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<title>Control in the Frame of the Legs applied on the Simscape Model</title>
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<h1 class="title">Control in the Frame of the Legs applied on the Simscape Model</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org1f22cdb">1. Decentralized Control</a>
<li><a href="#org1a08332">1. Decentralized Control</a>
<ul>
<li><a href="#org01937c0">1.1. Control Schematic</a></li>
<li><a href="#orgc9e3b66">1.2. Initialize the Simscape Model</a></li>
<li><a href="#org42afc36">1.3. Identification of the plant</a></li>
<li><a href="#org871560e">1.4. Plant Analysis</a></li>
<li><a href="#org296e3de">1.5. Controller Design</a></li>
<li><a href="#orgb7afa1e">1.6. Simulation</a></li>
<li><a href="#orgbb1dc16">1.7. Results</a></li>
<li><a href="#org88b6ca3">1.1. Control Schematic</a></li>
<li><a href="#org9041934">1.2. Initialize the Simscape Model</a></li>
<li><a href="#org78bce32">1.3. Identification of the plant</a></li>
<li><a href="#org3a56a98">1.4. Plant Analysis</a></li>
<li><a href="#org36df689">1.5. Controller Design</a></li>
<li><a href="#orgac5ea1c">1.6. Simulation</a></li>
<li><a href="#orga044079">1.7. Results</a></li>
</ul>
</li>
<li><a href="#orgfa4be92">2. HAC-LAC (IFF) Decentralized Control</a>
<li><a href="#orgeeaa041">2. HAC-LAC (IFF) Decentralized Control</a>
<ul>
<li><a href="#orgbc4af09">2.1. Control Schematic</a></li>
<li><a href="#org5ac6c37">2.2. Initialize the Simscape Model</a></li>
<li><a href="#org0903106">2.3. Initialization</a></li>
<li><a href="#orge739f61">2.4. Identification for IFF</a></li>
<li><a href="#org08b6a99">2.5. Integral Force Feedback Controller</a></li>
<li><a href="#org06b5c75">2.6. Identification of the damped plant</a></li>
<li><a href="#org85a0730">2.7. Controller Design</a></li>
<li><a href="#org58ffd80">2.8. Simulation</a></li>
<li><a href="#orga01ccc6">2.9. Results</a></li>
<li><a href="#orge42dfda">2.1. Control Schematic</a></li>
<li><a href="#org790d1db">2.2. Initialize the Simscape Model</a></li>
<li><a href="#org110a4e9">2.3. Initialization</a></li>
<li><a href="#org8f68ab2">2.4. Identification for IFF</a></li>
<li><a href="#orgbe68cd0">2.5. Integral Force Feedback Controller</a></li>
<li><a href="#orgca29231">2.6. Identification of the damped plant</a></li>
<li><a href="#org95df29b">2.7. Controller Design</a></li>
<li><a href="#org8b5710f">2.8. Simulation</a></li>
<li><a href="#org791c2a5">2.9. Results</a></li>
</ul>
</li>
<li><a href="#org21a9294">3. Conclusion</a></li>
<li><a href="#orgf9b95b3">3. Conclusion</a></li>
</ul>
</div>
</div>
@@ -68,15 +72,15 @@
In this document, we apply some decentralized control to the NASS and see what level of performance can be obtained.
</p>
<div id="outline-container-org1f22cdb" class="outline-2">
<h2 id="org1f22cdb"><span class="section-number-2">1</span> Decentralized Control</h2>
<div id="outline-container-org1a08332" class="outline-2">
<h2 id="org1a08332"><span class="section-number-2">1</span> Decentralized Control</h2>
<div class="outline-text-2" id="text-1">
</div>
<div id="outline-container-org01937c0" class="outline-3">
<h3 id="org01937c0"><span class="section-number-3">1.1</span> Control Schematic</h3>
<div id="outline-container-org88b6ca3" class="outline-3">
<h3 id="org88b6ca3"><span class="section-number-3">1.1</span> Control Schematic</h3>
<div class="outline-text-3" id="text-1-1">
<p>
The control architecture is shown in Figure <a href="#org5b9133f">1</a>.
The control architecture is shown in Figure <a href="#orgd4d73cb">1</a>.
