
<p> <p>
The obtained loop gains are shown in figure <a href="#orge5257d3">13</a>. The obtained loop gains are shown in figure <a href="#orgd5f1986">13</a>.
</p> </p>
<div id="orge5257d3" class="figure"> <div id="orgd5f1986" class="figure">
<p><img src="figs/dvf_open_loop.png" alt="dvf_open_loop.png" /> <p><img src="figs/dvf_open_loop.png" alt="dvf_open_loop.png" />
</p> </p>
<p><span class="figure-number">Figure 13: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/dvf_open_loop.png">png</a>, <a href="./figs/dvf_open_loop.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 13: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/dvf_open_loop.png">png</a>, <a href="./figs/dvf_open_loop.pdf">pdf</a>)</p>
@ -999,8 +999,8 @@ The obtained loop gains are shown in figure <a href="#orge5257d3">13</a>.
</div> </div>
</div> </div>
<div id="outline-container-org2b8ee35" class="outline-4"> <div id="outline-container-orgfe022fd" class="outline-4">
<h4 id="org2b8ee35"><span class="section-number-4">3.1.3</span> Diagonal Controller</h4> <h4 id="orgfe022fd"><span class="section-number-4">3.1.3</span> Diagonal Controller</h4>
<div class="outline-text-4" id="text-3-1-3"> <div class="outline-text-4" id="text-3-1-3">
<p> <p>
We create the diagonal controller and we add a minus sign as we have a positive feedback architecture. We create the diagonal controller and we add a minus sign as we have a positive feedback architecture.
@ -1021,12 +1021,12 @@ We save the controller for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-org508cd3e" class="outline-3"> <div id="outline-container-orgfbc2c6e" class="outline-3">
<h3 id="org508cd3e"><span class="section-number-3">3.2</span> Tomography Experiment</h3> <h3 id="orgfbc2c6e"><span class="section-number-3">3.2</span> Tomography Experiment</h3>
<div class="outline-text-3" id="text-3-2"> <div class="outline-text-3" id="text-3-2">
</div> </div>
<div id="outline-container-org8f01b99" class="outline-4"> <div id="outline-container-org06c8b9d" class="outline-4">
<h4 id="org8f01b99"><span class="section-number-4">3.2.1</span> Initialize the Simulation</h4> <h4 id="org06c8b9d"><span class="section-number-4">3.2.1</span> Initialize the Simulation</h4>
<div class="outline-text-4" id="text-3-2-1"> <div class="outline-text-4" id="text-3-2-1">
<p> <p>
We initialize elements for the tomography experiment. We initialize elements for the tomography experiment.
@ -1047,8 +1047,8 @@ save(<span class="org-string">'./mat/controllers.mat'</span>, <span class="org-s
</div> </div>
</div> </div>
<div id="outline-container-org57c8573" class="outline-4"> <div id="outline-container-org1172467" class="outline-4">
<h4 id="org57c8573"><span class="section-number-4">3.2.2</span> Simulation</h4> <h4 id="org1172467"><span class="section-number-4">3.2.2</span> Simulation</h4>
<div class="outline-text-4" id="text-3-2-2"> <div class="outline-text-4" id="text-3-2-2">
<p> <p>
We change the simulation stop time. We change the simulation stop time.
@ -1079,8 +1079,8 @@ save(<span class="org-string">'./active_damping/mat/tomo_exp.mat'</span>, <span
</div> </div>
</div> </div>
<div id="outline-container-org3b80a89" class="outline-4"> <div id="outline-container-org712bc79" class="outline-4">
<h4 id="org3b80a89"><span class="section-number-4">3.2.3</span> Compare with Undamped system</h4> <h4 id="org712bc79"><span class="section-number-4">3.2.3</span> Compare with Undamped system</h4>
<div class="outline-text-4" id="text-3-2-3"> <div class="outline-text-4" id="text-3-2-3">
<p> <p>
We load the results of tomography experiments. We load the results of tomography experiments.
