Update active damping analysis
This commit is contained in:
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<!-- 2020-02-11 mar. 15:50 -->
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<!-- 2020-02-11 mar. 18:04 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<title>Stewart Platform - Decentralized Active Damping</title>
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@@ -271,25 +271,25 @@ for the JavaScript code in this tag.
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<li><a href="#orgd59c804">1. Inertial Control</a>
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<ul>
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<li><a href="#org5f749c8">1.1. Identification of the Dynamics</a></li>
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<li><a href="#org41a6913">1.2. Effect of the Flexible Joint stiffness on the Dynamics</a></li>
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<li><a href="#orgbcd94dc">1.3. Obtained Damping</a></li>
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<li><a href="#orgb81ed64">1.4. Conclusion</a></li>
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<li><a href="#orgec430e2">1.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
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<li><a href="#orgaa11f3d">1.3. Obtained Damping</a></li>
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<li><a href="#orgcd93557">1.4. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org74c7eb4">2. Integral Force Feedback</a>
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<ul>
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<li><a href="#org04cb1dc">2.1. Identification of the Dynamics with perfect Joints</a></li>
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<li><a href="#org7f576ce">2.2. Effect of the Flexible Joint stiffness on the Dynamics</a></li>
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<li><a href="#orgb927f01">2.3. Obtained Damping</a></li>
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<li><a href="#orgf5f2135">2.4. Conclusion</a></li>
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<li><a href="#orga217cbb">2.1. Identification of the Dynamics with perfect Joints</a></li>
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<li><a href="#org5ab90ff">2.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
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<li><a href="#org8dd8d32">2.3. Obtained Damping</a></li>
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<li><a href="#org14503d2">2.4. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org08917d6">3. Direct Velocity Feedback</a>
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<ul>
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<li><a href="#orgbfe0af6">3.1. Identification of the Dynamics with perfect Joints</a></li>
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<li><a href="#org62438da">3.2. Effect of the Flexible Joint stiffness on the Dynamics</a></li>
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<li><a href="#orgb4fcddf">3.3. Obtained Damping</a></li>
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<li><a href="#org31a4bb6">3.4. Conclusion</a></li>
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<li><a href="#org025d6da">3.1. Identification of the Dynamics with perfect Joints</a></li>
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<li><a href="#org6dd3dfd">3.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
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<li><a href="#orge3fb12b">3.3. Obtained Damping</a></li>
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<li><a href="#org049f0ec">3.4. Conclusion</a></li>
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</ul>
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</li>
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</ul>
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@@ -322,11 +322,12 @@ stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>
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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">'disable'</span>, <span class="org-constant">true</span>);
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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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@@ -362,20 +363,31 @@ 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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<div id="outline-container-org41a6913" class="outline-3">
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<h3 id="org41a6913"><span class="section-number-3">1.2</span> Effect of the Flexible Joint stiffness on the Dynamics</h3>
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<div id="outline-container-orgec430e2" class="outline-3">
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<h3 id="orgec430e2"><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);
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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>);
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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>};
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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>};
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</pre>
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</div>
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<p>
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We now use the amplified actuators and 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 = initializeAmplifiedStrutDynamics(stewart);
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Ga = linearize(mdl, io, options);
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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>};
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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>};
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</pre>
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</div>
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<p>
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The new dynamics from force actuator to force sensor is shown in Figure <a href="#org683c779">2</a>.
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</p>
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@@ -388,8 +400,8 @@ The new dynamics from force actuator to force sensor is shown in Figure <a href=
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</div>
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</div>
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<div id="outline-container-orgbcd94dc" class="outline-3">
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<h3 id="orgbcd94dc"><span class="section-number-3">1.3</span> Obtained Damping</h3>
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<div id="outline-container-orgaa11f3d" class="outline-3">
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<h3 id="orgaa11f3d"><span class="section-number-3">1.3</span> Obtained Damping</h3>
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<div class="outline-text-3" id="text-1-3">
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<p>
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The control is a performed in a decentralized manner.
