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@@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2020-05-25 lun. 11:13 -->
<!-- 2020-09-01 mar. 13:48 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Amplified Piezoelectric Stack Actuator</title>
<meta name="generator" content="Org mode" />
@@ -36,30 +36,64 @@
<ul>
<li><a href="#org996fd7c">1. Simplified Model</a>
<ul>
<li><a href="#orgd4866c5">1.1. Parameters</a></li>
<li><a href="#orgf0cb0e7">1.2. Identification</a></li>
<li><a href="#org8d3f9bd">1.3. Root Locus</a></li>
<li><a href="#org76fe747">1.1. Parameters</a></li>
<li><a href="#orgbe95c15">1.2. Identification</a></li>
<li><a href="#orgeaad673">1.3. Root Locus</a></li>
<li><a href="#orged9310d">1.4. Analytical Model</a></li>
<li><a href="#org2f351a4">1.5. Analytical Analysis</a></li>
</ul>
</li>
<li><a href="#orgf1a765f">2. Rotating X-Y platform</a>
<ul>
<li><a href="#org6594475">2.1. Parameters</a></li>
<li><a href="#orgf86cabd">2.2. Identification</a></li>
<li><a href="#org5c898f6">2.3. Root Locus</a></li>
<li><a href="#orga31e2d2">2.1. Parameters</a></li>
<li><a href="#orgb7a6747">2.2. Identification</a></li>
<li><a href="#org290de6f">2.3. Root Locus</a></li>
<li><a href="#org069f401">2.4. Analysis</a></li>
</ul>
</li>
<li><a href="#org3c74f7f">3. Stewart Platform with Amplified Actuators</a>
<ul>
<li><a href="#org5a7c6dc">3.1. Initialization</a></li>
<li><a href="#org206d2b9">3.2. Identification</a></li>
<li><a href="#org14c7063">3.3. Controller Design</a></li>
<li><a href="#org043ce40">3.4. Effect of the Low Authority Control on the Primary Plant</a></li>
<li><a href="#orgbc2f246">3.5. Effect of the Low Authority Control on the Sensibility to Disturbances</a></li>
<li><a href="#org297c2ad">3.6. Optimal Stiffnesses</a></li>
<li><a href="#org1e2f810">3.7. Direct Velocity Feedback with Amplified Actuators</a></li>
<li><a href="#orgdfe4eeb">3.2. APA-100 Amplified Actuator</a>
<ul>
<li><a href="#org7798ce9">3.2.1. Identification</a></li>
<li><a href="#orgb943e63">3.2.2. Controller Design</a></li>
<li><a href="#org0bf79ae">3.2.3. Effect of the Low Authority Control on the Primary Plant</a></li>
<li><a href="#org96f3a8d">3.2.4. Effect of the Low Authority Control on the Sensibility to Disturbances</a></li>
</ul>
</li>
<li><a href="#org297c2ad">3.3. Optimal Stiffnesses</a>
<ul>
<li><a href="#org5dc2ac7">3.3.1. Low Authority Controller</a>
<ul>
<li><a href="#orgf339f37">3.3.1.1. Identification</a></li>
<li><a href="#orgfcd4ad7">3.3.1.2. Effect of the Low Authority Control on the Primary Plant</a></li>
<li><a href="#org32c3422">3.3.1.3. Effect of the Low Authority Control on the Sensibility to Disturbances</a></li>
</ul>
</li>
<li><a href="#orgce4f07c">3.3.2. High Authority Controller</a>
<ul>
<li><a href="#orgc16003c">3.3.2.1. Controller Design</a></li>
<li><a href="#orgbcf7749">3.3.2.2. Sensibility to Disturbances and Noise Budget</a></li>
<li><a href="#orga0e8915">3.3.2.3. Simulations of Tomography Experiment</a></li>
<li><a href="#orgb6ec250">3.3.2.4. Results</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#org1e2f810">3.4. Direct Velocity Feedback with Amplified Actuators</a></li>
</ul>
</li>
<li><a href="#org936810c">4. APA300ML</a>
<ul>
<li><a href="#org797e3ca">4.1. Initialization</a></li>
<li><a href="#org2300f00">4.2. Identification</a></li>
<li><a href="#org4ec1cb7">4.3. Controller Design</a></li>
<li><a href="#org1b67874">4.4. Effect of the Low Authority Control on the Primary Plant</a></li>
<li><a href="#org655c28c">4.5. Control in the leg space</a></li>
<li><a href="#org92df47e">4.6. Sensibility to Disturbances and Noise Budget</a></li>
<li><a href="#orge84cedc">4.7. Simulations of Tomography Experiment</a></li>
<li><a href="#org05ce41a">4.8. Results</a></li>
</ul>
</li>
</ul>
@@ -67,7 +101,7 @@
</div>
<p>
The presented model is based on <a class='org-ref-reference' href="#souleille18_concep_activ_mount_space_applic">souleille18_concep_activ_mount_space_applic</a>.
