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@@ -3,7 +3,7 @@
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<!-- 2021-01-08 ven. 15:30 -->
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<!-- 2021-01-08 ven. 15:53 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Stewart Platform - Decentralized Active Damping</title>
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<meta name="generator" content="Org mode" />
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@@ -42,25 +42,25 @@
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<li><a href="#orgddaf52f">1. Inertial Control</a>
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<ul>
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||||
<li><a href="#org933440d">1.1. Identification of the Dynamics</a></li>
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||||
<li><a href="#orged6d23c">1.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
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||||
<li><a href="#org533c409">1.3. Obtained Damping</a></li>
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||||
<li><a href="#orgc76021e">1.4. Conclusion</a></li>
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<li><a href="#org2875dd1">1.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
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||||
<li><a href="#org0cea759">1.3. Obtained Damping</a></li>
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<li><a href="#orga866100">1.4. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#orgf8ed544">2. Integral Force Feedback</a>
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<ul>
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<li><a href="#org7b81fe5">2.1. Identification of the Dynamics with perfect Joints</a></li>
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<li><a href="#org3dca396">2.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
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<li><a href="#org7044ed4">2.3. Obtained Damping</a></li>
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||||
<li><a href="#org9c769b9">2.4. Conclusion</a></li>
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||||
<li><a href="#orga2d019b">2.1. Identification of the Dynamics with perfect Joints</a></li>
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||||
<li><a href="#org6ac04ee">2.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
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||||
<li><a href="#org06e1086">2.3. Obtained Damping</a></li>
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<li><a href="#orgfa832d6">2.4. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#orgabec4e1">3. Direct Velocity Feedback</a>
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<ul>
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<li><a href="#orga2d019b">3.1. Identification of the Dynamics with perfect Joints</a></li>
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<li><a href="#org2875dd1">3.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
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<li><a href="#org0cea759">3.3. Obtained Damping</a></li>
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||||
<li><a href="#orga866100">3.4. Conclusion</a></li>
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<li><a href="#org19cbcee">3.1. Identification of the Dynamics with perfect Joints</a></li>
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<li><a href="#org0fabf01">3.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
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<li><a href="#org6c74c9a">3.3. Obtained Damping</a></li>
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<li><a href="#org81b2156">3.4. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#orgc7e2089">4. Compliance and Transmissibility Comparison</a>
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@@ -90,7 +90,7 @@ The following decentralized active damping techniques are briefly studied:
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<a id="org709d56c"></a>
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</p>
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<div class="note" id="org8a14d8c">
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<div class="note" id="org1ae7526">
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<p>
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The Matlab script corresponding to this section is accessible <a href="../matlab/active_damping_inertial.m">here</a>.
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||||
</p>
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||||
@@ -106,44 +106,44 @@ To run the script, open the Simulink Project, and type <code>run active_damping_
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<h3 id="org933440d"><span class="section-number-3">1.1</span> Identification of the Dynamics</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"> stewart = initializeStewartPlatform();
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stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
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stewart = generateGeneralConfiguration(stewart);
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stewart = computeJointsPose(stewart);
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stewart = initializeStrutDynamics(stewart);
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||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
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stewart = initializeCylindricalPlatforms(stewart);
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stewart = initializeCylindricalStruts(stewart);
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||||
stewart = computeJacobian(stewart);
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||||
stewart = initializeStewartPose(stewart);
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||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'accelerometer'</span>, <span class="org-string">'freq'</span>, 5e3);
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<pre class="src src-matlab">stewart = initializeStewartPlatform();
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stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
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||||
stewart = generateGeneralConfiguration(stewart);
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||||
stewart = computeJointsPose(stewart);
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||||
stewart = initializeStrutDynamics(stewart);
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stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
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||||
stewart = initializeCylindricalPlatforms(stewart);
