Update link to journal and matlab scripts
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index.html
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index.html
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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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<!-- 2020-11-12 jeu. 10:44 -->
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<!-- 2021-06-21 lun. 11:42 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Complementary Filters Shaping Using \(\mathcal{H}_\infty\) Synthesis</title>
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<meta name="generator" content="Org mode" />
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<title>Complementary Filters Shaping Using $\mathcal{H}_\infty$ Synthesis</title>
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<meta name="author" content="Thomas Dehaeze" />
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<meta name="generator" content="Org Mode" />
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<link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
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<script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
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<script>MathJax = {
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<script>
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MathJax = {
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svg: {
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scale: 1,
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fontCache: "global"
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},
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tex: {
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tags: 'ams',
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macros: {bm: ["\\boldsymbol{#1}",1],}
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tags: "ams",
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multlineWidth: "%MULTLINEWIDTH",
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tagSide: "right",
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macros: {bm: ["\\boldsymbol{#1}",1],},
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tagIndent: ".8em"
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}
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};
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</script>
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<script type="text/javascript" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
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<script id="MathJax-script" async
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src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js"></script>
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</head>
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<body>
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<div id="org-div-home-and-up">
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@ -41,18 +50,27 @@ This method is shown to be easily applicable for the synthesis of complex comple
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</p>
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</blockquote>
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<div id="outline-container-org51c6c0b" class="outline-2">
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<h2 id="org51c6c0b">Paper (<a href="paper/paper.pdf">link</a>)</h2>
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<div class="outline-text-2" id="text-org51c6c0b">
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<div id="outline-container-org16737c1" class="outline-2">
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<h2 id="org16737c1">Paper (<a href="journal/journal.pdf">link</a>)</h2>
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<div class="outline-text-2" id="text-org16737c1">
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<p>
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The paper has been created <a href="https://orgmode.org/">Org Mode</a> (generating <a href="https://www.latex-project.org/">LaTeX</a> code) under <a href="https://www.gnu.org/software/emacs/">Emacs</a>.
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</p>
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</div>
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</div>
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<div id="outline-container-org6820ca5" class="outline-2">
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<h2 id="org6820ca5">Tikz Figures (<a href="tikz/index.html">link</a>)</h2>
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<div class="outline-text-2" id="text-org6820ca5">
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<div id="outline-container-orgb50a720" class="outline-2">
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<h2 id="orgb50a720">Matlab Scripts (<a href="matlab/index.html">link</a>)</h2>
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<div class="outline-text-2" id="text-orgb50a720">
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<p>
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All the <a href="https://fr.mathworks.com/">Matlab</a> code that was used for the paper are accessible so that all the results are reproducible.
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</p>
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</div>
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</div>
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<div id="outline-container-org06a9b71" class="outline-2">
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<h2 id="org06a9b71">Tikz Figures (<a href="tikz/index.html">link</a>)</h2>
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<div class="outline-text-2" id="text-org06a9b71">
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<p>
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All the figures for the paper have been generated using <a href="https://sourceforge.net/projects/pgf/">TikZ</a>.
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</p>
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@ -20,13 +20,13 @@
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This method is shown to be easily applicable for the synthesis of complex complementary filters.
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#+end_quote
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* Paper ([[file:paper/paper.pdf][link]])
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* Paper ([[file:journal/journal.pdf][link]])
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:PROPERTIES:
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:UNNUMBERED: t
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:END:
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The paper has been created [[https://orgmode.org/][Org Mode]] (generating [[https://www.latex-project.org/][LaTeX]] code) under [[https://www.gnu.org/software/emacs/][Emacs]].
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* Matlab Scripts ([[file:matlab/index.org][link]]) :noexport:
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* Matlab Scripts ([[file:matlab/index.org][link]])
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:PROPERTIES:
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:UNNUMBERED: t
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:END:
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247
matlab/index.org
247
matlab/index.org
@ -167,10 +167,10 @@ exportFig('figs/weight_formula.pdf', 'width', 'wide', 'height', 'normal');
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[[file:figs/weight_formula.png]]
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#+begin_src matlab
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n = 2; w0 = 2*pi*10; G0 = 1/10; G1 = 1000; Gc = 0.45;
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n = 3; w0 = 2*pi*10; G0 = 1000; G1 = 0.1; Gc = 0.45;
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W1 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n;
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n = 3; w0 = 2*pi*10; G0 = 1000; G1 = 0.1; Gc = 0.45;
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n = 2; w0 = 2*pi*10; G0 = 1/10; G1 = 1000; Gc = 0.45;
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W2 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n;
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#+end_src
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@ -249,6 +249,28 @@ H1 = 1 - H2;
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** Obtained Complementary Filters
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The obtained complementary filters are shown on figure [[fig:hinf_filters_results]].
