973 lines
66 KiB
HTML
973 lines
66 KiB
HTML
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<a accesskey="h" href="../index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Complementary Filters Shaping Using \(\mathcal{H}_\infty\) Synthesis - Tikz Figures</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<ul>
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<li><a href="#orge7053aa">1. Fig 1: Sensor Fusion Architecture</a></li>
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<li><a href="#org39b5d0c">2. Fig 2: Sensor fusion architecture with sensor dynamics uncertainty</a></li>
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<li><a href="#orgfc9382d">3. Fig 3: Uncertainty set of the super sensor dynamics</a></li>
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<li><a href="#orgb356b70">4. Fig 4: Architecture used for \(\mathcal{H}_\infty\) synthesis of complementary filters</a></li>
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<li><a href="#orgdeaeaf4">5. Fig 5: Magnitude of a weighting function generated using the proposed formula</a></li>
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<li><a href="#org8ce545c">6. Fig 6: Frequency response of the weighting functions and complementary filters obtained using \(\mathcal{H}_\infty\) synthesis</a></li>
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<li><a href="#orgac21d24">7. Fig 7: Architecture for \(\mathcal{H}_\infty\) synthesis of three complementary filters</a></li>
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<li><a href="#org9688457">8. Fig 8: Frequency response of the weighting functions and three complementary filters obtained using \(\mathcal{H}_\infty\) synthesis</a></li>
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<li><a href="#org8d6867c">9. Fig 9: Specifications and weighting functions magnitude used for \(\mathcal{H}_\infty\) synthesis</a></li>
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<li><a href="#orgb6ae2f5">10. Fig 10: Comparison of the FIR filters (solid) with the filters obtained with \(\mathcal{H}_\infty\) synthesis (dashed)</a></li>
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<h2 id="orge7053aa"><span class="section-number-2">1</span> Fig 1: Sensor Fusion Architecture</h2>
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<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">scope</span>}
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgc3d769f" class="figure">
|
|
<p><img src="figs/fusion_super_sensor.png" alt="fusion_super_sensor.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 1: </span>Sensor Fusion Architecture (<a href="./figs/fusion_super_sensor.png">png</a>, <a href="./figs/fusion_super_sensor.pdf">pdf</a>, <a href="./figs/fusion_super_sensor.tex">tex</a>).</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org39b5d0c" class="outline-2">
|
|
<h2 id="org39b5d0c"><span class="section-number-2">2</span> Fig 2: Sensor fusion architecture with sensor dynamics uncertainty</h2>
|
|
<div class="outline-text-2" id="text-2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
|
|
<span class="org-font-latex-sedate">\node</span>[branch] (x) at (0, 0);
|
|
<span class="org-font-latex-sedate">\node</span>[addb, above right=0.8 and 4 of x](add1){};
|
|
<span class="org-font-latex-sedate">\node</span>[addb, below right=0.8 and 4 of x](add2){};
|
|
<span class="org-font-latex-sedate">\node</span>[block, above left=0.2 and 0.1 of add1](delta1){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Delta</span></span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">(s)$</span>};
|
|
<span class="org-font-latex-sedate">\node</span>[block, above left=0.2 and 0.1 of add2](delta2){<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Delta</span></span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">(s)$</span>};
|
|
<span class="org-font-latex-sedate">\node</span>[block, left=0.5 of delta1](W1){<span class="org-font-latex-math">$w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">(s)$</span>};
|
|
<span class="org-font-latex-sedate">\node</span>[block, left=0.5 of delta2](W2){<span class="org-font-latex-math">$w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">(s)$</span>};
|
|
<span class="org-font-latex-sedate">\node</span>[block, right=0.5 of add1](H1){<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">(s)$</span>};
|
|
<span class="org-font-latex-sedate">\node</span>[block, right=0.5 of add2](H2){<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">(s)$</span>};
|
|
<span class="org-font-latex-sedate">\node</span>[addb, right=6 of x](add){};
|
|
|
|
<span class="org-font-latex-sedate">\draw</span>[] (<span class="org-font-latex-math">$(x)+(-0.7, 0)$</span>) node[above right]{<span class="org-font-latex-math">$x$</span>} -- (x.center);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (x.center) |- (add1.west);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (x.center) |- (add2.west);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (<span class="org-font-latex-math">$(add1-|W1.west)+(-0.5, 0)$</span>)node[branch](S1){} |- (W1.west);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (<span class="org-font-latex-math">$(add2-|W2.west)+(-0.5, 0)$</span>)node[branch](S1){} |- (W2.west);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (W1.east) -- (delta1.west);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (W2.east) -- (delta2.west);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (delta1.east) -| (add1.north);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (delta2.east) -| (add2.north);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (add1.east) -- (H1.west);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (add2.east) -- (H2.west);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (H1.east) -| (add.north);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (H2.east) -| (add.south);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (add.east) -- ++(0.7, 0) node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\hat</span></span><span class="org-font-latex-math">{x}$</span>};
