Update files for new definition of hexapods
This commit is contained in:
@@ -4,7 +4,7 @@
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<!-- 2020-04-17 ven. 09:35 -->
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<!-- 2020-05-05 mar. 10:34 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>HAC-LAC applied on the Simscape Model</title>
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<meta name="generator" content="Org mode" />
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@@ -94,8 +94,8 @@ initializeMirror();
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The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeNanoHexapod(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
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initializeSample(<span class="org-string">'mass'</span>, 1);
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<pre class="src src-matlab">initializeNanoHexapod('actuator', 'piezo');
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initializeSample('mass', 1);
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</pre>
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</div>
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@@ -103,7 +103,7 @@ initializeSample(<span class="org-string">'mass'</span>, 1);
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We set the references that corresponds to a tomography experiment.
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</p>
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<div class="org-src-container">
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<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);
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<pre class="src src-matlab">initializeReferences('Rz_type', 'rotating', 'Rz_period', 1);
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</pre>
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</div>
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@@ -116,7 +116,7 @@ We set the references that corresponds to a tomography experiment.
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Open Loop.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
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<pre class="src src-matlab">initializeController('type', 'open-loop');
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</pre>
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</div>
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@@ -124,7 +124,7 @@ Open Loop.
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And we put some gravity.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">true</span>);
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<pre class="src src-matlab">initializeSimscapeConfiguration('gravity', true);
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</pre>
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</div>
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@@ -132,7 +132,7 @@ And we put some gravity.
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We log the signals.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'all'</span>);
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<pre class="src src-matlab">initializeLoggingConfiguration('log', 'all');
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</pre>
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</div>
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</div>
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@@ -154,18 +154,18 @@ The design of the associated decentralized controller is explained in <a href="c
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<h3 id="orga860160"><span class="section-number-3">2.1</span> Identification</h3>
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<div class="outline-text-3" id="text-2-1">
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
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mdl = <span class="org-string">'nass_model'</span>;
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<pre class="src src-matlab">%% Name of the Simulink File
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mdl = 'nass_model';
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
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%% Input/Output definition
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clear io; io_i = 1;
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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>
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io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station'</span>], 3, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Dnlm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Motion Outputs</span>
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io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Inputs
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io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Dnlm'); io_i = io_i + 1; % Relative Motion Outputs
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
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%% Run the linearization
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G_dvf = linearize(mdl, io, 0);
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G_dvf.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>};
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G_dvf.OutputName = {<span class="org-string">'Dnlm1'</span>, <span class="org-string">'Dnlm2'</span>, <span class="org-string">'Dnlm3'</span>, <span class="org-string">'Dnlm4'</span>, <span class="org-string">'Dnlm5'</span>, <span class="org-string">'Dnlm6'</span>};
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G_dvf.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
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G_dvf.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'};
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</pre>
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</div>
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</div>
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@@ -181,12 +181,12 @@ G_dvf.OutputName = {<span class="org-string">'Dnlm1'</span>, <span class="org-st
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<h3 id="orgafbd7d0"><span class="section-number-3">2.4</span> Controller and Loop Gain</h3>
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<div class="outline-text-3" id="text-2-4">
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<div class="org-src-container">
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<pre class="src src-matlab">K_dvf = s<span class="org-type">*</span>15000<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>10000);
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<pre class="src src-matlab">K_dvf = s*15000/(1 + s/2/pi/10000);
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">K_dvf = <span class="org-type">-</span>K_dvf<span class="org-type">*</span>eye(6);
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<pre class="src src-matlab">K_dvf = -K_dvf*eye(6);
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</pre>
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</div>
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</div>
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@@ -198,23 +198,23 @@ G_dvf.OutputName = {<span class="org-string">'Dnlm1'</span>, <span class="org-st
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<div class="outline-text-2" id="text-3">
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<div class="org-src-container">
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<pre class="src src-matlab">K_dvf_backup = K_dvf;
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initializeController(<span class="org-string">'type'</span>, <span class="org-string">'hac-dvf'</span>);
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initializeController('type', 'hac-dvf');
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">masses = [1, 10, 50]; <span class="org-comment">% [kg]</span>
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<pre class="src src-matlab">masses = [1, 10, 50]; % [kg]
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
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mdl = <span class="org-string">'nass_model'</span>;
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<pre class="src src-matlab">%% Name of the Simulink File
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mdl = 'nass_model';
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
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%% Input/Output definition
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clear io; io_i = 1;
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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>
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io(io_i) = linio([mdl, <span class="org-string">'/Tracking Error'</span>], 1, <span class="org-string">'output'</span>, [], <span class="org-string">'En'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Position Errror</span>
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io(io_i) = linio([mdl, '/Controller'], 1, 'input'); io_i = io_i + 1; % Actuator Inputs
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io(io_i) = linio([mdl, '/Tracking Error'], 1, 'output', [], 'En'); io_i = io_i + 1; % Position Errror
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</pre>
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</div>
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</div>
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@@ -233,23 +233,23 @@ io(io_i) = linio([mdl, <span class="org-string">'/Tracking Error'</span>], 1, <s
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'hac-dvf'</span>);
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<pre class="src src-matlab">initializeController('type', 'hac-dvf');
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
