Rework the disturbance file
This commit is contained in:
@@ -4,7 +4,7 @@
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<!-- 2020-03-13 ven. 17:39 -->
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<!-- 2020-03-17 mar. 11:21 -->
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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>Identification of the disturbances</title>
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@@ -254,7 +254,6 @@
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<li><a href="#Compute-the-Power-Spectral-Density-of-the-disturbance-force">5. Compute the Power Spectral Density of the disturbance force</a></li>
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<li><a href="#Noise-Budget">6. Noise Budget</a></li>
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<li><a href="#Save">7. Save</a></li>
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<li><a href="#org9a1d0a9">8. Error motion of the Sample without Control</a></li>
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</ul>
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</div>
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</div>
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@@ -277,7 +276,6 @@ Because we cannot measure directly the perturbation forces, we have the measure
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</p>
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<div id="org3b8025c" class="figure">
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<p><img src="figs/uniaxial-model-micro-station.png" alt="uniaxial-model-micro-station.png" />
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</p>
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@@ -324,7 +322,8 @@ We load the configuration and we set a small <code>StopTime</code>.
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</div>
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<p>
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We initialize all the stages.
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We initialize all the stages without the sample nor the nano-hexapod.
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The obtained system corresponds to the status micro-station when the vibration measurements were conducted.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeGround();
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@@ -339,6 +338,30 @@ initializeNanoHexapod(<span class="org-string">'type'</span>, <span class="org-s
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initializeSample(<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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<p>
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Open Loop Control.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
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</pre>
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</div>
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<p>
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We don’t need gravity here.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">false</span>);
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</pre>
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</div>
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<p>
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We log the signals.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'all'</span>);
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</pre>
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</div>
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</div>
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</div>
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@@ -351,41 +374,41 @@ The transfer functions from the disturbance forces to the relative velocity of t
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
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options = linearizeOptions;
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options.SampleTime = 0;
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
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<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
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mdl = <span class="org-string">'nass_model'</span>;
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</pre>
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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">%% Micro-Hexapod</span></span>
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clear io; io_i = 1;
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io(io_i) = linio([mdl, <span class="org-string">'/Disturbances'</span>], 1, <span class="org-string">'openinput'</span>, [], <span class="org-string">'Dwz'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Vertical Ground Motion</span>
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io(io_i) = linio([mdl, <span class="org-string">'/Disturbances'</span>], 1, <span class="org-string">'openinput'</span>, [], <span class="org-string">'Fty_z'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Parasitic force Ty</span>
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io(io_i) = linio([mdl, <span class="org-string">'/Disturbances'</span>], 1, <span class="org-string">'openinput'</span>, [], <span class="org-string">'Frz_z'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Parasitic force Rz</span>
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io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station/Granite/Modal Analysis/accelerometer'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute motion - Granite</span>
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io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station/Micro Hexapod/Modal Analysis/accelerometer'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute Motion - Hexapod</span>
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<span class="org-comment">% io(io_i) = linio([mdl, '/Vm'], 1, 'openoutput'); io_i = io_i + 1; % Relative Velocity hexapod/granite</span>
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</pre>
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</div>
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Micro-Hexapod</span></span>
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clear io; io_i = 1;
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io(io_i) = linio([mdl, <span class="org-string">'/Disturbances'</span>], 1, <span class="org-string">'openinput'</span>, [], <span class="org-string">'Dwz'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Vertical Ground Motion</span>
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io(io_i) = linio([mdl, <span class="org-string">'/Disturbances'</span>], 1, <span class="org-string">'openinput'</span>, [], <span class="org-string">'Fty_z'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Parasitic force Ty</span>
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io(io_i) = linio([mdl, <span class="org-string">'/Disturbances'</span>], 1, <span class="org-string">'openinput'</span>, [], <span class="org-string">'Frz_z'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Parasitic force Rz</span>
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-comment">% Run the linearization</span>
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io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station/Granite/Modal Analysis/accelerometer'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute motion - Granite</span>