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#+begin_src matlab :results output replace :exports results :tangle no
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zpk(H1)
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zpk(H2)
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#+end_src
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#+RESULTS:
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#+begin_example
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zpk(H1)
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ans =
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(s+1.289e05) (s+153.6) (s+3.842)^3
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-------------------------------------------------------
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(s+1.29e05) (s^2 + 102.1s + 2733) (s^2 + 69.45s + 3272)
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zpk(H2)
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ans =
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125.61 (s+3358)^2 (s^2 + 46.61s + 813.8)
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-------------------------------------------------------
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(s+1.29e05) (s^2 + 102.1s + 2733) (s^2 + 69.45s + 3272)
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#+end_example
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#+begin_src matlab :exports none
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figure;
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tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
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@ -1315,45 +1337,67 @@ exportFig('figs/hinf_comp_H1_H2_syn.pdf', 'width', 'wide', 'height', 'normal');
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[[file:figs/hinf_comp_H1_H2_syn.png]]
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** Using Feedback architecture
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#+begin_src matlab
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n = 2; w0 = 2*pi*11; G0 = 1/10; G1 = 1000; Gc = 1/2;
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n = 3; w0 = 2*pi*10; G0 = 1000; G1 = 0.1; Gc = 0.45;
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W1 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n;
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n = 3; w0 = 2*pi*10; G0 = 1000; G1 = 0.1; Gc = 1/2;
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n = 2; w0 = 2*pi*10; G0 = 1/10; G1 = 1000; Gc = 0.45;
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W2 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n;
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#+end_src
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Let's first synthesize $H_1(s)$:
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#+begin_src matlab
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P = [W1 -W1;
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0 W2;
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1 -1];
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P = [ W1 0 1;
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-W1 W2 -1];
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#+end_src
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#+begin_src matlab :results output replace :exports both
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[K, ~, gamma, ~] = hinfsyn(P, 1, 1,'TOLGAM', 0.001, 'METHOD', 'lmi', 'DISPLAY', 'on');
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[L, ~, gamma, ~] = hinfsyn(P, 1, 1,'TOLGAM', 0.001, 'METHOD', 'lmi', 'DISPLAY', 'on');
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#+end_src
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#+begin_src matlab
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H1 = inv(1 + K);
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H1 = inv(1 + L);
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H2 = 1 - H1;
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#+end_src
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#+begin_src matlab :results output replace :exports results :tangle no
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zpk(H1)
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zpk(H2)
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#+end_src
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#+RESULTS:
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#+begin_example
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zpk(H1)
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ans =
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(s+2.115e07) (s+153.6) (s+4.613) (s^2 + 6.858s + 12.03)
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--------------------------------------------------------
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(s+2.117e07) (s^2 + 102.1s + 2732) (s^2 + 69.43s + 3271)
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zpk(H2)
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ans =
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20455 (s+3425) (s+3318) (s^2 + 46.58s + 813.2)
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--------------------------------------------------------
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(s+2.117e07) (s^2 + 102.1s + 2732) (s^2 + 69.43s + 3271)
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#+end_example
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#+begin_src matlab :exports none
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freqs = logspace(-2, 4, 1000);
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figure;
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hold on;
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plot(freqs, abs(squeeze(freqresp(H1, freqs, 'Hz'))), '-', 'DisplayName', '$H_1$');
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plot(freqs, abs(squeeze(freqresp(H2, freqs, 'Hz'))), '-', 'DisplayName', '$H_2$');
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set(gca,'ColorOrderIndex',1);
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plot(freqs, 1./abs(squeeze(freqresp(W1, freqs, 'Hz'))), '--', 'DisplayName', '$|W_1|^{-1}$');
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plot(freqs, 1./abs(squeeze(freqresp(W2, freqs, 'Hz'))), '--', 'DisplayName', '$|W_2|^{-1}$');
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set(gca,'ColorOrderIndex',1);
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plot(freqs, abs(squeeze(freqresp(H1, freqs, 'Hz'))), '-', 'DisplayName', '$|H_1|$');
