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< title > Sensor Fusion Paper - Tikz Figures< / title >
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< h1 class = "title" > Sensor Fusion Paper - Tikz Figures< / h1 >
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< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
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< li > < a href = "#org3a7fde8" > 1. Change some default< / a > < / li >
< li > < a href = "#orgad52b16" > 2. Sensor Fusion with complementary filters< / a > < / li >
< li > < a href = "#org5b2f979" > 3. Equivalent configuration< / a > < / li >
< li > < a href = "#org78058a3" > 4. Equivalent configuration - classical Feedback< / a > < / li >
< li > < a href = "#orgfaf2e59" > 5. Equivalent configuration - classical Feedback with pre-filter< / a > < / li >
< li > < a href = "#org1e815b2" > 6. Equivalent configuration - bis< / a > < / li >
< li > < a href = "#orge3cecd1" > 7. H-Infinity - Complementary filters - Generalized plant< / a > < / li >
< li > < a href = "#org3d2bd22" > 8. H-Infinity - Complementary filters< / a > < / li >
< li > < a href = "#org408fe0c" > 9. H-Infinity - 3 Complementary filters< / a > < / li >
< li > < a href = "#orgf18dc35" > 10. Input Multiplicative Uncertainty< / a > < / li >
< li > < a href = "#org922fc19" > 11. One mass< / a > < / li >
< li > < a href = "#org10c0552" > 12. One mass - Control< / a > < / li >
< li > < a href = "#org9d5c45c" > 13. Piezoelectric Actuator< / a > < / li >
< li > < a href = "#org867350f" > 14. Upper bounds< / a > < / li >
< li > < a href = "#org6a90bb1" > 15. Bode plot of the mechanical system< / a > < / li >
< li > < a href = "#org16e0cef" > 16. Bode plot of the mechanical system - Uncertainty< / a > < / li >
< li > < a href = "#orgb234097" > 17. Bode plot of the controller< / a > < / li >
< li > < a href = "#org6fb49a0" > 18. Bode plot of the loop gain< / a > < / li >
< li > < a href = "#org6dc8522" > 19. Upper bounds with weights< / a > < / li >
< li > < a href = "#org3f273a2" > 20. Upper bounds with Complementary Filters< / a > < / li >
< li > < a href = "#org666f416" > 21. Upper bounds with weights and Complementary Filters< / a > < / li >
< li > < a href = "#org4296f42" > 22. Robustness - Nyquist< / a > < / li >
< li > < a href = "#org07ffae0" > 23. Robustness - Loop Gain< / a > < / li >
< li > < a href = "#org7dc679b" > 24. Robust performance< / a > < / li >
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Configuration file is accessible < a href = "config.html" > here< / a > .
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< h2 id = "org3a7fde8" > < span class = "section-number-2" > 1< / span > Change some default< / h2 >
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< h2 id = "orgad52b16" > < span class = "section-number-2" > 2< / span > Sensor Fusion with complementary filters< / h2 >
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< div id = "org4fd4aa4" class = "figure" >
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< p > < img src = "figs/sf_arch.png" alt = "sf_arch.png" / >
< / p >
< p > < span class = "figure-number" > Figure 1: < / span > Sensor Fusion with complementary filters (< a href = "./figs/sf_arch.png" > png< / a > , < a href = "./figs/sf_arch.pdf" > pdf< / a > , < a href = "./figs/sf_arch.tex" > tex< / a > ).< / p >
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< div id = "outline-container-org5b2f979" class = "outline-2" >
< h2 id = "org5b2f979" > < span class = "section-number-2" > 3< / span > Equivalent configuration< / h2 >
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< p > < img src = "figs/sf_arch_eq.png" alt = "sf_arch_eq.png" / >
< / p >
< p > < span class = "figure-number" > Figure 2: < / span > Equivalent configuration (< a href = "./figs/sf_arch_eq.png" > png< / a > , < a href = "./figs/sf_arch_eq.pdf" > pdf< / a > , < a href = "./figs/sf_arch_eq.tex" > tex< / a > ).< / p >
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< h2 id = "org78058a3" > < span class = "section-number-2" > 4< / span > Equivalent configuration - classical Feedback< / h2 >
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< div id = "org62499fb" class = "figure" >
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< p > < img src = "figs/sf_arch_class.png" alt = "sf_arch_class.png" / >
< / p >
< p > < span class = "figure-number" > Figure 3: < / span > Equivalent configuration - classical Feedback (< a href = "./figs/sf_arch_class.png" > png< / a > , < a href = "./figs/sf_arch_class.pdf" > pdf< / a > , < a href = "./figs/sf_arch_class.tex" > tex< / a > ).< / p >
< / div >
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< div id = "outline-container-orgfaf2e59" class = "outline-2" >
< h2 id = "orgfaf2e59" > < span class = "section-number-2" > 5< / span > Equivalent configuration - classical Feedback with pre-filter< / h2 >
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< span class = "org-font-latex-sedate" > \definecolor< / span > {T}{rgb}{0.230, 0.299, 0.754}< span class = "org-comment" > %< / span >