The presented model is based on (<a href="#citeproc_bib_item_2">Souleille et al. 2018</a>).
</p>
<p>
@@ -136,8 +170,8 @@ The parameters are shown in the table below.
<h2 id="org996fd7c"><span class="section-number-2">1</span> Simplified Model</h2>
<div class="outline-text-2" id="text-1">
</div>
<div id="outline-container-orgd4866c5" class="outline-3">
<h3 id="orgd4866c5"><span class="section-number-3">1.1</span> Parameters</h3>
<div id="outline-container-org76fe747" class="outline-3">
<h3 id="org76fe747"><span class="section-number-3">1.1</span> Parameters</h3>
<div class="outline-text-3" id="text-1-1">
<div class="org-src-container">
<pre class="src src-matlab">m = 1; % [kg]
@@ -167,8 +201,8 @@ IFF Controller:
</div>
</div>
<div id="outline-container-orgf0cb0e7" class="outline-3">
<h3 id="orgf0cb0e7"><span class="section-number-3">1.2</span> Identification</h3>
<div id="outline-container-orgbe95c15" class="outline-3">
<h3 id="orgbe95c15"><span class="section-number-3">1.2</span> Identification</h3>
<div class="outline-text-3" id="text-1-2">
<p>
Identification in open-loop.
@@ -223,8 +257,8 @@ Giff.OutputName = {'Fs', 'x1'};
</div>
</div>
<div id="outline-container-org8d3f9bd" class="outline-3">
<h3 id="org8d3f9bd"><span class="section-number-3">1.3</span> Root Locus</h3>
<div id="outline-container-orgeaad673" class="outline-3">
<h3 id="orgeaad673"><span class="section-number-3">1.3</span> Root Locus</h3>
<div class="outline-text-3" id="text-1-3">
<div id="org85cd6e5" class="figure">
@@ -300,6 +334,17 @@ And two complex conjugate poles at:
If maximal damping is to be attained with IFF, the distance between the zero and the pole is to be maximized.
Thus, we wish to maximize \(p/z\), which is equivalent as to minimize \(k_1\) and have \(k_e \approx k_a\) (supposing \(k_e + k_a \approx \text{cst}\)).
</p>
<div class="org-src-container">
<pre class="src src-matlab">m = 1;
k1 = 1e6;
ka = 1e6;
ke = 1e6;
Giff.InputName = {'f'};
Giff.OutputName = {'Fs'};
</pre>
</div>
</div>
</div>
</div>
@@ -307,9 +352,13 @@ Thus, we wish to maximize \(p/z\), which is equivalent as to minimize \(k_1\) an
<div id="outline-container-orgf1a765f" class="outline-2">
<h2 id="orgf1a765f"><span class="section-number-2">2</span> Rotating X-Y platform</h2>
<div class="outline-text-2" id="text-2">
<p>
This analysis gave rise to a paper (<a href="#citeproc_bib_item_1">Dehaeze and Collette 2020</a>).