</p>
<p>
@@ -92,7 +96,7 @@ The signals are:
</ul>
<div id="org5b9133f" class="figure">
<div id="orgd4d73cb" class="figure">
<p><img src="figs/decentralized_reference_tracking_L.png" alt="decentralized_reference_tracking_L.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Decentralized control for reference tracking</p>
@@ -100,21 +104,21 @@ The signals are:
</div>
</div>
<div id="outline-container-orgc9e3b66" class="outline-3">
<h3 id="orgc9e3b66"><span class="section-number-3">1.2</span> Initialize the Simscape Model</h3>
<div id="outline-container-org9041934" class="outline-3">
<h3 id="org9041934"><span class="section-number-3">1.2</span> Initialize the Simscape Model</h3>
<div class="outline-text-3" id="text-1-2">
<p>
We initialize all the stages with the default parameters.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
<pre class="src src-matlab"> initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
</pre>
</div>
@@ -122,8 +126,8 @@ initializeMirror();
The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeNanoHexapod(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
initializeSample(<span class="org-string">'mass'</span>, 1);
<pre class="src src-matlab"> initializeNanoHexapod(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
initializeSample(<span class="org-string">'mass'</span>, 1);
</pre>
</div>
@@ -131,12 +135,12 @@ initializeSample(<span class="org-string">'mass'</span>, 1);
We set the references that corresponds to a tomography experiment.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeReferences(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, 1);
<pre class="src src-matlab"> initializeReferences(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, 1);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">initializeDisturbances();
<pre class="src src-matlab"> initializeDisturbances();
</pre>
</div>
@@ -144,8 +148,8 @@ We set the references that corresponds to a tomography experiment.
Open Loop.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-L'</span>);
Kl = tf(zeros(6));
<pre class="src src-matlab"> initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-L'</span>);
Kl = tf(zeros(6));
</pre>
</div>
@@ -153,7 +157,7 @@ Kl = tf(zeros(6));
And we put some gravity.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">true</span>);
<pre class="src src-matlab"> initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">true</span>);
</pre>
</div>
@@ -161,41 +165,41 @@ And we put some gravity.
We log the signals.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'all'</span>);
<pre class="src src-matlab"> initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'all'</span>);
</pre>
</div>
</div>
</div>
<div id="outline-container-org42afc36" class="outline-3">
<h3 id="org42afc36"><span class="section-number-3">1.3</span> Identification of the plant</h3>
<div id="outline-container-org78bce32" class="outline-3">
<h3 id="org78bce32"><span class="section-number-3">1.3</span> Identification of the plant</h3>
<div class="outline-text-3" id="text-1-3">
<p>
Let&rsquo;s identify the transfer function from \(\bm{\tau}\) to \(\bm{\mathcal{L}}\).
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
mdl = <span class="org-string">'nass_model'</span>;
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
mdl = <span class="org-string">'nass_model'</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
clear io; io_i = 1;
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Inputs</span>
io(io_i) = linio([mdl, <span class="org-string">'/Controller/Reference-Tracking-L/Sum'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Leg length error</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
clear io; io_i = 1;
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Inputs</span>
io(io_i) = linio([mdl, <span class="org-string">'/Controller/Reference-Tracking-L/Sum'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Leg length error</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
G = linearize(mdl, io, 0);
G.InputName = {<span class="org-string">'Fnl1'</span>, <span class="org-string">'Fnl2'</span>, <span class="org-string">'Fnl3'</span>, <span class="org-string">'Fnl4'</span>, <span class="org-string">'Fnl5'</span>, <span class="org-string">'Fnl6'</span>};
G.OutputName = {<span class="org-string">'El1'</span>, <span class="org-string">'El2'</span>, <span class="org-string">'El3'</span>, <span class="org-string">'El4'</span>, <span class="org-string">'El5'</span>, <span class="org-string">'El6'</span>};
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
G = linearize(mdl, io, 0);
G.InputName = {<span class="org-string">'Fnl1'</span>, <span class="org-string">'Fnl2'</span>, <span class="org-string">'Fnl3'</span>, <span class="org-string">'Fnl4'</span>, <span class="org-string">'Fnl5'</span>, <span class="org-string">'Fnl6'</span>};
G.OutputName = {<span class="org-string">'El1'</span>, <span class="org-string">'El2'</span>, <span class="org-string">'El3'</span>, <span class="org-string">'El4'</span>, <span class="org-string">'El5'</span>, <span class="org-string">'El6'</span>};
</pre>
</div>
</div>
</div>
<div id="outline-container-org871560e" class="outline-3">
<h3 id="org871560e"><span class="section-number-3">1.4</span> Plant Analysis</h3>
<div id="outline-container-org3a56a98" class="outline-3">
<h3 id="org3a56a98"><span class="section-number-3">1.4</span> Plant Analysis</h3>
<div class="outline-text-3" id="text-1-4">
<p>
The diagonal and off-diagonal terms of the plant are shown in Figure <a href="#org68ea839">2</a>.
