770 lines
33 KiB
HTML
770 lines
33 KiB
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#org-div-home-and-up
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/*]]>*/-->
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// @license magnet:?xt=urn:btih:1f739d935676111cfff4b4693e3816e664797050&dn=gpl-3.0.txt GPL-v3-or-Later
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<script>
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MathJax = {
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tex: { macros: {
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bm: ["\\boldsymbol{#1}",1],
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</head>
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<body>
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<div id="org-div-home-and-up">
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<a accesskey="h" href="./index.html"> UP </a>
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<a accesskey="H" href="./index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Control in the Frame of the Legs applied on the Simscape Model</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#org1f22cdb">1. Decentralized Control</a>
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<ul>
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<li><a href="#orgf7b3c37">1.1. Control Schematic</a></li>
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<li><a href="#org15ed002">1.2. Initialize the Simscape Model</a></li>
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<li><a href="#org42afc36">1.3. Identification of the plant</a></li>
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<li><a href="#org871560e">1.4. Plant Analysis</a></li>
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<li><a href="#orgb0aa319">1.5. Controller Design</a></li>
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<li><a href="#org564e3b0">1.6. Simulation</a></li>
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<li><a href="#org0f36edb">1.7. Results</a></li>
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</ul>
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</li>
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<li><a href="#orgfa4be92">2. HAC-LAC (IFF) Decentralized Control</a>
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<ul>
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<li><a href="#orgcd58f5e">2.1. Control Schematic</a></li>
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<li><a href="#org4318f13">2.2. Initialize the Simscape Model</a></li>
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<li><a href="#org0903106">2.3. Initialization</a></li>
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<li><a href="#orge739f61">2.4. Identification for IFF</a></li>
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<li><a href="#org08b6a99">2.5. Integral Force Feedback Controller</a></li>
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<li><a href="#org06b5c75">2.6. Identification of the damped plant</a></li>
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<li><a href="#orgdf3c9aa">2.7. Controller Design</a></li>
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<li><a href="#org753f2c4">2.8. Simulation</a></li>
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<li><a href="#orgd8c14ee">2.9. Results</a></li>
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</ul>
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</li>
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<li><a href="#org21a9294">3. Conclusion</a></li>
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</ul>
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</div>
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</div>
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<p>
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In this document, we apply some decentralized control to the NASS and see what level of performance can be obtained.
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</p>
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<div id="outline-container-org1f22cdb" class="outline-2">
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<h2 id="org1f22cdb"><span class="section-number-2">1</span> Decentralized Control</h2>
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<div class="outline-text-2" id="text-1">
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</div>
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<div id="outline-container-orgf7b3c37" class="outline-3">
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<h3 id="orgf7b3c37"><span class="section-number-3">1.1</span> Control Schematic</h3>
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<div class="outline-text-3" id="text-1-1">
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<p>
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The control architecture is shown in Figure <a href="#org7503773">1</a>.
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</p>
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<p>
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The signals are:
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</p>
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<ul class="org-ul">
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<li>\(\bm{r}_\mathcal{X}\): wanted position of the sample with respect to the granite</li>
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<li>\(\bm{r}_{\mathcal{X}_n}\): wanted position of the sample with respect to the nano-hexapod</li>
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<li>\(\bm{r}_\mathcal{L}\): wanted length of each of the nano-hexapod’s legs</li>
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<li>\(\bm{\tau}\): forces applied in each actuator</li>
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<li>\(\bm{\mathcal{L}}\): measured displacement of each leg</li>
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<li>\(\bm{\mathcal{X}}\): measured position of the sample with respect to the granite</li>
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||
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|
</ul>
|
||
|
|
|
||
|
|
|
||
|
|
<div id="org7503773" 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>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-org15ed002" class="outline-3">
|
||
|
|
<h3 id="org15ed002"><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>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
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>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
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>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-matlab">initializeDisturbances();
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
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>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
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>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
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>
|
||
|
|
</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 class="outline-text-3" id="text-1-3">
|
||
|
|
<p>
|
||
|
|
Let’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>;
|
||
|
|
|
||
|
|
<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>};
|
||
|
|
</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 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>.