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< p > < img src = "figs/sf_arch_class_prefilter.png" alt = "sf_arch_class_prefilter.png" / >
< / p >
< p > < span class = "figure-number" > Figure 4: < / span > Equivalent configuration - classical Feedback with pre-filter (< a href = "./figs/sf_arch_class_prefilter.png" > png< / a > , < a href = "./figs/sf_arch_class_prefilter.pdf" > pdf< / a > , < a href = "./figs/sf_arch_class_prefilter.tex" > tex< / a > ).< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org1e815b2" class = "outline-2" >
< h2 id = "org1e815b2" > < span class = "section-number-2" > 6< / span > Equivalent configuration - bis< / h2 >
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< p > < img src = "figs/sf_arch_class_bis.png" alt = "sf_arch_class_bis.png" / >
< / p >
< p > < span class = "figure-number" > Figure 5: < / span > Equivalent configuration - bis (< a href = "./figs/sf_arch_class_bis.png" > png< / a > , < a href = "./figs/sf_arch_class_bis.pdf" > pdf< / a > , < a href = "./figs/sf_arch_class_bis.tex" > tex< / a > ).< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-orge3cecd1" class = "outline-2" >
< h2 id = "orge3cecd1" > < span class = "section-number-2" > 7< / span > H-Infinity - Complementary filters - Generalized plant< / h2 >
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< p > < img src = "figs/sf_hinf_filters_plant_b.png" alt = "sf_hinf_filters_plant_b.png" / >
< / p >
< p > < span class = "figure-number" > Figure 6: < / span > H-Infinity - Complementary filters - Generalized plant (< a href = "./figs/sf_hinf_filters_plant_b.png" > png< / a > , < a href = "./figs/sf_hinf_filters_plant_b.pdf" > pdf< / a > , < a href = "./figs/sf_hinf_filters_plant_b.tex" > tex< / a > ).< / p >
< / div >
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< div id = "outline-container-org3d2bd22" class = "outline-2" >
< h2 id = "org3d2bd22" > < span class = "section-number-2" > 8< / span > H-Infinity - Complementary filters< / h2 >
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< div class = "outline-text-2" id = "text-8" >
< div class = "org-src-container" >
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< span class = "org-font-latex-sedate" > \definecolor< / span > {T}{rgb}{0.230, 0.299, 0.754}< span class = "org-comment" > %< / span >
< span class = "org-font-latex-sedate" > \definecolor< / span > {S}{rgb}{0.706, 0.016, 0.150}< span class = "org-comment" > %< / span >
< span class = "org-font-latex-sedate" > < span class = "org-keyword" > \begin< / span > < / span > {< span class = "org-function-name" > tikzpicture< / span > }
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< span class = "org-font-latex-sedate" > \node< / span > [addb={+}{}{}{}{-}, left=of WH] (sub) {};
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< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (HL.west) -| (< span class = "org-font-latex-math" > $(inputu)+(0.5*< / span > < span class = "org-font-latex-sedate" > < span class = "org-font-latex-math" > \cdist< / span > < / span > < span class = "org-font-latex-math" > , 0)$< / span > ) -- (WL.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) -- (WH.west);
< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (< span class = "org-font-latex-math" > $(inputw)+(2*< / span > < span class = "org-font-latex-sedate" > < span class = "org-font-latex-math" > \cdist< / span > < / span > < span class = "org-font-latex-math" > , 0)$< / span > ) node[branch]{} |- (< span class = "org-font-latex-math" > $(outputv)+(-0.5*< / span > < span class = "org-font-latex-sedate" > < span class = "org-font-latex-math" > \cdist< / span > < / span > < span class = "org-font-latex-math" > , 0)$< / span > ) |- (HL.east);
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< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (WH.east) -- (outputh)node[above left]{< span class = "org-font-latex-math" > $z< / span > < span class = "org-font-latex-math" > < span class = "org-font-latex-script-char" > _< / span > < / span > < span class = "org-font-latex-math" > H$< / span > };
< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (WL.east) -- (outputl)node[above left]{< span class = "org-font-latex-math" > $z< / span > < span class = "org-font-latex-math" > < span class = "org-font-latex-script-char" > _< / span > < / span > < span class = "org-font-latex-math" > L$< / span > };
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< span class = "org-font-latex-sedate" > < span class = "org-keyword" > \end< / span > < / span > {< span class = "org-function-name" > tikzpicture< / span > }
< / pre >
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< div id = "org2a9bc75" class = "figure" >
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< p > < img src = "figs/sf_hinf_filters_b.png" alt = "sf_hinf_filters_b.png" / >
< / p >
< p > < span class = "figure-number" > Figure 7: < / span > H-Infinity - Complementary filters (< a href = "./figs/sf_hinf_filters_b.png" > png< / a > , < a href = "./figs/sf_hinf_filters_b.pdf" > pdf< / a > , < a href = "./figs/sf_hinf_filters_b.tex" > tex< / a > ).< / p >