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io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station/Micro Hexapod/Modal Analysis/accelerometer'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute Motion - Hexapod</span>
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<span class="org-comment">% io(io_i) = linio([mdl, '/Vm'], 1, 'openoutput'); io_i = io_i + 1; % Relative Velocity hexapod/granite</span>
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<span class="org-comment">% Run the linearization</span>
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G = linearize(mdl, io, 0);
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</pre>
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</div>
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<span class="org-comment">% We Take only the outputs corresponding to the vertical acceleration</span>
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G = G([3,9], <span class="org-type">:</span>);
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<p>
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We Take only the outputs corresponding to the vertical acceleration.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">G = G([3,9], <span class="org-type">:</span>);
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<span class="org-comment">% Input/Output names</span>
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G.InputName = {<span class="org-string">'Dw'</span>, <span class="org-string">'Fty'</span>, <span class="org-string">'Frz'</span>};
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G.OutputName = {<span class="org-string">'Agm'</span>, <span class="org-string">'Ahm'</span>};
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</pre>
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</div>
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<span class="org-comment">% We integrate 1 time the output to have the velocity and we</span>
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<span class="org-comment">% substract the absolute velocities to have the relative velocity</span>
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G = (1<span class="org-type">/</span>s)<span class="org-type">*</span>tf([<span class="org-type">-</span>1, 1])<span class="org-type">*</span>G;
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<p>
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We integrate 1 time the output to have the velocity and we substract the absolute velocities to have the relative velocity.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">G = (1<span class="org-type">/</span>s)<span class="org-type">*</span>tf([<span class="org-type">-</span>1, 1])<span class="org-type">*</span>G;
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<span class="org-comment">% Input/Output names</span>
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G.InputName = {<span class="org-string">'Dw'</span>, <span class="org-string">'Fty'</span>, <span class="org-string">'Frz'</span>};
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@@ -402,6 +425,14 @@ G.OutputName = {<span class="org-string">'Vm'</span>};
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<a id="org5636fee"></a>
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</p>
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<p>
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The obtained sensitivity to disturbances are shown bellow:
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</p>
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<ul class="org-ul">
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<li>The transfer function from vertical ground motion \(D_w\) to the vertical relative displacement from the micro-hexapod to the granite \(D\) is shown in Figure <a href="#org7fe296c">2</a></li>
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<li>The sensitive from vertical forces applied in the Translation stage is shown in Figure <a href="#orgce9715c">3</a></li>
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</ul>
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<div id="org7fe296c" class="figure">
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<p><img src="figs/sensitivity_dist_gm.png" alt="sensitivity_dist_gm.png" />
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@@ -432,10 +463,13 @@ G.OutputName = {<span class="org-string">'Vm'</span>};
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<div class="outline-text-2" id="text-Power-Spectral-Density-of-the-effect-of-the-disturbances">
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<p>
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<a id="org40a7e4e"></a>
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The PSD of the relative velocity between the hexapod and the marble in \([(m/s)^2/Hz]\) are loaded for the following sources of disturbance:
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</p>
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<p>
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The Power Spectral Densities of the relative velocity between the hexapod and the marble in \([(m/s)^2/Hz]\) are loaded for the following sources of disturbance:
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</p>
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<ul class="org-ul">
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<li>Slip Ring Rotation</li>
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<li>Slip Ring Rotation (\(F_{r_z}\))</li>
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<li>Scan of the translation stage (effect in the vertical direction and in the horizontal direction)</li>
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</ul>
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@@ -460,7 +494,7 @@ We now compute the relative velocity between the hexapod and the granite due to
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</div>
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<p>
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The Power Spectral Density of the relative motion/velocity of the hexapod with respect to the granite are shown in figures <a href="#orgb815ef2">5</a> and <a href="#org4c2c215">6</a>.
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The Power Spectral Density of the relative motion and velocity of the hexapod with respect to the granite are shown in figures <a href="#orgb815ef2">5</a> and <a href="#org4c2c215">6</a>.
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</p>
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<p>
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@@ -487,6 +521,14 @@ The Cumulative Amplitude Spectrum of the relative motion is shown in figure <a h
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<p><img src="figs/dist_effect_relative_motion_cas.png" alt="dist_effect_relative_motion_cas.png" />
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</p>
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<p><span class="figure-number">Figure 7: </span>Cumulative Amplitude Spectrum of the relative motion due to different sources of perturbation (<a href="./figs/dist_effect_relative_motion_cas.png">png</a>, <a href="./figs/dist_effect_relative_motion_cas.pdf">pdf</a>)</p>
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</div>
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<div class="important">
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<p>
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From Figure <a href="#orgaf910f1">7</a>, we can see that the translation stage and the rotation stage have almost the same effect on the position error.