|
|
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">scope</span>}[on background layer]
|
|
<span class="org-font-latex-sedate">\node</span>[block, fit={(<span class="org-font-latex-math">$(W1.north-|S1)+(-0.2, 0.2)$</span>) (<span class="org-font-latex-math">$(add1.south east)+(0.2, -0.3)$</span>)}, fill=black!20!white, dashed, inner sep=0pt] (sensor1) {};
|
|
<span class="org-font-latex-sedate">\node</span>[above right] at (sensor1.south west) {Sensor 1};
|
|
<span class="org-font-latex-sedate">\node</span>[block, fit={(<span class="org-font-latex-math">$(W2.north-|S1)+(-0.2, 0.2)$</span>) (<span class="org-font-latex-math">$(add2.south east)+(0.2, -0.3)$</span>)}, fill=black!20!white, dashed, inner sep=0pt] (sensor2) {};
|
|
<span class="org-font-latex-sedate">\node</span>[above right] at (sensor2.south west) {Sensor 2};
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">scope</span>}
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgde2b8c0" class="figure">
|
|
<p><img src="figs/sensor_fusion_dynamic_uncertainty.png" alt="sensor_fusion_dynamic_uncertainty.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 2: </span>Sensor fusion architecture with sensor dynamics uncertainty (<a href="./figs/sensor_fusion_dynamic_uncertainty.png">png</a>, <a href="./figs/sensor_fusion_dynamic_uncertainty.pdf">pdf</a>, <a href="./figs/sensor_fusion_dynamic_uncertainty.tex">tex</a>).</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgfc9382d" class="outline-2">
|
|
<h2 id="orgfc9382d"><span class="section-number-2">3</span> Fig 3: Uncertainty set of the super sensor dynamics</h2>
|
|
<div class="outline-text-2" id="text-3">
|
|
<div class="org-src-container">
|
|
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">scope</span>}[shift={(4, 0)}]
|
|
|
|
<span class="org-comment">% Uncertainty Circle</span>
|
|
<span class="org-font-latex-sedate">\node</span>[draw, circle, fill=black!20!white, minimum size=3.6cm] (c) at (0, 0) {};
|
|
<span class="org-font-latex-sedate">\path</span>[draw, dotted] (0, 0) circle [radius=1.0];
|
|
<span class="org-font-latex-sedate">\path</span>[draw, dashed] (135:1.0) circle [radius=0.8];
|
|
|
|
<span class="org-comment">% Center of Circle</span>
|
|
<span class="org-font-latex-sedate">\node</span>[below] at (0, 0){<span class="org-font-latex-math">$1$</span>};
|
|
|
|
<span class="org-font-latex-sedate">\draw</span>[<->, dashed] (0, 0) node[branch]{} -- coordinate[midway](r1) ++(45:1.0);
|
|
<span class="org-font-latex-sedate">\draw</span>[<->, dashed] (135:1.0)node[branch]{} -- coordinate[midway](r2) ++(90:0.8);
|
|
|
|
<span class="org-font-latex-sedate">\node</span>[] (l1) at (2, 1.5) {<span class="org-font-latex-math">$|w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math"> H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">|$</span>};
|
|
<span class="org-font-latex-sedate">\draw</span>[->, dashed, out=-90, in=0] (l1.south) to (r1);
|
|
|
|
<span class="org-font-latex-sedate">\node</span>[] (l2) at (0, 2.0) {<span class="org-font-latex-math">$|w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math"> H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">|$</span>};
|
|
<span class="org-font-latex-sedate">\draw</span>[->, dashed, out=-90, in=0] (l2.south) to (r2);
|
|
|
|
<span class="org-font-latex-sedate">\draw</span>[<->, dashed] (0, 0) -- coordinate[near end](r3) ++(200:1.8);
|
|
<span class="org-font-latex-sedate">\node</span>[] (l3) at (-2.5, -1.5) {<span class="org-font-latex-math">$|w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math"> H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">| + |w</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math"> H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">|$</span>};
|
|
<span class="org-font-latex-sedate">\draw</span>[->, dashed, out=90, in=-90] (l3.north) to (r3);
|
|
|
|
<span class="org-comment">% % Uncertainty Regions</span>
|
|
<span class="org-comment">% </span><span class="org-font-latex-sedate"><span class="org-comment">\node</span></span><span class="org-comment">[below left] at (45:1.8) {$</span><span class="org-font-latex-sedate"><span class="org-comment">\Pi</span></span><span class="org-comment">_{</span><span class="org-font-latex-sedate"><span class="org-comment">\text</span></span><span class="org-comment">{ss}}$};</span>
|
|
<span class="org-comment">% </span><span class="org-font-latex-sedate"><span class="org-comment">\node</span></span><span class="org-comment">[above left] at (-45:1.0) {$</span><span class="org-font-latex-sedate"><span class="org-comment">\Pi</span></span><span class="org-comment">_{1}$};</span>
|
|
<span class="org-comment">% </span><span class="org-font-latex-sedate"><span class="org-comment">\node</span></span><span class="org-comment">[below] at ($(135:1.0)+(0, 0.8)$) {$</span><span class="org-font-latex-sedate"><span class="org-comment">\Pi</span></span><span class="org-comment">_{2}$};</span>
