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<!-- 2021-01-08 ven. 15:29 -->
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<!-- 2021-01-08 ven. 15:52 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Stewart Platform with Flexible Elements</title>
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<meta name="generator" content="Org mode" />
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@@ -24,48 +24,48 @@
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<ul>
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<li><a href="#orgc309c7b">1. Simscape Model</a>
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<ul>
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<li><a href="#orgae23ac5">1.1. Flexible APA</a></li>
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<li><a href="#org0e00e94">1.1. Flexible APA</a></li>
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||||
<li><a href="#orgf337fe9">1.2. Flexible Joint</a></li>
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<li><a href="#orga8d83ce">1.3. Identification</a></li>
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<li><a href="#orgc239ed1">1.3. Identification</a></li>
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<li><a href="#org59e4972">1.4. No Flexible Elements</a></li>
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<li><a href="#orgb06052a">1.5. Flexible joints</a></li>
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<li><a href="#org0e00e94">1.6. Flexible APA</a></li>
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<li><a href="#org4cccff6">1.6. Flexible APA</a></li>
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<li><a href="#org4f41f14">1.7. Flexible Joints and APA</a></li>
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<li><a href="#orga39e477">1.8. Save</a></li>
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<li><a href="#org1e66228">1.9. Direct Velocity Feedback</a></li>
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<li><a href="#orgef60bbc">1.10. Integral Force Feedback</a></li>
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<li><a href="#org50fdd32">1.11. Procedure to include flexible elements into Simscape</a></li>
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<li><a href="#org52c4099">1.12. Conclusion</a></li>
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<li><a href="#org55fe34f">1.12. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org2d65f84">2. Control with flexible elements</a>
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<ul>
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<li><a href="#org7f0d75c">2.1. Flexible APA and Flexible Joint</a></li>
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<li><a href="#orgc239ed1">2.2. Identification</a></li>
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<li><a href="#org5f84aea">2.2. Identification</a></li>
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<li><a href="#org5ae25be">2.3. Decentralized Direct Velocity Feedback</a></li>
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<li><a href="#org3d014d0">2.4. HAC</a></li>
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</ul>
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</li>
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<li><a href="#org2b937bc">3. Flexible Joint Specifications</a>
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<ul>
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<li><a href="#org166293c">3.1. Stewart Platform Initialization</a></li>
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<li><a href="#org775a387">3.1. Stewart Platform Initialization</a></li>
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<li><a href="#orgc430963">3.2. Effect of the Bending Stiffness</a></li>
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<li><a href="#orgb29824b">3.3. Effect of the Torsion Stiffness</a></li>
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<li><a href="#org6d029b0">3.4. Effect of the Axial Stiffness</a></li>
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<li><a href="#org5177329">3.5. Effect of the Radial (Shear) Stiffness</a></li>
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<li><a href="#orgd67ef9e">3.6. Comparison of perfect joint and worst specified joint</a></li>
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<li><a href="#org55fe34f">3.7. Conclusion</a></li>
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<li><a href="#orge0f8240">3.6. Comparison of perfect joint and worst specified joint</a></li>
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<li><a href="#org79b6e2d">3.7. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org8798d60">4. Flexible Joint Specifications with the APA300ML</a>
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<ul>
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<li><a href="#org6fc554b">4.1. Stewart Platform Initialization</a></li>
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<li><a href="#orge0f8240">4.2. Comparison of perfect joint and worst specified joint</a></li>
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<li><a href="#org6d56b33">4.1. Stewart Platform Initialization</a></li>
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<li><a href="#orgdc3d576">4.2. Comparison of perfect joint and worst specified joint</a></li>
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</ul>
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</li>
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<li><a href="#orgbae1ad3">5. Relative Motion Sensors</a>
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<ul>
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<li><a href="#org775a387">5.1. Stewart Platform Initialization</a></li>
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<li><a href="#org74f7ec9">5.1. Stewart Platform Initialization</a></li>
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</ul>
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</li>
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<li><a href="#orgb454975">6. Struts with Encoders</a>
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@@ -82,11 +82,11 @@
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<h2 id="orgc309c7b"><span class="section-number-2">1</span> Simscape Model</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-orgae23ac5" class="outline-3">
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<h3 id="orgae23ac5"><span class="section-number-3">1.1</span> Flexible APA</h3>
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<div id="outline-container-org0e00e94" class="outline-3">
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<h3 id="org0e00e94"><span class="section-number-3">1.1</span> Flexible APA</h3>
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<div class="outline-text-3" id="text-1-1">
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<div class="org-src-container">
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<pre class="src src-matlab"> apa = load(<span class="org-string">'./mat/APA300ML.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
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<pre class="src src-matlab">apa = load(<span class="org-string">'./mat/APA300ML.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
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</pre>
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</div>
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@@ -209,7 +209,7 @@
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<h3 id="orgf337fe9"><span class="section-number-3">1.2</span> Flexible Joint</h3>
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<div class="outline-text-3" id="text-1-2">
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<div class="org-src-container">
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<pre class="src src-matlab"> flex_joint = load(<span class="org-string">'./mat/flexor_025.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
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<pre class="src src-matlab">flex_joint = load(<span class="org-string">'./mat/flexor_025.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
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</pre>
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</div>
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@@ -325,37 +325,37 @@
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</div>
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</div>
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<div id="outline-container-orga8d83ce" class="outline-3">
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<h3 id="orga8d83ce"><span class="section-number-3">1.3</span> Identification</h3>
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<div id="outline-container-orgc239ed1" class="outline-3">
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<h3 id="orgc239ed1"><span class="section-number-3">1.3</span> Identification</h3>
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<div class="outline-text-3" id="text-1-3">
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<p>
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And we identify the dynamics from force actuators to force sensors.