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||||
stewart = initializeCylindricalStruts(stewart);
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stewart = computeJacobian(stewart);
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stewart = initializeStewartPose(stewart);
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stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'accelerometer'</span>, <span class="org-string">'freq'</span>, 5e3);
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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">'rigid'</span>, <span class="org-string">'rot_point'</span>, stewart.platform_F.FO_A);
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payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
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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">'rigid'</span>, <span class="org-string">'rot_point'</span>, stewart.platform_F.FO_A);
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payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
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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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<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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||||
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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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||||
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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">'Vm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute velocity of each leg [m/s]</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">'Vm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute velocity of each leg [m/s]</span>
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
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||||
G = linearize(mdl, io, options);
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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>};
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||||
G.OutputName = {<span class="org-string">'Vm1'</span>, <span class="org-string">'Vm2'</span>, <span class="org-string">'Vm3'</span>, <span class="org-string">'Vm4'</span>, <span class="org-string">'Vm5'</span>, <span class="org-string">'Vm6'</span>};
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||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
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||||
G = linearize(mdl, io, options);
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||||
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>};
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||||
G.OutputName = {<span class="org-string">'Vm1'</span>, <span class="org-string">'Vm2'</span>, <span class="org-string">'Vm3'</span>, <span class="org-string">'Vm4'</span>, <span class="org-string">'Vm5'</span>, <span class="org-string">'Vm6'</span>};
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||||
</pre>
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||||
</div>
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||||
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||||
@@ -159,17 +159,17 @@ The transfer function from actuator forces to force sensors is shown in Figure <
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||||
</div>
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||||
</div>
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||||
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||||
<div id="outline-container-orged6d23c" class="outline-3">
|
||||
<h3 id="orged6d23c"><span class="section-number-3">1.2</span> Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</h3>
|
||||
<div id="outline-container-org2875dd1" class="outline-3">
|
||||
<h3 id="org2875dd1"><span class="section-number-3">1.2</span> Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</h3>
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||||
<div class="outline-text-3" id="text-1-2">
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||||
<p>
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||||
We add some stiffness and damping in the flexible joints and we re-identify the dynamics.
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||||
</p>
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||||
<div class="org-src-container">
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||||
<pre class="src src-matlab"> stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical'</span>);
|
||||
Gf = linearize(mdl, io, options);
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||||
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">'Vm1'</span>, <span class="org-string">'Vm2'</span>, <span class="org-string">'Vm3'</span>, <span class="org-string">'Vm4'</span>, <span class="org-string">'Vm5'</span>, <span class="org-string">'Vm6'</span>};
|
||||
<pre class="src src-matlab">stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical'</span>);
|
||||
Gf = 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">'Vm1'</span>, <span class="org-string">'Vm2'</span>, <span class="org-string">'Vm3'</span>, <span class="org-string">'Vm4'</span>, <span class="org-string">'Vm5'</span>, <span class="org-string">'Vm6'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -177,10 +177,10 @@ We add some stiffness and damping in the flexible joints and we re-identify the
|
||||
We now use the amplified actuators and re-identify the dynamics
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeAmplifiedStrutDynamics(stewart);
|
||||
Ga = 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">'Vm1'</span>, <span class="org-string">'Vm2'</span>, <span class="org-string">'Vm3'</span>, <span class="org-string">'Vm4'</span>, <span class="org-string">'Vm5'</span>, <span class="org-string">'Vm6'</span>};
|
||||
<pre class="src src-matlab">stewart = initializeAmplifiedStrutDynamics(stewart);
|
||||
Ga = 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">'Vm1'</span>, <span class="org-string">'Vm2'</span>, <span class="org-string">'Vm3'</span>, <span class="org-string">'Vm4'</span>, <span class="org-string">'Vm5'</span>, <span class="org-string">'Vm6'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -196,8 +196,8 @@ The new dynamics from force actuator to force sensor is shown in Figure <a href=
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org533c409" class="outline-3">
|
||||
<h3 id="org533c409"><span class="section-number-3">1.3</span> Obtained Damping</h3>
|
||||
<div id="outline-container-org0cea759" class="outline-3">
|
||||
<h3 id="org0cea759"><span class="section-number-3">1.3</span> Obtained Damping</h3>
|
||||
<div class="outline-text-3" id="text-1-3">
|
||||
<p>
|
||||
The control is a performed in a decentralized manner.