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">scope</span>}
|
|
|
|
<span class="org-comment">% Real and Imaginary Axis</span>
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (-0.5, 0) -- (7.0, 0) node[below left]{Re};
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (0, -1.8) -- (0, 2.0) node[below left]{Im};
|
|
|
|
<span class="org-font-latex-sedate">\draw</span>[dashed] (0, 0) -- (tangent cs:node=c,point={(0, 0)},solution=2);
|
|
<span class="org-font-latex-sedate">\draw</span>[dashed] (1, 0) arc (0:28:1) node[midway, right]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\Delta</span></span><span class="org-font-latex-math"> </span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\phi</span></span><span class="org-font-latex-math">$</span>};
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgf3182a4" class="figure">
|
|
<p><img src="figs/uncertainty_set_super_sensor.png" alt="uncertainty_set_super_sensor.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 3: </span>Uncertainty region of the super sensor dynamics in the complex plane (solid circle), of the sensor 1 (dotted circle) and of the sensor 2 (dashed circle) (<a href="./figs/uncertainty_set_super_sensor.png">png</a>, <a href="./figs/uncertainty_set_super_sensor.pdf">pdf</a>, <a href="./figs/uncertainty_set_super_sensor.tex">tex</a>).</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb356b70" class="outline-2">
|
|
<h2 id="orgb356b70"><span class="section-number-2">4</span> Fig 4: Architecture used for \(\mathcal{H}_\infty\) synthesis of complementary filters</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
<div class="org-src-container">
|
|
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
|
|
<span class="org-font-latex-sedate">\node</span>[block={4.0cm}{2.5cm}, fill=black!20!white, dashed] (P) {};
|
|
<span class="org-font-latex-sedate">\node</span>[above] at (P.north) {<span class="org-font-latex-math">$P(s)$</span>};
|
|
|
|
<span class="org-font-latex-sedate">\coordinate</span>[] (inputw) at (<span class="org-font-latex-math">$(P.south west)!0.75!(P.north west) + (-0.7, 0)$</span>);
|
|
<span class="org-font-latex-sedate">\coordinate</span>[] (inputu) at (<span class="org-font-latex-math">$(P.south west)!0.35!(P.north west) + (-0.7, 0)$</span>);
|
|
|
|
<span class="org-font-latex-sedate">\coordinate</span>[] (output1) at (<span class="org-font-latex-math">$(P.south east)!0.75!(P.north east) + ( 0.7, 0)$</span>);
|
|
<span class="org-font-latex-sedate">\coordinate</span>[] (output2) at (<span class="org-font-latex-math">$(P.south east)!0.35!(P.north east) + ( 0.7, 0)$</span>);
|
|
<span class="org-font-latex-sedate">\coordinate</span>[] (outputv) at (<span class="org-font-latex-math">$(P.south east)!0.1!(P.north east) + ( 0.7, 0)$</span>);
|
|
|
|
<span class="org-font-latex-sedate">\node</span>[block, left=1.4 of output1] (W1){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">(s)$</span>};
|
|
<span class="org-font-latex-sedate">\node</span>[block, left=1.4 of output2] (W2){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">(s)$</span>};
|
|
<span class="org-font-latex-sedate">\node</span>[addb={+}{}{}{}{-}, left=of W1] (sub) {};
|
|
|
|
<span class="org-font-latex-sedate">\node</span>[block, below=0.3 of P] (H2) {<span class="org-font-latex-math">$H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">(s)$</span>};
|
|
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (inputw) node[above right]{<span class="org-font-latex-math">$w$</span>} -- (sub.west);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (H2.west) -| (<span class="org-font-latex-math">$(inputu)+(0.35, 0)$</span>) node[above]{<span class="org-font-latex-math">$u$</span>} -- (W2.west);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (inputu-|sub) node[branch]{} -- (sub.south);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (sub.east) -- (W1.west);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (<span class="org-font-latex-math">$(sub.west)+(-0.6, 0)$</span>) node[branch]{} |- (<span class="org-font-latex-math">$(outputv)+(-0.35, 0)$</span>) node[above]{<span class="org-font-latex-math">$v$</span>} |- (H2.east);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (W1.east) -- (output1)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (W2.east) -- (output2)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org3cb8226" class="figure">
|
|
<p><img src="figs/h_infinity_robust_fusion.png" alt="h_infinity_robust_fusion.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 4: </span>Architecture used for \(\mathcal{H}_\infty\) synthesis of complementary filters (<a href="./figs/h_infinity_robust_fusion.png">png</a>, <a href="./figs/h_infinity_robust_fusion.pdf">pdf</a>, <a href="./figs/h_infinity_robust_fusion.tex">tex</a>).</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgdeaeaf4" class="outline-2">
|
|
<h2 id="orgdeaeaf4"><span class="section-number-2">5</span> Fig 5: Magnitude of a weighting function generated using the proposed formula</h2>
|
|
<div class="outline-text-2" id="text-5">
|
|
<div class="org-src-container">
|
|
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\setlength</span></span><span class="org-font-latex-sedate"><span class="org-variable-name">\fwidth</span></span>{<span class="org-variable-name">6.5cm</span>}
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\setlength</span></span><span class="org-font-latex-sedate"><span class="org-variable-name">\fheight</span></span>{<span class="org-variable-name">3.5cm</span>}
|
|