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plot(freqs, abs(squeeze(freqresp(H2, freqs, 'Hz'))), '-', 'DisplayName', '$|H_2|$');
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plot(freqs, abs(squeeze(freqresp(L, freqs, 'Hz'))), 'k--', 'DisplayName', '$|L|$');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Magnitude');
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legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 2);
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legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 3);
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#+end_src
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** Adding feature in the filters
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@ -1999,6 +2043,183 @@ There is no difference between " open-loop" shaping and "close-loop" shaping:
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- same obtained filter orders
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#+end_important
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** Integral Action
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*** Test
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#+begin_src matlab
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freqs = logspace(-2, 3, 1000);
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#+end_src
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\begin{equation}
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W_1(s) = \frac{W_{10}(s)}{s}
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\end{equation}
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with $W_{10}(0) \neq 0$
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#+begin_src matlab
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W10 = 0.1*(s+125.7)^2/(s+1.257)^2*(s + 0.0001)/(1 + s/1000);
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W1 = W10/s;
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#+end_src
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#+begin_src matlab
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n = 2; w0 = 2*pi*10; G0 = 1/10; G1 = 1000; Gc = 0.5;
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W2 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n;
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#+end_src
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#+begin_src matlab :exports none
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figure;
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hold on;
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set(gca,'ColorOrderIndex',1)
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plot(freqs, 1./abs(squeeze(freqresp(W1, freqs, 'Hz'))), '--', 'DisplayName', '$|W_1|^{-1}$');
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set(gca,'ColorOrderIndex',2)
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plot(freqs, 1./abs(squeeze(freqresp(W2, freqs, 'Hz'))), '--', 'DisplayName', '$|W_2|^{-1}$');
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Magnitude');
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hold off;
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xlim([freqs(1), freqs(end)]);
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ylim([1e-4, 20]);
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xticks([0.1, 1, 10, 100, 1000]);
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leg = legend('location', 'southeast', 'FontSize', 8);
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leg.ItemTokenSize(1) = 18;
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#+end_src
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#+begin_src matlab
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V = 1;
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#+end_src
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#+begin_src matlab
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P = [ V*W10 W10;
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0 W2;
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-V -1];
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#+end_src
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And we do the $\mathcal{H}_\infty$ synthesis using the =hinfsyn= command.
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#+begin_src matlab :results output replace :exports both
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[H2, ~, gamma, ~] = hinfsyn(P, 1, 1,'TOLGAM', 0.001, 'METHOD', 'lmi', 'DISPLAY', 'on');
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#+end_src
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#+begin_src matlab
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H1 = 1 - H2;
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#+end_src
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#+begin_src matlab :exports none
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figure;
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tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
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% Magnitude
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ax1 = nexttile([2, 1]);
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hold on;
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set(gca,'ColorOrderIndex',1)
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plot(freqs, 1./abs(squeeze(freqresp(W1, freqs, 'Hz'))), '--', 'DisplayName', '$w_1$');
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set(gca,'ColorOrderIndex',2)
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plot(freqs, 1./abs(squeeze(freqresp(W2, freqs, 'Hz'))), '--', 'DisplayName', '$w_2$');
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set(gca,'ColorOrderIndex',1)
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plot(freqs, abs(squeeze(freqresp(H1, freqs, 'Hz'))), '-', 'DisplayName', '$H_1$');
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set(gca,'ColorOrderIndex',2)
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plot(freqs, abs(squeeze(freqresp(H2, freqs, 'Hz'))), '-', 'DisplayName', '$H_2$');
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Magnitude');
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set(gca, 'XTickLabel',[]);
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ylim([1e-4, 20]);
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yticks([1e-4, 1e-3, 1e-2, 1e-1, 1, 1e1]);
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leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);
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leg.ItemTokenSize(1) = 18;
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% Phase
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ax2 = nexttile;