</p>
</div>
<div id="outline-container-org6594475" class="outline-3">
<h3 id="org6594475"><span class="section-number-3">2.1</span> Parameters</h3>
<div id="outline-container-orga31e2d2" class="outline-3">
<h3 id="orga31e2d2"><span class="section-number-3">2.1</span> Parameters</h3>
<div class="outline-text-3" id="text-2-1">
<div class="org-src-container">
<pre class="src src-matlab">m = 1; % [kg]
@@ -336,8 +385,8 @@ h = 0.2; % [m]
</div>
</div>
<div id="outline-container-orgf86cabd" class="outline-3">
<h3 id="orgf86cabd"><span class="section-number-3">2.2</span> Identification</h3>
<div id="outline-container-orgb7a6747" class="outline-3">
<h3 id="orgb7a6747"><span class="section-number-3">2.2</span> Identification</h3>
<div class="outline-text-3" id="text-2-2">
<p>
Rotating speed in rad/s:
@@ -386,8 +435,8 @@ end
</div>
</div>
<div id="outline-container-org5c898f6" class="outline-3">
<h3 id="org5c898f6"><span class="section-number-3">2.3</span> Root Locus</h3>
<div id="outline-container-org290de6f" class="outline-3">
<h3 id="org290de6f"><span class="section-number-3">2.3</span> Root Locus</h3>
<div class="outline-text-3" id="text-2-3">
<div id="orgccd3396" class="figure">
@@ -485,9 +534,13 @@ We set the stiffness of the payload fixation:
</div>
</div>
<div id="outline-container-org206d2b9" class="outline-3">
<h3 id="org206d2b9"><span class="section-number-3">3.2</span> Identification</h3>
<div id="outline-container-orgdfe4eeb" class="outline-3">
<h3 id="orgdfe4eeb"><span class="section-number-3">3.2</span> APA-100 Amplified Actuator</h3>
<div class="outline-text-3" id="text-3-2">
</div>
<div id="outline-container-org7798ce9" class="outline-4">
<h4 id="org7798ce9"><span class="section-number-4">3.2.1</span> Identification</h4>
<div class="outline-text-4" id="text-3-2-1">
<div class="org-src-container">
<pre class="src src-matlab">K = tf(zeros(6));
Kiff = tf(zeros(6));
@@ -512,9 +565,21 @@ The nano-hexapod has the following leg&rsquo;s stiffness and damping.
</div>
</div>
<div id="outline-container-org14c7063" class="outline-3">
<h3 id="org14c7063"><span class="section-number-3">3.3</span> Controller Design</h3>
<div class="outline-text-3" id="text-3-3">
<div id="outline-container-orgb943e63" class="outline-4">
<h4 id="orgb943e63"><span class="section-number-4">3.2.2</span> Controller Design</h4>
<div class="outline-text-4" id="text-3-2-2">
<p>
The loop gain for IFF is shown in Figure <a href="#org0e2911a">8</a>.
</p>
<p>
The corresponding root locus is shown in Figure <a href="#org5d7f6d3">9</a>.
</p>
<p>
Finally, the damping as function of the gain is display in Figure <a href="#org4743c83">10</a>.
</p>
<div id="org0e2911a" class="figure">
<p><img src="figs/amplified_piezo_iff_loop_gain.png" alt="amplified_piezo_iff_loop_gain.png" />
@@ -530,9 +595,6 @@ The nano-hexapod has the following leg&rsquo;s stiffness and damping.