The diagonal and off-diagonal terms of the plant are shown in Figure <a href="#orgbc5977b">2</a>.
</p>
<p>
@@ -207,7 +211,7 @@ We can see that:
</ul>
<div id="org68ea839" class="figure">
<div id="orgbc5977b" class="figure">
<p><img src="figs/decentralized_control_plant_L.png" alt="decentralized_control_plant_L.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Transfer Functions from forces applied in each actuator \(\tau_i\) to the relative motion of each leg \(d\mathcal{L}_i\) (<a href="./figs/decentralized_control_plant_L.png">png</a>, <a href="./figs/decentralized_control_plant_L.pdf">pdf</a>)</p>
@@ -215,8 +219,8 @@ We can see that:
</div>
</div>
<div id="outline-container-org296e3de" class="outline-3">
<h3 id="org296e3de"><span class="section-number-3">1.5</span> Controller Design</h3>
<div id="outline-container-org36df689" class="outline-3">
<h3 id="org36df689"><span class="section-number-3">1.5</span> Controller Design</h3>
<div class="outline-text-3" id="text-1-5">
<p>
The controller consists of:
@@ -229,24 +233,24 @@ The controller consists of:
</ul>
<p>
The obtained loop gains corresponding to the diagonal elements are shown in Figure <a href="#org3bd29d4">3</a>.
The obtained loop gains corresponding to the diagonal elements are shown in Figure <a href="#org0e9c3e8">3</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>20;
h = 1.5;
<pre class="src src-matlab"> wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>20;
h = 1.5;
Kl = diag(1<span class="org-type">./</span>diag(abs(freqresp(G, wc)))) <span class="org-type">*</span> ...
wc<span class="org-type">/</span>s <span class="org-type">*</span> ...<span class="org-comment"> % Pure Integrator</span>
((s<span class="org-type">/</span>wc<span class="org-type">*</span>2 <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>wc<span class="org-type">*</span>2)) <span class="org-type">*</span> ...<span class="org-comment"> % Integrator up to wc/2</span>
1<span class="org-type">/</span>h <span class="org-type">*</span> (1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">*</span>h)<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">/</span>h) <span class="org-type">*</span> ...<span class="org-comment"> % Lead</span>
1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>3<span class="org-type">/</span>wc) <span class="org-type">*</span> ...<span class="org-comment"> % Low pass Filter</span>
1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>3<span class="org-type">/</span>wc);
Kl = diag(1<span class="org-type">./</span>diag(abs(freqresp(G, wc)))) <span class="org-type">*</span> ...
wc<span class="org-type">/</span>s <span class="org-type">*</span> ...<span class="org-comment"> % Pure Integrator</span>
((s<span class="org-type">/</span>wc<span class="org-type">*</span>2 <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>wc<span class="org-type">*</span>2)) <span class="org-type">*</span> ...<span class="org-comment"> % Integrator up to wc/2</span>
1<span class="org-type">/</span>h <span class="org-type">*</span> (1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">*</span>h)<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">/</span>h) <span class="org-type">*</span> ...<span class="org-comment"> % Lead</span>
1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>3<span class="org-type">/</span>wc) <span class="org-type">*</span> ...<span class="org-comment"> % Low pass Filter</span>
1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>3<span class="org-type">/</span>wc);
</pre>
</div>
<div id="org3bd29d4" class="figure">
<div id="org0e9c3e8" class="figure">
<p><img src="figs/decentralized_control_L_loop_gain.png" alt="decentralized_control_L_loop_gain.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Obtained Loop Gain (<a href="./figs/decentralized_control_L_loop_gain.png">png</a>, <a href="./figs/decentralized_control_L_loop_gain.pdf">pdf</a>)</p>
@@ -256,54 +260,54 @@ Kl = diag(1<span class="org-type">./</span>diag(abs(freqresp(G, wc)))) <span cla
We add a minus sign to the controller as it is not included in the Simscape model.