@ -1092,21 +1092,21 @@ t = linspace(0, 3, length(En(<span class="org-type">:</span>,1)));
</div> </div>
<div id="org9c27ffd" class="figure"> <div id="orgcf6c283" class="figure">
<p><img src="figs/nass_act_damp_dvf_sim_tomo_xy.png" alt="nass_act_damp_dvf_sim_tomo_xy.png" /> <p><img src="figs/nass_act_damp_dvf_sim_tomo_xy.png" alt="nass_act_damp_dvf_sim_tomo_xy.png" />
</p> </p>
<p><span class="figure-number">Figure 14: </span>Position Error during tomography experiment - XY Motion (<a href="./figs/nass_act_damp_dvf_sim_tomo_xy.png">png</a>, <a href="./figs/nass_act_damp_dvf_sim_tomo_xy.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 14: </span>Position Error during tomography experiment - XY Motion (<a href="./figs/nass_act_damp_dvf_sim_tomo_xy.png">png</a>, <a href="./figs/nass_act_damp_dvf_sim_tomo_xy.pdf">pdf</a>)</p>
</div> </div>
<div id="org9e590a1" class="figure"> <div id="org03ea40c" class="figure">
<p><img src="figs/nass_act_damp_dvf_sim_tomo_trans.png" alt="nass_act_damp_dvf_sim_tomo_trans.png" /> <p><img src="figs/nass_act_damp_dvf_sim_tomo_trans.png" alt="nass_act_damp_dvf_sim_tomo_trans.png" />
</p> </p>
<p><span class="figure-number">Figure 15: </span>Position Error during tomography experiment - Translations (<a href="./figs/nass_act_damp_dvf_sim_tomo_trans.png">png</a>, <a href="./figs/nass_act_damp_dvf_sim_tomo_trans.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 15: </span>Position Error during tomography experiment - Translations (<a href="./figs/nass_act_damp_dvf_sim_tomo_trans.png">png</a>, <a href="./figs/nass_act_damp_dvf_sim_tomo_trans.pdf">pdf</a>)</p>
</div> </div>
<div id="orgf861835" class="figure"> <div id="org258bfdb" class="figure">
<p><img src="figs/nass_act_damp_dvf_sim_tomo_rot.png" alt="nass_act_damp_dvf_sim_tomo_rot.png" /> <p><img src="figs/nass_act_damp_dvf_sim_tomo_rot.png" alt="nass_act_damp_dvf_sim_tomo_rot.png" />
</p> </p>
<p><span class="figure-number">Figure 16: </span>Position Error during tomography experiment - Rotations (<a href="./figs/nass_act_damp_dvf_sim_tomo_rot.png">png</a>, <a href="./figs/nass_act_damp_dvf_sim_tomo_rot.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 16: </span>Position Error during tomography experiment - Rotations (<a href="./figs/nass_act_damp_dvf_sim_tomo_rot.png">png</a>, <a href="./figs/nass_act_damp_dvf_sim_tomo_rot.pdf">pdf</a>)</p>
@ -1115,8 +1115,8 @@ t = linspace(0, 3, length(En(<span class="org-type">:</span>,1)));
</div> </div>
</div> </div>
<div id="outline-container-orgbfc0305" class="outline-3"> <div id="outline-container-orgb7038fc" class="outline-3">
<h3 id="orgbfc0305"><span class="section-number-3">3.3</span> Conclusion</h3> <h3 id="orgb7038fc"><span class="section-number-3">3.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-3"> <div class="outline-text-3" id="text-3-3">
<div class="important"> <div class="important">
<p> <p>
@ -1131,11 +1131,11 @@ Direct Velocity Feedback:
</div> </div>
</div> </div>
<div id="outline-container-org97c7099" class="outline-2"> <div id="outline-container-org189c37a" class="outline-2">
<h2 id="org97c7099"><span class="section-number-2">4</span> Inertial Control</h2> <h2 id="org189c37a"><span class="section-number-2">4</span> Inertial Control</h2>
<div class="outline-text-2" id="text-4"> <div class="outline-text-2" id="text-4">
<p> <p>
<a id="org431eadf"></a> <a id="org79aba2e"></a>
</p> </p>
<div class="note"> <div class="note">
<p> <p>
@ -1148,12 +1148,12 @@ In Inertial Control, a feedback is applied between the measured <b>absolute</b>
</p> </p>
</div> </div>
<div id="outline-container-org3d0c40e" class="outline-3"> <div id="outline-container-org0b527cf" class="outline-3">
<h3 id="org3d0c40e"><span class="section-number-3">4.1</span> Control Design</h3> <h3 id="org0b527cf"><span class="section-number-3">4.1</span> Control Design</h3>
<div class="outline-text-3" id="text-4-1"> <div class="outline-text-3" id="text-4-1">
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<div id="outline-container-org7d50913" class="outline-4"> <div id="outline-container-org8f10824" class="outline-4">
<h4 id="org7d50913"><span class="section-number-4">4.1.1</span> Plant</h4> <h4 id="org8f10824"><span class="section-number-4">4.1.1</span> Plant</h4>
<div class="outline-text-4" id="text-4-1-1"> <div class="outline-text-4" id="text-4-1-1">
<p> <p>
Let&rsquo;s load the undamped plant: Let&rsquo;s load the undamped plant:
@ -1164,11 +1164,11 @@ Let&rsquo;s load the undamped plant:
</div> </div>
<p> <p>
Let&rsquo;s look at the transfer function from actuator forces in the nano-hexapod to the measured velocity of the nano-hexapod platform in the direction of the corresponding actuator for all 6 pairs of actuator/sensor (figure <a href="#org5d67443">17</a>). Let&rsquo;s look at the transfer function from actuator forces in the nano-hexapod to the measured velocity of the nano-hexapod platform in the direction of the corresponding actuator for all 6 pairs of actuator/sensor (figure <a href="#org524e9d1">17</a>).