|
||
|
|
</p>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
We can see that:
|
||
|
|
</p>
|
||
|
|
<ul class="org-ul">
|
||
|
|
<li>the diagonal terms have similar dynamics</li>
|
||
|
|
<li>the plant is decoupled at low frequency</li>
|
||
|
|
</ul>
|
||
|
|
|
||
|
|
|
||
|
|
<div id="org68ea839" 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>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-orgb0aa319" class="outline-3">
|
||
|
|
<h3 id="orgb0aa319"><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:
|
||
|
|
</p>
|
||
|
|
<ul class="org-ul">
|
||
|
|
<li>A pure integrator</li>
|
||
|
|
<li>An integrator up to little before the crossover</li>
|
||
|
|
<li>A lead around the crossover</li>
|
||
|
|
<li>A low pass filter with a cut-off frequency 3 times the crossover to increase the gain margin</li>
|
||
|
|
</ul>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
The obtained loop gains corresponding to the diagonal elements are shown in Figure <a href="#org3bd29d4">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;
|
||
|
|
|
||
|
|
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">
|
||
|
|
<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>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
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>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-org564e3b0" class="outline-3">
|
||
|
|
<h3 id="org564e3b0"><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>
|
||
|
|
</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>
|
||
|
|
</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>
|
||
|
|
</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>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-org0f36edb" class="outline-3">
|
||
|
|
<h3 id="org0f36edb"><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>.
|
||
|
|
</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>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
|
||
|
|
<div id="org247b3a0" 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>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</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 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-orgcd58f5e" class="outline-3">
|
||
|
|
<h3 id="orgcd58f5e"><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="#org7503773">1</a>.
|
||
|
|
</p>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
The signals are:
|
||
|
|
</p>
|
||
|
|
<ul class="org-ul">
|
||
|
|
<li>\(\bm{r}_\mathcal{X}\): wanted position of the sample with respect to the granite</li>
|
||
|
|
<li>\(\bm{r}_{\mathcal{X}_n}\): wanted position of the sample with respect to the nano-hexapod</li>
|
||
|
|
<li>\(\bm{r}_\mathcal{L}\): wanted length of each of the nano-hexapod’s legs</li>
|
||
|
|
<li>\(\bm{\tau}\): forces applied in each actuator</li>
|
||
|
|
<li>\(\bm{\mathcal{L}}\): measured displacement of each leg</li>
|
||
|
|
<li>\(\bm{\mathcal{X}}\): measured position of the sample with respect to the granite</li>
|
||
|
|
</ul>
|
||
|
|
|
||
|
|
|
||
|
|
<div id="org5b991df" 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>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-org4318f13" class="outline-3">
|
||
|
|
<h3 id="org4318f13"><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>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
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>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
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>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-matlab">initializeDisturbances();
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
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>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
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>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
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>
|
||
|
|
</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 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>
|
||
|
|
</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 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>;
|
||
|
|
|
||
|
|
<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>};
|
||
|
|
</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 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>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<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 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>;
|
||
|
|
|
||
|
|
<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>};
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-orgdf3c9aa" class="outline-3">
|
||
|
|
<h3 id="orgdf3c9aa"><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;
|
||
|
|
|
||
|
|
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>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-matlab">Kl = <span class="org-type">-</span>Kl;
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
|
||
|
|
<div id="outline-container-org753f2c4" class="outline-3">
|
||
|
|
<h3 id="org753f2c4"><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>
|
||
|
|
</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>
|
||
|
|
</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>
|
||
|
|
</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>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-orgd8c14ee" class="outline-3">
|
||
|
|
<h3 id="orgd8c14ee"><span class="section-number-3">2.9</span> Results</h3>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
<div id="outline-container-org21a9294" class="outline-2">
|
||
|
|
<h2 id="org21a9294"><span class="section-number-2">3</span> Conclusion</h2>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
<div id="postamble" class="status">
|
||
|
|
<p class="author">Author: Dehaeze Thomas</p>
|
||
|
|
<p class="date">Created: 2020-03-20 ven. 16:35</p>
|
||
|
|
</div>
|
||
|
|
</body>
|
||
|
|
</html>
|