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< div id = "outline-container-org408fe0c" class = "outline-2" >
< h2 id = "org408fe0c" > < span class = "section-number-2" > 9< / span > H-Infinity - 3 Complementary filters< / h2 >
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< div class = "outline-text-2" id = "text-9" >
< div class = "org-src-container" >
< pre class = "src src-latex" > < span class = "org-font-latex-sedate" > \tikzset< / span > {block/.default={0.8cm}{0.6cm}}
< span class = "org-font-latex-sedate" > \tikzset< / span > {addb/.append style={scale=0.7}}
< span class = "org-font-latex-sedate" > \tikzset< / span > {node distance=0.6}
< span class = "org-font-latex-sedate" > \def\cdist< / span > {0.7}
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< span class = "org-font-latex-sedate" > \definecolor< / span > {T}{rgb}{0.230, 0.299, 0.754}< span class = "org-comment" > %< / span >
< span class = "org-font-latex-sedate" > \definecolor< / span > {S}{rgb}{0.706, 0.016, 0.150}< span class = "org-comment" > %< / span >
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< span class = "org-font-latex-sedate" > \coordinate< / span > [] (outputv) at (< span class = "org-font-latex-math" > $(P.south east)!0.1!(P.north east) + ( < / span > < span class = "org-font-latex-sedate" > < span class = "org-font-latex-math" > \cdist< / span > < / span > < span class = "org-font-latex-math" > , 0)$< / span > );
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< / pre >
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< div id = "org2b18902" class = "figure" >
< p > < img src = "figs/comp_filter_three_hinf.png" alt = "comp_filter_three_hinf.png" / >
< / p >
< p > < span class = "figure-number" > Figure 8: < / span > H-Infinity - 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 >
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< div id = "outline-container-orgf18dc35" class = "outline-2" >
< h2 id = "orgf18dc35" > < span class = "section-number-2" > 10< / span > Input Multiplicative Uncertainty< / 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" > \tikzset< / span > {block/.default={0.8cm}{0.6cm}}
< span class = "org-font-latex-sedate" > \tikzset< / span > {addb/.append style={scale=0.7}}
< span class = "org-font-latex-sedate" > \tikzset< / span > {node distance=0.6}
< span class = "org-font-latex-sedate" > \def\cdist< / span > {0.7}
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< span class = "org-font-latex-sedate" > \definecolor< / span > {T}{rgb}{0.230, 0.299, 0.754}< span class = "org-comment" > %< / span >
< span class = "org-font-latex-sedate" > \definecolor< / span > {S}{rgb}{0.706, 0.016, 0.150}< span class = "org-comment" > %< / span >
< span class = "org-font-latex-sedate" > < span class = "org-keyword" > \begin< / span > < / span > {< span class = "org-function-name" > tikzpicture< / span > }
< span class = "org-comment" > % Blocs< / span >
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< span class = "org-comment" > % Connections and labels< / span >
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< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (wi.east) -- (deltai.west);
< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (deltai.east) -| (addi.north);
< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (addi.east) -- (G.west);
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< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (G.east) -- ++(0.6, 0);
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< 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 > [fit={(branch|-wi.north) (G.south east)}, inner sep=6pt, draw, dashed, fill=black!20!white] (Gp) {};
< span class = "org-font-latex-sedate" > \node< / span > [below left] at (Gp.north east) {< span class = "org-font-latex-math" > $G< / span > < span class = "org-font-latex-sedate" > < span class = "org-font-latex-math" > \prime< / 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" > scope< / span > }
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< span class = "org-font-latex-sedate" > < span class = "org-keyword" > \end< / span > < / span > {< span class = "org-function-name" > tikzpicture< / span > }
< / pre >
< / div >
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< div id = "orgb4b8084" class = "figure" >
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< p > < img src = "figs/input_uncertainty.png" alt = "input_uncertainty.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 9: < / span > Input Multiplicative Uncertainty (< a href = "./figs/input_uncertainty.png" > png< / a > , < a href = "./figs/input_uncertainty.pdf" > pdf< / a > , < a href = "./figs/input_uncertainty.tex" > tex< / a > ).< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org922fc19" class = "outline-2" >
< h2 id = "org922fc19" > < span class = "section-number-2" > 11< / span > One mass< / h2 >
< div class = "outline-text-2" id = "text-11" >
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< div class = "org-src-container" >
< pre class = "src src-latex" > < span class = "org-font-latex-sedate" > \tikzset< / span > {block/.default={0.8cm}{0.6cm}}