</p> </p>
<div id="org5d67443" class="figure"> <div id="org524e9d1" class="figure">
<p><img src="figs/ine_plant.png" alt="ine_plant.png" /> <p><img src="figs/ine_plant.png" alt="ine_plant.png" />
</p> </p>
<p><span class="figure-number">Figure 17: </span>Transfer function from forces applied in the legs to leg velocity sensor (<a href="./figs/ine_plant.png">png</a>, <a href="./figs/ine_plant.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 17: </span>Transfer function from forces applied in the legs to leg velocity sensor (<a href="./figs/ine_plant.png">png</a>, <a href="./figs/ine_plant.pdf">pdf</a>)</p>
@ -1176,11 +1176,11 @@ Let&rsquo;s look at the transfer function from actuator forces in the nano-hexap
</div> </div>
</div> </div>
<div id="outline-container-org3bd6be5" class="outline-4"> <div id="outline-container-orgbf5fc59" class="outline-4">
<h4 id="org3bd6be5"><span class="section-number-4">4.1.2</span> Control Design</h4> <h4 id="orgbf5fc59"><span class="section-number-4">4.1.2</span> Control Design</h4>
<div class="outline-text-4" id="text-4-1-2"> <div class="outline-text-4" id="text-4-1-2">
<p> <p>
The controller is defined below and the obtained loop gain is shown in figure <a href="#org2b27a68">18</a>. The controller is defined below and the obtained loop gain is shown in figure <a href="#org9d25b5e">18</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -1189,7 +1189,7 @@ The controller is defined below and the obtained loop gain is shown in figure <a
</div> </div>
<div id="org2b27a68" class="figure"> <div id="org9d25b5e" class="figure">
<p><img src="figs/ine_open_loop_gain.png" alt="ine_open_loop_gain.png" /> <p><img src="figs/ine_open_loop_gain.png" alt="ine_open_loop_gain.png" />
</p> </p>
<p><span class="figure-number">Figure 18: </span>Loop Gain for Inertial Control (<a href="./figs/ine_open_loop_gain.png">png</a>, <a href="./figs/ine_open_loop_gain.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 18: </span>Loop Gain for Inertial Control (<a href="./figs/ine_open_loop_gain.png">png</a>, <a href="./figs/ine_open_loop_gain.pdf">pdf</a>)</p>
@ -1197,8 +1197,8 @@ The controller is defined below and the obtained loop gain is shown in figure <a
</div> </div>
</div> </div>
<div id="outline-container-orgb77c3b3" class="outline-4"> <div id="outline-container-org26c423f" class="outline-4">
<h4 id="orgb77c3b3"><span class="section-number-4">4.1.3</span> Diagonal Controller</h4> <h4 id="org26c423f"><span class="section-number-4">4.1.3</span> Diagonal Controller</h4>
<div class="outline-text-4" id="text-4-1-3"> <div class="outline-text-4" id="text-4-1-3">
<p> <p>
We create the diagonal controller and we add a minus sign as we have a positive feedback architecture. We create the diagonal controller and we add a minus sign as we have a positive feedback architecture.
@ -1219,12 +1219,12 @@ We save the controller for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-orgfa1ca32" class="outline-3"> <div id="outline-container-org4354127" class="outline-3">
<h3 id="orgfa1ca32"><span class="section-number-3">4.2</span> Tomography Experiment</h3> <h3 id="org4354127"><span class="section-number-3">4.2</span> Tomography Experiment</h3>
<div class="outline-text-3" id="text-4-2"> <div class="outline-text-3" id="text-4-2">
</div> </div>
<div id="outline-container-orgf686c33" class="outline-4"> <div id="outline-container-org7a7d0fe" class="outline-4">
<h4 id="orgf686c33"><span class="section-number-4">4.2.1</span> Initialize the Simulation</h4> <h4 id="org7a7d0fe"><span class="section-number-4">4.2.1</span> Initialize the Simulation</h4>
<div class="outline-text-4" id="text-4-2-1"> <div class="outline-text-4" id="text-4-2-1">
<p> <p>
We initialize elements for the tomography experiment. We initialize elements for the tomography experiment.
@ -1245,8 +1245,8 @@ save(<span class="org-string">'./mat/controllers.mat'</span>, <span class="org-s
</div> </div>
</div> </div>
<div id="outline-container-org1a7fe63" class="outline-4"> <div id="outline-container-org4e1a6ec" class="outline-4">
<h4 id="org1a7fe63"><span class="section-number-4">4.2.2</span> Simulation</h4> <h4 id="org4e1a6ec"><span class="section-number-4">4.2.2</span> Simulation</h4>
<div class="outline-text-4" id="text-4-2-2"> <div class="outline-text-4" id="text-4-2-2">
<p> <p>
We change the simulation stop time. We change the simulation stop time.