</p>
<div class="org-src-container">
<pre class="src src-matlab">Kl = <span class="org-type">-</span>Kl;
<pre class="src src-matlab"> Kl = <span class="org-type">-</span>Kl;
</pre>
</div>
</div>
</div>
<div id="outline-container-orgb7afa1e" class="outline-3">
<h3 id="orgb7afa1e"><span class="section-number-3">1.6</span> Simulation</h3>
<div id="outline-container-orgac5ea1c" class="outline-3">
<h3 id="orgac5ea1c"><span class="section-number-3">1.6</span> Simulation</h3>
<div class="outline-text-3" id="text-1-6">
<div class="org-src-container">
<pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-L'</span>);
<pre class="src src-matlab"> initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-L'</span>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'mat/conf_simulink.mat'</span>);
<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'2'</span>);
<pre class="src src-matlab"> load(<span class="org-string">'mat/conf_simulink.mat'</span>);
<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'2'</span>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
<pre class="src src-matlab"> <span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">decentralized_L = simout;
save(<span class="org-string">'./mat/tomo_exp_decentalized.mat'</span>, <span class="org-string">'decentralized_L'</span>, <span class="org-string">'-append'</span>);
<pre class="src src-matlab"> decentralized_L = simout;
save(<span class="org-string">'./mat/tomo_exp_decentalized.mat'</span>, <span class="org-string">'decentralized_L'</span>, <span class="org-string">'-append'</span>);
</pre>
</div>
</div>
</div>
<div id="outline-container-orgbb1dc16" class="outline-3">
<h3 id="orgbb1dc16"><span class="section-number-3">1.7</span> Results</h3>
<div id="outline-container-orga044079" class="outline-3">
<h3 id="orga044079"><span class="section-number-3">1.7</span> Results</h3>
<div class="outline-text-3" id="text-1-7">
<p>
The reference path and the position of the mobile platform are shown in Figure <a href="#org247b3a0">4</a>.
The reference path and the position of the mobile platform are shown in Figure <a href="#org5b1621d">4</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_align_dist'</span>);
load(<span class="org-string">'./mat/tomo_exp_decentalized.mat'</span>, <span class="org-string">'decentralized_L'</span>);
<pre class="src src-matlab"> load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_align_dist'</span>);
load(<span class="org-string">'./mat/tomo_exp_decentalized.mat'</span>, <span class="org-string">'decentralized_L'</span>);
</pre>
</div>
<div id="org247b3a0" class="figure">
<div id="org5b1621d" class="figure">
<p><img src="figs/decentralized_L_position_errors.png" alt="decentralized_L_position_errors.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Position Errors when using the Decentralized Control Architecture (<a href="./figs/decentralized_L_position_errors.png">png</a>, <a href="./figs/decentralized_L_position_errors.pdf">pdf</a>)</p>
@@ -312,19 +316,19 @@ load(<span class="org-string">'./mat/tomo_exp_decentalized.mat'</span>, <span cl
</div>
</div>
<div id="outline-container-orgfa4be92" class="outline-2">
<h2 id="orgfa4be92"><span class="section-number-2">2</span> HAC-LAC (IFF) Decentralized Control</h2>
<div id="outline-container-orgeeaa041" class="outline-2">
<h2 id="orgeeaa041"><span class="section-number-2">2</span> HAC-LAC (IFF) Decentralized Control</h2>
<div class="outline-text-2" id="text-2">
<p>
We here add an Active Damping Loop (Integral Force Feedback) prior to using the Decentralized control architecture using \(\bm{\mathcal{L}}\).
</p>
</div>
<div id="outline-container-orgbc4af09" class="outline-3">
<h3 id="orgbc4af09"><span class="section-number-3">2.1</span> Control Schematic</h3>
<div id="outline-container-orge42dfda" class="outline-3">
<h3 id="orge42dfda"><span class="section-number-3">2.1</span> Control Schematic</h3>
<div class="outline-text-3" id="text-2-1">
<p>
The control architecture is shown in Figure <a href="#org5b9133f">1</a>.
The control architecture is shown in Figure <a href="#orgd4d73cb">1</a>.