|
||||
@@ -222,10 +222,10 @@ The root locus is shown in figure <a href="#orgaea8656">3</a>.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgc76021e" class="outline-3">
|
||||
<h3 id="orgc76021e"><span class="section-number-3">1.4</span> Conclusion</h3>
|
||||
<div id="outline-container-orga866100" class="outline-3">
|
||||
<h3 id="orga866100"><span class="section-number-3">1.4</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-1-4">
|
||||
<div class="important" id="org37b8ef0">
|
||||
<div class="important" id="org91c21ee">
|
||||
<p>
|
||||
We do not have guaranteed stability with Inertial control. This is because of the flexibility inside the internal sensor.
|
||||
</p>
|
||||
@@ -242,7 +242,7 @@ We do not have guaranteed stability with Inertial control. This is because of th
|
||||
<a id="org1f0d316"></a>
|
||||
</p>
|
||||
|
||||
<div class="note" id="org54cec4b">
|
||||
<div class="note" id="org30f755d">
|
||||
<p>
|
||||
The Matlab script corresponding to this section is accessible <a href="../matlab/active_damping_iff.m">here</a>.
|
||||
</p>
|
||||
@@ -254,31 +254,31 @@ To run the script, open the Simulink Project, and type <code>run active_damping_
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org7b81fe5" class="outline-3">
|
||||
<h3 id="org7b81fe5"><span class="section-number-3">2.1</span> Identification of the Dynamics with perfect Joints</h3>
|
||||
<div id="outline-container-orga2d019b" class="outline-3">
|
||||
<h3 id="orga2d019b"><span class="section-number-3">2.1</span> Identification of the Dynamics with perfect Joints</h3>
|
||||
<div class="outline-text-3" id="text-2-1">
|
||||
<p>
|
||||
We first initialize the Stewart platform without joint stiffness.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStrutDynamics(stewart);
|
||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStrutDynamics(stewart);
|
||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'rot_point'</span>, stewart.platform_F.FO_A);
|
||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
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">'rigid'</span>, <span class="org-string">'rot_point'</span>, stewart.platform_F.FO_A);
|
||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -286,18 +286,18 @@ We first initialize the Stewart platform without joint stiffness.
|
||||
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">%% 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">'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">'Taum'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Force Sensor Outputs [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">'Taum'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Force Sensor Outputs [N]</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">'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>};
|
||||
<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">'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>
|
||||
|
||||
@@ -313,17 +313,17 @@ The transfer function from actuator forces to force sensors is shown in Figure <
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org3dca396" class="outline-3">
|
||||
<h3 id="org3dca396"><span class="section-number-3">2.2</span> Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</h3>
|
||||
<div id="outline-container-org6ac04ee" class="outline-3">
|
||||
<h3 id="org6ac04ee"><span class="section-number-3">2.2</span> Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</h3>
|
||||
<div class="outline-text-3" id="text-2-2">
|
||||
<p>
|
||||
We add some stiffness and damping in the flexible joints and we re-identify the dynamics.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical'</span>);
|
||||
Gf = linearize(mdl, io);
|
||||
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">'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">stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical'</span>);
|
||||
Gf = linearize(mdl, io);
|
||||
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">'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>
|
||||
|
||||
@@ -331,10 +331,10 @@ We add some stiffness and damping in the flexible joints and we re-identify the
|
||||
We now use the amplified actuators and re-identify the dynamics
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeAmplifiedStrutDynamics(stewart);
|
||||
Ga = linearize(mdl, io);
|
||||
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">'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">stewart = initializeAmplifiedStrutDynamics(stewart);
|
||||
Ga = linearize(mdl, io);
|
||||
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">'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>
|
||||
|
||||
@@ -350,8 +350,8 @@ The new dynamics from force actuator to force sensor is shown in Figure <a href=
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org7044ed4" class="outline-3">
|
||||
<h3 id="org7044ed4"><span class="section-number-3">2.3</span> Obtained Damping</h3>
|
||||
<div id="outline-container-org06e1086" class="outline-3">
|
||||
<h3 id="org06e1086"><span class="section-number-3">2.3</span> Obtained Damping</h3>
|
||||
<div class="outline-text-3" id="text-2-3">
|
||||
<p>
|
||||
The control is a performed in a decentralized manner.