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@@ -403,7 +415,7 @@ The \(6 \times 6\) control is a diagonal matrix with pure proportional action on
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</p>
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<p>
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The root locus is shown in figure <a href="#org9af9e33">3</a> and the obtained pole damping function of the control gain is shown in figure <a href="#org4e6b73b">4</a>.
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The root locus is shown in figure <a href="#org9af9e33">3</a>.
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</p>
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<div id="org9af9e33" class="figure">
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@@ -411,22 +423,15 @@ The root locus is shown in figure <a href="#org9af9e33">3</a> and the obtained p
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</p>
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<p><span class="figure-number">Figure 3: </span>Root Locus plot with Decentralized Inertial Control when considering the stiffness of flexible joints (<a href="./figs/root_locus_inertial_rot_stiffness.png">png</a>, <a href="./figs/root_locus_inertial_rot_stiffness.pdf">pdf</a>)</p>
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</div>
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<div id="org4e6b73b" class="figure">
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<p><img src="figs/pole_damping_gain_inertial_rot_stiffness.png" alt="pole_damping_gain_inertial_rot_stiffness.png" />
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</p>
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<p><span class="figure-number">Figure 4: </span>Damping of the poles with respect to the gain of the Decentralized Inertial Control when considering the stiffness of flexible joints (<a href="./figs/pole_damping_gain_inertial_rot_stiffness.png">png</a>, <a href="./figs/pole_damping_gain_inertial_rot_stiffness.pdf">pdf</a>)</p>
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</div>
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</div>
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</div>
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<div id="outline-container-orgb81ed64" class="outline-3">
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<h3 id="orgb81ed64"><span class="section-number-3">1.4</span> Conclusion</h3>
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<div id="outline-container-orgcd93557" class="outline-3">
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<h3 id="orgcd93557"><span class="section-number-3">1.4</span> Conclusion</h3>
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<div class="outline-text-3" id="text-1-4">
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<div class="important">
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<p>
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Joint stiffness does increase the resonance frequencies of the system but does not change the attainable damping when using relative motion sensors.
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We do not have guaranteed stability with Inertial control. This is because of the flexibility inside the internal sensor.
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</p>
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</div>
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@@ -442,8 +447,8 @@ Joint stiffness does increase the resonance frequencies of the system but does n
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</p>
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</div>
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<div id="outline-container-org04cb1dc" class="outline-3">
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<h3 id="org04cb1dc"><span class="section-number-3">2.1</span> Identification of the Dynamics with perfect Joints</h3>
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<div id="outline-container-orga217cbb" class="outline-3">
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<h3 id="orga217cbb"><span class="section-number-3">2.1</span> Identification of the Dynamics with perfect Joints</h3>
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<div class="outline-text-3" id="text-2-1">
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<p>
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We first initialize the Stewart platform without joint stiffness.
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@@ -454,12 +459,12 @@ stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>
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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 = initializeAmplifiedStrutDynamics(stewart);
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stewart = initializeJointDynamics(stewart, <span class="org-string">'disable'</span>, <span class="org-constant">true</span>);
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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">'none'</span>);
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</pre>
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</div>
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@@ -487,25 +492,25 @@ G.OutputName = {<span class="org-string">'Fm1'</span>, <span class="org-string">
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</div>
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<p>
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The transfer function from actuator forces to force sensors is shown in Figure <a href="#org3fca9dd">5</a>.
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The transfer function from actuator forces to force sensors is shown in Figure <a href="#org3fca9dd">4</a>.