@ -1277,8 +1277,8 @@ save(<span class="org-string">'./active_damping/mat/tomo_exp.mat'</span>, <span
</div> </div>
</div> </div>
<div id="outline-container-orge8b8bf8" class="outline-4"> <div id="outline-container-org43213af" class="outline-4">
<h4 id="orge8b8bf8"><span class="section-number-4">4.2.3</span> Compare with Undamped system</h4> <h4 id="org43213af"><span class="section-number-4">4.2.3</span> Compare with Undamped system</h4>
<div class="outline-text-4" id="text-4-2-3"> <div class="outline-text-4" id="text-4-2-3">
<p> <p>
We load the results of tomography experiments. We load the results of tomography experiments.
@ -1290,21 +1290,21 @@ t = linspace(0, 3, length(En_ine(<span class="org-type">:</span>,1)));
</div> </div>
<div id="orgab8bdcc" class="figure"> <div id="org0914dbb" class="figure">
<p><img src="figs/nass_act_damp_ine_sim_tomo_xy.png" alt="nass_act_damp_ine_sim_tomo_xy.png" /> <p><img src="figs/nass_act_damp_ine_sim_tomo_xy.png" alt="nass_act_damp_ine_sim_tomo_xy.png" />
</p> </p>
<p><span class="figure-number">Figure 19: </span>Position Error during tomography experiment - XY Motion (<a href="./figs/nass_act_damp_ine_sim_tomo_xy.png">png</a>, <a href="./figs/nass_act_damp_ine_sim_tomo_xy.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 19: </span>Position Error during tomography experiment - XY Motion (<a href="./figs/nass_act_damp_ine_sim_tomo_xy.png">png</a>, <a href="./figs/nass_act_damp_ine_sim_tomo_xy.pdf">pdf</a>)</p>
</div> </div>
<div id="org179b8c0" class="figure"> <div id="org48f6bf5" class="figure">
<p><img src="figs/nass_act_damp_ine_sim_tomo_trans.png" alt="nass_act_damp_ine_sim_tomo_trans.png" /> <p><img src="figs/nass_act_damp_ine_sim_tomo_trans.png" alt="nass_act_damp_ine_sim_tomo_trans.png" />
</p> </p>
<p><span class="figure-number">Figure 20: </span>Position Error during tomography experiment - Translations (<a href="./figs/nass_act_damp_ine_sim_tomo_trans.png">png</a>, <a href="./figs/nass_act_damp_ine_sim_tomo_trans.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 20: </span>Position Error during tomography experiment - Translations (<a href="./figs/nass_act_damp_ine_sim_tomo_trans.png">png</a>, <a href="./figs/nass_act_damp_ine_sim_tomo_trans.pdf">pdf</a>)</p>
</div> </div>
<div id="org5050229" class="figure"> <div id="org89ebbf9" class="figure">
<p><img src="figs/nass_act_damp_ine_sim_tomo_rot.png" alt="nass_act_damp_ine_sim_tomo_rot.png" /> <p><img src="figs/nass_act_damp_ine_sim_tomo_rot.png" alt="nass_act_damp_ine_sim_tomo_rot.png" />
</p> </p>
<p><span class="figure-number">Figure 21: </span>Position Error during tomography experiment - Rotations (<a href="./figs/nass_act_damp_ine_sim_tomo_rot.png">png</a>, <a href="./figs/nass_act_damp_ine_sim_tomo_rot.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 21: </span>Position Error during tomography experiment - Rotations (<a href="./figs/nass_act_damp_ine_sim_tomo_rot.png">png</a>, <a href="./figs/nass_act_damp_ine_sim_tomo_rot.pdf">pdf</a>)</p>
@ -1313,8 +1313,8 @@ t = linspace(0, 3, length(En_ine(<span class="org-type">:</span>,1)));
</div> </div>
</div> </div>
<div id="outline-container-orgde615df" class="outline-3"> <div id="outline-container-org1583f6b" class="outline-3">
<h3 id="orgde615df"><span class="section-number-3">4.3</span> Conclusion</h3> <h3 id="org1583f6b"><span class="section-number-3">4.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-4-3"> <div class="outline-text-3" id="text-4-3">
<div class="important"> <div class="important">
<p> <p>
@ -1326,15 +1326,15 @@ Inertial Control:
</div> </div>
</div> </div>
<div id="outline-container-orgada4654" class="outline-2"> <div id="outline-container-org60a7861" class="outline-2">
<h2 id="orgada4654"><span class="section-number-2">5</span> Comparison</h2> <h2 id="org60a7861"><span class="section-number-2">5</span> Comparison</h2>
<div class="outline-text-2" id="text-5"> <div class="outline-text-2" id="text-5">
<p> <p>
<a id="org98830ef"></a> <a id="org7d71743"></a>
</p> </p>
</div> </div>
<div id="outline-container-org2976576" class="outline-3"> <div id="outline-container-orgcfb94b6" class="outline-3">