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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-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
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options = linearizeOptions;
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options.SampleTime = 0;
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<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
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options = linearizeOptions;
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options.SampleTime = 0;
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<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">'stewart_platform_model'</span>;
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<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">'stewart_platform_model'</span>;
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
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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 Force Inputs [N]</span>
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io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
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io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Taum'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Force Sensors [N]</span>
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
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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 Force Inputs [N]</span>
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io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
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io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Taum'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Force Sensors [N]</span>
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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"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
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payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 50);
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controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
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||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
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||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 50);
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||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
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||||
</pre>
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||||
</div>
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||||
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||||
<div class="org-src-container">
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||||
<pre class="src src-matlab"> disturbances = initializeDisturbances();
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<pre class="src src-matlab">disturbances = initializeDisturbances();
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||||
</pre>
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||||
</div>
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||||
</div>
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||||
@@ -365,36 +365,36 @@ And we identify the dynamics from force actuators to force sensors.
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<h3 id="org59e4972"><span class="section-number-3">1.4</span> No Flexible Elements</h3>
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||||
<div class="outline-text-3" id="text-1-4">
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||||
<div class="org-src-container">
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||||
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
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stewart = initializeFramesPositions(stewart);
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stewart = generateGeneralConfiguration(stewart);
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stewart = computeJointsPose(stewart);
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||||
stewart = initializeAmplifiedStrutDynamics(stewart, <span class="org-string">'Ke'</span>, 1.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ka'</span>, 40.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'K1'</span>, 0.4e6<span class="org-type">*</span>ones(6,1));
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stewart = initializeJointDynamics(stewart, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_3dof'</span>, ...
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<span class="org-string">'Kr_M'</span>, flex_joint.K(1,1)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Ka_M'</span>, flex_joint.K(3,3)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kf_M'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kt_M'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'type_F'</span>, <span class="org-string">'universal_3dof'</span>, ...
|
||||
<span class="org-string">'Kr_F'</span>, flex_joint.K(1,1)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Ka_F'</span>, flex_joint.K(3,3)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kf_F'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kt_F'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1));
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeAmplifiedStrutDynamics(stewart, <span class="org-string">'Ke'</span>, 1.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ka'</span>, 40.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'K1'</span>, 0.4e6<span class="org-type">*</span>ones(6,1));
|
||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_3dof'</span>, ...
|
||||
<span class="org-string">'Kr_M'</span>, flex_joint.K(1,1)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Ka_M'</span>, flex_joint.K(3,3)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kf_M'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kt_M'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'type_F'</span>, <span class="org-string">'universal_3dof'</span>, ...
|
||||
<span class="org-string">'Kr_F'</span>, flex_joint.K(1,1)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Ka_F'</span>, flex_joint.K(3,3)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kf_F'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kt_F'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1));
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
|
||||
references = initializeReferences(stewart);
|
||||
references = initializeReferences(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
G = linearize(mdl, io, options);
|
||||
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||
G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>, <span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>};
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
G = linearize(mdl, io, options);
|
||||
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||
G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>, <span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -411,32 +411,32 @@ And we identify the dynamics from force actuators to force sensors.
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeAmplifiedStrutDynamics(stewart, <span class="org-string">'Ke'</span>, 1.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ka'</span>, 40.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'K1'</span>, 0.4e6<span class="org-type">*</span>ones(6,1));
|
||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_F'</span>, flex_joint.K, <span class="org-string">'M_F'</span>, flex_joint.M, <span class="org-string">'n_xyz_F'</span>, flex_joint.n_xyz, <span class="org-string">'xi_F'</span>, 0.1, <span class="org-string">'step_file_F'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_M'</span>, flex_joint.K, <span class="org-string">'M_M'</span>, flex_joint.M, <span class="org-string">'n_xyz_M'</span>, flex_joint.n_xyz, <span class="org-string">'xi_M'</span>, 0.1, <span class="org-string">'step_file_M'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>);
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeAmplifiedStrutDynamics(stewart, <span class="org-string">'Ke'</span>, 1.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ka'</span>, 40.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'K1'</span>, 0.4e6<span class="org-type">*</span>ones(6,1));
|
||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_F'</span>, flex_joint.K, <span class="org-string">'M_F'</span>, flex_joint.M, <span class="org-string">'n_xyz_F'</span>, flex_joint.n_xyz, <span class="org-string">'xi_F'</span>, 0.1, <span class="org-string">'step_file_F'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_M'</span>, flex_joint.K, <span class="org-string">'M_M'</span>, flex_joint.M, <span class="org-string">'n_xyz_M'</span>, flex_joint.n_xyz, <span class="org-string">'xi_M'</span>, 0.1, <span class="org-string">'step_file_M'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>);
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
Gj = linearize(mdl, io, options);
|
||||
Gj.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||
Gj.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>, <span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>};
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
Gj = linearize(mdl, io, options);
|
||||
Gj.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||
Gj.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>, <span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0e00e94" class="outline-3">
|
||||
<h3 id="org0e00e94"><span class="section-number-3">1.6</span> Flexible APA</h3>
|
||||
<div id="outline-container-org4cccff6" class="outline-3">
|
||||
<h3 id="org4cccff6"><span class="section-number-3">1.6</span> Flexible APA</h3>
|
||||
<div class="outline-text-3" id="text-1-6">
|
||||
|
||||
<div id="org6abb282" class="figure">
|
||||
@@ -446,34 +446,34 @@ And we identify the dynamics from force actuators to force sensors.