<p><span class="figure-number">Figure 9: </span>Root Locus for the IFF control for three payload masses</p>
</div>
<p>
Damping as function of the gain
</p>
<div id="org4743c83" class="figure">
<p><img src="figs/amplified_piezo_iff_damping_gain.png" alt="amplified_piezo_iff_damping_gain.png" />
@@ -541,7 +603,7 @@ Damping as function of the gain
</div>
<p>
Finally, we use the following controller for the Decentralized Direct Velocity Feedback:
The following controller for the Decentralized Integral Force Feedback is used:
</p>
<div class="org-src-container">
<pre class="src src-matlab">Kiff = -1e4/s*eye(6);
@@ -550,9 +612,9 @@ Finally, we use the following controller for the Decentralized Direct Velocity F
</div>
</div>
<div id="outline-container-org043ce40" class="outline-3">
<h3 id="org043ce40"><span class="section-number-3">3.4</span> Effect of the Low Authority Control on the Primary Plant</h3>
<div class="outline-text-3" id="text-3-4">
<div id="outline-container-org0bf79ae" class="outline-4">
<h4 id="org0bf79ae"><span class="section-number-4">3.2.3</span> Effect of the Low Authority Control on the Primary Plant</h4>
<div class="outline-text-4" id="text-3-2-3">
<div id="org904efc3" class="figure">
<p><img src="figs/amplified_piezo_iff_plant_damped_X.png" alt="amplified_piezo_iff_plant_damped_X.png" />
@@ -584,15 +646,19 @@ Finally, we use the following controller for the Decentralized Direct Velocity F
</div>
</div>
<div id="outline-container-orgbc2f246" class="outline-3">
<h3 id="orgbc2f246"><span class="section-number-3">3.5</span> Effect of the Low Authority Control on the Sensibility to Disturbances</h3>
<div class="outline-text-3" id="text-3-5">
<div id="outline-container-org96f3a8d" class="outline-4">
<h4 id="org96f3a8d"><span class="section-number-4">3.2.4</span> Effect of the Low Authority Control on the Sensibility to Disturbances</h4>
<div class="outline-text-4" id="text-3-2-4">
<div id="org56179cd" class="figure">
<p><img src="figs/amplified_piezo_iff_disturbances.png" alt="amplified_piezo_iff_disturbances.png" />
</p>
<p><span class="figure-number">Figure 15: </span>Norm of the transfer function from vertical disturbances to vertical position error with (dashed) and without (solid) Integral Force Feedback applied</p>
</div>
</div>
</div>
<div class="outline-text-3" id="text-3-2">
<div class="important">
</div>
@@ -601,16 +667,387 @@ Finally, we use the following controller for the Decentralized Direct Velocity F
<div id="outline-container-org297c2ad" class="outline-3">
<h3 id="org297c2ad"><span class="section-number-3">3.6</span> Optimal Stiffnesses</h3>
<h3 id="org297c2ad"><span class="section-number-3">3.3</span> Optimal Stiffnesses</h3>
<div class="outline-text-3" id="text-3-3">
<p>
Based on the analytical analysis, we can determine the parameters of the amplified piezoelectric actuator in order to be able to add a lots of damping using IFF:
</p>
<ul class="org-ul">
<li>\(k_1\) should be minimized.</li>
<li>\(k_e \approx k_a \approx 10^5 - 10^6\,[N/m]\)</li>
</ul>
<p>
However, this might not be realizable.
</p>
</div>
<div id="outline-container-org5dc2ac7" class="outline-4">
<h4 id="org5dc2ac7"><span class="section-number-4">3.3.1</span> Low Authority Controller</h4>
<div class="outline-text-4" id="text-3-3-1">
</div>
<div id="outline-container-orgf339f37" class="outline-5">
<h5 id="orgf339f37"><span class="section-number-5">3.3.1.1</span> Identification</h5>
<div class="outline-text-5" id="text-3-3-1-1">
<p>
The nano-hexapod is initialized with the following parameters:
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeNanoHexapod('actuator', 'amplified', ...
'k1', 1e4, ...
'ke', 1e6, ...
'ka', 1e6);
</pre>
</div>
<p>
The obtain plan for the IFF control is shown in Figure <a href="#orgafcb4d0">16</a>.
The associated Root Locus is shown in Figure <a href="#org62c3e69">17</a>.