<h3 id="org2976576"><span class="section-number-3">5.1</span> Load the plants</h3> <h3 id="orgcfb94b6"><span class="section-number-3">5.1</span> Load the plants</h3>
<div class="outline-text-3" id="text-5-1"> <div class="outline-text-3" id="text-5-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'./active_damping/mat/plants.mat'</span>, <span class="org-string">'G'</span>, <span class="org-string">'G_iff'</span>, <span class="org-string">'G_ine'</span>, <span class="org-string">'G_dvf'</span>); <pre class="src src-matlab">load(<span class="org-string">'./active_damping/mat/plants.mat'</span>, <span class="org-string">'G'</span>, <span class="org-string">'G_iff'</span>, <span class="org-string">'G_ine'</span>, <span class="org-string">'G_dvf'</span>);
@ -1343,11 +1343,11 @@ Inertial Control:
</div> </div>
</div> </div>
<div id="outline-container-org835d9db" class="outline-3"> <div id="outline-container-org478cd23" class="outline-3">
<h3 id="org835d9db"><span class="section-number-3">5.2</span> Sensitivity to Disturbance</h3> <h3 id="org478cd23"><span class="section-number-3">5.2</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-5-2"> <div class="outline-text-3" id="text-5-2">
<div id="orgdf47c67" class="figure"> <div id="org766a5d0" class="figure">
<p><img src="figs/sensitivity_comp_ground_motion_z.png" alt="sensitivity_comp_ground_motion_z.png" /> <p><img src="figs/sensitivity_comp_ground_motion_z.png" alt="sensitivity_comp_ground_motion_z.png" />
</p> </p>
<p><span class="figure-number">Figure 22: </span>Sensitivity to ground motion in the Z direction on the Z motion error (<a href="./figs/sensitivity_comp_ground_motion_z.png">png</a>, <a href="./figs/sensitivity_comp_ground_motion_z.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 22: </span>Sensitivity to ground motion in the Z direction on the Z motion error (<a href="./figs/sensitivity_comp_ground_motion_z.png">png</a>, <a href="./figs/sensitivity_comp_ground_motion_z.pdf">pdf</a>)</p>
@ -1355,21 +1355,21 @@ Inertial Control:
<div id="orgfc493eb" class="figure"> <div id="orgb662906" class="figure">
<p><img src="figs/sensitivity_comp_direct_forces_z.png" alt="sensitivity_comp_direct_forces_z.png" /> <p><img src="figs/sensitivity_comp_direct_forces_z.png" alt="sensitivity_comp_direct_forces_z.png" />
</p> </p>
<p><span class="figure-number">Figure 23: </span>Compliance in the Z direction: Sensitivity of direct forces applied on the sample in the Z direction on the Z motion error (<a href="./figs/sensitivity_comp_direct_forces_z.png">png</a>, <a href="./figs/sensitivity_comp_direct_forces_z.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 23: </span>Compliance in the Z direction: Sensitivity of direct forces applied on the sample in the Z direction on the Z motion error (<a href="./figs/sensitivity_comp_direct_forces_z.png">png</a>, <a href="./figs/sensitivity_comp_direct_forces_z.pdf">pdf</a>)</p>
</div> </div>
<div id="org31dee6d" class="figure"> <div id="orgd7e090b" class="figure">
<p><img src="figs/sensitivity_comp_spindle_z.png" alt="sensitivity_comp_spindle_z.png" /> <p><img src="figs/sensitivity_comp_spindle_z.png" alt="sensitivity_comp_spindle_z.png" />
</p> </p>
<p><span class="figure-number">Figure 24: </span>Sensitivity to forces applied in the Z direction by the Spindle on the Z motion error (<a href="./figs/sensitivity_comp_spindle_z.png">png</a>, <a href="./figs/sensitivity_comp_spindle_z.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 24: </span>Sensitivity to forces applied in the Z direction by the Spindle on the Z motion error (<a href="./figs/sensitivity_comp_spindle_z.png">png</a>, <a href="./figs/sensitivity_comp_spindle_z.pdf">pdf</a>)</p>
</div> </div>
<div id="orgc54a0c8" class="figure"> <div id="orge64e918" class="figure">
<p><img src="figs/sensitivity_comp_ty_z.png" alt="sensitivity_comp_ty_z.png" /> <p><img src="figs/sensitivity_comp_ty_z.png" alt="sensitivity_comp_ty_z.png" />
</p> </p>