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeFlexibleStrutDynamics(stewart, <span class="org-string">'H'</span>, 0.03, <span class="org-string">'K'</span>, apa.K, <span class="org-string">'M'</span>, apa.M, <span class="org-string">'n_xyz'</span>, apa.n_xyz, <span class="org-string">'xi'</span>, 0.1, <span class="org-string">'Gf'</span>, <span class="org-type">-</span>2.65e7, <span class="org-string">'step_file'</span>, <span class="org-string">'mat/APA300ML.STEP'</span>);
|
||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_3dof'</span>, ...
|
||||
<span class="org-string">'Kr_M'</span>, flex_joint.K(1,1)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Ka_M'</span>, flex_joint.K(3,3)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kf_M'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kt_M'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'type_F'</span>, <span class="org-string">'universal_3dof'</span>, ...
|
||||
<span class="org-string">'Kr_F'</span>, flex_joint.K(1,1)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Ka_F'</span>, flex_joint.K(3,3)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kf_F'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kt_F'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1));
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'none'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'none'</span>);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeFlexibleStrutDynamics(stewart, <span class="org-string">'H'</span>, 0.03, <span class="org-string">'K'</span>, apa.K, <span class="org-string">'M'</span>, apa.M, <span class="org-string">'n_xyz'</span>, apa.n_xyz, <span class="org-string">'xi'</span>, 0.1, <span class="org-string">'Gf'</span>, <span class="org-type">-</span>2.65e7, <span class="org-string">'step_file'</span>, <span class="org-string">'mat/APA300ML.STEP'</span>);
|
||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_3dof'</span>, ...
|
||||
<span class="org-string">'Kr_M'</span>, flex_joint.K(1,1)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Ka_M'</span>, flex_joint.K(3,3)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kf_M'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kt_M'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'type_F'</span>, <span class="org-string">'universal_3dof'</span>, ...
|
||||
<span class="org-string">'Kr_F'</span>, flex_joint.K(1,1)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Ka_F'</span>, flex_joint.K(3,3)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kf_F'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kt_F'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1));
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'none'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'none'</span>);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
Ga = <span class="org-type">-</span>linearize(mdl, io, options);
|
||||
Ga.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||
Ga.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>, <span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>};
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
Ga = <span class="org-type">-</span>linearize(mdl, io, options);
|
||||
Ga.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||
Ga.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>, <span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -490,24 +490,24 @@ And we identify the dynamics from force actuators to force sensors.
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeFlexibleStrutDynamics(stewart, <span class="org-string">'H'</span>, 0.03, <span class="org-string">'K'</span>, apa.K, <span class="org-string">'M'</span>, apa.M, <span class="org-string">'n_xyz'</span>, apa.n_xyz, <span class="org-string">'xi'</span>, 0.1, <span class="org-string">'Gf'</span>, <span class="org-type">-</span>2.65e7, <span class="org-string">'step_file'</span>, <span class="org-string">'mat/APA300ML.STEP'</span>);
|
||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_F'</span>, flex_joint.K, <span class="org-string">'M_F'</span>, flex_joint.M, <span class="org-string">'n_xyz_F'</span>, flex_joint.n_xyz, <span class="org-string">'xi_F'</span>, 0.1, <span class="org-string">'step_file_F'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_M'</span>, flex_joint.K, <span class="org-string">'M_M'</span>, flex_joint.M, <span class="org-string">'n_xyz_M'</span>, flex_joint.n_xyz, <span class="org-string">'xi_M'</span>, 0.1, <span class="org-string">'step_file_M'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>);
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'none'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'none'</span>);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeFlexibleStrutDynamics(stewart, <span class="org-string">'H'</span>, 0.03, <span class="org-string">'K'</span>, apa.K, <span class="org-string">'M'</span>, apa.M, <span class="org-string">'n_xyz'</span>, apa.n_xyz, <span class="org-string">'xi'</span>, 0.1, <span class="org-string">'Gf'</span>, <span class="org-type">-</span>2.65e7, <span class="org-string">'step_file'</span>, <span class="org-string">'mat/APA300ML.STEP'</span>);
|
||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_F'</span>, flex_joint.K, <span class="org-string">'M_F'</span>, flex_joint.M, <span class="org-string">'n_xyz_F'</span>, flex_joint.n_xyz, <span class="org-string">'xi_F'</span>, 0.1, <span class="org-string">'step_file_F'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_M'</span>, flex_joint.K, <span class="org-string">'M_M'</span>, flex_joint.M, <span class="org-string">'n_xyz_M'</span>, flex_joint.n_xyz, <span class="org-string">'xi_M'</span>, 0.1, <span class="org-string">'step_file_M'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>);
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'none'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'none'</span>);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> Gf = <span class="org-type">-</span>linearize(mdl, io, options);
|
||||
Gf.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||
Gf.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>, <span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>};
|
||||
<pre class="src src-matlab">Gf = <span class="org-type">-</span>linearize(mdl, io, options);
|
||||
Gf.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||
Gf.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>, <span class="org-string">'Fm1'</span>, <span class="org-string">'Fm2'</span>, <span class="org-string">'Fm3'</span>, <span class="org-string">'Fm4'</span>, <span class="org-string">'Fm5'</span>, <span class="org-string">'Fm6'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -517,7 +517,7 @@ And we identify the dynamics from force actuators to force sensors.