|
||||
@@ -383,10 +383,10 @@ The root locus is shown in figure <a href="#orgce5d8d8">6</a> and the obtained p
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org9c769b9" class="outline-3">
|
||||
<h3 id="org9c769b9"><span class="section-number-3">2.4</span> Conclusion</h3>
|
||||
<div id="outline-container-orgfa832d6" class="outline-3">
|
||||
<h3 id="orgfa832d6"><span class="section-number-3">2.4</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-2-4">
|
||||
<div class="important" id="orged36719">
|
||||
<div class="important" id="orgad0c17b">
|
||||
<p>
|
||||
The joint stiffness has a huge impact on the attainable active damping performance when using force sensors.
|
||||
Thus, if Integral Force Feedback is to be used in a Stewart platform with flexible joints, the rotational stiffness of the joints should be minimized.
|
||||
@@ -404,7 +404,7 @@ Thus, if Integral Force Feedback is to be used in a Stewart platform with flexib
|
||||
<a id="org63027d0"></a>
|
||||
</p>
|
||||
|
||||
<div class="note" id="orgfb739d8">
|
||||
<div class="note" id="orgadea9d6">
|
||||
<p>
|
||||
The Matlab script corresponding to this section is accessible <a href="../matlab/active_damping_dvf.m">here</a>.
|
||||
</p>
|
||||
@@ -416,31 +416,31 @@ To run the script, open the Simulink Project, and type <code>run active_damping_
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga2d019b" class="outline-3">
|
||||
<h3 id="orga2d019b"><span class="section-number-3">3.1</span> Identification of the Dynamics with perfect Joints</h3>
|
||||
<div id="outline-container-org19cbcee" class="outline-3">
|
||||
<h3 id="org19cbcee"><span class="section-number-3">3.1</span> Identification of the Dynamics with perfect Joints</h3>
|
||||
<div class="outline-text-3" id="text-3-1">
|
||||
<p>
|
||||
We first initialize the Stewart platform without joint stiffness.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStrutDynamics(stewart);
|
||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStrutDynamics(stewart);
|
||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'rot_point'</span>, stewart.platform_F.FO_A);
|
||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
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">'rigid'</span>, <span class="org-string">'rot_point'</span>, stewart.platform_F.FO_A);
|
||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -448,22 +448,22 @@ We first initialize the Stewart platform without joint stiffness.
|
||||
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>
|
||||
|
||||
<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-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>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -480,17 +480,17 @@ The transfer function from actuator forces to relative motion sensors is shown i
|
||||
</div>
|
||||
|
||||
|
||||
<div id="outline-container-org2875dd1" class="outline-3">
|
||||
<h3 id="org2875dd1"><span class="section-number-3">3.2</span> Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</h3>
|
||||
<div id="outline-container-org0fabf01" class="outline-3">
|
||||
<h3 id="org0fabf01"><span class="section-number-3">3.2</span> Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</h3>
|
||||
<div class="outline-text-3" id="text-3-2">
|
||||
<p>
|
||||
We add some stiffness and damping in the flexible joints and we re-identify the dynamics.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical'</span>);
|
||||
Gf = 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>};
|
||||
<pre class="src src-matlab">stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical'</span>);
|
||||
Gf = 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>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -498,10 +498,10 @@ We add some stiffness and damping in the flexible joints and we re-identify the
|
||||
We now use the amplified actuators and re-identify the dynamics
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeAmplifiedStrutDynamics(stewart);
|
||||
Ga = 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>};
|
||||
<pre class="src src-matlab">stewart = initializeAmplifiedStrutDynamics(stewart);
|
||||
Ga = 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>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -517,8 +517,8 @@ The new dynamics from force actuator to relative motion sensor is shown in Figur
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0cea759" class="outline-3">
|
||||
<h3 id="org0cea759"><span class="section-number-3">3.3</span> Obtained Damping</h3>
|
||||
<div id="outline-container-org6c74c9a" class="outline-3">
|
||||
<h3 id="org6c74c9a"><span class="section-number-3">3.3</span> Obtained Damping</h3>
|
||||
<div class="outline-text-3" id="text-3-3">
|
||||
<p>
|
||||
The control is a performed in a decentralized manner.