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">axis</span>}[<span class="org-comment">%</span>
|
|
width=1.0<span class="org-font-latex-sedate">\fwidth</span>,
|
|
height=1.0<span class="org-font-latex-sedate">\fheight</span>,
|
|
at={(0.0<span class="org-font-latex-sedate">\fwidth</span>, 0.0<span class="org-font-latex-sedate">\fheight</span>)},
|
|
scale only axis,
|
|
xmode=log,
|
|
xmin=0.1,
|
|
xmax=100,
|
|
xtick={0.1,1,10, 100},
|
|
xminorticks=true,
|
|
ymode=log,
|
|
ymin=0.0005,
|
|
ymax=20,
|
|
ytick={0.001, 0.01, 0.1, 1, 10},
|
|
yminorticks=true,
|
|
ylabel={Magnitude},
|
|
xlabel={Frequency [Hz]},
|
|
xminorgrids,
|
|
yminorgrids,
|
|
]
|
|
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=black, line width=1.5pt, forget plot]
|
|
table [x=freqs, y=ampl, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matweight_formula.csv};
|
|
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=black, dashed, line width=1.5pt]
|
|
table[row sep=crcr]{<span class="org-comment">%</span>
|
|
1 10<span class="org-font-latex-warning">\\</span>
|
|
100 10<span class="org-font-latex-warning">\\</span>
|
|
};
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=black, dashed, line width=1.5pt]
|
|
table[row sep=crcr]{<span class="org-comment">%</span>
|
|
0.1 0.001<span class="org-font-latex-warning">\\</span>
|
|
3 0.001<span class="org-font-latex-warning">\\</span>
|
|
};
|
|
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=black, line width=1.5pt]
|
|
table[row sep=crcr]{<span class="org-comment">%</span>
|
|
0.1 1<span class="org-font-latex-warning">\\</span>
|
|
100 1<span class="org-font-latex-warning">\\</span>
|
|
};
|
|
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=black, dashed, line width=1.5pt]
|
|
table[row sep=crcr]{<span class="org-comment">%</span>
|
|
10 2<span class="org-font-latex-warning">\\</span>
|
|
10 1<span class="org-font-latex-warning">\\</span>
|
|
};
|
|
|
|
<span class="org-font-latex-sedate">\node</span>[below] at (2, 10) {<span class="org-font-latex-math">$G_\infty$</span>};
|
|
<span class="org-font-latex-sedate">\node</span>[above] at (2, 0.001) {<span class="org-font-latex-math">$G_0$</span>};
|
|
|
|
<span class="org-font-latex-sedate">\node</span>[branch] at (10, 2){};
|
|
<span class="org-font-latex-sedate">\draw</span>[dashed, line cap=round] (7, 2) -- (20, 2) node[right]{<span class="org-font-latex-math">$G_c$</span>};
|
|
<span class="org-font-latex-sedate">\draw</span>[dashed, line cap=round] (10, 2) -- (10, 1) node[below]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\omega</span></span><span class="org-font-latex-math">_c$</span>};
|
|
|
|
<span class="org-font-latex-sedate">\node</span>[right] at (3, 0.1) {<span class="org-font-latex-math">$+n$</span>};
|
|
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">axis</span>}
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orga3a1174" class="figure">
|
|
<p><img src="figs/weight_formula.png" alt="weight_formula.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 5: </span>Magnitude of a weighting function generated using the proposed formula (<a href="./figs/weight_formula.png">png</a>, <a href="./figs/weight_formula.pdf">pdf</a>, <a href="./figs/weight_formula.tex">tex</a>).</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org8ce545c" class="outline-2">
|
|
<h2 id="org8ce545c"><span class="section-number-2">6</span> Fig 6: Frequency response of the weighting functions and complementary filters obtained using \(\mathcal{H}_\infty\) synthesis</h2>
|
|
<div class="outline-text-2" id="text-6">
|
|
<div class="org-src-container">
|
|
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\setlength</span></span><span class="org-font-latex-sedate"><span class="org-variable-name">\fwidth</span></span>{<span class="org-variable-name">6.5cm</span>}
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\setlength</span></span><span class="org-font-latex-sedate"><span class="org-variable-name">\fheight</span></span>{<span class="org-variable-name">6cm</span>}
|
|
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">axis</span>}[<span class="org-comment">%</span>
|
|
width=1.0<span class="org-font-latex-sedate">\fwidth</span>,
|
|
height=0.5<span class="org-font-latex-sedate">\fheight</span>,
|
|
at={(0.0<span class="org-font-latex-sedate">\fwidth</span>, 0.5<span class="org-font-latex-sedate">\fheight</span>)},
|
|
scale only axis,
|
|
xmode=log,
|
|
xmin=0.1,
|
|
xmax=1000,
|
|
xtick={0.1, 1, 10, 100, 1000},
|
|
xticklabels={{}},
|
|
xminorticks=true,
|
|
ymode=log,
|
|
ymin=0.0005,
|
|
ymax=20,
|
|
ytick={0.001, 0.01, 0.1, 1, 10},
|
|
yminorticks=true,
|
|
ylabel={Magnitude},
|
|
xminorgrids,
|
|
yminorgrids,
|
|
]
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor1, line width=1.5pt, forget plot]
|
|
table [x=freqs, y=H1, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_filters_results.csv};
|
|
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor2, line width=1.5pt, forget plot]
|
|
table [x=freqs, y=H2, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_filters_results.csv};
|
|
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor1, dashed, line width=1.5pt, forget plot]
|
|
table [x=freqs, y=W1, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_weights.csv};
|
|
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor2, dashed, line width=1.5pt, forget plot]
|
|
table [x=freqs, y=W2, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_weights.csv};
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">axis</span>}
|
|