</p>
<p>
Based on that, the following IFF gain is chosen:
</p>
<div class="org-src-container">
<pre class="src src-matlab">Kiff = -1e3/s*eye(6);
</pre>
</div>
<div id="orgafcb4d0" class="figure">
<p><img src="figs/amplified_piezo_opt_stiff_iff_plant.png" alt="amplified_piezo_opt_stiff_iff_plant.png" />
</p>
<p><span class="figure-number">Figure 16: </span>Plant dynamics for IFF with the amplified piezoelectric stack actuator</p>
</div>
<div id="org62c3e69" class="figure">
<p><img src="figs/amplified_piezo_opt_stiff_iff_root_locus.png" alt="amplified_piezo_opt_stiff_iff_root_locus.png" />
</p>
<p><span class="figure-number">Figure 17: </span>Root Locus for IFF with the amplified piezoelectric stack actuator</p>
</div>
<div id="orgaf25c91" class="figure">
<p><img src="figs/amplified_piezo_opt_stiff_gain_damping.png" alt="amplified_piezo_opt_stiff_gain_damping.png" />
</p>
<p><span class="figure-number">Figure 18: </span>Damping of the modes as a function of the IFF gain</p>
</div>
</div>
</div>
<div id="outline-container-orgfcd4ad7" class="outline-5">
<h5 id="orgfcd4ad7"><span class="section-number-5">3.3.1.2</span> Effect of the Low Authority Control on the Primary Plant</h5>
</div>
<div id="outline-container-org32c3422" class="outline-5">
<h5 id="org32c3422"><span class="section-number-5">3.3.1.3</span> Effect of the Low Authority Control on the Sensibility to Disturbances</h5>
<div class="outline-text-5" id="text-3-3-1-3">
<div id="orgf43f9ed" class="figure">
<p><img src="figs/amplified_piezo_opt_stiff_iff_dist.png" alt="amplified_piezo_opt_stiff_iff_dist.png" />
</p>
<p><span class="figure-number">Figure 19: </span>Effect of disturbance with and without IFF</p>
</div>
<div class="important">
<p>
</p>
</div>
</div>
</div>
</div>
<div id="outline-container-orgce4f07c" class="outline-4">
<h4 id="orgce4f07c"><span class="section-number-4">3.3.2</span> High Authority Controller</h4>
<div class="outline-text-4" id="text-3-3-2">
</div>
<div id="outline-container-orgc16003c" class="outline-5">
<h5 id="orgc16003c"><span class="section-number-5">3.3.2.1</span> Controller Design</h5>
<div class="outline-text-5" id="text-3-3-2-1">
<div class="org-src-container">
<pre class="src src-matlab">h = 2.5;
Kl = 5e6 * eye(6) * ...
1/h*(s/(2*pi*40/h) + 1)/(s/(2*pi*40*h) + 1) * ...
1/h*(s/(2*pi*100/h) + 1)/(s/(2*pi*100*h) + 1) * ...
(s/2/pi/50 + 1)/(s/2/pi/50) * ...
(s/2/pi/10 + 1)/(s/2/pi/10) * ...
1/(1 + s/2/pi/200);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">Kl = 3e10 * eye(6) * ...
1/s * ...
(s+0.8)/s * ...
(s+50)/(s+0.01) * ...
(s+120)/(s+1000) * ...
(s+150)/(s+1000);
</pre>
</div>
<p>
Finally, we include the Jacobian in the control and we ignore the measurement of the vertical rotation as for the real system.
</p>
<div class="org-src-container">
<pre class="src src-matlab">load('mat/stages.mat', 'nano_hexapod');
K = Kl*nano_hexapod.kinematics.J*diag([1, 1, 1, 1, 1, 0]);
</pre>
</div>
</div>
</div>
<div id="outline-container-orgbcf7749" class="outline-5">
<h5 id="orgbcf7749"><span class="section-number-5">3.3.2.2</span> Sensibility to Disturbances and Noise Budget</h5>
<div class="outline-text-5" id="text-3-3-2-2">
<p>
We identify the transfer function from disturbances to the position error of the sample when the HAC-LAC control is applied.
</p>
</div>
</div>
<div id="outline-container-orga0e8915" class="outline-5">
<h5 id="orga0e8915"><span class="section-number-5">3.3.2.3</span> Simulations of Tomography Experiment</h5>
<div class="outline-text-5" id="text-3-3-2-3">
<p>
Let&rsquo;s now simulate a tomography experiment.
To do so, we include all disturbances except vibrations of the translation stage.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeDisturbances();
initializeSimscapeConfiguration('gravity', false);
initializeLoggingConfiguration('log', 'all');
</pre>
</div>
<p>
And we run the simulation for all three payload Masses.