< span class = "org-font-latex-sedate" > \tikzset< / span > {addb/.append style={scale=0.7}}
< span class = "org-font-latex-sedate" > \tikzset< / span > {node distance=0.6}
< span class = "org-font-latex-sedate" > \def\cdist< / span > {0.7}
< span class = "org-font-latex-sedate" > \definecolor< / span > {T}{rgb}{0.230, 0.299, 0.754}< span class = "org-comment" > %< / span >
< span class = "org-font-latex-sedate" > \definecolor< / span > {S}{rgb}{0.706, 0.016, 0.150}< span class = "org-comment" > %< / span >
< span class = "org-font-latex-sedate" > < span class = "org-keyword" > \begin< / span > < / span > {< span class = "org-function-name" > tikzpicture< / span > }
< span class = "org-comment" > % ====================< / span >
< span class = "org-comment" > % Parameters< / span >
< span class = "org-comment" > % ====================< / span >
< span class = "org-font-latex-sedate" > \def\massw< / span > {2.2} < span class = "org-comment" > % Width of the masses< / span >
< span class = "org-font-latex-sedate" > \def\massh< / span > {0.8} < span class = "org-comment" > % Height of the masses< / span >
< span class = "org-font-latex-sedate" > \def\spaceh< / span > {1.2} < span class = "org-comment" > % Height of the springs/dampers< / span >
< span class = "org-font-latex-sedate" > \def\dispw< / span > {0.3} < span class = "org-comment" > % Width of the dashed line for the displacement< / span >
< span class = "org-font-latex-sedate" > \def\disph< / span > {0.5} < span class = "org-comment" > % Height of the arrow for the displacements< / span >
< span class = "org-font-latex-sedate" > \def\bracs< / span > {0.05} < span class = "org-comment" > % Brace spacing vertically< / span >
< span class = "org-font-latex-sedate" > \def\brach< / span > {-10pt} < span class = "org-comment" > % Brace shift horizontaly< / span >
< span class = "org-comment" > % ====================< / span >
< span class = "org-comment" > % ====================< / span >
< span class = "org-comment" > % Ground< / span >
< span class = "org-comment" > % ====================< / span >
< span class = "org-font-latex-sedate" > \draw< / span > (-0.5*< span class = "org-font-latex-sedate" > \massw< / span > , 0) -- (0.5*< span class = "org-font-latex-sedate" > \massw< / span > , 0);
< span class = "org-font-latex-sedate" > \draw< / span > [dashed] (0.5*< span class = "org-font-latex-sedate" > \massw< / span > , 0) -- ++(< span class = "org-font-latex-sedate" > \dispw< / span > , 0);
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< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (0.5*< span class = "org-font-latex-sedate" > \massw< / span > +0.5*< span class = "org-font-latex-sedate" > \dispw< / span > , 0) -- ++(0, < span class = "org-font-latex-sedate" > \disph< / span > ) node[right]{< span class = "org-font-latex-math" > $w$< / span > };
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< span class = "org-comment" > % ====================< / span >
< span class = "org-font-latex-sedate" > < span class = "org-keyword" > \begin< / span > < / span > {< span class = "org-function-name" > scope< / span > }[shift={(0, 0)}]
< span class = "org-comment" > % Mass< / span >
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< span class = "org-font-latex-sedate" > \draw< / span > [fill=white] (-0.5*< span class = "org-font-latex-sedate" > \massw< / span > , < span class = "org-font-latex-sedate" > \spaceh< / span > ) rectangle (0.5*< span class = "org-font-latex-sedate" > \massw< / span > , < span class = "org-font-latex-sedate" > \spaceh< / span > +< span class = "org-font-latex-sedate" > \massh< / span > ) node[pos=0.5]{< span class = "org-font-latex-math" > $m$< / span > };
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< span class = "org-comment" > % Spring, Damper, and Actuator< / span >
< span class = "org-font-latex-sedate" > \draw< / span > [spring] (-0.4*< span class = "org-font-latex-sedate" > \massw< / span > , 0) -- (-0.4*< span class = "org-font-latex-sedate" > \massw< / span > , < span class = "org-font-latex-sedate" > \spaceh< / span > ) node[midway, left=0.1]{< span class = "org-font-latex-math" > $k$< / span > };
< span class = "org-font-latex-sedate" > \draw< / span > [damper] (0, 0) -- ( 0, < span class = "org-font-latex-sedate" > \spaceh< / span > ) node[midway, left=0.2]{< span class = "org-font-latex-math" > $c$< / span > };
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< span class = "org-font-latex-sedate" > \draw< / span > [actuator] ( 0.4*< span class = "org-font-latex-sedate" > \massw< / span > , 0) -- ( 0.4*< span class = "org-font-latex-sedate" > \massw< / span > , < span class = "org-font-latex-sedate" > \spaceh< / span > ) node[midway, left=0.1](F){< span class = "org-font-latex-math" > $F$< / span > };
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< span class = "org-comment" > % Displacements< / span >
< span class = "org-font-latex-sedate" > \draw< / span > [dashed] (0.5*< span class = "org-font-latex-sedate" > \massw< / span > , < span class = "org-font-latex-sedate" > \spaceh< / span > ) -- ++(< span class = "org-font-latex-sedate" > \dispw< / span > , 0);