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">axis</span>}[<span class="org-comment">%</span>
|
|
width=1.0<span class="org-font-latex-sedate">\fwidth</span>,
|
|
height=0.45<span class="org-font-latex-sedate">\fheight</span>,
|
|
at={(0.0<span class="org-font-latex-sedate">\fwidth</span>, 0.0<span class="org-font-latex-sedate">\fheight</span>)},
|
|
scale only axis,
|
|
xmode=log,
|
|
xmin=0.1,
|
|
xmax=1000,
|
|
xtick={0.1, 1, 10, 100, 1000},
|
|
xminorticks=true,
|
|
xlabel={Frequency [Hz]},
|
|
ymin=-200,
|
|
ymax=200,
|
|
ytick={-180, -90, 0, 90, 180},
|
|
ylabel={Phase [deg]},
|
|
xminorgrids,
|
|
legend style={at={(1,1.1)}, outer sep=2pt , anchor=north east, legend cell align=left, align=left, draw=black, nodes={scale=0.7, transform shape}},
|
|
]
|
|
<span class="org-font-latex-sedate">\addlegendimage</span>{color=mycolor1, dashed, line width=1.5pt}
|
|
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$W_1^{-1}$</span>};
|
|
<span class="org-font-latex-sedate">\addlegendimage</span>{color=mycolor2, dashed, line width=1.5pt}
|
|
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$W_2^{-1}$</span>};
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor1, line width=1.5pt]
|
|
table [x=freqs, y=H1p, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_filters_results.csv};
|
|
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$H_1$</span>};
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor2, line width=1.5pt]
|
|
table [x=freqs, y=H2p, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_filters_results.csv};
|
|
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$H_2$</span>};
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">axis</span>}
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org49f0f1e" class="figure">
|
|
<p><img src="figs/hinf_synthesis_results.png" alt="hinf_synthesis_results.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 6: </span>Frequency response of the weighting functions and complementary filters obtained using \(\mathcal{H}_\infty\) synthesis (<a href="./figs/hinf_synthesis_results.png">png</a>, <a href="./figs/hinf_synthesis_results.pdf">pdf</a>, <a href="./figs/hinf_synthesis_results.tex">tex</a>).</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgac21d24" class="outline-2">
|
|
<h2 id="orgac21d24"><span class="section-number-2">7</span> Fig 7: Architecture for \(\mathcal{H}_\infty\) synthesis of three complementary filters</h2>
|
|
<div class="outline-text-2" id="text-7">
|
|
<div class="org-src-container">
|
|
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
|
|
<span class="org-font-latex-sedate">\node</span>[block={5.0cm}{3.5cm}, fill=black!20!white, dashed] (P) {};
|
|
<span class="org-font-latex-sedate">\node</span>[above] at (P.north) {<span class="org-font-latex-math">$P(s)$</span>};
|
|
|
|
<span class="org-font-latex-sedate">\coordinate</span>[] (inputw) at (<span class="org-font-latex-math">$(P.south west)!0.8!(P.north west) + (-0.7, 0)$</span>);
|
|
<span class="org-font-latex-sedate">\coordinate</span>[] (inputu) at (<span class="org-font-latex-math">$(P.south west)!0.4!(P.north west) + (-0.7, 0)$</span>);
|
|
|
|
<span class="org-font-latex-sedate">\coordinate</span>[] (output1) at (<span class="org-font-latex-math">$(P.south east)!0.8!(P.north east) + (0.7, 0)$</span>);
|
|
<span class="org-font-latex-sedate">\coordinate</span>[] (output2) at (<span class="org-font-latex-math">$(P.south east)!0.55!(P.north east) + (0.7, 0)$</span>);
|
|
<span class="org-font-latex-sedate">\coordinate</span>[] (output3) at (<span class="org-font-latex-math">$(P.south east)!0.3!(P.north east) + (0.7, 0)$</span>);
|
|
<span class="org-font-latex-sedate">\coordinate</span>[] (outputv) at (<span class="org-font-latex-math">$(P.south east)!0.1!(P.north east) + (0.7, 0)$</span>);
|
|
|
|
<span class="org-font-latex-sedate">\node</span>[block, left=1.4 of output1] (W1){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">(s)$</span>};
|
|
<span class="org-font-latex-sedate">\node</span>[block, left=1.4 of output2] (W2){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">(s)$</span>};
|
|
<span class="org-font-latex-sedate">\node</span>[block, left=1.4 of output3] (W3){<span class="org-font-latex-math">$W</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_3</span></span><span class="org-font-latex-math">(s)$</span>};
|
|
<span class="org-font-latex-sedate">\node</span>[addb={+}{}{}{}{-}, left=of W1] (sub1) {};
|
|
<span class="org-font-latex-sedate">\node</span>[addb={+}{}{}{}{-}, left=of sub1] (sub2) {};
|
|
|
|
<span class="org-font-latex-sedate">\node</span>[block, below=0.3 of P] (H) {<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-keyword"><span class="org-font-latex-math">\begin</span></span></span><span class="org-font-latex-math">{</span><span class="org-function-name"><span class="org-font-latex-math">bmatrix</span></span><span class="org-font-latex-math">}H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">(s) \\ H</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_3</span></span><span class="org-font-latex-math">(s)</span><span class="org-font-latex-sedate"><span class="org-keyword"><span class="org-font-latex-math">\end</span></span></span><span class="org-font-latex-math">{</span><span class="org-function-name"><span class="org-font-latex-math">bmatrix</span></span><span class="org-font-latex-math">}$</span>};
|
|