</p>
</div>
</div>
<div id="outline-container-orgb6ec250" class="outline-5">
<h5 id="orgb6ec250"><span class="section-number-5">3.3.2.4</span> Results</h5>
</div>
</div>
</div>
<div id="outline-container-org1e2f810" class="outline-3">
<h3 id="org1e2f810"><span class="section-number-3">3.7</span> Direct Velocity Feedback with Amplified Actuators</h3>
<h3 id="org1e2f810"><span class="section-number-3">3.4</span> Direct Velocity Feedback with Amplified Actuators</h3>
<div class="outline-text-3" id="text-3-4">
<p>
Lack of collocation.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeController('type', 'hac-dvf');
K = tf(zeros(6));
Kdvf = tf(zeros(6));
</pre>
</div>
<p>
We identify the system for the following payload masses:
</p>
<div class="org-src-container">
<pre class="src src-matlab">Ms = [1, 10, 50];
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">initializeNanoHexapod('actuator', 'amplified', ...
'k1', 1e4, ...
'ke', 1e6, ...
'ka', 1e6);
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-org936810c" class="outline-2">
<h2 id="org936810c"><span class="section-number-2">4</span> APA300ML</h2>
<div class="outline-text-2" id="text-4">
</div>
<div id="outline-container-org797e3ca" class="outline-3">
<h3 id="org797e3ca"><span class="section-number-3">4.1</span> Initialization</h3>
<div class="outline-text-3" id="text-4-1">
<div class="org-src-container">
<pre class="src src-matlab">initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
initializeSimscapeConfiguration();
initializeDisturbances('enable', false);
initializeLoggingConfiguration('log', 'none');
initializeController('type', 'hac-dvf');
</pre>
</div>
<p>
We set the stiffness of the payload fixation:
</p>
<div class="org-src-container">
<pre class="src src-matlab">Kp = 1e8; % [N/m]
</pre>
</div>
</div>
</div>
<div id="outline-container-org2300f00" class="outline-3">
<h3 id="org2300f00"><span class="section-number-3">4.2</span> Identification</h3>
<div class="outline-text-3" id="text-4-2">
<div class="org-src-container">
<pre class="src src-matlab">K = tf(zeros(6));
Kdvf = tf(zeros(6));
</pre>
</div>
<p>
We identify the system for the following payload masses:
</p>
<div class="org-src-container">
<pre class="src src-matlab">Ms = [1, 10, 50];
</pre>
</div>
<p>
The nano-hexapod has the following leg&rsquo;s stiffness and damping.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeNanoHexapod('actuator', 'amplified', 'k1', 0.4e6, 'ka', 43e6, 'ke', 1.5e6);
</pre>
</div>
</div>
</div>
<div id="outline-container-org4ec1cb7" class="outline-3">
<h3 id="org4ec1cb7"><span class="section-number-3">4.3</span> Controller Design</h3>
<div class="outline-text-3" id="text-4-3">
<p>
Damping as function of the gain
Finally, we use the following controller for the Decentralized Direct Velocity Feedback:
</p>
<div class="org-src-container">
<pre class="src src-matlab">Kdvf = 5e5*s/(1+s/2/pi/1e3)*eye(6);
</pre>
</div>
</div>
</div>
<div id="outline-container-org1b67874" class="outline-3">
<h3 id="org1b67874"><span class="section-number-3">4.4</span> Effect of the Low Authority Control on the Primary Plant</h3>
</div>
<div id="outline-container-org655c28c" class="outline-3">
<h3 id="org655c28c"><span class="section-number-3">4.5</span> Control in the leg space</h3>
<div class="outline-text-3" id="text-4-5">
<p>
We design a diagonal controller with all the same diagonal elements.
</p>
<p>
The requirements for the controller are:
</p>
<ul class="org-ul">
<li>Crossover frequency of around 100Hz</li>
<li>Stable for all the considered payload masses</li>
<li>Sufficient phase and gain margin</li>
<li>Integral action at low frequency</li>
</ul>
<p>
The design controller is as follows:
</p>
<ul class="org-ul">
<li>Lead centered around the crossover</li>
<li>An integrator below 10Hz</li>
<li>A low pass filter at 250Hz</li>
</ul>
<div class="org-src-container">
<pre class="src src-matlab">h = 2.0;
Kl = 1e9 * eye(6) * ...