<p><span class="figure-number">Figure 25: </span>Sensitivity to forces applied in the Z direction by the Y translation stage on the Z motion error (<a href="./figs/sensitivity_comp_ty_z.png">png</a>, <a href="./figs/sensitivity_comp_ty_z.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 25: </span>Sensitivity to forces applied in the Z direction by the Y translation stage on the Z motion error (<a href="./figs/sensitivity_comp_ty_z.png">png</a>, <a href="./figs/sensitivity_comp_ty_z.pdf">pdf</a>)</p>
@ -1377,7 +1377,7 @@ Inertial Control:
<div id="orgf732728" class="figure"> <div id="org6d663d9" class="figure">
<p><img src="figs/sensitivity_comp_ty_x.png" alt="sensitivity_comp_ty_x.png" /> <p><img src="figs/sensitivity_comp_ty_x.png" alt="sensitivity_comp_ty_x.png" />
</p> </p>
<p><span class="figure-number">Figure 26: </span>Sensitivity to forces applied in the X direction by the Y translation stage on the X motion error (<a href="./figs/sensitivity_comp_ty_x.png">png</a>, <a href="./figs/sensitivity_comp_ty_x.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 26: </span>Sensitivity to forces applied in the X direction by the Y translation stage on the X motion error (<a href="./figs/sensitivity_comp_ty_x.png">png</a>, <a href="./figs/sensitivity_comp_ty_x.pdf">pdf</a>)</p>
@ -1385,25 +1385,25 @@ Inertial Control:
</div> </div>
</div> </div>
<div id="outline-container-orga94123d" class="outline-3"> <div id="outline-container-org0c15520" class="outline-3">
<h3 id="orga94123d"><span class="section-number-3">5.3</span> Damped Plant</h3> <h3 id="org0c15520"><span class="section-number-3">5.3</span> Damped Plant</h3>
<div class="outline-text-3" id="text-5-3"> <div class="outline-text-3" id="text-5-3">
<div id="org7f947f5" class="figure"> <div id="org8336dec" class="figure">
<p><img src="figs/plant_comp_damping_z.png" alt="plant_comp_damping_z.png" /> <p><img src="figs/plant_comp_damping_z.png" alt="plant_comp_damping_z.png" />
</p> </p>
<p><span class="figure-number">Figure 27: </span>Plant for the \(z\) direction for different active damping technique used (<a href="./figs/plant_comp_damping_z.png">png</a>, <a href="./figs/plant_comp_damping_z.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 27: </span>Plant for the \(z\) direction for different active damping technique used (<a href="./figs/plant_comp_damping_z.png">png</a>, <a href="./figs/plant_comp_damping_z.pdf">pdf</a>)</p>
</div> </div>
<div id="orgaf1a7e2" class="figure"> <div id="orgfe252f1" class="figure">
<p><img src="figs/plant_comp_damping_x.png" alt="plant_comp_damping_x.png" /> <p><img src="figs/plant_comp_damping_x.png" alt="plant_comp_damping_x.png" />
</p> </p>
<p><span class="figure-number">Figure 28: </span>Plant for the \(x\) direction for different active damping technique used (<a href="./figs/plant_comp_damping_x.png">png</a>, <a href="./figs/plant_comp_damping_x.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 28: </span>Plant for the \(x\) direction for different active damping technique used (<a href="./figs/plant_comp_damping_x.png">png</a>, <a href="./figs/plant_comp_damping_x.pdf">pdf</a>)</p>
</div> </div>
<div id="org421e4e1" class="figure"> <div id="orgd70da06" class="figure">
<p><img src="figs/plant_comp_damping_coupling.png" alt="plant_comp_damping_coupling.png" /> <p><img src="figs/plant_comp_damping_coupling.png" alt="plant_comp_damping_coupling.png" />
</p> </p>
<p><span class="figure-number">Figure 29: </span>Comparison of one off-diagonal plant for different damping technique applied (<a href="./figs/plant_comp_damping_coupling.png">png</a>, <a href="./figs/plant_comp_damping_coupling.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 29: </span>Comparison of one off-diagonal plant for different damping technique applied (<a href="./figs/plant_comp_damping_coupling.png">png</a>, <a href="./figs/plant_comp_damping_coupling.pdf">pdf</a>)</p>
@ -1411,12 +1411,12 @@ Inertial Control:
</div> </div>
</div> </div>
<div id="outline-container-org75eccc0" class="outline-3"> <div id="outline-container-org7cec242" class="outline-3">
<h3 id="org75eccc0"><span class="section-number-3">5.4</span> Tomography Experiment</h3> <h3 id="org7cec242"><span class="section-number-3">5.4</span> Tomography Experiment</h3>
<div class="outline-text-3" id="text-5-4"> <div class="outline-text-3" id="text-5-4">
</div> </div>