</p>
<p>
@@ -340,7 +344,7 @@ The signals are:
</ul>
<div id="org657383b" class="figure">
<div id="org9b33c60" class="figure">
<p><img src="figs/decentralized_reference_tracking_L.png" alt="decentralized_reference_tracking_L.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Decentralized control for reference tracking</p>
@@ -348,21 +352,21 @@ The signals are:
</div>
</div>
<div id="outline-container-org5ac6c37" class="outline-3">
<h3 id="org5ac6c37"><span class="section-number-3">2.2</span> Initialize the Simscape Model</h3>
<div id="outline-container-org790d1db" class="outline-3">
<h3 id="org790d1db"><span class="section-number-3">2.2</span> Initialize the Simscape Model</h3>
<div class="outline-text-3" id="text-2-2">
<p>
We initialize all the stages with the default parameters.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
<pre class="src src-matlab"> initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeAxisc();
initializeMirror();
</pre>
</div>
@@ -370,8 +374,8 @@ initializeMirror();
The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeNanoHexapod(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
initializeSample(<span class="org-string">'mass'</span>, 1);
<pre class="src src-matlab"> initializeNanoHexapod(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
initializeSample(<span class="org-string">'mass'</span>, 1);
</pre>
</div>
@@ -379,12 +383,12 @@ initializeSample(<span class="org-string">'mass'</span>, 1);
We set the references that corresponds to a tomography experiment.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeReferences(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, 1);
<pre class="src src-matlab"> initializeReferences(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, 1);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">initializeDisturbances();
<pre class="src src-matlab"> initializeDisturbances();
</pre>
</div>
@@ -392,8 +396,8 @@ We set the references that corresponds to a tomography experiment.
Open Loop.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-L'</span>);
Kl = tf(zeros(6));
<pre class="src src-matlab"> initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-L'</span>);
Kl = tf(zeros(6));
</pre>
</div>
@@ -401,7 +405,7 @@ Kl = tf(zeros(6));
And we put some gravity.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">true</span>);
<pre class="src src-matlab"> initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">true</span>);
</pre>
</div>
@@ -409,149 +413,149 @@ And we put some gravity.
We log the signals.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'all'</span>);
<pre class="src src-matlab"> initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'all'</span>);
</pre>
</div>
</div>
</div>
<div id="outline-container-org0903106" class="outline-3">
<h3 id="org0903106"><span class="section-number-3">2.3</span> Initialization</h3>
<div id="outline-container-org110a4e9" class="outline-3">
<h3 id="org110a4e9"><span class="section-number-3">2.3</span> Initialization</h3>
<div class="outline-text-3" id="text-2-3">
<div class="org-src-container">
<pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-iff-L'</span>);
K_iff = tf(zeros(6));
Kl = tf(zeros(6));
<pre class="src src-matlab"> initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-iff-L'</span>);
K_iff = tf(zeros(6));
Kl = tf(zeros(6));
</pre>
</div>
</div>
</div>
<div id="outline-container-orge739f61" class="outline-3">
<h3 id="orge739f61"><span class="section-number-3">2.4</span> Identification for IFF</h3>
<div id="outline-container-org8f68ab2" class="outline-3">
<h3 id="org8f68ab2"><span class="section-number-3">2.4</span> Identification for IFF</h3>
<div class="outline-text-3" id="text-2-4">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
mdl = <span class="org-string">'nass_model'</span>;
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
mdl = <span class="org-string">'nass_model'</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
clear io; io_i = 1;
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Inputs</span>
io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station'</span>], 3, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Fnlm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Force Sensors</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
clear io; io_i = 1;
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Inputs</span>
io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station'</span>], 3, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Fnlm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Force Sensors</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
G_iff = linearize(mdl, io, 0);
G_iff.InputName = {<span class="org-string">'Fnl1'</span>, <span class="org-string">'Fnl2'</span>, <span class="org-string">'Fnl3'</span>, <span class="org-string">'Fnl4'</span>, <span class="org-string">'Fnl5'</span>, <span class="org-string">'Fnl6'</span>};
G_iff.OutputName = {<span class="org-string">'Fnlm1'</span>, <span class="org-string">'Fnlm2'</span>, <span class="org-string">'Fnlm3'</span>, <span class="org-string">'Fnlm4'</span>, <span class="org-string">'Fnlm5'</span>, <span class="org-string">'Fnlm6'</span>};