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< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (0.5*< span class = "org-font-latex-sedate" > \massw< / span > +0.5*< span class = "org-font-latex-sedate" > \dispw< / span > , < span class = "org-font-latex-sedate" > \spaceh< / span > ) -- ++(0, < span class = "org-font-latex-sedate" > \disph< / span > ) node[right]{< span class = "org-font-latex-math" > $x$< / span > };
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< span class = "org-comment" > % Legend< / span >
< span class = "org-comment" > % < / span > < span class = "org-font-latex-sedate" > < span class = "org-comment" > \draw< / span > < / span > < span class = "org-comment" > [decorate, decoration={brace, amplitude=8pt}, xshift=< / span > < span class = "org-font-latex-sedate" > < span class = "org-comment" > \brach< / span > < / span > < span class = "org-comment" > ] %< / span >
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< span class = "org-comment" > % (-0.5*< / span > < span class = "org-font-latex-sedate" > < span class = "org-comment" > \massw< / span > < / span > < span class = "org-comment" > , < / span > < span class = "org-font-latex-sedate" > < span class = "org-comment" > \bracs< / span > < / span > < span class = "org-comment" > ) -- (-0.5*< / span > < span class = "org-font-latex-sedate" > < span class = "org-comment" > \massw< / span > < / span > < span class = "org-comment" > , < / span > < span class = "org-font-latex-sedate" > < span class = "org-comment" > \spaceh< / span > < / span > < span class = "org-comment" > +< / span > < span class = "org-font-latex-sedate" > < span class = "org-comment" > \massh< / span > < / span > < span class = "org-comment" > -< / span > < span class = "org-font-latex-sedate" > < span class = "org-comment" > \bracs< / span > < / span > < span class = "org-comment" > ) %< / span >
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< span class = "org-comment" > % node[midway,rotate=90,anchor=south,yshift=10pt]{};< / span >
< 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 >
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< div id = "orgafce3e6" class = "figure" >
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< p > < img src = "figs/mech_sys_alone.png" alt = "mech_sys_alone.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 10: < / span > One mass (< a href = "./figs/mech_sys_alone.png" > png< / a > , < a href = "./figs/mech_sys_alone.pdf" > pdf< / a > , < a href = "./figs/mech_sys_alone.tex" > tex< / a > ).< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org10c0552" class = "outline-2" >
< h2 id = "org10c0552" > < span class = "section-number-2" > 12< / span > One mass - Control< / h2 >
< div class = "outline-text-2" id = "text-12" >
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< div class = "org-src-container" >
< pre class = "src src-latex" > < span class = "org-font-latex-sedate" > \tikzset< / span > {block/.default={0.8cm}{0.6cm}}
< span class = "org-font-latex-sedate" > \tikzset< / span > {addb/.append style={scale=0.7}}
< span class = "org-font-latex-sedate" > \tikzset< / span > {node distance=0.6}
< span class = "org-font-latex-sedate" > \def\cdist< / span > {0.7}
< span class = "org-font-latex-sedate" > \definecolor< / span > {T}{rgb}{0.230, 0.299, 0.754}< span class = "org-comment" > %< / span >
< span class = "org-font-latex-sedate" > \definecolor< / span > {S}{rgb}{0.706, 0.016, 0.150}< span class = "org-comment" > %< / span >
< span class = "org-font-latex-sedate" > < span class = "org-keyword" > \begin< / span > < / span > {< span class = "org-function-name" > tikzpicture< / span > }
< span class = "org-comment" > % ====================< / span >
< span class = "org-comment" > % Parameters< / span >
< span class = "org-comment" > % ====================< / span >
< span class = "org-font-latex-sedate" > \def\massw< / span > {2.2} < span class = "org-comment" > % Width of the masses< / span >
< span class = "org-font-latex-sedate" > \def\massh< / span > {0.8} < span class = "org-comment" > % Height of the masses< / span >
< span class = "org-font-latex-sedate" > \def\spaceh< / span > {1.2} < span class = "org-comment" > % Height of the springs/dampers< / span >
< span class = "org-font-latex-sedate" > \def\dispw< / span > {0.3} < span class = "org-comment" > % Width of the dashed line for the displacement< / span >
< span class = "org-font-latex-sedate" > \def\disph< / span > {0.5} < span class = "org-comment" > % Height of the arrow for the displacements< / span >
< span class = "org-font-latex-sedate" > \def\bracs< / span > {0.05} < span class = "org-comment" > % Brace spacing vertically< / span >
< span class = "org-font-latex-sedate" > \def\brach< / span > {-10pt} < span class = "org-comment" > % Brace shift horizontaly< / span >
< span class = "org-comment" > % ====================< / span >
< span class = "org-comment" > % ====================< / span >
< span class = "org-comment" > % Ground< / span >