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Also, the ground motion has a relatively negligible effect on the position error.
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</p>
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</div>
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</div>
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</div>
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@@ -499,15 +541,22 @@ The Cumulative Amplitude Spectrum of the relative motion is shown in figure <a h
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</p>
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<p>
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Now, from the extracted transfer functions from the disturbance force to the relative motion of the hexapod with respect to the granite (section <a href="#org5636fee">3</a>) and from the measured PSD of the relative motion (section <a href="#org40a7e4e">4</a>), we can compute the PSD of the disturbance force.
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Using the extracted transfer functions from the disturbance force to the relative motion of the hexapod with respect to the granite (section <a href="#org5636fee">3</a>) and using the measured PSD of the relative motion (section <a href="#org40a7e4e">4</a>), we can compute the PSD of the disturbance force.
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</p>
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<p>
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This is done below.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">rz.psd_f = rz.pxsp_r<span class="org-type">./</span>abs(squeeze(freqresp(G(<span class="org-string">'Vm'</span>, <span class="org-string">'Frz'</span>), rz.f, <span class="org-string">'Hz'</span>)))<span class="org-type">.^</span>2;
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tyz.psd_f = tyz.pxz_ty_r<span class="org-type">./</span>abs(squeeze(freqresp(G(<span class="org-string">'Vm'</span>, <span class="org-string">'Fty'</span>), tyz.f, <span class="org-string">'Hz'</span>)))<span class="org-type">.^</span>2;
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</pre>
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</div>
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<p>
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The obtained amplitude spectral densities of the disturbance forces are shown in Figure <a href="#org45cf35c">8</a>.
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</p>
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<div id="org45cf35c" class="figure">
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<p><img src="figs/dist_force_psd.png" alt="dist_force_psd.png" />
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@@ -525,24 +574,31 @@ tyz.psd_f = tyz.pxz_ty_r<span class="org-type">./</span>abs(squeeze(freqresp(G(<
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</p>
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<p>
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Now, from the compute spectral density of the disturbance sources, we can compute the resulting relative motion of the Hexapod with respect to the granite using the model.
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We should verify that this is coherent with the measurements.
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From the obtained spectral density of the disturbance sources, we can compute the resulting relative motion of the Hexapod with respect to the granite using the model.
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</p>
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<p>
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This is equivalent as doing the inverse that was done in the previous section.
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This is done in order to verify that this is coherent with the measurements.
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</p>
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<p>
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The power spectral density of the relative motion is computed below and the result is shown in Figure <a href="#orgcacf809">9</a>.
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We can see that this is exactly the same as the Figure <a href="#org4c2c215">6</a>.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">psd_gm_d = gm.psd_gm<span class="org-type">.*</span>abs(squeeze(freqresp(G(<span class="org-string">'Vm'</span>, <span class="org-string">'Dw'</span>)<span class="org-type">/</span>s, gm.f, <span class="org-string">'Hz'</span>)))<span class="org-type">.^</span>2;
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psd_ty_d = tyz.psd_f<span class="org-type">.*</span>abs(squeeze(freqresp(G(<span class="org-string">'Vm'</span>, <span class="org-string">'Fty'</span>)<span class="org-type">/</span>s, tyz.f, <span class="org-string">'Hz'</span>)))<span class="org-type">.^</span>2;
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psd_rz_d = rz.psd_f<span class="org-type">.*</span>abs(squeeze(freqresp(G(<span class="org-string">'Vm'</span>, <span class="org-string">'Frz'</span>)<span class="org-type">/</span>s, rz.f, <span class="org-string">'Hz'</span>)))<span class="org-type">.^</span>2;
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</pre>
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||||
</div>
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||||
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<div id="orgcacf809" class="figure">
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<p><img src="figs/psd_effect_dist_verif.png" alt="psd_effect_dist_verif.png" />
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</p>