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
G_iff = linearize(mdl, io, 0);
G_iff.InputName = {<span class="org-string">'Fnl1'</span>, <span class="org-string">'Fnl2'</span>, <span class="org-string">'Fnl3'</span>, <span class="org-string">'Fnl4'</span>, <span class="org-string">'Fnl5'</span>, <span class="org-string">'Fnl6'</span>};
G_iff.OutputName = {<span class="org-string">'Fnlm1'</span>, <span class="org-string">'Fnlm2'</span>, <span class="org-string">'Fnlm3'</span>, <span class="org-string">'Fnlm4'</span>, <span class="org-string">'Fnlm5'</span>, <span class="org-string">'Fnlm6'</span>};
</pre>
</div>
</div>
</div>
<div id="outline-container-org08b6a99" class="outline-3">
<h3 id="org08b6a99"><span class="section-number-3">2.5</span> Integral Force Feedback Controller</h3>
<div id="outline-container-orgbe68cd0" class="outline-3">
<h3 id="orgbe68cd0"><span class="section-number-3">2.5</span> Integral Force Feedback Controller</h3>
<div class="outline-text-3" id="text-2-5">
<div class="org-src-container">
<pre class="src src-matlab">w0 = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>50;
K_iff = <span class="org-type">-</span>5000<span class="org-type">/</span>s <span class="org-type">*</span> (s<span class="org-type">/</span>w0)<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>w0) <span class="org-type">*</span> eye(6);
<pre class="src src-matlab"> w0 = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>50;
K_iff = <span class="org-type">-</span>5000<span class="org-type">/</span>s <span class="org-type">*</span> (s<span class="org-type">/</span>w0)<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>w0) <span class="org-type">*</span> eye(6);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">K_iff = <span class="org-type">-</span>K_iff;
<pre class="src src-matlab"> K_iff = <span class="org-type">-</span>K_iff;
</pre>
</div>
</div>
</div>
<div id="outline-container-org06b5c75" class="outline-3">
<h3 id="org06b5c75"><span class="section-number-3">2.6</span> Identification of the damped plant</h3>
<div id="outline-container-orgca29231" class="outline-3">
<h3 id="orgca29231"><span class="section-number-3">2.6</span> Identification of the damped plant</h3>
<div class="outline-text-3" id="text-2-6">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink DehaezeFile</span></span>
mdl = <span class="org-string">'nass_model'</span>;
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink DehaezeFile</span></span>
mdl = <span class="org-string">'nass_model'</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
clear io; io_i = 1;
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'input'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Inputs</span>
io(io_i) = linio([mdl, <span class="org-string">'/Controller/Reference-Tracking-IFF-L/Sum'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Leg length error</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
clear io; io_i = 1;
io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'input'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Inputs</span>
io(io_i) = linio([mdl, <span class="org-string">'/Controller/Reference-Tracking-IFF-L/Sum'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Leg length error</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
Gd = linearize(mdl, io, 0);
Gd.InputName = {<span class="org-string">'Fnl1'</span>, <span class="org-string">'Fnl2'</span>, <span class="org-string">'Fnl3'</span>, <span class="org-string">'Fnl4'</span>, <span class="org-string">'Fnl5'</span>, <span class="org-string">'Fnl6'</span>};
Gd.OutputName = {<span class="org-string">'El1'</span>, <span class="org-string">'El2'</span>, <span class="org-string">'El3'</span>, <span class="org-string">'El4'</span>, <span class="org-string">'El5'</span>, <span class="org-string">'El6'</span>};
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
Gd = linearize(mdl, io, 0);
Gd.InputName = {<span class="org-string">'Fnl1'</span>, <span class="org-string">'Fnl2'</span>, <span class="org-string">'Fnl3'</span>, <span class="org-string">'Fnl4'</span>, <span class="org-string">'Fnl5'</span>, <span class="org-string">'Fnl6'</span>};
Gd.OutputName = {<span class="org-string">'El1'</span>, <span class="org-string">'El2'</span>, <span class="org-string">'El3'</span>, <span class="org-string">'El4'</span>, <span class="org-string">'El5'</span>, <span class="org-string">'El6'</span>};
</pre>
</div>
</div>
</div>
<div id="outline-container-org85a0730" class="outline-3">
<h3 id="org85a0730"><span class="section-number-3">2.7</span> Controller Design</h3>
<div id="outline-container-org95df29b" class="outline-3">
<h3 id="org95df29b"><span class="section-number-3">2.7</span> Controller Design</h3>
<div class="outline-text-3" id="text-2-7">
<div class="org-src-container">
<pre class="src src-matlab">wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>300;
h = 3;
<pre class="src src-matlab"> wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>300;
h = 3;
Kl = diag(1<span class="org-type">./</span>diag(abs(freqresp(Gd, wc)))) <span class="org-type">*</span> ...