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (inputw) node[above right](w){<span class="org-font-latex-math">$w$</span>} -- (sub2.west);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (W3-|sub1)node[branch]{} -- (sub1.south);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (W2-|sub2)node[branch]{} -- (sub2.south);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (<span class="org-font-latex-math">$(sub2.west)+(-0.5, 0)$</span>) node[branch]{} |- (outputv) |- (H.east);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (<span class="org-font-latex-math">$(H.south west)!0.7!(H.north west)$</span>) -| (inputu|-W2) -- (W2.west);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (<span class="org-font-latex-math">$(H.south west)!0.3!(H.north west)$</span>) -| (<span class="org-font-latex-math">$(inputu|-W3)+(0.4, 0)$</span>) -- (W3.west);
|
|
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (sub2.east) -- (sub1.west);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (sub1.east) -- (W1.west);
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (W1.east) -- (output1)node[above left](z){<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (W2.east) -- (output2)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
|
|
<span class="org-font-latex-sedate">\draw</span>[->] (W3.east) -- (output3)node[above left]{<span class="org-font-latex-math">$z</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_3</span></span><span class="org-font-latex-math">$</span>};
|
|
<span class="org-font-latex-sedate">\node</span>[above] at (W2-|w){<span class="org-font-latex-math">$u</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_1</span></span><span class="org-font-latex-math">$</span>};
|
|
<span class="org-font-latex-sedate">\node</span>[above] at (W3-|w){<span class="org-font-latex-math">$u</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_2</span></span><span class="org-font-latex-math">$</span>};
|
|
<span class="org-font-latex-sedate">\node</span>[above] at (outputv-|z){<span class="org-font-latex-math">$v$</span>};
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgd2b8673" class="figure">
|
|
<p><img src="figs/comp_filter_three_hinf.png" alt="comp_filter_three_hinf.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 7: </span>Architecture for \(\mathcal{H}_\infty\) synthesis of three complementary filters (<a href="./figs/comp_filter_three_hinf.png">png</a>, <a href="./figs/comp_filter_three_hinf.pdf">pdf</a>, <a href="./figs/comp_filter_three_hinf.tex">tex</a>).</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org9688457" class="outline-2">
|
|
<h2 id="org9688457"><span class="section-number-2">8</span> Fig 8: Frequency response of the weighting functions and three complementary filters obtained using \(\mathcal{H}_\infty\) synthesis</h2>
|
|
<div class="outline-text-2" id="text-8">
|
|
<div class="org-src-container">
|
|
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\setlength</span></span><span class="org-font-latex-sedate"><span class="org-variable-name">\fwidth</span></span>{<span class="org-variable-name">6.5cm</span>}
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\setlength</span></span><span class="org-font-latex-sedate"><span class="org-variable-name">\fheight</span></span>{<span class="org-variable-name">6cm</span>}
|
|
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">axis</span>}[<span class="org-comment">%</span>
|
|
width=1.0<span class="org-font-latex-sedate">\fwidth</span>,
|
|
height=0.55<span class="org-font-latex-sedate">\fheight</span>,
|
|
at={(0.0<span class="org-font-latex-sedate">\fwidth</span>, 0.45<span class="org-font-latex-sedate">\fheight</span>)},
|
|
scale only axis,
|
|
xmode=log,
|
|
xmin=0.1,
|
|
xmax=100,
|
|
xticklabels={{}},
|
|
xminorticks=true,
|
|
ymode=log,
|
|
ymin=0.0005,
|
|
ymax=20,
|
|
ytick={0.001, 0.01, 0.1, 1, 10},
|
|
yminorticks=true,
|
|
ylabel={Magnitude},
|
|
xminorgrids,
|
|
yminorgrids,
|
|
legend columns=2,
|
|
legend style={
|
|
/tikz/column 2/.style={
|
|
column sep=5pt,
|
|
},
|
|
at={(1,0)}, outer sep=2pt , anchor=south east, legend cell align=left, align=left, draw=black, nodes={scale=0.7, transform shape}
|
|
},
|
|
]
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor1, dashed, line width=1.5pt]
|
|
table [x=freqs, y=W1, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_weights.csv};
|
|
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">${W_1}^{-1}$</span>};
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor1, line width=1.5pt]
|
|
table [x=freqs, y=H1, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
|
|
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$H_1$</span>};
|
|
|
|
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor2, dashed, line width=1.5pt]
|
|
table [x=freqs, y=W2, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_weights.csv};
|
|
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">${W_2}^{-1}$</span>};
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor2, line width=1.5pt]
|
|
table [x=freqs, y=H2, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
|
|
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$H_2$</span>};
|
|
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor3, dashed, line width=1.5pt]
|
|
table [x=freqs, y=W3, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_weights.csv};
|
|
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">${W_3}^{-1}$</span>};
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor3, line width=1.5pt]
|
|
table [x=freqs, y=H3, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
|
|
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$H_3$</span>};