|
||||
@@ -543,10 +543,10 @@ The root locus is shown in figure <a href="#org0436b4d">10</a>.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga866100" class="outline-3">
|
||||
<h3 id="orga866100"><span class="section-number-3">3.4</span> Conclusion</h3>
|
||||
<div id="outline-container-org81b2156" class="outline-3">
|
||||
<h3 id="org81b2156"><span class="section-number-3">3.4</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-3-4">
|
||||
<div class="important" id="org2640d3c">
|
||||
<div class="important" id="orgb486ca9">
|
||||
<p>
|
||||
Joint stiffness does increase the resonance frequencies of the system but does not change the attainable damping when using relative motion sensors.
|
||||
</p>
|
||||
@@ -567,17 +567,17 @@ Joint stiffness does increase the resonance frequencies of the system but does n
|
||||
We first initialize the Stewart platform without joint stiffness.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStrutDynamics(stewart);
|
||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||||
stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStrutDynamics(stewart);
|
||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
|
||||
stewart = initializeCylindricalPlatforms(stewart);
|
||||
stewart = initializeCylindricalStruts(stewart);
|
||||
stewart = computeJacobian(stewart);
|
||||
stewart = initializeStewartPose(stewart);
|
||||
stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -585,9 +585,9 @@ We first initialize the Stewart platform without joint stiffness.
|
||||
The rotation point of the ground is located at the origin of frame \(\{A\}\).
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'rot_point'</span>, stewart.platform_F.FO_A);
|
||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
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">'rigid'</span>, <span class="org-string">'rot_point'</span>, stewart.platform_F.FO_A);
|
||||
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
|
||||
controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -600,9 +600,9 @@ The rotation point of the ground is located at the origin of frame \(\{A\}\).
|
||||
Let’s first identify the transmissibility and compliance in the open-loop case.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
[T_ol, T_norm_ol, freqs] = computeTransmissibility();
|
||||
[C_ol, C_norm_ol, freqs] = computeCompliance();
|
||||
<pre class="src src-matlab">controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
[T_ol, T_norm_ol, freqs] = computeTransmissibility();
|
||||
[C_ol, C_norm_ol, freqs] = computeCompliance();
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -610,11 +610,11 @@ Let’s first identify the transmissibility and compliance in the open-loop
|
||||
Now, let’s identify the transmissibility and compliance for the Integral Force Feedback architecture.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'iff'</span>);
|
||||
K_iff = (1e4<span class="org-type">/</span>s)<span class="org-type">*</span>eye(6);
|
||||
<pre class="src src-matlab">controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'iff'</span>);
|
||||
K_iff = (1e4<span class="org-type">/</span>s)<span class="org-type">*</span>eye(6);
|
||||
|
||||
[T_iff, T_norm_iff, <span class="org-type">~</span>] = computeTransmissibility();
|
||||
[C_iff, C_norm_iff, <span class="org-type">~</span>] = computeCompliance();
|
||||
[T_iff, T_norm_iff, <span class="org-type">~</span>] = computeTransmissibility();
|
||||
[C_iff, C_norm_iff, <span class="org-type">~</span>] = computeCompliance();
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -622,11 +622,11 @@ Now, let’s identify the transmissibility and compliance for the Integral F
|
||||
And for the Direct Velocity Feedback.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"> controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'dvf'</span>);
|
||||
K_dvf = 1e4<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>5000)<span class="org-type">*</span>eye(6);
|
||||
<pre class="src src-matlab">controller = initializeController(<span class="org-string">'type'</span>, <span class="org-string">'dvf'</span>);
|
||||
K_dvf = 1e4<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>5000)<span class="org-type">*</span>eye(6);
|
||||
|
||||
[T_dvf, T_norm_dvf, <span class="org-type">~</span>] = computeTransmissibility();
|
||||
[C_dvf, C_norm_dvf, <span class="org-type">~</span>] = computeCompliance();
|
||||
[T_dvf, T_norm_dvf, <span class="org-type">~</span>] = computeTransmissibility();
|
||||
[C_dvf, C_norm_dvf, <span class="org-type">~</span>] = computeCompliance();
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
@@ -661,7 +661,7 @@ And for the Direct Velocity Feedback.
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:30</p>
|
||||
<p class="date">Created: 2021-01-08 ven. 15:53</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
Reference in New Issue
Block a user