< span class = "org-comment" > % ====================< / span >
< span class = "org-font-latex-sedate" > \draw< / span > (-0.5*< span class = "org-font-latex-sedate" > \massw< / span > , 0) -- (0.5*< span class = "org-font-latex-sedate" > \massw< / span > , 0);
< span class = "org-font-latex-sedate" > \draw< / span > [dashed] (0.5*< span class = "org-font-latex-sedate" > \massw< / span > , 0) -- ++(< span class = "org-font-latex-sedate" > \dispw< / span > , 0);
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< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (0.5*< span class = "org-font-latex-sedate" > \massw< / span > +0.5*< span class = "org-font-latex-sedate" > \dispw< / span > , 0) -- ++(0, < span class = "org-font-latex-sedate" > \disph< / span > ) node[below right]{< span class = "org-font-latex-math" > $w$< / span > };
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< span class = "org-comment" > % ====================< / span >
< span class = "org-font-latex-sedate" > < span class = "org-keyword" > \begin< / span > < / span > {< span class = "org-function-name" > scope< / span > }[shift={(0, 0)}]
< span class = "org-comment" > % Mass< / span >
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< span class = "org-font-latex-sedate" > \draw< / span > [fill=white] (-0.5*< span class = "org-font-latex-sedate" > \massw< / span > , < span class = "org-font-latex-sedate" > \spaceh< / span > ) rectangle (0.5*< span class = "org-font-latex-sedate" > \massw< / span > , < span class = "org-font-latex-sedate" > \spaceh< / span > +< span class = "org-font-latex-sedate" > \massh< / span > ) node[pos=0.5]{< span class = "org-font-latex-math" > $m$< / span > };
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< span class = "org-comment" > % Spring, Damper, and Actuator< / span >
< span class = "org-font-latex-sedate" > \draw< / span > [spring] (-0.4*< span class = "org-font-latex-sedate" > \massw< / span > , 0) -- (-0.4*< span class = "org-font-latex-sedate" > \massw< / span > , < span class = "org-font-latex-sedate" > \spaceh< / span > ) node[midway, left=0.1]{< span class = "org-font-latex-math" > $k$< / span > };
< span class = "org-font-latex-sedate" > \draw< / span > [damper] (0, 0) -- ( 0, < span class = "org-font-latex-sedate" > \spaceh< / span > ) node[midway, left=0.2]{< span class = "org-font-latex-math" > $c$< / span > };
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< span class = "org-font-latex-sedate" > \draw< / span > [actuator] ( 0.4*< span class = "org-font-latex-sedate" > \massw< / span > , 0) -- ( 0.4*< span class = "org-font-latex-sedate" > \massw< / span > , < span class = "org-font-latex-sedate" > \spaceh< / span > ) coordinate[midway, right=0.15](F);
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< span class = "org-comment" > % Displacements< / span >
< span class = "org-font-latex-sedate" > \draw< / span > [dashed] (0.5*< span class = "org-font-latex-sedate" > \massw< / span > , < span class = "org-font-latex-sedate" > \spaceh< / span > ) -- ++(< span class = "org-font-latex-sedate" > \dispw< / span > , 0);
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< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (0.5*< span class = "org-font-latex-sedate" > \massw< / span > +0.5*< span class = "org-font-latex-sedate" > \dispw< / span > , < span class = "org-font-latex-sedate" > \spaceh< / span > ) -- ++(0, < span class = "org-font-latex-sedate" > \disph< / span > ) node[right](x){< span class = "org-font-latex-math" > $x$< / span > };
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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" > \node< / span > [block, right=1 of F] (Kfb) {< span class = "org-font-latex-math" > $K$< / span > };
< span class = "org-font-latex-sedate" > \node< / span > [addb={+}{}{-}{}{}, right=2*< span class = "org-font-latex-sedate" > \cdist< / span > of Kfb] (add) {};
< span class = "org-font-latex-sedate" > \node< / span > [addb] (addn) at (x-|Kfb) {};
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< span class = "org-font-latex-sedate" > \node< / span > [block, right=of addn] (Hl) {< span class = "org-font-latex-math" > $H< / span > < span class = "org-font-latex-math" > < span class = "org-font-latex-script-char" > _< / span > < / span > < span class = "org-font-latex-math" > L$< / span > };
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< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (x) -- (addn.west);
< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (addn.east) -- (Hl.west);
< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (Hl.east) -| (add.north);
< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (add.west) -- (Kfb.east);
< span class = "org-font-latex-sedate" > \draw< / span > [-> ] (Kfb.west) -- (F) node[above right]{< span class = "org-font-latex-math" > $F$< / span > };
< span class = "org-font-latex-sedate" > \draw< / span > [< -] (addn.north) -- ++(0,< span class = "org-font-latex-sedate" > \cdist< / span > ) node[below right]{< span class = "org-font-latex-math" > $n$< / span > };