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</p>
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<div id="org3fca9dd" class="figure">
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<p><img src="figs/iff_plant_coupling.png" alt="iff_plant_coupling.png" />
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</p>
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<p><span class="figure-number">Figure 5: </span>Transfer function from the Actuator force \(F_{i}\) to the Force sensor of the same leg \(F_{m,i}\) and to the force sensor of the other legs \(F_{m,j}\) with \(i \neq j\) in grey (<a href="./figs/iff_plant_coupling.png">png</a>, <a href="./figs/iff_plant_coupling.pdf">pdf</a>)</p>
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<p><span class="figure-number">Figure 4: </span>Transfer function from the Actuator force \(F_{i}\) to the Force sensor of the same leg \(F_{m,i}\) and to the force sensor of the other legs \(F_{m,j}\) with \(i \neq j\) in grey (<a href="./figs/iff_plant_coupling.png">png</a>, <a href="./figs/iff_plant_coupling.pdf">pdf</a>)</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org7f576ce" class="outline-3">
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<h3 id="org7f576ce"><span class="section-number-3">2.2</span> Effect of the Flexible Joint stiffness on the Dynamics</h3>
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<div id="outline-container-org5ab90ff" class="outline-3">
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<h3 id="org5ab90ff"><span class="section-number-3">2.2</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-2-2">
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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);
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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>);
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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>};
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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>};
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@@ -513,19 +518,30 @@ Gf.OutputName = {<span class="org-string">'Fm1'</span>, <span class="org-string"
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</div>
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<p>
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The new dynamics from force actuator to force sensor is shown in Figure <a href="#org090868b">6</a>.
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We now use the amplified actuators and 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 = initializeAmplifiedStrutDynamics(stewart);
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Ga = linearize(mdl, io, options);
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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>};
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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>};
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</pre>
|
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</div>
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<p>
|
||||
The new dynamics from force actuator to force sensor is shown in Figure <a href="#org090868b">5</a>.
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</p>
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<div id="org090868b" class="figure">
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<p><img src="figs/iff_plant_flexible_joint_decentralized.png" alt="iff_plant_flexible_joint_decentralized.png" />
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</p>
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<p><span class="figure-number">Figure 6: </span>Transfer function from the Actuator force \(F_{i}\) to the force sensor \(F_{m,i}\) (<a href="./figs/iff_plant_flexible_joint_decentralized.png">png</a>, <a href="./figs/iff_plant_flexible_joint_decentralized.pdf">pdf</a>)</p>
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<p><span class="figure-number">Figure 5: </span>Transfer function from the Actuator force \(F_{i}\) to the force sensor \(F_{m,i}\) (<a href="./figs/iff_plant_flexible_joint_decentralized.png">png</a>, <a href="./figs/iff_plant_flexible_joint_decentralized.pdf">pdf</a>)</p>
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</div>
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||||
</div>
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||||
</div>
|
||||
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||||
<div id="outline-container-orgb927f01" class="outline-3">
|
||||
<h3 id="orgb927f01"><span class="section-number-3">2.3</span> Obtained Damping</h3>
|
||||
<div id="outline-container-org8dd8d32" class="outline-3">
|
||||
<h3 id="org8dd8d32"><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.
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||||
@@ -539,26 +555,26 @@ The \(6 \times 6\) control is a diagonal matrix with pure integration action on
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</p>
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<p>
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||||
The root locus is shown in figure <a href="#orge21bbea">7</a> and the obtained pole damping function of the control gain is shown in figure <a href="#org94d6943">8</a>.
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||||
The root locus is shown in figure <a href="#orge21bbea">6</a> and the obtained pole damping function of the control gain is shown in figure <a href="#org94d6943">7</a>.