((s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>20) <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>20))) <span class="org-type">*</span> ...<span class="org-comment"> % Pure Integrator</span>
((s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>50) <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>50))) <span class="org-type">*</span> ...<span class="org-comment"> % Integrator up to wc/2</span>
1<span class="org-type">/</span>h <span class="org-type">*</span> (1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">*</span>h)<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">/</span>h) <span class="org-type">*</span> ...
1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>(2<span class="org-type">*</span>wc)) <span class="org-type">*</span> ...
1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>(3<span class="org-type">*</span>wc));
Kl = diag(1<span class="org-type">./</span>diag(abs(freqresp(Gd, wc)))) <span class="org-type">*</span> ...
((s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>20) <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>20))) <span class="org-type">*</span> ...<span class="org-comment"> % Pure Integrator</span>
((s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>50) <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>50))) <span class="org-type">*</span> ...<span class="org-comment"> % Integrator up to wc/2</span>
1<span class="org-type">/</span>h <span class="org-type">*</span> (1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">*</span>h)<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">/</span>h) <span class="org-type">*</span> ...
1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>(2<span class="org-type">*</span>wc)) <span class="org-type">*</span> ...
1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>(3<span class="org-type">*</span>wc));
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">isstable(feedback(Gd<span class="org-type">*</span>Kl, eye(6), <span class="org-type">-</span>1))
<pre class="src src-matlab"> isstable(feedback(Gd<span class="org-type">*</span>Kl, eye(6), <span class="org-type">-</span>1))
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">Kl = <span class="org-type">-</span>Kl;
<pre class="src src-matlab"> Kl = <span class="org-type">-</span>Kl;
</pre>
</div>
</div>
</div>
<div id="outline-container-org58ffd80" class="outline-3">
<h3 id="org58ffd80"><span class="section-number-3">2.8</span> Simulation</h3>
<div id="outline-container-org8b5710f" class="outline-3">
<h3 id="org8b5710f"><span class="section-number-3">2.8</span> Simulation</h3>
<div class="outline-text-3" id="text-2-8">
<div class="org-src-container">
<pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-iff-L'</span>);
<pre class="src src-matlab"> initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-iff-L'</span>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'mat/conf_simulink.mat'</span>);
<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'2'</span>);
<pre class="src src-matlab"> load(<span class="org-string">'mat/conf_simulink.mat'</span>);
<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'2'</span>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
<pre class="src src-matlab"> <span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">decentralized_iff_L = simout;
save(<span class="org-string">'./mat/tomo_exp_decentalized.mat'</span>, <span class="org-string">'decentralized_iff_L'</span>, <span class="org-string">'-append'</span>);
<pre class="src src-matlab"> decentralized_iff_L = simout;
save(<span class="org-string">'./mat/tomo_exp_decentalized.mat'</span>, <span class="org-string">'decentralized_iff_L'</span>, <span class="org-string">'-append'</span>);
</pre>
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<div id="outline-container-orga01ccc6" class="outline-3">
<h3 id="orga01ccc6"><span class="section-number-3">2.9</span> Results</h3>
<div id="outline-container-org791c2a5" class="outline-3">
<h3 id="org791c2a5"><span class="section-number-3">2.9</span> Results</h3>
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<div id="outline-container-org21a9294" class="outline-2">
<h2 id="org21a9294"><span class="section-number-2">3</span> Conclusion</h2>
<div id="outline-container-orgf9b95b3" class="outline-2">
<h2 id="orgf9b95b3"><span class="section-number-2">3</span> Conclusion</h2>
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<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-04-17 ven. 09:35</p>
<p class="date">Created: 2021-02-20 sam. 23:08</p>
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