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mdl = <span class="org-string">'nass_model'</span>;
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<pre class="src src-matlab">%% Name of the Simulink File
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mdl = 'nass_model';
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
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%% Input/Output definition
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clear io; io_i = 1;
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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>
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io(io_i) = linio([mdl, <span class="org-string">'/Tracking Error'</span>], 1, <span class="org-string">'output'</span>, [], <span class="org-string">'En'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Position Errror</span>
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io(io_i) = linio([mdl, '/Controller'], 1, 'input'); io_i = io_i + 1; % Actuator Inputs
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io(io_i) = linio([mdl, '/Tracking Error'], 1, 'output', [], 'En'); io_i = io_i + 1; % Position Errror
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
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%% Run the linearization
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G = linearize(mdl, io, 0);
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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>};
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G.OutputName = {<span class="org-string">'Ex'</span>, <span class="org-string">'Ey'</span>, <span class="org-string">'Ez'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
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G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
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G.OutputName = {'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'};
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</pre>
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</div>
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@@ -257,10 +257,10 @@ G.OutputName = {<span class="org-string">'Ex'</span>, <span class="org-string">'
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The minus sine is put here because there is already a minus sign included due to the computation of the position error.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">load(<span class="org-string">'mat/stages.mat'</span>, <span class="org-string">'nano_hexapod'</span>);
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<pre class="src src-matlab">load('mat/stages.mat', 'nano_hexapod');
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Gx = <span class="org-type">-</span>G<span class="org-type">*</span>inv(nano_hexapod.J<span class="org-type">'</span>);
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Gx.InputName = {<span class="org-string">'Fx'</span>, <span class="org-string">'Fy'</span>, <span class="org-string">'Fz'</span>, <span class="org-string">'Mx'</span>, <span class="org-string">'My'</span>, <span class="org-string">'Mz'</span>};
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Gx = -G*inv(nano_hexapod.kinematics.J');
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Gx.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
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</pre>
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</div>
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</div>
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@@ -280,29 +280,29 @@ The controller consists of:
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</ul>
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<div class="org-src-container">
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<pre class="src src-matlab">wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>15; <span class="org-comment">% Bandwidth Bandwidth [rad/s]</span>
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<pre class="src src-matlab">wc = 2*pi*15; % Bandwidth Bandwidth [rad/s]
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h = 1.5; <span class="org-comment">% Lead parameter</span>
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h = 1.5; % Lead parameter
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Kx = (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> wc<span class="org-type">/</span>s <span class="org-type">*</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> (1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">/</span>2));
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Kx = (1/h) * (1 + s/wc*h)/(1 + s/wc/h) * wc/s * ((s/wc*2 + 1)/(s/wc*2)) * (1/(1 + s/wc/2));
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<span class="org-comment">% Normalization of the gain of have a loop gain of 1 at frequency wc</span>
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Kx = Kx<span class="org-type">.*</span>diag(1<span class="org-type">./</span>diag(abs(freqresp(Gx<span class="org-type">*</span>Kx, wc))));
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% Normalization of the gain of have a loop gain of 1 at frequency wc
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Kx = Kx.*diag(1./diag(abs(freqresp(Gx*Kx, wc))));
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">isstable(feedback(Gx<span class="org-type">*</span>Kx, eye(6), <span class="org-type">-</span>1))
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<pre class="src src-matlab">isstable(feedback(Gx*Kx, eye(6), -1))
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">Kx = inv(nano_hexapod.J<span class="org-type">'</span>)<span class="org-type">*</span>Kx;
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<pre class="src src-matlab">Kx = inv(nano_hexapod.kinematics.J')*Kx;
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">isstable(feedback(G<span class="org-type">*</span>Kx, eye(6), 1))
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<pre class="src src-matlab">isstable(feedback(G*Kx, eye(6), 1))
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</pre>
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</div>
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</div>
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@@ -313,8 +313,8 @@ Kx = Kx<span class="org-type">.*</span>diag(1<span class="org-type">./</span>dia
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<h2 id="orgb7ffa65"><span class="section-number-2">5</span> Simulation</h2>
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<div class="outline-text-2" id="text-5">
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<div class="org-src-container">
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<pre class="src src-matlab">load(<span class="org-string">'mat/conf_simulink.mat'</span>);
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<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>);
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<pre class="src src-matlab">load('mat/conf_simulink.mat');
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set_param(conf_simulink, 'StopTime', '2');
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</pre>
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</div>
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@@ -322,13 +322,13 @@ Kx = Kx<span class="org-type">.*</span>diag(1<span class="org-type">./</span>dia
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And we simulate the system.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
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<pre class="src src-matlab">sim('nass_model');
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">hac_dvf = simout;
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save(<span class="org-string">'./mat/tomo_exp_hac_lac.mat'</span>, <span class="org-string">'hac_dvf'</span>);
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save('./mat/tomo_exp_hac_lac.mat', 'hac_dvf');
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</pre>
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</div>
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</div>
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@@ -341,8 +341,8 @@ save(<span class="org-string">'./mat/tomo_exp_hac_lac.mat'</span>, <span class="
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Let’s load the simulation when no control is applied.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_align_dist'</span>);
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load(<span class="org-string">'./mat/tomo_exp_hac_lac.mat'</span>, <span class="org-string">'hac_dvf'</span>);
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<pre class="src src-matlab">load('./mat/experiment_tomography.mat', 'tomo_align_dist');
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load('./mat/tomo_exp_hac_lac.mat', 'hac_dvf');
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</pre>
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</div>
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</div>
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@@ -350,7 +350,7 @@ load(<span class="org-string">'./mat/tomo_exp_hac_lac.mat'</span>, <span class="
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</div>
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<div id="postamble" class="status">
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<p class="author">Author: Dehaeze Thomas</p>
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<p class="date">Created: 2020-04-17 ven. 09:35</p>
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<p class="date">Created: 2020-05-05 mar. 10:34</p>
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</div>
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</body>
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</html>
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Block a user