<div id="outline-container-org341a139" class="outline-4"> <div id="outline-container-org9cc6c6a" class="outline-4">
<h4 id="org341a139"><span class="section-number-4">5.4.1</span> Load the Simulation Data</h4> <h4 id="org9cc6c6a"><span class="section-number-4">5.4.1</span> Load the Simulation Data</h4>
<div class="outline-text-4" id="text-5-4-1"> <div class="outline-text-4" id="text-5-4-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'./active_damping/mat/tomo_exp.mat'</span>, <span class="org-string">'En'</span>, <span class="org-string">'En_iff_hpf'</span>, <span class="org-string">'En_dvf'</span>, <span class="org-string">'En_ine'</span>); <pre class="src src-matlab">load(<span class="org-string">'./active_damping/mat/tomo_exp.mat'</span>, <span class="org-string">'En'</span>, <span class="org-string">'En_iff_hpf'</span>, <span class="org-string">'En_dvf'</span>, <span class="org-string">'En_ine'</span>);
@ -1427,8 +1427,8 @@ t = linspace(0, 3, length(En(<span class="org-type">:</span>,1)));
</div> </div>
</div> </div>
<div id="outline-container-org267c98c" class="outline-4"> <div id="outline-container-org68b07c1" class="outline-4">
<h4 id="org267c98c"><span class="section-number-4">5.4.2</span> Frequency Domain Analysis</h4> <h4 id="org68b07c1"><span class="section-number-4">5.4.2</span> Frequency Domain Analysis</h4>
<div class="outline-text-4" id="text-5-4-2"> <div class="outline-text-4" id="text-5-4-2">
<p> <p>
Window used for <code>pwelch</code> function. Window used for <code>pwelch</code> function.
@ -1440,28 +1440,28 @@ han_win = hanning(ceil(length(En(<span class="org-type">:</span>, 1))<span class
</div> </div>
<div id="orga580e07" class="figure"> <div id="org520876a" class="figure">
<p><img src="figs/act_damp_tomo_exp_comp_psd_trans.png" alt="act_damp_tomo_exp_comp_psd_trans.png" /> <p><img src="figs/act_damp_tomo_exp_comp_psd_trans.png" alt="act_damp_tomo_exp_comp_psd_trans.png" />
</p> </p>
<p><span class="figure-number">Figure 30: </span>PSD of the translation errors for applied Active Damping techniques (<a href="./figs/act_damp_tomo_exp_comp_psd_trans.png">png</a>, <a href="./figs/act_damp_tomo_exp_comp_psd_trans.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 30: </span>PSD of the translation errors for applied Active Damping techniques (<a href="./figs/act_damp_tomo_exp_comp_psd_trans.png">png</a>, <a href="./figs/act_damp_tomo_exp_comp_psd_trans.pdf">pdf</a>)</p>
</div> </div>
<div id="orgdf9a147" class="figure"> <div id="org23a6962" class="figure">
<p><img src="figs/act_damp_tomo_exp_comp_psd_rot.png" alt="act_damp_tomo_exp_comp_psd_rot.png" /> <p><img src="figs/act_damp_tomo_exp_comp_psd_rot.png" alt="act_damp_tomo_exp_comp_psd_rot.png" />
</p> </p>
<p><span class="figure-number">Figure 31: </span>PSD of the rotation errors for applied Active Damping techniques (<a href="./figs/act_damp_tomo_exp_comp_psd_rot.png">png</a>, <a href="./figs/act_damp_tomo_exp_comp_psd_rot.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 31: </span>PSD of the rotation errors for applied Active Damping techniques (<a href="./figs/act_damp_tomo_exp_comp_psd_rot.png">png</a>, <a href="./figs/act_damp_tomo_exp_comp_psd_rot.pdf">pdf</a>)</p>
</div> </div>
<div id="orge199cbc" class="figure"> <div id="org3b5e07b" class="figure">
<p><img src="figs/act_damp_tomo_exp_comp_cps_trans.png" alt="act_damp_tomo_exp_comp_cps_trans.png" /> <p><img src="figs/act_damp_tomo_exp_comp_cps_trans.png" alt="act_damp_tomo_exp_comp_cps_trans.png" />
</p> </p>
<p><span class="figure-number">Figure 32: </span>CPS of the translation errors for applied Active Damping techniques (<a href="./figs/act_damp_tomo_exp_comp_cps_trans.png">png</a>, <a href="./figs/act_damp_tomo_exp_comp_cps_trans.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 32: </span>CPS of the translation errors for applied Active Damping techniques (<a href="./figs/act_damp_tomo_exp_comp_cps_trans.png">png</a>, <a href="./figs/act_damp_tomo_exp_comp_cps_trans.pdf">pdf</a>)</p>
</div> </div>
<div id="org4b2375c" class="figure"> <div id="org31dea9b" class="figure">