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hold on;
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set(gca,'ColorOrderIndex',1)
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plot(freqs, 180/pi*phase(squeeze(freqresp(H1, freqs, 'Hz'))), '-');
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set(gca,'ColorOrderIndex',2)
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plot(freqs, 180/pi*phase(squeeze(freqresp(H2, freqs, 'Hz'))), '-');
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hold off;
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xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
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set(gca, 'XScale', 'log');
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yticks([-180:90:180]);
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linkaxes([ax1,ax2],'x');
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xlim([freqs(1), freqs(end)]);
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#+end_src
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*** Example 6.7.3
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#+begin_src matlab
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n = 2; w0 = 2*pi*10; G0 = 1000; G1 = 0.1; Gc = 0.45;
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W1 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n;
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n = 2; w0 = 2*pi*10; G0 = 1/10; G1 = 1000; Gc = 0.45;
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W2 = (((1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (G0/Gc)^(1/n))/((1/G1)^(1/n)*(1/w0)*sqrt((1-(G0/Gc)^(2/n))/(1-(Gc/G1)^(2/n)))*s + (1/Gc)^(1/n)))^n;
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#+end_src
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#+begin_src matlab
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V = 1/(1 + s/2/pi/100);
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#+end_src
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#+begin_src matlab
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V = W2;
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W2 = tf(1);
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#+end_src
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#+begin_src matlab
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P = [W1 -W1;
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0 W2;
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V 0];
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#+end_src
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#+begin_src matlab :results output replace :exports both
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[H2, ~, gamma, ~] = hinfsyn(P, 1, 1,'TOLGAM', 0.001, 'METHOD', 'ric', 'DISPLAY', 'on');
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#+end_src
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#+begin_src matlab
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H2 = H2*V;
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#+end_src
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#+begin_src matlab
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H1 = 1 - H2;
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#+end_src
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#+begin_src matlab :exports none
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figure;
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tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
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% Magnitude
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ax1 = nexttile([2, 1]);
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hold on;
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set(gca,'ColorOrderIndex',1)
|
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plot(freqs, 1./abs(squeeze(freqresp(W1, freqs, 'Hz'))), '--', 'DisplayName', '$w_1$');
|
||||
set(gca,'ColorOrderIndex',2)
|
||||
plot(freqs, 1./abs(squeeze(freqresp(W2, freqs, 'Hz'))), '--', 'DisplayName', '$w_2$');
|
||||
|
||||
set(gca,'ColorOrderIndex',1)
|
||||
plot(freqs, abs(squeeze(freqresp(H1, freqs, 'Hz'))), '-', 'DisplayName', '$H_1$');
|
||||
set(gca,'ColorOrderIndex',2)
|
||||
plot(freqs, abs(squeeze(freqresp(H2, freqs, 'Hz'))), '-', 'DisplayName', '$H_2$');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Magnitude');
|
||||
set(gca, 'XTickLabel',[]);
|
||||
ylim([1e-4, 20]);
|
||||
yticks([1e-4, 1e-3, 1e-2, 1e-1, 1, 1e1]);
|
||||
leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);
|
||||
leg.ItemTokenSize(1) = 18;
|
||||
|
||||
% Phase
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
set(gca,'ColorOrderIndex',1)
|
||||
plot(freqs, 180/pi*phase(squeeze(freqresp(H1, freqs, 'Hz'))), '-');
|
||||
set(gca,'ColorOrderIndex',2)
|
||||
plot(freqs, 180/pi*phase(squeeze(freqresp(H2, freqs, 'Hz'))), '-');
|
||||
hold off;
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
set(gca, 'XScale', 'log');
|
||||
yticks([-180:90:180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([freqs(1), freqs(end)]);
|
||||
#+end_src
|
||||
|
||||
* Impose a positive slope at DC or a negative slope at infinite frequency
|
||||
** Introduction :ignore:
|
||||
|
||||
|
||||
@ -213,17 +213,17 @@ Configuration file is accessible [[file:config.org][here]].
|
||||
\node[addb] (addu) at ($(delta1.east|-input) + (0.4, 0)$) {};
|
||||
\node[addb, right=0.4 of addu] (addn) {};
|
||||
|
||||
\draw[->] ($(input)+(-0.7, 0)$) node[above right]{$x$} -- (addu);
|
||||
\draw[->] ($(input)+(-0.8, 0)$) node[above right]{$x$} -- (addu);
|
||||
\draw[->] (input.center) |- (W1.west);
|
||||
\draw[->] (W1.east) -- (delta1.west);
|
||||
\draw[->] (delta1.east) -| (addu.north);
|
||||
\draw[->] (addu.east) -- (addn.west);
|
||||
\draw[<-] (addn.north) -- ++(0, 0.7)node[below right](n1){$n_1$};
|
||||
\draw[<-] (addn.north) -- ++(0, 0.6)node[below right](n1){$n_1$};
|
||||
\draw[->] (addn.east) -- ++(0.9, 0) node[above left]{$\hat{x}_1$};
|
||||
|
||||
\begin{scope}[on background layer]
|
||||
\node[fit={(input.west |- addu.south) ($(delta1.north -| addn.east) + (0.1, 0.4)$)}, fill=black!10!white, draw, inner sep=6pt] (sensor1cal) {};
|
||||
\node[below] at (sensor1cal.north) {Normalized Sensor};
|
||||
\node[fit={(input.west |- addu.south) ($(delta1.north -| addn.east) + (0.1, 0)$)}, fill=black!10!white, draw, inner sep=6pt] (sensor1cal) {};
|
||||
\node[below left, align=right] at (sensor1cal.north east) {{\tiny Normalized}\\[-0.5em]{\tiny sensor}};
|
||||
\end{scope}
|
||||
\end{tikzpicture}
|
||||
#+end_src
|
||||
@ -423,19 +423,19 @@ Configuration file is accessible [[file:config.org][here]].