|
||||
<h3 id="orga39e477"><span class="section-number-3">1.8</span> Save</h3>
|
||||
<div class="outline-text-3" id="text-1-8">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> save(<span class="org-string">'./mat/flexible_stewart_platform.mat'</span>, <span class="org-string">'G'</span>, <span class="org-string">'Gj'</span>, <span class="org-string">'Ga'</span>, <span class="org-string">'Gf'</span>);
|
||||
<pre class="src src-matlab">save(<span class="org-string">'./mat/flexible_stewart_platform.mat'</span>, <span class="org-string">'G'</span>, <span class="org-string">'Gj'</span>, <span class="org-string">'Ga'</span>, <span class="org-string">'Gf'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -566,10 +566,10 @@ In order to model a flexible element with only few mass-spring-damper elements:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org52c4099" class="outline-3">
|
||||
<h3 id="org52c4099"><span class="section-number-3">1.12</span> Conclusion</h3>
|
||||
<div id="outline-container-org55fe34f" class="outline-3">
|
||||
<h3 id="org55fe34f"><span class="section-number-3">1.12</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-1-12">
|
||||
<div class="important" id="org7acf160">
|
||||
<div class="important" id="orgba069e0">
|
||||
<p>
|
||||
The results seems to indicate that the model is well represented with only few degrees of freedom.
|
||||
This permit to have a relatively sane number of states for the model.
|
||||
@@ -588,66 +588,66 @@ This permit to have a relatively sane number of states for the model.
|
||||
<h3 id="org7f0d75c"><span class="section-number-3">2.1</span> Flexible APA and Flexible Joint</h3>
|
||||
<div class="outline-text-3" id="text-2-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> apa = load(<span class="org-string">'./mat/APA300ML.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
||||
flex_joint = load(<span class="org-string">'./mat/flexor_ID16.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
||||
<pre class="src src-matlab">apa = load(<span class="org-string">'./mat/APA300ML.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
||||
flex_joint = load(<span class="org-string">'./mat/flexor_ID16.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeFlexibleStrutDynamics(stewart, <span class="org-string">'H'</span>, 0.03, <span class="org-string">'K'</span>, apa.K, <span class="org-string">'M'</span>, apa.M, <span class="org-string">'n_xyz'</span>, apa.n_xyz, <span class="org-string">'xi'</span>, 0.1, <span class="org-string">'step_file'</span>, <span class="org-string">'mat/APA300ML.STEP'</span>);
|
||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_F'</span>, flex_joint.K, <span class="org-string">'M_F'</span>, flex_joint.M, <span class="org-string">'n_xyz_F'</span>, flex_joint.n_xyz, <span class="org-string">'xi_F'</span>, 0.1, <span class="org-string">'step_file_F'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_M'</span>, flex_joint.K, <span class="org-string">'M_M'</span>, flex_joint.M, <span class="org-string">'n_xyz_M'</span>, flex_joint.n_xyz, <span class="org-string">'xi_M'</span>, 0.1, <span class="org-string">'step_file_M'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>);
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'none'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'none'</span>);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeFlexibleStrutDynamics(stewart, <span class="org-string">'H'</span>, 0.03, <span class="org-string">'K'</span>, apa.K, <span class="org-string">'M'</span>, apa.M, <span class="org-string">'n_xyz'</span>, apa.n_xyz, <span class="org-string">'xi'</span>, 0.1, <span class="org-string">'step_file'</span>, <span class="org-string">'mat/APA300ML.STEP'</span>);
|
||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_F'</span>, flex_joint.K, <span class="org-string">'M_F'</span>, flex_joint.M, <span class="org-string">'n_xyz_F'</span>, flex_joint.n_xyz, <span class="org-string">'xi_F'</span>, 0.1, <span class="org-string">'step_file_F'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'K_M'</span>, flex_joint.K, <span class="org-string">'M_M'</span>, flex_joint.M, <span class="org-string">'n_xyz_M'</span>, flex_joint.n_xyz, <span class="org-string">'xi_M'</span>, 0.1, <span class="org-string">'step_file_M'</span>, <span class="org-string">'mat/flexor_ID16.STEP'</span>);
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'none'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'none'</span>);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 50);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 50);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> disturbances = initializeDisturbances();
|
||||
references = initializeReferences(stewart);
|
||||
<pre class="src src-matlab">disturbances = initializeDisturbances();
|
||||
references = initializeReferences(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgc239ed1" class="outline-3">
|
||||
<h3 id="orgc239ed1"><span class="section-number-3">2.2</span> Identification</h3>
|
||||
<div id="outline-container-org5f84aea" class="outline-3">
|
||||
<h3 id="org5f84aea"><span class="section-number-3">2.2</span> Identification</h3>
|
||||
<div class="outline-text-3" id="text-2-2">
|
||||
<p>
|
||||
And we identify the dynamics from force actuators to force sensors.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||
mdl = <span class="org-string">'stewart_platform_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 Force Inputs [N]</span>
|
||||
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</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 Force Inputs [N]</span>
|
||||
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> G = <span class="org-type">-</span>linearize(mdl, io, options);
|
||||
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||
G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>};
|
||||
<pre class="src src-matlab">G = <span class="org-type">-</span>linearize(mdl, io, options);
|
||||
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||
G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -660,12 +660,12 @@ And we identify the dynamics from force actuators to force sensors.