<p><img src="figs/act_damp_tomo_exp_comp_cps_rot.png" alt="act_damp_tomo_exp_comp_cps_rot.png" /> <p><img src="figs/act_damp_tomo_exp_comp_cps_rot.png" alt="act_damp_tomo_exp_comp_cps_rot.png" />
</p> </p>
<p><span class="figure-number">Figure 33: </span>CPS of the rotation errors for applied Active Damping techniques (<a href="./figs/act_damp_tomo_exp_comp_cps_rot.png">png</a>, <a href="./figs/act_damp_tomo_exp_comp_cps_rot.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 33: </span>CPS of the rotation errors for applied Active Damping techniques (<a href="./figs/act_damp_tomo_exp_comp_cps_rot.png">png</a>, <a href="./figs/act_damp_tomo_exp_comp_cps_rot.pdf">pdf</a>)</p>
@ -1471,15 +1471,15 @@ han_win = hanning(ceil(length(En(<span class="org-type">:</span>, 1))<span class
</div> </div>
</div> </div>
<div id="outline-container-org5f0f434" class="outline-2"> <div id="outline-container-orgd1af630" class="outline-2">
<h2 id="org5f0f434"><span class="section-number-2">6</span> Useful Functions</h2> <h2 id="orgd1af630"><span class="section-number-2">6</span> Useful Functions</h2>
<div class="outline-text-2" id="text-6"> <div class="outline-text-2" id="text-6">
</div> </div>
<div id="outline-container-org6ecc4dc" class="outline-3"> <div id="outline-container-org4da4ec2" class="outline-3">
<h3 id="org6ecc4dc"><span class="section-number-3">6.1</span> prepareTomographyExperiment</h3> <h3 id="org4da4ec2"><span class="section-number-3">6.1</span> prepareTomographyExperiment</h3>
<div class="outline-text-3" id="text-6-1"> <div class="outline-text-3" id="text-6-1">
<p> <p>
<a id="orgf80e6d6"></a> <a id="orgfe1b669"></a>
</p> </p>
<p> <p>
@ -1487,9 +1487,9 @@ This Matlab function is accessible <a href="src/prepareTomographyExperiment.m">h
</p> </p>
</div> </div>
<div id="outline-container-org435d4b8" class="outline-4"> <div id="outline-container-orgd77a897" class="outline-4">
<h4 id="org435d4b8">Function Description</h4> <h4 id="orgd77a897">Function Description</h4>
<div class="outline-text-4" id="text-org435d4b8"> <div class="outline-text-4" id="text-orgd77a897">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[]</span> = <span class="org-function-name">prepareTomographyExperiment</span>(<span class="org-variable-name">args</span>) <pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[]</span> = <span class="org-function-name">prepareTomographyExperiment</span>(<span class="org-variable-name">args</span>)
</pre> </pre>
@ -1497,9 +1497,9 @@ This Matlab function is accessible <a href="src/prepareTomographyExperiment.m">h
</div> </div>
</div> </div>
<div id="outline-container-org45dbf99" class="outline-4"> <div id="outline-container-org8bc4916" class="outline-4">
<h4 id="org45dbf99">Optional Parameters</h4> <h4 id="org8bc4916">Optional Parameters</h4>
<div class="outline-text-4" id="text-org45dbf99"> <div class="outline-text-4" id="text-org8bc4916">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">arguments <pre class="src src-matlab">arguments
args.nass_actuator char {mustBeMember(args.nass_actuator,{<span class="org-string">'piezo'</span>, <span class="org-string">'lorentz'</span>})} = <span class="org-string">'piezo'</span> args.nass_actuator char {mustBeMember(args.nass_actuator,{<span class="org-string">'piezo'</span>, <span class="org-string">'lorentz'</span>})} = <span class="org-string">'piezo'</span>
@ -1511,9 +1511,9 @@ This Matlab function is accessible <a href="src/prepareTomographyExperiment.m">h
</div> </div>
</div> </div>
<div id="outline-container-org80d47ea" class="outline-4"> <div id="outline-container-org2b62851" class="outline-4">
<h4 id="org80d47ea">Initialize the Simulation</h4> <h4 id="org2b62851">Initialize the Simulation</h4>
<div class="outline-text-4" id="text-org80d47ea"> <div class="outline-text-4" id="text-org2b62851">
<p> <p>
We initialize all the stages with the default parameters. We initialize all the stages with the default parameters.
</p> </p>
@ -1567,7 +1567,7 @@ save(<span class="org-string">'./mat/controllers.mat'</span>, <span class="org-s
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-01-20 lun. 17:40</p> <p class="date">Created: 2020-01-20 lun. 17:45</p>
</div> </div>
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