|
||||
#+RESULTS:
|
||||
[[file:figs/ligo_super_sensor_architecture.png]]
|
||||
|
||||
* Feedback Loop Sensor Fusion Architecture
|
||||
* Closed-Loop Complementary Filters
|
||||
#+begin_src latex :file feedback_sensor_fusion.pdf :tangle figs/feedback_sensor_fusion.tex
|
||||
\begin{tikzpicture}
|
||||
\node[addb={+}{}{}{}{-}] (addfb) at (0, 0){};
|
||||
\node[block, right=1 of addfb] (L){$L$};
|
||||
\node[block, right=1 of addfb] (L){$L(s)$};
|
||||
\node[addb={+}{}{}{}{}, right=1 of L] (adddy){};
|
||||
|
||||
\draw[<-] (addfb.west) -- ++(-1, 0) node[above right]{$\hat{x}_1$};
|
||||
\draw[<-] (addfb.west) -- ++(-1, 0) node[above right]{$\hat{x}_2$};
|
||||
\draw[->] (addfb.east) -- (L.west);
|
||||
\draw[->] (L.east) -- (adddy.west);
|
||||
\draw[->] (adddy.east) -- ++(1.4, 0) node[above left]{$\hat{x}$};
|
||||
\draw[->] ($(adddy.east) + (0.5, 0)$) node[branch]{} -- ++(0, -0.8) coordinate(botc) -| (addfb.south);
|
||||
\draw[<-] (adddy.north) -- ++(0, 1) node[below right]{$\hat{x}_2$};
|
||||
\draw[<-] (adddy.north) -- ++(0, 1) node[below right]{$\hat{x}_1$};
|
||||
|
||||
\begin{scope}[on background layer]
|
||||
\node[fit={(L.north-|addfb.west) (botc)}, fill=black!10!white, draw, inner sep=6pt] (supersensor) {};
|
||||
@ -445,25 +445,61 @@ Configuration file is accessible [[file:config.org][here]].
|
||||
#+end_src
|
||||
|
||||
#+name: fig:feedback_sensor_fusion
|
||||
#+caption: ([[./figs/feedback_sensor_fusion.png][png]], [[./figs/feedback_sensor_fusion.pdf][pdf]], [[./figs/feedback_sensor_fusion.tex][tex]]).
|
||||
#+caption: "Closed-Loop" complementary filters ([[./figs/feedback_sensor_fusion.png][png]], [[./figs/feedback_sensor_fusion.pdf][pdf]], [[./figs/feedback_sensor_fusion.tex][tex]]).