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</p>
|
||||
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||||
<div id="orge21bbea" class="figure">
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<p><img src="figs/root_locus_iff_rot_stiffness.png" alt="root_locus_iff_rot_stiffness.png" />
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</p>
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<p><span class="figure-number">Figure 7: </span>Root Locus plot with Decentralized Integral Force Feedback when considering the stiffness of flexible joints (<a href="./figs/root_locus_iff_rot_stiffness.png">png</a>, <a href="./figs/root_locus_iff_rot_stiffness.pdf">pdf</a>)</p>
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||||
<p><span class="figure-number">Figure 6: </span>Root Locus plot with Decentralized Integral Force Feedback when considering the stiffness of flexible joints (<a href="./figs/root_locus_iff_rot_stiffness.png">png</a>, <a href="./figs/root_locus_iff_rot_stiffness.pdf">pdf</a>)</p>
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</div>
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||||
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<div id="org94d6943" class="figure">
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||||
<p><img src="figs/pole_damping_gain_iff_rot_stiffness.png" alt="pole_damping_gain_iff_rot_stiffness.png" />
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||||
</p>
|
||||
<p><span class="figure-number">Figure 8: </span>Damping of the poles with respect to the gain of the Decentralized Integral Force Feedback when considering the stiffness of flexible joints (<a href="./figs/pole_damping_gain_iff_rot_stiffness.png">png</a>, <a href="./figs/pole_damping_gain_iff_rot_stiffness.pdf">pdf</a>)</p>
|
||||
<p><span class="figure-number">Figure 7: </span>Damping of the poles with respect to the gain of the Decentralized Integral Force Feedback when considering the stiffness of flexible joints (<a href="./figs/pole_damping_gain_iff_rot_stiffness.png">png</a>, <a href="./figs/pole_damping_gain_iff_rot_stiffness.pdf">pdf</a>)</p>
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</div>
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||||
</div>
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||||
</div>
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||||
<div id="outline-container-orgf5f2135" class="outline-3">
|
||||
<h3 id="orgf5f2135"><span class="section-number-3">2.4</span> Conclusion</h3>
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||||
<div id="outline-container-org14503d2" class="outline-3">
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||||
<h3 id="org14503d2"><span class="section-number-3">2.4</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-2-4">
|
||||
<div class="important">
|
||||
<p>
|
||||
@@ -579,8 +595,8 @@ Thus, if Integral Force Feedback is to be used in a Stewart platform with flexib
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgbfe0af6" class="outline-3">
|
||||
<h3 id="orgbfe0af6"><span class="section-number-3">3.1</span> Identification of the Dynamics with perfect Joints</h3>
|
||||
<div id="outline-container-org025d6da" class="outline-3">
|
||||
<h3 id="org025d6da"><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.
|
||||
@@ -591,11 +607,12 @@ stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStrutDynamics(stewart);
|
||||
stewart = initializeJointDynamics(stewart, <span class="org-string">'disable'</span>, <span class="org-constant">true</span>);
|
||||
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>
|
||||
|
||||
@@ -623,26 +640,26 @@ G.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string">
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The transfer function from actuator forces to relative motion sensors is shown in Figure <a href="#orgcc86228">9</a>.
|
||||
The transfer function from actuator forces to relative motion sensors is shown in Figure <a href="#orgcc86228">8</a>.
|
||||
</p>
|
||||
|
||||
<div id="orgcc86228" class="figure">
|
||||
<p><img src="figs/dvf_plant_coupling.png" alt="dvf_plant_coupling.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 9: </span>Transfer function from the Actuator force \(F_{i}\) to the Relative Motion Sensor \(D_{m,j}\) with \(i \neq j\) (<a href="./figs/dvf_plant_coupling.png">png</a>, <a href="./figs/dvf_plant_coupling.pdf">pdf</a>)</p>
|
||||
<p><span class="figure-number">Figure 8: </span>Transfer function from the Actuator force \(F_{i}\) to the Relative Motion Sensor \(D_{m,j}\) with \(i \neq j\) (<a href="./figs/dvf_plant_coupling.png">png</a>, <a href="./figs/dvf_plant_coupling.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="outline-container-org62438da" class="outline-3">
|
||||
<h3 id="org62438da"><span class="section-number-3">3.2</span> Effect of the Flexible Joint stiffness on the Dynamics</h3>
|
||||
<div id="outline-container-org6dd3dfd" class="outline-3">
|
||||
<h3 id="org6dd3dfd"><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);
|
||||
<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>};
|
||||
@@ -650,19 +667,30 @@ Gf.OutputName = {<span class="org-string">'Dm1'</span>, <span class="org-string"
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The new dynamics from force actuator to relative motion sensor is shown in Figure <a href="#org5a86447">10</a>.