|
||||
Controller Design
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> Kl = <span class="org-type">-</span>1e5<span class="org-type">*</span>s<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>2e2)<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>5e2) <span class="org-type">*</span> eye(6);
|
||||
<pre class="src src-matlab">Kl = <span class="org-type">-</span>1e5<span class="org-type">*</span>s<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>2e2)<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>5e2) <span class="org-type">*</span> eye(6);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> isstable(feedback(G(1<span class="org-type">:</span>6,1<span class="org-type">:</span>6)<span class="org-type">*</span>Kl, eye(6), <span class="org-type">-</span>1))
|
||||
<pre class="src src-matlab">isstable(feedback(G(1<span class="org-type">:</span>6,1<span class="org-type">:</span>6)<span class="org-type">*</span>Kl, eye(6), <span class="org-type">-</span>1))
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -679,37 +679,37 @@ Controller Design
|
||||
<h3 id="org3d014d0"><span class="section-number-3">2.4</span> HAC</h3>
|
||||
<div class="outline-text-3" id="text-2-4">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> Kx = tf(zeros(6));
|
||||
<pre class="src src-matlab">Kx = tf(zeros(6));
|
||||
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-hac-dvf'</span>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-hac-dvf'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<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">'stewart_platform_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">'stewart_platform_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 Force Inputs [N]</span>
|
||||
io(io_i) = linio([mdl, <span class="org-string">'/Relative Motion Sensor'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</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 Force Inputs [N]</span>
|
||||
io(io_i) = linio([mdl, <span class="org-string">'/Relative Motion Sensor'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
G = linearize(mdl, io);
|
||||
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||
G.OutputName = {<span class="org-string">'Dx'</span>, <span class="org-string">'Dy'</span>, <span class="org-string">'Dz'</span>, <span class="org-string">'Rx'</span>, <span class="org-string">'Ry'</span>, <span class="org-string">'Rz'</span>};
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
G = linearize(mdl, io);
|
||||
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||
G.OutputName = {<span class="org-string">'Dx'</span>, <span class="org-string">'Dy'</span>, <span class="org-string">'Dz'</span>, <span class="org-string">'Rx'</span>, <span class="org-string">'Ry'</span>, <span class="org-string">'Rz'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> Gl = <span class="org-type">-</span>stewart.kinematics.J<span class="org-type">*</span>G;
|
||||
Gl.OutputName = {<span class="org-string">'D1'</span>, <span class="org-string">'D2'</span>, <span class="org-string">'D3'</span>, <span class="org-string">'D4'</span>, <span class="org-string">'D5'</span>, <span class="org-string">'D6'</span>};
|
||||
<pre class="src src-matlab">Gl = <span class="org-type">-</span>stewart.kinematics.J<span class="org-type">*</span>G;
|
||||
Gl.OutputName = {<span class="org-string">'D1'</span>, <span class="org-string">'D2'</span>, <span class="org-string">'D3'</span>, <span class="org-string">'D4'</span>, <span class="org-string">'D5'</span>, <span class="org-string">'D6'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<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;
|
||||
Kl = diag(1<span class="org-type">./</span>diag(abs(freqresp(Gl, wc)))) <span class="org-type">*</span> wc<span class="org-type">/</span>s <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 class="src src-matlab">wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>300;
|
||||
Kl = diag(1<span class="org-type">./</span>diag(abs(freqresp(Gl, wc)))) <span class="org-type">*</span> wc<span class="org-type">/</span>s <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>
|
||||
@@ -720,39 +720,39 @@ Controller Design
|
||||
<h2 id="org2b937bc"><span class="section-number-2">3</span> Flexible Joint Specifications</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
</div>
|
||||
<div id="outline-container-org166293c" class="outline-3">
|
||||
<h3 id="org166293c"><span class="section-number-3">3.1</span> Stewart Platform Initialization</h3>
|
||||
<div id="outline-container-org775a387" class="outline-3">
|
||||
<h3 id="org775a387"><span class="section-number-3">3.1</span> Stewart Platform Initialization</h3>
|
||||
<div class="outline-text-3" id="text-3-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeAmplifiedStrutDynamics(stewart, <span class="org-string">'Ke'</span>, 1.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ka'</span>, 43e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'K1'</span>, 0.4e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'C1'</span>, 10<span class="org-type">*</span>ones(6,1));
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeAmplifiedStrutDynamics(stewart, <span class="org-string">'Ke'</span>, 1.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ka'</span>, 43e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'K1'</span>, 0.4e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'C1'</span>, 10<span class="org-type">*</span>ones(6,1));
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
|
||||
references = initializeReferences(stewart);
|
||||
references = initializeReferences(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 50);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 50);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> disturbances = initializeDisturbances();
|
||||
<pre class="src src-matlab">disturbances = initializeDisturbances();
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> open(<span class="org-string">'stewart_platform_model.slx'</span>)