|
||||
#+RESULTS:
|
||||
[[file:figs/feedback_sensor_fusion.png]]
|
||||
|
||||
* Feedback Loop Sensor Fusion Architecture
|
||||
* Closed-Loop Fusion Architecture
|
||||
#+begin_src latex :file feedback_sensor_fusion_arch.pdf :tangle figs/feedback_sensor_fusion_arch.tex
|
||||
\begin{tikzpicture}
|
||||
\node[addb={+}{}{}{}{-}] (addfb) at (0, 0){};
|
||||
\node[block, right=1 of addfb] (L){$L(s)$};
|
||||
\node[addb={+}{}{}{}{}, right=1 of L] (adddy){};
|
||||
|
||||
\node[block, left=1.2 of addfb] (sensor2){Sensor 2};
|
||||
\node[block, above=0.4 of sensor2] (sensor1){Sensor 1};
|
||||
\node[branch, left=0.6 of sensor2] (x){};
|
||||
|
||||
\draw[->] (addfb.east) -- (L.west);
|
||||
\draw[->] (L.east) -- (adddy.west);
|
||||
\draw[->] (adddy.east) -- ++(1.4, 0) node[above left]{$\hat{x}$};
|
||||
\draw[->] ($(adddy.east) + (0.5, 0)$) node[branch]{} -- ++(0, -0.8) coordinate(botc) -| (addfb.south);
|
||||
\draw[->] (x.center) |- (sensor1.west);
|
||||
\draw[->] ($(x)-(0.8,0)$) node[above right]{$x$} -- (sensor2.west);
|
||||
\draw[->] (sensor2.east)node[above right=0 and 0.25]{$\hat{x}_2$} -- (addfb.west);
|
||||
\draw[->] (sensor1.east)node[above right=0 and 0.25]{$\hat{x}_1$} -| (adddy.north);
|
||||
|
||||
\begin{scope}[on background layer]
|
||||
\node[fit={(x|-sensor1.north) (botc)}, fill=black!10!white, draw, inner sep=9pt] (supersensor) {};
|
||||
\node[fit={(sensor1.north-|addfb.west) (botc)}, fill=black!20!white, draw, inner sep=6pt] (feedbackfilter) {};
|
||||
\node[fit={(sensor2.west|-botc) (sensor1.north east)}, fill=black!20!white, draw, inner sep=6pt] (sensors) {};
|
||||
\node[above, align=center] at (sensors.south) {{\tiny Normalized}\\[-0.5em]{\tiny sensors}};
|
||||
\node[below, align=center] at (feedbackfilter.north) {{\tiny "Closed-Loop"}\\[-0.5em]{\tiny complementary filters}};
|
||||
% \node[above, align=center] at (supersensor.north) {Super Sensor};
|
||||
\end{scope}
|
||||
\end{tikzpicture}
|
||||
#+end_src
|
||||
|
||||
#+name: fig:feedback_sensor_fusion_arch
|
||||
#+caption: ([[./figs/feedback_sensor_fusion_arch.png][png]], [[./figs/feedback_sensor_fusion_arch.pdf][pdf]], [[./figs/feedback_sensor_fusion_arch.tex][tex]]).
|
||||
#+RESULTS:
|
||||
[[file:figs/feedback_sensor_fusion_arch.png]]
|
||||
|
||||
* TODO Feedback Loop Sensor Fusion Architecture
|
||||
#+begin_src latex :file feedback_synthesis_architecture.pdf :tangle figs/feedback_synthesis_architecture.tex
|
||||
\begin{tikzpicture}
|
||||
\node[block] (W1) at (0,0) {$W_1$};
|
||||
\node[addb={+}{}{}{}{-}, right=1 of W1] (addfb){};
|
||||
\node[addb={+}{}{}{}{}, right=4.5 of W1] (adddy){};
|
||||
\node[block, above=0.8 of adddy] (W2){$W_2$};
|
||||
\node[block] (W2) at (0,0) {$W_2$};
|
||||
\node[addb={+}{}{}{}{-}, right=1 of W2] (addfb){};
|
||||
\node[addb={+}{}{}{}{}, right=4.5 of W2] (adddy){};
|
||||
\node[block, above=0.8 of adddy] (W1){$W_1$};
|
||||
|
||||
\draw[<-] (W1.west) -- ++(-1, 0) node[above right]{$w_1$};
|
||||
\draw[->] (W1.east) -- (addfb.west) node[above left]{$\tilde{w}_1$};
|
||||
\draw[<-] (W2.west) -- ++(-1, 0) node[above right]{$w_2$};
|
||||
\draw[->] (W2.east) -- (addfb.west) node[above left]{$\tilde{w}_2$};
|
||||
\draw[->] (addfb.east) -- ++(1, 0) node[above left]{$v$};
|
||||
\draw[<-] (adddy.west) -- ++(-1, 0) node[above right]{$u$};
|
||||
\draw[->] (adddy.east) -- ++(1.4, 0) node[above left]{$z$};
|
||||
\draw[->] (W2.south) -- (adddy.north) node[above right]{$\tilde{w}_2$};
|
||||
\draw[<-] (W2.north) -- ++(0, 1) node[below right]{$w_2$};
|
||||
\draw[->] (W1.south) -- (adddy.north) node[above right]{$\tilde{w}_1$};
|
||||
\draw[<-] (W1.north) -- ++(0, 1) node[below right]{$w_1$};
|
||||
\draw[->] ($(adddy.east) + (0.5, 0)$) node[branch]{} -- ++(0, -0.8) -| (addfb.south);
|
||||
\end{tikzpicture}
|
||||
#+end_src
|
||||
@ -473,29 +509,29 @@ Configuration file is accessible [[file:config.org][here]].