|
||||
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>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The new dynamics from force actuator to relative motion sensor is shown in Figure <a href="#org5a86447">9</a>.
|
||||
</p>
|
||||
|
||||
<div id="org5a86447" class="figure">
|
||||
<p><img src="figs/dvf_plant_flexible_joint_decentralized.png" alt="dvf_plant_flexible_joint_decentralized.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 10: </span>Transfer function from the Actuator force \(F_{i}\) to the relative displacement sensor \(D_{m,i}\) (<a href="./figs/dvf_plant_flexible_joint_decentralized.png">png</a>, <a href="./figs/dvf_plant_flexible_joint_decentralized.pdf">pdf</a>)</p>
|
||||
<p><span class="figure-number">Figure 9: </span>Transfer function from the Actuator force \(F_{i}\) to the relative displacement sensor \(D_{m,i}\) (<a href="./figs/dvf_plant_flexible_joint_decentralized.png">png</a>, <a href="./figs/dvf_plant_flexible_joint_decentralized.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb4fcddf" class="outline-3">
|
||||
<h3 id="orgb4fcddf"><span class="section-number-3">3.3</span> Obtained Damping</h3>
|
||||
<div id="outline-container-orge3fb12b" class="outline-3">
|
||||
<h3 id="orge3fb12b"><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.
|
||||
@@ -676,26 +704,19 @@ The \(6 \times 6\) control is a diagonal matrix with pure derivative action on t
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The root locus is shown in figure <a href="#org277d60d">11</a> and the obtained pole damping function of the control gain is shown in figure <a href="#orgd673396">12</a>.
|
||||
The root locus is shown in figure <a href="#org277d60d">10</a>.
|
||||
</p>
|
||||
|
||||
<div id="org277d60d" class="figure">
|
||||
<p><img src="figs/root_locus_dvf_rot_stiffness.png" alt="root_locus_dvf_rot_stiffness.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 11: </span>Root Locus plot with Direct Velocity Feedback when considering the Stiffness of flexible joints (<a href="./figs/root_locus_dvf_rot_stiffness.png">png</a>, <a href="./figs/root_locus_dvf_rot_stiffness.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgd673396" class="figure">
|
||||
<p><img src="figs/pole_damping_gain_dvf_rot_stiffness.png" alt="pole_damping_gain_dvf_rot_stiffness.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 12: </span>Damping of the poles with respect to the gain of the Direct Velocity Feedback when considering the Stiffness of flexible joints (<a href="./figs/pole_damping_gain_dvf_rot_stiffness.png">png</a>, <a href="./figs/pole_damping_gain_dvf_rot_stiffness.pdf">pdf</a>)</p>
|
||||
<p><span class="figure-number">Figure 10: </span>Root Locus plot with Direct Velocity Feedback when considering the Stiffness of flexible joints (<a href="./figs/root_locus_dvf_rot_stiffness.png">png</a>, <a href="./figs/root_locus_dvf_rot_stiffness.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org31a4bb6" class="outline-3">
|
||||
<h3 id="org31a4bb6"><span class="section-number-3">3.4</span> Conclusion</h3>
|
||||
<div id="outline-container-org049f0ec" class="outline-3">
|
||||
<h3 id="org049f0ec"><span class="section-number-3">3.4</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-3-4">
|
||||
<div class="important">
|
||||
<p>
|
||||
@@ -709,7 +730,7 @@ Joint stiffness does increase the resonance frequencies of the system but does n
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2020-02-11 mar. 15:50</p>
|
||||
<p class="date">Created: 2020-02-11 mar. 18:04</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
Reference in New Issue
Block a user