|
||||
<pre class="src src-matlab">open(<span class="org-string">'stewart_platform_model.slx'</span>)
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -762,7 +762,7 @@ Controller Design
|
||||
<h3 id="orgc430963"><span class="section-number-3">3.2</span> Effect of the Bending Stiffness</h3>
|
||||
<div class="outline-text-3" id="text-3-2">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> Kfs = [1, 10, 100, 1000]; <span class="org-comment">% [Nm/rad]</span>
|
||||
<pre class="src src-matlab">Kfs = [1, 10, 100, 1000]; <span class="org-comment">% [Nm/rad]</span>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -772,7 +772,7 @@ Controller Design
|
||||
<h3 id="orgb29824b"><span class="section-number-3">3.3</span> Effect of the Torsion Stiffness</h3>
|
||||
<div class="outline-text-3" id="text-3-3">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> Kts = [10, 100, 500, 1000]; <span class="org-comment">% [Nm/rad]</span>
|
||||
<pre class="src src-matlab">Kts = [10, 100, 500, 1000]; <span class="org-comment">% [Nm/rad]</span>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -782,7 +782,7 @@ Controller Design
|
||||
<h3 id="org6d029b0"><span class="section-number-3">3.4</span> Effect of the Axial Stiffness</h3>
|
||||
<div class="outline-text-3" id="text-3-4">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> Kas = [1e6, 1e7, 1e8, 5e8, 1e9]; <span class="org-comment">% [N/m]</span>
|
||||
<pre class="src src-matlab">Kas = [1e6, 1e7, 1e8, 5e8, 1e9]; <span class="org-comment">% [N/m]</span>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -792,17 +792,17 @@ Controller Design
|
||||
<h3 id="org5177329"><span class="section-number-3">3.5</span> Effect of the Radial (Shear) Stiffness</h3>
|
||||
<div class="outline-text-3" id="text-3-5">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> Krs = [1e4, 1e5, 1e6, 1e7]; <span class="org-comment">% [N/m]</span>
|
||||
<pre class="src src-matlab">Krs = [1e4, 1e5, 1e6, 1e7]; <span class="org-comment">% [N/m]</span>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd67ef9e" class="outline-3">
|
||||
<h3 id="orgd67ef9e"><span class="section-number-3">3.6</span> Comparison of perfect joint and worst specified joint</h3>
|
||||
<div id="outline-container-orge0f8240" class="outline-3">
|
||||
<h3 id="orge0f8240"><span class="section-number-3">3.6</span> Comparison of perfect joint and worst specified joint</h3>
|
||||
</div>
|
||||
<div id="outline-container-org55fe34f" class="outline-3">
|
||||
<h3 id="org55fe34f"><span class="section-number-3">3.7</span> Conclusion</h3>
|
||||
<div id="outline-container-org79b6e2d" class="outline-3">
|
||||
<h3 id="org79b6e2d"><span class="section-number-3">3.7</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-3-7">
|
||||
<p>
|
||||
Qualitatively:
|
||||
@@ -891,118 +891,118 @@ Quantitatively:
|
||||
<h2 id="org8798d60"><span class="section-number-2">4</span> Flexible Joint Specifications with the APA300ML</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
</div>
|
||||
<div id="outline-container-org6fc554b" class="outline-3">
|
||||
<h3 id="org6fc554b"><span class="section-number-3">4.1</span> Stewart Platform Initialization</h3>
|
||||
<div id="outline-container-org6d56b33" class="outline-3">
|
||||
<h3 id="org6d56b33"><span class="section-number-3">4.1</span> Stewart Platform Initialization</h3>
|
||||
<div class="outline-text-3" id="text-4-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> apa = load(<span class="org-string">'./mat/APA300ML.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
||||
<pre class="src src-matlab">apa = load(<span class="org-string">'./mat/APA300ML.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeFlexibleStrutDynamics(stewart, <span class="org-string">'H'</span>, 0.03, <span class="org-string">'K'</span>, apa.K, <span class="org-string">'M'</span>, apa.M, <span class="org-string">'n_xyz'</span>, apa.n_xyz, <span class="org-string">'xi'</span>, 0.1, <span class="org-string">'step_file'</span>, <span class="org-string">'mat/APA300ML.STEP'</span>);
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'none'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'none'</span>);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeFlexibleStrutDynamics(stewart, <span class="org-string">'H'</span>, 0.03, <span class="org-string">'K'</span>, apa.K, <span class="org-string">'M'</span>, apa.M, <span class="org-string">'n_xyz'</span>, apa.n_xyz, <span class="org-string">'xi'</span>, 0.1, <span class="org-string">'step_file'</span>, <span class="org-string">'mat/APA300ML.STEP'</span>);
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'none'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'none'</span>);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
|
||||
references = initializeReferences(stewart);
|
||||
references = initializeReferences(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 50);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 50);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> disturbances = initializeDisturbances();
|
||||
<pre class="src src-matlab">disturbances = initializeDisturbances();
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> open(<span class="org-string">'stewart_platform_model.slx'</span>)
|
||||
<pre class="src src-matlab">open(<span class="org-string">'stewart_platform_model.slx'</span>)
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orge0f8240" class="outline-3">
|
||||
<h3 id="orge0f8240"><span class="section-number-3">4.2</span> Comparison of perfect joint and worst specified joint</h3>
|
||||
<div id="outline-container-orgdc3d576" class="outline-3">
|
||||
<h3 id="orgdc3d576"><span class="section-number-3">4.2</span> Comparison of perfect joint and worst specified joint</h3>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-orgbae1ad3" class="outline-2">
|
||||
<h2 id="orgbae1ad3"><span class="section-number-2">5</span> Relative Motion Sensors</h2>
|
||||