1/h*(s/(2*pi*100/h) + 1)/(s/(2*pi*100*h) + 1) * ...
1/h*(s/(2*pi*200/h) + 1)/(s/(2*pi*200*h) + 1) * ...
(s/2/pi/10 + 1)/(s/2/pi/10) * ...
1/(1 + s/2/pi/300);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">load('mat/stages.mat', 'nano_hexapod');
K = Kl*nano_hexapod.kinematics.J*diag([1, 1, 1, 1, 1, 0]);
</pre>
</div>
</div>
</div>
<div id="outline-container-org92df47e" class="outline-3">
<h3 id="org92df47e"><span class="section-number-3">4.6</span> Sensibility to Disturbances and Noise Budget</h3>
<div class="outline-text-3" id="text-4-6">
<p>
We identify the transfer function from disturbances to the position error of the sample when the HAC-LAC control is applied.
</p>
<div id="org44696dd" class="figure">
<p><img src="figs/opt_stiff_primary_control_L_psd_dist.png" alt="opt_stiff_primary_control_L_psd_dist.png" />
</p>
<p><span class="figure-number">Figure 20: </span>Amplitude Spectral Density of the vertical position error of the sample when the HAC-DVF control is applied due to both the ground motion and spindle vibrations</p>
</div>
<div id="org15d4b96" class="figure">
<p><img src="figs/opt_stiff_primary_control_L_psd_tot.png" alt="opt_stiff_primary_control_L_psd_tot.png" />
</p>
<p><span class="figure-number">Figure 21: </span>Amplitude Spectral Density of the vertical position error of the sample in Open-Loop and when the HAC-DVF control is applied</p>
</div>
<div id="org7a31e40" class="figure">
<p><img src="figs/opt_stiff_primary_control_L_cas_tot.png" alt="opt_stiff_primary_control_L_cas_tot.png" />
</p>
<p><span class="figure-number">Figure 22: </span>Cumulative Amplitude Spectrum of the vertical position error of the sample in Open-Loop and when the HAC-DVF control is applied</p>
</div>
</div>
</div>
<div id="outline-container-orge84cedc" class="outline-3">
<h3 id="orge84cedc"><span class="section-number-3">4.7</span> Simulations of Tomography Experiment</h3>
<div class="outline-text-3" id="text-4-7">
<p>
Let&rsquo;s now simulate a tomography experiment.
To do so, we include all disturbances except vibrations of the translation stage.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeDisturbances();
initializeSimscapeConfiguration('gravity', false);
initializeLoggingConfiguration('log', 'all');
</pre>
</div>
<p>
And we run the simulation for all three payload Masses.
</p>
</div>
</div>
<div id="outline-container-org05ce41a" class="outline-3">
<h3 id="org05ce41a"><span class="section-number-3">4.8</span> Results</h3>
<div class="outline-text-3" id="text-4-8">
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><h2 class='citeproc-org-bib-h2'>Bibliography</h2>
<div class="csl-bib-body">
<div class="csl-entry"><a name="citeproc_bib_item_1"></a>Dehaeze, T., and C. Collette. 2020. “Active Damping of Rotating Platforms Using Integral Force Feedback.” In <i>Proceedings of the International Conference on Modal Analysis Noise and Vibration Engineering (ISMA)</i>.</div>
<div class="csl-entry"><a name="citeproc_bib_item_2"></a>Souleille, Adrien, Thibault Lampert, V Lafarga, Sylvain Hellegouarch, Alan Rondineau, Gonçalo Rodrigues, and Christophe Collette. 2018. “A Concept of Active Mount for Space Applications.” <i>CEAS Space Journal</i> 10 (2). Springer:157–65.</div>
</div>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-05-25 lun. 11:13</p>
<p class="date">Created: 2020-09-01 mar. 13:48</p>
</div>
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</html>