< span class = "org-font-latex-sedate" > \draw< / span > [< -] (add.east) -- ++(< span class = "org-font-latex-sedate" > \cdist< / span > ,0) node[above left]{< span class = "org-font-latex-math" > $r$< / span > };
< span class = "org-font-latex-sedate" > < span class = "org-keyword" > \end< / span > < / span > {< span class = "org-function-name" > tikzpicture< / span > }
< / pre >
< / div >
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< div id = "orgfbc8e17" class = "figure" >
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< p > < img src = "figs/mech_sys_alone_ctrl.png" alt = "mech_sys_alone_ctrl.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 11: < / span > One mass - Control (< a href = "./figs/mech_sys_alone_ctrl.png" > png< / a > , < a href = "./figs/mech_sys_alone_ctrl.pdf" > pdf< / a > , < a href = "./figs/mech_sys_alone_ctrl.tex" > tex< / a > ).< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org9d5c45c" class = "outline-2" >
< h2 id = "org9d5c45c" > < span class = "section-number-2" > 13< / span > Piezoelectric Actuator< / h2 >
< div class = "outline-text-2" id = "text-13" >
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< div class = "org-src-container" >
< pre class = "src src-latex" > < span class = "org-font-latex-sedate" > \tikzset< / span > {block/.default={0.8cm}{0.6cm}}
< span class = "org-font-latex-sedate" > \tikzset< / span > {addb/.append style={scale=0.7}}
< span class = "org-font-latex-sedate" > \tikzset< / span > {node distance=0.6}
< span class = "org-font-latex-sedate" > \def\cdist< / span > {0.7}
< span class = "org-font-latex-sedate" > \definecolor< / span > {T}{rgb}{0.230, 0.299, 0.754}< span class = "org-comment" > %< / span >
< span class = "org-font-latex-sedate" > \definecolor< / span > {S}{rgb}{0.706, 0.016, 0.150}< span class = "org-comment" > %< / 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" > \node< / span > [piezo={2}{3}{10}] (piezo) at (0, 0){};
< span class = "org-font-latex-sedate" > \node< / span > [draw, fill=white, anchor=south, minimum width=3cm, minimum height=1.5cm] (mass) at (< span class = "org-font-latex-math" > $(piezo.north)+(0, 0.5)$< / span > ) {Mass};
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< / p >
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< p > < span class = "figure-number" > Figure 12: < / span > Piezoelectric Actuator (< a href = "./figs/1dof_isolation_piezo.png" > png< / a > , < a href = "./figs/1dof_isolation_piezo.pdf" > pdf< / a > , < a href = "./figs/1dof_isolation_piezo.tex" > tex< / a > ).< / p >
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< / div >
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< div id = "orgbfa9c4e" class = "figure" >
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< p > < img src = "figs/spec_S_T.png" alt = "spec_S_T.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 13: < / span > Upper bounds (< a href = "./figs/spec_S_T.png" > png< / a > , < a href = "./figs/spec_S_T.pdf" > pdf< / a > , < a href = "./figs/spec_S_T.tex" > tex< / a > ).< / p >
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< / div >
< / div >
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< div id = "outline-container-org6a90bb1" class = "outline-2" >
< h2 id = "org6a90bb1" > < span class = "section-number-2" > 15< / span > Bode plot of the mechanical system< / h2 >
< div class = "outline-text-2" id = "text-15" >
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< div id = "orge128c4f" class = "figure" >
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< p > < img src = "figs/bode_plot_mech_sys.png" alt = "bode_plot_mech_sys.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 14: < / span > Bode plot of the mechanical system (< a href = "./figs/bode_plot_mech_sys.png" > png< / a > , < a href = "./figs/bode_plot_mech_sys.pdf" > pdf< / a > , < a href = "./figs/bode_plot_mech_sys.tex" > tex< / a > ).< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org16e0cef" class = "outline-2" >
< h2 id = "org16e0cef" > < span class = "section-number-2" > 16< / span > Bode plot of the mechanical system - Uncertainty< / h2 >
< div class = "outline-text-2" id = "text-16" >
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< div id = "org2632bf6" class = "figure" >
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< p > < img src = "figs/bode_plot_mech_sys_uncertainty.png" alt = "bode_plot_mech_sys_uncertainty.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 15: < / span > Bode plot of the mechanical system - Uncertainty (< a href = "./figs/bode_plot_mech_sys_uncertainty.png" > png< / a > , < a href = "./figs/bode_plot_mech_sys_uncertainty.pdf" > pdf< / a > , < a href = "./figs/bode_plot_mech_sys_uncertainty.tex" > tex< / a > ).< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-orgb234097" class = "outline-2" >
< h2 id = "orgb234097" > < span class = "section-number-2" > 17< / span > Bode plot of the controller< / h2 >
< div class = "outline-text-2" id = "text-17" >
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< div id = "org5e72d6c" class = "figure" >