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">axis</span>}
|
|
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">axis</span>}[<span class="org-comment">%</span>
|
|
width=1.0<span class="org-font-latex-sedate">\fwidth</span>,
|
|
height=0.4<span class="org-font-latex-sedate">\fheight</span>,
|
|
at={(0.0<span class="org-font-latex-sedate">\fwidth</span>, 0.0<span class="org-font-latex-sedate">\fheight</span>)},
|
|
scale only axis,
|
|
xmode=log,
|
|
xmin=0.1,
|
|
xmax=100,
|
|
xminorticks=true,
|
|
xlabel={Frequency [Hz]},
|
|
ymin=-240,
|
|
ymax=240,
|
|
ytick={-180, -90, 0, 90, 180},
|
|
ylabel={Phase [deg]},
|
|
xminorgrids,
|
|
]
|
|
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor1, line width=1.5pt]
|
|
table [x=freqs, y=H1p, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
|
|
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor2, line width=1.5pt]
|
|
table [x=freqs, y=H2p, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
|
|
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor3, line width=1.5pt]
|
|
table [x=freqs, y=H3p, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/mathinf_three_results.csv};
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">axis</span>}
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org044b17c" class="figure">
|
|
<p><img src="figs/hinf_three_synthesis_results.png" alt="hinf_three_synthesis_results.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 8: </span>Frequency response of the weighting functions and three complementary filters obtained using \(\mathcal{H}_\infty\) synthesis (<a href="./figs/hinf_three_synthesis_results.png">png</a>, <a href="./figs/hinf_three_synthesis_results.pdf">pdf</a>, <a href="./figs/hinf_three_synthesis_results.tex">tex</a>).</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org8d6867c" class="outline-2">
|
|
<h2 id="org8d6867c"><span class="section-number-2">9</span> Fig 9: Specifications and weighting functions magnitude used for \(\mathcal{H}_\infty\) synthesis</h2>
|
|
<div class="outline-text-2" id="text-9">
|
|
<div class="org-src-container">
|
|
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\setlength</span></span><span class="org-font-latex-sedate"><span class="org-variable-name">\fwidth</span></span>{<span class="org-variable-name">6.5cm</span>}
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\setlength</span></span><span class="org-font-latex-sedate"><span class="org-variable-name">\fheight</span></span>{<span class="org-variable-name">4cm</span>}
|
|
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">axis</span>}[<span class="org-comment">%</span>
|
|
width=1.0<span class="org-font-latex-sedate">\fwidth</span>,
|
|
height=1.0<span class="org-font-latex-sedate">\fheight</span>,
|
|
at={(0.0<span class="org-font-latex-sedate">\fwidth</span>, 0.0<span class="org-font-latex-sedate">\fheight</span>)},
|
|
scale only axis,
|
|
separate axis lines,
|
|
every outer x axis line/.append style={black},
|
|
every x tick label/.append style={font=<span class="org-font-latex-sedate">\color</span>{black}},
|
|
every x tick/.append style={black},
|
|
xmode=log,
|
|
xmin=0.001,
|
|
xmax=1,
|
|
xminorticks=true,
|
|
xlabel={Frequency [Hz]},
|
|
every outer y axis line/.append style={black},
|
|
every y tick label/.append style={font=<span class="org-font-latex-sedate">\color</span>{black}},
|
|
every y tick/.append style={black},
|
|
ymode=log,
|
|
ymin=0.005,
|
|
ymax=20,
|
|
yminorticks=true,
|
|
ylabel={Magnitude},
|
|
axis background/.style={fill=white},
|
|
xmajorgrids,
|
|
xminorgrids,
|
|
ymajorgrids,
|
|
yminorgrids,
|
|
legend style={at={(0,1)}, outer sep=2pt, anchor=north west, legend cell align=left, align=left, draw=black, nodes={scale=0.7, transform shape}}
|
|
]
|
|
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor1, line width=1.5pt]
|
|
table [x=freqs, y=wHm, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matligo_weights.csv};
|
|
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$|w_H|^{-1}$</span>}
|
|
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor2, line width=1.5pt]
|
|
table [x=freqs, y=wLm, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matligo_weights.csv};
|
|
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$|w_L|^{-1}$</span>}
|
|
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=black, dotted, line width=1.5pt]
|
|
table[row sep=crcr]{<span class="org-comment">%</span>
|
|
0.0005 0.008<span class="org-font-latex-warning">\\</span>
|
|
0.008 0.008<span class="org-font-latex-warning">\\</span>
|
|
};
|
|
<span class="org-font-latex-sedate">\addlegendentry</span>{Specifications}
|
|
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=black, dotted, line width=1.5pt, forget plot]
|
|
table[row sep=crcr]{<span class="org-comment">%</span>
|
|
0.008 0.008<span class="org-font-latex-warning">\\</span>
|
|
0.04 1<span class="org-font-latex-warning">\\</span>
|
|
};
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=black, dotted, line width=1.5pt, forget plot]
|
|
table[row sep=crcr]{<span class="org-comment">%</span>
|
|
0.04 3<span class="org-font-latex-warning">\\</span>
|
|
0.1 3<span class="org-font-latex-warning">\\</span>
|
|
};
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=black, dotted, line width=1.5pt]
|
|
table[row sep=crcr]{<span class="org-comment">%</span>
|
|
0.1 0.045<span class="org-font-latex-warning">\\</span>
|
|
2 0.045<span class="org-font-latex-warning">\\</span>
|
|
};
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">axis</span>}