<div class="outline-text-2" id="text-5">
|
||||
</div>
|
||||
<div id="outline-container-org775a387" class="outline-3">
|
||||
<h3 id="org775a387"><span class="section-number-3">5.1</span> Stewart Platform Initialization</h3>
|
||||
<div id="outline-container-org74f7ec9" class="outline-3">
|
||||
<h3 id="org74f7ec9"><span class="section-number-3">5.1</span> Stewart Platform Initialization</h3>
|
||||
<div class="outline-text-3" id="text-5-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> apa = load(<span class="org-string">'./mat/APA300ML.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
||||
stewart = initializeAmplifiedStrutDynamics(stewart, <span class="org-string">'Ke'</span>, 1.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ka'</span>, 40.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'K1'</span>, 0.4e6<span class="org-type">*</span>ones(6,1));
|
||||
<span class="org-comment">% stewart = initializeFlexibleStrutDynamics(stewart, 'H', 0.03, 'K', apa.K, 'M', apa.M, 'n_xyz', apa.n_xyz, 'xi', 0.1, 'step_file', 'mat/APA300ML.STEP');</span>
|
||||
<pre class="src src-matlab">apa = load(<span class="org-string">'./mat/APA300ML.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
||||
stewart = initializeAmplifiedStrutDynamics(stewart, <span class="org-string">'Ke'</span>, 1.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ka'</span>, 40.5e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'K1'</span>, 0.4e6<span class="org-type">*</span>ones(6,1));
|
||||
<span class="org-comment">% stewart = initializeFlexibleStrutDynamics(stewart, 'H', 0.03, 'K', apa.K, 'M', apa.M, 'n_xyz', apa.n_xyz, 'xi', 0.1, 'step_file', 'mat/APA300ML.STEP');</span>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> flex_joint = load(<span class="org-string">'./mat/flexor_025.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_3dof'</span>, ...
|
||||
<span class="org-string">'Kr_M'</span>, flex_joint.K(1,1)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Ka_M'</span>, flex_joint.K(3,3)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kf_M'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kt_M'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'type_F'</span>, <span class="org-string">'universal_3dof'</span>, ...
|
||||
<span class="org-string">'Kr_F'</span>, flex_joint.K(1,1)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Ka_F'</span>, flex_joint.K(3,3)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kf_F'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kt_F'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1));
|
||||
<pre class="src src-matlab">flex_joint = load(<span class="org-string">'./mat/flexor_025.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_3dof'</span>, ...
|
||||
<span class="org-string">'Kr_M'</span>, flex_joint.K(1,1)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Ka_M'</span>, flex_joint.K(3,3)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kf_M'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kt_M'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'type_F'</span>, <span class="org-string">'universal_3dof'</span>, ...
|
||||
<span class="org-string">'Kr_F'</span>, flex_joint.K(1,1)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Ka_F'</span>, flex_joint.K(3,3)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kf_F'</span>, flex_joint.K(4,4)<span class="org-type">*</span>ones(6,1), ...
|
||||
<span class="org-string">'Kt_F'</span>, flex_joint.K(6,6)<span class="org-type">*</span>ones(6,1));
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeCylindricalPlatforms(stewart);
|
||||
<pre class="src src-matlab">stewart = initializeCylindricalPlatforms(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeCylindricalStruts(stewart);
|
||||
<pre class="src src-matlab">stewart = initializeCylindricalStruts(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
<pre class="src src-matlab">stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
|
||||
references = initializeReferences(stewart);
|
||||
references = initializeReferences(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 50);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 50);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> disturbances = initializeDisturbances();
|
||||
<pre class="src src-matlab">disturbances = initializeDisturbances();
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1017,7 +1017,7 @@ Quantitatively:
|
||||
<h3 id="org6bde940"><span class="section-number-3">6.1</span> Flexible Strut</h3>
|
||||
<div class="outline-text-3" id="text-6-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> apa = load(<span class="org-string">'./mat/strut_encoder.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
||||
<pre class="src src-matlab">apa = load(<span class="org-string">'./mat/strut_encoder.mat'</span>, <span class="org-string">'int_xyz'</span>, <span class="org-string">'int_i'</span>, <span class="org-string">'n_xyz'</span>, <span class="org-string">'n_i'</span>, <span class="org-string">'nodes'</span>, <span class="org-string">'M'</span>, <span class="org-string">'K'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1148,60 +1148,60 @@ Quantitatively:
|
||||
<h3 id="org4b369e6"><span class="section-number-3">6.2</span> Stewart Platform</h3>
|
||||
<div class="outline-text-3" id="text-6-2">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 95e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 220e<span class="org-type">-</span>3);
|
||||
stewart = generateGeneralConfiguration(stewart, <span class="org-string">'FH'</span>, 22.5e<span class="org-type">-</span>3, <span class="org-string">'FR'</span>, 114e<span class="org-type">-</span>3, <span class="org-string">'FTh'</span>, [ <span class="org-type">-</span>11, 11, 120<span class="org-type">-</span>11, 120<span class="org-type">+</span>11, 240<span class="org-type">-</span>11, 240<span class="org-type">+</span>11]<span class="org-type">*</span>(<span class="org-constant">pi</span><span class="org-type">/</span>180), ...
