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Active Damping Rework for new simscape model

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Thomas Dehaeze 2020-02-13 14:50:30 +01:00
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2 changed files with 89 additions and 56 deletions
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docs/active-damping.html
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@ -4,7 +4,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2020-02-11 mar. 18:04 -->
<!-- 2020-02-13 jeu. 14:50 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Stewart Platform - Decentralized Active Damping</title>
@ -271,25 +271,25 @@ for the JavaScript code in this tag.
<li><a href="#orgd59c804">1. Inertial Control</a>
<ul>
<li><a href="#org5f749c8">1.1. Identification of the Dynamics</a></li>
<li><a href="#orgec430e2">1.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
<li><a href="#orgaa11f3d">1.3. Obtained Damping</a></li>
<li><a href="#orgcd93557">1.4. Conclusion</a></li>
<li><a href="#orgd5c2ca3">1.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
<li><a href="#org2123b01">1.3. Obtained Damping</a></li>
<li><a href="#org3471687">1.4. Conclusion</a></li>
</ul>
</li>
<li><a href="#org74c7eb4">2. Integral Force Feedback</a>
<ul>
<li><a href="#orga217cbb">2.1. Identification of the Dynamics with perfect Joints</a></li>
<li><a href="#org5ab90ff">2.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
<li><a href="#org8dd8d32">2.3. Obtained Damping</a></li>
<li><a href="#org14503d2">2.4. Conclusion</a></li>
<li><a href="#org79e6a47">2.1. Identification of the Dynamics with perfect Joints</a></li>
<li><a href="#orgf71d9f1">2.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
<li><a href="#orgaaed0b1">2.3. Obtained Damping</a></li>
<li><a href="#orgf95ef97">2.4. Conclusion</a></li>
</ul>
</li>
<li><a href="#org08917d6">3. Direct Velocity Feedback</a>
<ul>
<li><a href="#org025d6da">3.1. Identification of the Dynamics with perfect Joints</a></li>
<li><a href="#org6dd3dfd">3.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
<li><a href="#orge3fb12b">3.3. Obtained Damping</a></li>
<li><a href="#org049f0ec">3.4. Conclusion</a></li>
<li><a href="#orgc7446b0">3.1. Identification of the Dynamics with perfect Joints</a></li>
<li><a href="#orged14fce">3.2. Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</a></li>
<li><a href="#orga745203">3.3. Obtained Damping</a></li>
<li><a href="#org711b15d">3.4. Conclusion</a></li>
</ul>
</li>
</ul>
@ -331,18 +331,24 @@ stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</spa
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
options = linearizeOptions;
options.SampleTime = 0;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
mdl = <span class="org-string">'stewart_active_damping'</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">'/F'</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">'/Vm'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute velocity of each leg [m/s]</span>
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">'Vm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute velocity of each leg [m/s]</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
G = linearize(mdl, io, options);
@ -363,8 +369,8 @@ The transfer function from actuator forces to force sensors is shown in Figure <
</div>
</div>
<div id="outline-container-orgec430e2" class="outline-3">
<h3 id="orgec430e2"><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-orgd5c2ca3" class="outline-3">
<h3 id="orgd5c2ca3"><span class="section-number-3">1.2</span> Effect of the Flexible Joint stiffness and Actuator amplification on the Dynamics</h3>
<div class="outline-text-3" id="text-1-2">
<p>
We add some stiffness and damping in the flexible joints and we re-identify the dynamics.
@ -400,8 +406,8 @@ The new dynamics from force actuator to force sensor is shown in Figure <a href=
</div>
</div>
<div id="outline-container-orgaa11f3d" class="outline-3">
<h3 id="orgaa11f3d"><span class="section-number-3">1.3</span> Obtained Damping</h3>
<div id="outline-container-org2123b01" class="outline-3">
<h3 id="org2123b01"><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.
@ -426,8 +432,8 @@ The root locus is shown in figure <a href="#org9af9e33">3</a>.
</div>
</div>
<div id="outline-container-orgcd93557" class="outline-3">
<h3 id="orgcd93557"><span class="section-number-3">1.4</span> Conclusion</h3>
<div id="outline-container-org3471687" class="outline-3">
<h3 id="org3471687"><span class="section-number-3">1.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-1-4">
<div class="important">
<p>
@ -447,8 +453,8 @@ We do not have guaranteed stability with Inertial control. This is because of th
</p>
</div>
<div id="outline-container-orga217cbb" class="outline-3">
<h3 id="orga217cbb"><span class="section-number-3">2.1</span> Identification of the Dynamics with perfect Joints</h3>
<div id="outline-container-org79e6a47" class="outline-3">
<h3 id="org79e6a47"><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.
@ -468,6 +474,12 @@ stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</spa
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
</pre>
</div>
<p>
And we identify the dynamics from force actuators to force sensors.
</p>
@ -477,12 +489,12 @@ 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_active_damping'</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">'/F'</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">'/Fm'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Force Sensor Outputs [N]</span>
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, options);
@ -503,8 +515,8 @@ The transfer function from actuator forces to force sensors is shown in Figure <
</div>
</div>
<div id="outline-container-org5ab90ff" class="outline-3">
<h3 id="org5ab90ff"><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-orgf71d9f1" class="outline-3">
<h3 id="orgf71d9f1"><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.
@ -540,8 +552,8 @@ The new dynamics from force actuator to force sensor is shown in Figure <a href=
</div>
</div>
<div id="outline-container-org8dd8d32" class="outline-3">
<h3 id="org8dd8d32"><span class="section-number-3">2.3</span> Obtained Damping</h3>
<div id="outline-container-orgaaed0b1" class="outline-3">
<h3 id="orgaaed0b1"><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.