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< p > < img src = "figs/bode_Kfb.png" alt = "bode_Kfb.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 16: < / span > Bode plot of the controller (< a href = "./figs/bode_Kfb.png" > png< / a > , < a href = "./figs/bode_Kfb.pdf" > pdf< / a > , < a href = "./figs/bode_Kfb.tex" > tex< / a > ).< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org6fb49a0" class = "outline-2" >
< h2 id = "org6fb49a0" > < span class = "section-number-2" > 18< / span > Bode plot of the loop gain< / h2 >
< div class = "outline-text-2" id = "text-18" >
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< div id = "org1e1e8b1" class = "figure" >
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< p > < img src = "figs/bode_plot_loop_gain.png" alt = "bode_plot_loop_gain.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 17: < / span > Bode plot of the loop gain (< a href = "./figs/bode_plot_loop_gain.png" > png< / a > , < a href = "./figs/bode_plot_loop_gain.pdf" > pdf< / a > , < a href = "./figs/bode_plot_loop_gain.tex" > tex< / a > ).< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org6dc8522" class = "outline-2" >
< h2 id = "org6dc8522" > < span class = "section-number-2" > 19< / span > Upper bounds with weights< / h2 >
< div class = "outline-text-2" id = "text-19" >
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< div id = "orgfc5d0ac" class = "figure" >
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< p > < img src = "figs/spec_S_T_weights.png" alt = "spec_S_T_weights.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 18: < / span > Upper bounds with weights (< a href = "./figs/spec_S_T_weights.png" > png< / a > , < a href = "./figs/spec_S_T_weights.pdf" > pdf< / a > , < a href = "./figs/spec_S_T_weights.tex" > tex< / a > ).< / p >
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< / div >
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< div id = "outline-container-org3f273a2" class = "outline-2" >
< h2 id = "org3f273a2" > < span class = "section-number-2" > 20< / span > Upper bounds with Complementary Filters< / h2 >
< div class = "outline-text-2" id = "text-20" >
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< div id = "orgddcf95e" class = "figure" >
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< p > < img src = "figs/hinf_filters_result_tikz.png" alt = "hinf_filters_result_tikz.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 19: < / span > Upper bounds with Complementary Filters (< a href = "./figs/hinf_filters_result_tikz.png" > png< / a > , < a href = "./figs/hinf_filters_result_tikz.pdf" > pdf< / a > , < a href = "./figs/hinf_filters_result_tikz.tex" > tex< / a > ).< / p >
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< / div >
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< div id = "outline-container-org666f416" class = "outline-2" >
< h2 id = "org666f416" > < span class = "section-number-2" > 21< / span > Upper bounds with weights and Complementary Filters< / h2 >
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< p > < span class = "figure-number" > Figure 20: < / span > Upper bounds with weights and Complementary Filters (< a href = "./figs/hinf_filters_result_weights.png" > png< / a > , < a href = "./figs/hinf_filters_result_weights.pdf" > pdf< / a > , < a href = "./figs/hinf_filters_result_weights.tex" > tex< / a > ).< / p >
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< h2 id = "org4296f42" > < span class = "section-number-2" > 22< / span > Robustness - Nyquist< / h2 >
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< p > < img src = "figs/nyquist_robustness.png" alt = "nyquist_robustness.png" / >
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< p > < span class = "figure-number" > Figure 21: < / span > Robustness - Nyquist (< a href = "./figs/nyquist_robustness.png" > png< / a > , < a href = "./figs/nyquist_robustness.pdf" > pdf< / a > , < a href = "./figs/nyquist_robustness.tex" > tex< / a > ).< / p >
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< h2 id = "org07ffae0" > < span class = "section-number-2" > 23< / span > Robustness - Loop Gain< / h2 >
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< p > < span class = "figure-number" > Figure 22: < / span > Robustness - Loop Gain (< a href = "./figs/sf_arch.png" > png< / a > , < a href = "./figs/sf_arch.pdf" > pdf< / a > , < a href = "./figs/sf_arch.tex" > tex< / a > ).< / p >
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< h2 id = "org7dc679b" > < span class = "section-number-2" > 24< / span > Robust performance< / h2 >
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< p > < span class = "figure-number" > Figure 23: < / span > Robust performance (< a href = "./figs/robust_perf.png" > png< / a > , < a href = "./figs/robust_perf.pdf" > pdf< / a > , < a href = "./figs/robust_perf.tex" > tex< / a > ).< / p >
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< p class = "author" > Author: Thomas Dehaeze< / p >
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< p class = "date" > Created: 2020-11-12 jeu. 10:43< / p >
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