|
||||
#+RESULTS:
|
||||
[[file:figs/feedback_synthesis_architecture.png]]
|
||||
|
||||
* Feedback Loop Sensor Fusion Architecture
|
||||
* Feedback Sensor Fusion - Generalized Plant
|
||||
#+begin_src latex :file feedback_synthesis_architecture_generalized_plant.pdf :tangle figs/feedback_synthesis_architecture_generalized_plant.tex
|
||||
\begin{tikzpicture}
|
||||
\node[block={4.5cm}{3.0cm}, fill=black!10!white] (P) {};
|
||||
\node[above] at (P.north) {$P_L(s)$};
|
||||
|
||||
\coordinate[] (inputw2) at ($(P.south west)!0.75!(P.north west) + (-0.7, 0)$);
|
||||
\coordinate[] (inputw1) at ($(P.south west)!0.40!(P.north west) + (-0.7, 0)$);
|
||||
\coordinate[] (inputw1) at ($(P.south west)!0.75!(P.north west) + (-0.7, 0)$);
|
||||
\coordinate[] (inputw2) at ($(P.south west)!0.40!(P.north west) + (-0.7, 0)$);
|
||||
\coordinate[] (inputu) at ($(P.south west)!0.15!(P.north west) + (-0.7, 0)$);
|
||||
|
||||
\coordinate[] (outputz) at ($(P.south east)!0.75!(P.north east) + ( 0.7, 0)$);
|
||||
\coordinate[] (outputv) at ($(P.south east)!0.40!(P.north east) + ( 0.7, 0)$);
|
||||
|
||||
\node[block, right=1.2 of inputw1] (W1){$W_1(s)$};
|
||||
\node[block, right=1.2 of inputw2] (W2){$W_2(s)$};
|
||||
\node[addb={+}{}{}{}{}, right=0.8 of W2] (add) {};
|
||||
\node[addb={+}{}{-}{}{}, right=1.8 of W1] (sub) {};
|
||||
\node[block, right=1.2 of inputw1] (W1){$W_1(s)$};
|
||||
\node[addb={+}{}{}{}{}, right=0.8 of W1] (add) {};
|
||||
\node[addb={+}{}{-}{}{}, right=1.8 of W2] (sub) {};
|
||||
|
||||
\draw[->] (inputw1) node[above right]{$w_1$} -- (W1.west);
|
||||
\draw[->] (inputw2) node[above right]{$w_2$} -- (W2.west);
|
||||
\draw[->] (inputw1) node[above right]{$w_1$} -- (W1.west);
|
||||
\draw[->] (inputu) node[above right]{$u$} -| (add.south);
|
||||
\draw[->] (W1.east) -- (sub.west);
|
||||
\draw[->] (W2.east) -- (add.west);
|
||||
\draw[->] (W2.east) -- (sub.west);
|
||||
\draw[->] (W1.east) -- (add.west);
|
||||
\draw[->] (add.east) -- (outputz)node[above left]{$z$};
|
||||
\draw[->] (sub.east) -- (outputv)node[above left]{$v$};
|
||||
\draw[->] (add-|sub) node[branch]{} -- (sub.north);
|
||||
@ -595,7 +631,7 @@ Configuration file is accessible [[file:config.org][here]].
|
||||
#+begin_src latex :file comp_filter_three_hinf.pdf :tangle figs/comp_filter_three_hinf.tex
|
||||
\begin{tikzpicture}
|
||||
\node[block={5.0cm}{4.5cm}, fill=black!10!white] (P) {};
|
||||
\node[above] at (P.north) {$P(s)$};
|
||||
\node[above] at (P.north) {$P_3(s)$};
|
||||
|
||||
\coordinate[] (inputw) at ($(P.south west)!0.8!(P.north west) + (-0.7, 0)$);
|
||||
\coordinate[] (inputu) at ($(P.south west)!0.4!(P.north west) + (-0.7, 0)$);
|
||||
|
||||
Loading…
Reference in New Issue
Block a user