@ -573,8 +585,8 @@ The root locus is shown in figure <a href="#orge21bbea">6</a> and the obtained p
</div>
</div>
<div id="outline-container-org14503d2" class="outline-3">
<h3 id="org14503d2"><span class="section-number-3">2.4</span> Conclusion</h3>
<div id="outline-container-orgf95ef97" class="outline-3">
<h3 id="orgf95ef97"><span class="section-number-3">2.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-4">
<div class="important">
<p>
@ -595,8 +607,8 @@ Thus, if Integral Force Feedback is to be used in a Stewart platform with flexib
</p>
</div>
<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 id="outline-container-orgc7446b0" class="outline-3">
<h3 id="orgc7446b0"><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.
@ -616,6 +628,12 @@ stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</spa
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
</pre>
</div>
<p>
And we identify the dynamics from force actuators to force sensors.
</p>
@ -625,12 +643,12 @@ 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_active_damping'</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">'/F'</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">'/Dm'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [N]</span>
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);
@ -652,8 +670,8 @@ The transfer function from actuator forces to relative motion sensors is shown i
</div>
<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 id="outline-container-orged14fce" class="outline-3">
<h3 id="orged14fce"><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.
@ -689,8 +707,8 @@ The new dynamics from force actuator to relative motion sensor is shown in Figur
</div>
</div>
<div id="outline-container-orge3fb12b" class="outline-3">
<h3 id="orge3fb12b"><span class="section-number-3">3.3</span> Obtained Damping</h3>
<div id="outline-container-orga745203" class="outline-3">
<h3 id="orga745203"><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.
@ -715,8 +733,8 @@ The root locus is shown in figure <a href="#org277d60d">10</a>.
</div>
</div>
<div id="outline-container-org049f0ec" class="outline-3">
<h3 id="org049f0ec"><span class="section-number-3">3.4</span> Conclusion</h3>
<div id="outline-container-org711b15d" class="outline-3">
<h3 id="org711b15d"><span class="section-number-3">3.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-4">
<div class="important">
<p>
@ -730,7 +748,7 @@ 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. 18:04</p>
<p class="date">Created: 2020-02-13 jeu. 14:50</p>
</div>
</body>
</html>

39
org/active-damping.org
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@ -66,7 +66,7 @@ The following decentralized active damping techniques are briefly studied:
#+end_src
#+begin_src matlab
open('simulink/stewart_active_damping.slx')
open('stewart_platform_model.slx')
#+end_src
** Identification of the Dynamics
@ -84,18 +84,23 @@ The following decentralized active damping techniques are briefly studied:
stewart = initializeInertialSensor(stewart, 'type', 'accelerometer', 'freq', 5e3);
#+end_src
#+begin_src matlab
ground = initializeGround('type', 'none');
payload = initializePayload('type', 'none');
#+end_src
#+begin_src matlab
%% Options for Linearized
options = linearizeOptions;
options.SampleTime = 0;
%% Name of the Simulink File
mdl = 'stewart_active_damping';
mdl = 'stewart_platform_model';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
io(io_i) = linio([mdl, '/Vm'], 1, 'openoutput'); io_i = io_i + 1; % Absolute velocity of each leg [m/s]
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'Vm'); io_i = io_i + 1; % Absolute velocity of each leg [m/s]
%% Run the linearization
G = linearize(mdl, io, options);
@ -284,7 +289,7 @@ The root locus is shown in figure [[fig:root_locus_inertial_rot_stiffness]].
#+end_src
#+begin_src matlab
open('simulink/stewart_active_damping.slx')
open('stewart_platform_model.slx')
#+end_src
** Identification of the Dynamics with perfect Joints
@ -303,6 +308,11 @@ We first initialize the Stewart platform without joint stiffness.
stewart = initializeInertialSensor(stewart, 'type', 'none');
#+end_src
#+begin_src matlab
ground = initializeGround('type', 'none');
payload = initializePayload('type', 'none');
#+end_src
And we identify the dynamics from force actuators to force sensors.
#+begin_src matlab
%% Options for Linearized
@ -310,12 +320,12 @@ And we identify the dynamics from force actuators to force sensors.
options.SampleTime = 0;
%% Name of the Simulink File
mdl = 'stewart_active_damping';
mdl = 'stewart_platform_model';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
io(io_i) = linio([mdl, '/Fm'], 1, 'openoutput'); io_i = io_i + 1; % Force Sensor Outputs [N]
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'Taum'); io_i = io_i + 1; % Force Sensor Outputs [N]
%% Run the linearization
G = linearize(mdl, io, options);
@ -542,7 +552,7 @@ The root locus is shown in figure [[fig:root_locus_iff_rot_stiffness]] and the o
#+end_src
#+begin_src matlab
open('simulink/stewart_active_damping.slx')
open('stewart_platform_model.slx')
#+end_src
** Identification of the Dynamics with perfect Joints
@ -561,6 +571,11 @@ We first initialize the Stewart platform without joint stiffness.
stewart = initializeInertialSensor(stewart, 'type', 'none');
#+end_src
#+begin_src matlab
ground = initializeGround('type', 'none');
payload = initializePayload('type', 'none');
#+end_src
And we identify the dynamics from force actuators to force sensors.
#+begin_src matlab
%% Options for Linearized
@ -568,12 +583,12 @@ And we identify the dynamics from force actuators to force sensors.
options.SampleTime = 0;
%% Name of the Simulink File
mdl = 'stewart_active_damping';
mdl = 'stewart_platform_model';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/F'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
io(io_i) = linio([mdl, '/Dm'], 1, 'openoutput'); io_i = io_i + 1; % Relative Displacement Outputs [N]
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'dLm'); io_i = io_i + 1; % Relative Displacement Outputs [m]
%% Run the linearization
G = linearize(mdl, io, options);