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgb9647cd" class="figure">
|
|
<p><img src="figs/ligo_weights.png" alt="ligo_weights.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 9: </span>Specifications and weighting functions magnitude used for \(\mathcal{H}_\infty\) synthesis (<a href="./figs/ligo_weights.png">png</a>, <a href="./figs/ligo_weights.pdf">pdf</a>, <a href="./figs/ligo_weights.tex">tex</a>).</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb6ae2f5" class="outline-2">
|
|
<h2 id="orgb6ae2f5"><span class="section-number-2">10</span> Fig 10: Comparison of the FIR filters (solid) with the filters obtained with \(\mathcal{H}_\infty\) synthesis (dashed)</h2>
|
|
<div class="outline-text-2" id="text-10">
|
|
<div class="org-src-container">
|
|
<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\setlength</span></span><span class="org-font-latex-sedate"><span class="org-variable-name">\fwidth</span></span>{<span class="org-variable-name">6.5cm</span>}
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\setlength</span></span><span class="org-font-latex-sedate"><span class="org-variable-name">\fheight</span></span>{<span class="org-variable-name">7cm</span>}
|
|
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">axis</span>}[<span class="org-comment">%</span>
|
|
width=1.0<span class="org-font-latex-sedate">\fwidth</span>,
|
|
height=0.60<span class="org-font-latex-sedate">\fheight</span>,
|
|
at={(0.0<span class="org-font-latex-sedate">\fwidth</span>, 0.35<span class="org-font-latex-sedate">\fheight</span>)},
|
|
scale only axis,
|
|
xmode=log,
|
|
xmin=0.001,
|
|
xmax=1,
|
|
xtick={0.001,0.01,0.1,1},
|
|
xticklabels={{}},
|
|
xminorticks=true,
|
|
ymode=log,
|
|
ymin=0.002,
|
|
ymax=5,
|
|
ytick={0.001, 0.01, 0.1, 1, 10},
|
|
yminorticks=true,
|
|
ylabel={Magnitude},
|
|
xminorgrids,
|
|
yminorgrids,
|
|
legend style={at={(1,0)}, outer sep=2pt, anchor=south east, legend cell align=left, align=left, draw=black, nodes={scale=0.7, transform shape}}
|
|
]
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor1, line width=1.5pt]
|
|
table [x=freqs, y=Hhm, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_hinf.csv};
|
|
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$H_H(s)$</span> - <span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\mathcal</span></span><span class="org-font-latex-math">{H}_\infty$</span>}
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor1, dashed, line width=1.5pt]
|
|
table [x=freqs, y=Hhm, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_fir.csv};
|
|
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$H_H(s)$</span> - FIR}
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor2, line width=1.5pt]
|
|
table [x=freqs, y=Hlm, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_hinf.csv};
|
|
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$H_L(s)$</span> - <span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\mathcal</span></span><span class="org-font-latex-math">{H}_\infty$</span>}
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor2, dashed, line width=1.5pt]
|
|
table [x=freqs, y=Hlm, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_fir.csv};
|
|
<span class="org-font-latex-sedate">\addlegendentry</span>{<span class="org-font-latex-math">$H_L(s)$</span> - FIR}
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">axis</span>}
|
|
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">axis</span>}[<span class="org-comment">%</span>
|
|
width=1.0<span class="org-font-latex-sedate">\fwidth</span>,
|
|
height=0.3<span class="org-font-latex-sedate">\fheight</span>,
|
|
at={(0.0<span class="org-font-latex-sedate">\fwidth</span>, 0.0<span class="org-font-latex-sedate">\fheight</span>)},
|
|
scale only axis,
|
|
xmode=log,
|
|
xmin=0.001,
|
|
xmax=1,
|
|
xtick={0.001, 0.01, 0.1, 1},
|
|
xminorticks=true,
|
|
xlabel={Frequency [Hz]},
|
|
ymin=-180,
|
|
ymax=180,
|
|
ytick={-180, -90, 0, 90, 180},
|
|
ylabel={Phase [deg]},
|
|
xminorgrids,
|
|
]
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor1, line width=1.5pt, forget plot]
|
|
table [x=freqs, y=Hhp, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_hinf.csv};
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor1, dashed, line width=1.5pt, forget plot]
|
|
table [x=freqs, y=Hhp, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_fir.csv};
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor2, line width=1.5pt, forget plot]
|
|
table [x=freqs, y=Hlp, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_hinf.csv};
|
|
<span class="org-font-latex-sedate">\addplot</span> [color=mycolor2, dashed, line width=1.5pt, forget plot]
|
|
table [x=freqs, y=Hlp, col sep=comma] {/home/thomas/Cloud/thesis/papers/dehaeze19_desig_compl_filte/matlab/matcomp_ligo_fir.csv};
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">axis</span>}
|
|
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgc99b299" class="figure">
|
|
<p><img src="figs/comp_fir_ligo_hinf.png" alt="comp_fir_ligo_hinf.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 10: </span>Comparison of the FIR filters (solid) with the filters obtained with \(\mathcal{H}_\infty\) synthesis (dashed) (<a href="./figs/comp_fir_ligo_hinf.png">png</a>, <a href="./figs/comp_fir_ligo_hinf.pdf">pdf</a>, <a href="./figs/comp_fir_ligo_hinf.tex">tex</a>).</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: Thomas Dehaeze</p>
|
|
<p class="date">Created: 2019-09-26 jeu. 17:46</p>
|
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
|
</div>
|
|
</body>
|
|
</html>
|