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<p><span class="figure-number">Figure 9: </span>Computed Effect of the disturbances on the relative displacement hexapod/granite (<a href="./figs/psd_effect_dist_verif.png">png</a>, <a href="./figs/psd_effect_dist_verif.pdf">pdf</a>)</p>
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</div>
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||||
|
||||
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||||
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||||
<div id="orgf872ab1" class="figure">
|
||||
<p><img src="figs/cas_computed_relative_displacement.png" alt="cas_computed_relative_displacement.png" />
|
||||
</p>
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||||
<p><span class="figure-number">Figure 10: </span>CAS of the total Relative Displacement due to all considered sources of perturbation (<a href="./figs/cas_computed_relative_displacement.png">png</a>, <a href="./figs/cas_computed_relative_displacement.pdf">pdf</a>)</p>
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||||
</div>
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||||
</div>
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||||
</div>
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||||
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@@ -567,117 +623,10 @@ save(<span class="org-string">'./mat/dist_psd.mat'</span>, <span class="org-stri
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</div>
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||||
</div>
|
||||
</div>
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<div id="outline-container-org9a1d0a9" class="outline-2">
|
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<h2 id="org9a1d0a9"><span class="section-number-2">8</span> Error motion of the Sample without Control</h2>
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<div class="outline-text-2" id="text-8">
|
||||
<div class="org-src-container">
|
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<pre class="src src-matlab">initializeGround();
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initializeGranite(<span class="org-string">'Foffset'</span>, <span class="org-constant">false</span>);
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initializeTy(<span class="org-string">'Foffset'</span>, <span class="org-constant">false</span>);
|
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initializeRy(<span class="org-string">'Foffset'</span>, <span class="org-constant">false</span>);
|
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initializeRz(<span class="org-string">'Foffset'</span>, <span class="org-constant">false</span>);
|
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initializeMicroHexapod(<span class="org-string">'Foffset'</span>, <span class="org-constant">false</span>);
|
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initializeAxisc(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>);
|
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initializeMirror(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>);
|
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</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">initializeNanoHexapod(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>);
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initializeSample(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>, <span class="org-string">'mass'</span>, 50);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
We set the references and disturbances to zero.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">initializeReferences();
|
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initializeDisturbances();
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
We set the controller type to Open-Loop.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
And we put some gravity.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">false</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
We do not need to log any signal.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'all'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">initializePosError(<span class="org-string">'error'</span>, <span class="org-constant">false</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">load(<span class="org-string">'mat/conf_simulink.mat'</span>);
|
||||
<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'1'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
We simulate the model.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
||||
subplot(1, 2, 1);
|
||||
hold on;
|
||||
plot(simout.Em.Eg.Time, simout.Em.Eg.Data(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'X'</span>);
|
||||
plot(simout.Em.Eg.Time, simout.Em.Eg.Data(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Y'</span>);
|
||||
plot(simout.Em.Eg.Time, simout.Em.Eg.Data(<span class="org-type">:</span>, 3), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Z'</span>);
|
||||
hold off;
|
||||
xlabel(<span class="org-string">'Time [s]'</span>);
|
||||
ylabel(<span class="org-string">'Position error [m]'</span>);
|
||||
legend();
|
||||
|
||||
subplot(1, 2, 2);
|
||||
hold on;
|
||||
plot(simout.Em.Eg.Time, simout.Em.Eg.Data(<span class="org-type">:</span>, 4));
|
||||
plot(simout.Em.Eg.Time, simout.Em.Eg.Data(<span class="org-type">:</span>, 5));
|
||||
plot(simout.Em.Eg.Time, simout.Em.Eg.Data(<span class="org-type">:</span>, 6));
|
||||
hold off;
|
||||
xlabel(<span class="org-string">'Time [s]'</span>);
|
||||
ylabel(<span class="org-string">'Orientation error [rad]'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Eg = simout.Em.Eg;
|
||||
save(<span class="org-string">'./mat/motion_error_ol.mat'</span>, <span class="org-string">'Eg'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2020-03-13 ven. 17:39</p>
|
||||
<p class="date">Created: 2020-03-17 mar. 11:21</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
Reference in New Issue
Block a user