|
||||
<span class="org-string">'MH'</span>, 22.5e<span class="org-type">-</span>3, <span class="org-string">'MR'</span>, 110e<span class="org-type">-</span>3, <span class="org-string">'MTh'</span>, [<span class="org-type">-</span>60<span class="org-type">+</span>15, 60<span class="org-type">-</span>15, 60<span class="org-type">+</span>15, 180<span class="org-type">-</span>15, 180<span class="org-type">+</span>15, <span class="org-type">-</span>60<span class="org-type">-</span>15]<span class="org-type">*</span>(<span class="org-constant">pi</span><span class="org-type">/</span>180));
|
||||
stewart = computeJointsPose(stewart);
|
||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 95e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 220e<span class="org-type">-</span>3);
|
||||
stewart = generateGeneralConfiguration(stewart, <span class="org-string">'FH'</span>, 22.5e<span class="org-type">-</span>3, <span class="org-string">'FR'</span>, 114e<span class="org-type">-</span>3, <span class="org-string">'FTh'</span>, [ <span class="org-type">-</span>11, 11, 120<span class="org-type">-</span>11, 120<span class="org-type">+</span>11, 240<span class="org-type">-</span>11, 240<span class="org-type">+</span>11]<span class="org-type">*</span>(<span class="org-constant">pi</span><span class="org-type">/</span>180), ...
|
||||
<span class="org-string">'MH'</span>, 22.5e<span class="org-type">-</span>3, <span class="org-string">'MR'</span>, 110e<span class="org-type">-</span>3, <span class="org-string">'MTh'</span>, [<span class="org-type">-</span>60<span class="org-type">+</span>15, 60<span class="org-type">-</span>15, 60<span class="org-type">+</span>15, 180<span class="org-type">-</span>15, 180<span class="org-type">+</span>15, <span class="org-type">-</span>60<span class="org-type">-</span>15]<span class="org-type">*</span>(<span class="org-constant">pi</span><span class="org-type">/</span>180));
|
||||
stewart = computeJointsPose(stewart);
|
||||
|
||||
stewart = initializeFlexibleStrutAndJointDynamics(stewart, <span class="org-string">'H'</span>, (apa.int_xyz(1,3) <span class="org-type">-</span> apa.int_xyz(2,3)), ...
|
||||
<span class="org-string">'K'</span>, apa.K, ...
|
||||
<span class="org-string">'M'</span>, apa.M, ...
|
||||
<span class="org-string">'n_xyz'</span>, apa.n_xyz, ...
|
||||
<span class="org-string">'xi'</span>, 0.1, ...
|
||||
<span class="org-string">'Gf'</span>, <span class="org-type">-</span>2.65e7, ...
|
||||
<span class="org-string">'step_file'</span>, <span class="org-string">'mat/APA300ML.STEP'</span>);
|
||||
stewart = initializeFlexibleStrutAndJointDynamics(stewart, <span class="org-string">'H'</span>, (apa.int_xyz(1,3) <span class="org-type">-</span> apa.int_xyz(2,3)), ...
|
||||
<span class="org-string">'K'</span>, apa.K, ...
|
||||
<span class="org-string">'M'</span>, apa.M, ...
|
||||
<span class="org-string">'n_xyz'</span>, apa.n_xyz, ...
|
||||
<span class="org-string">'xi'</span>, 0.1, ...
|
||||
<span class="org-string">'Gf'</span>, <span class="org-type">-</span>2.65e7, ...
|
||||
<span class="org-string">'step_file'</span>, <span class="org-string">'mat/APA300ML.STEP'</span>);
|
||||
|
||||
stewart = initializeSolidPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'none'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'none'</span>);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
stewart = initializeSolidPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'none'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'none'</span>);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> disturbances = initializeDisturbances();
|
||||
ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 1);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
references = initializeReferences(stewart);
|
||||
<pre class="src src-matlab">disturbances = initializeDisturbances();
|
||||
ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'m'</span>, 1);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
references = initializeReferences(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||
mdl = <span class="org-string">'stewart_platform_model'</span>;
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||
mdl = <span class="org-string">'stewart_platform_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 Force Inputs [N]</span>
|
||||
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
|
||||
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Lm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Force Sensors [N]</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 Force Inputs [N]</span>
|
||||
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
|
||||
io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Lm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Force Sensors [N]</span>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> <span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
G = linearize(mdl, io, options);
|
||||
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||
G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>, ...
|
||||
<span class="org-string">'D1'</span>, <span class="org-string">'D2'</span>, <span class="org-string">'D3'</span>, <span class="org-string">'D4'</span>, <span class="org-string">'D5'</span>, <span class="org-string">'D6'</span>};
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
G = linearize(mdl, io, options);
|
||||
G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
|
||||
G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">'Dm2'</span>, <span class="org-string">'Dm3'</span>, <span class="org-string">'Dm4'</span>, <span class="org-string">'Dm5'</span>, <span class="org-string">'Dm6'</span>, ...
|
||||
<span class="org-string">'D1'</span>, <span class="org-string">'D2'</span>, <span class="org-string">'D3'</span>, <span class="org-string">'D4'</span>, <span class="org-string">'D5'</span>, <span class="org-string">'D6'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -1216,7 +1216,7 @@ Quantitatively:
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:29</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:52</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
Reference in New Issue
Block a user