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Continue analysis about mixed H2/Hinf synthesis

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Thomas Dehaeze 2019-08-30 14:39:01 +02:00
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@ -104,42 +104,6 @@ Configuration file is accessible [[file:config.org][here]].
#+RESULTS:
[[file:figs/sf_hinf_filters_b.png]]
* H-Infinity - Optimal Complementary Filters
#+begin_src latex :file h_infinity_optimal_comp_filters.pdf :tangle figs/h_infinity_optimal_comp_filters.tex
<<tikz_default>>
\begin{tikzpicture}
\node[block={5.0cm}{3.0cm}, fill=black!20!white, dashed] (P) {};
\node[above] at (P.north) {$P$};
\coordinate[] (inputn1) at ($(P.south west)!0.8!(P.north west) + (-\cdist, 0)$);
\coordinate[] (inputn2) at ($(P.south west)!0.5!(P.north west) + (-\cdist, 0)$);
\coordinate[] (inputu) at ($(P.south west)!0.2!(P.north west) + (-\cdist, 0)$);
\coordinate[] (outputx) at ($(P.south east)!0.5!(P.north east) + ( \cdist, 0)$);
\coordinate[] (outputv) at ($(P.south east)!0.1!(P.north east) + ( \cdist, 0)$);
\node[block, right=1.5 of inputn1] (N1){$N_1$};
\node[block, right=1.5 of inputn2] (N2){$N_2$};
\node[addb={+}{}{}{}{-}, right=of N1] (sub) {};
\node[addb, right=2 of N2] (add) {};
\node[block, below=of P] (H1) {$H_1$};
\draw[->] (inputn1)node[above right]{$\tilde{n}_1$} -- (N1.west);
\draw[->] (inputn2)node[above right]{$\tilde{n}_2$} -- (N2.west);
\draw[->] (N1) -- (sub.west);
\draw[->] (N2) -| (sub.south);
\draw[->] (N2-|sub.south) node[branch]{} -- (add.west);
\draw[->] (sub.east) -- ++(0.5, 0) |- ($(outputv) + (-0.3, 0)$) |- (H1.east);
\draw[->] (H1.west) -| ($(inputu) + (0.3, 0)$) -| (add.south);
\draw[->] (add.east) -- (outputx) node[above left]{$\hat{x}$};
\end{tikzpicture}
#+end_src
#+name: fig:h_infinity_optimal_comp_filters
#+caption: H-Infinity - Optimal Complementary Filters ([[./figs/h_infinity_optimal_comp_filters.png][png]], [[./figs/h_infinity_optimal_comp_filters.pdf][pdf]], [[./figs/h_infinity_optimal_comp_filters.tex][tex]]).
#+RESULTS:
[[file:figs/h_infinity_optimal_comp_filters.png]]
* Generate Complementary Filters using Feedback Control Architecture
#+begin_src latex :file complementary_filters_feedback_architecture.pdf :tangle figs/complementary_filters_feedback_architecture.tex :exports both
\begin{tikzpicture}
@ -162,7 +126,7 @@ Configuration file is accessible [[file:config.org][here]].
[[file:figs/complementary_filters_feedback_architecture.png]]
* H-Infinity Synthesis for Robust Sensor Fusion
#+begin_src latex :file h_infinity_robust_fusion.pdf :tangle figs/h_infinity_robust_fusion.tex :exports both
#+begin_src latex :file h_infinity_robust_fusion_old.pdf :tangle figs/h_infinity_robust_fusion_old.tex :exports both
<<tikz_default>>
\begin{tikzpicture}
\node[block={4.0cm}{3.0cm}, dashed] (P) {};
@ -191,10 +155,11 @@ Configuration file is accessible [[file:config.org][here]].
\end{tikzpicture}
#+end_src
#+name: fig:h_infinity_robust_fusion
#+caption: H-Infinity Synthesis for Robust Sensor Fusion ([[./figs/h_infinity_robust_fusion.png][png]], [[./figs/h_infinity_robust_fusion.pdf][pdf]], [[./figs/h_infinity_robust_fusion.tex][tex]]).
#+name: fig:h_infinity_robust_fusion_old
#+caption: H-Infinity Synthesis for Robust Sensor Fusion ([[./figs/h_infinity_robust_fusion_old.png][png]], [[./figs/h_infinity_robust_fusion_old.pdf][pdf]], [[./figs/h_infinity_robust_fusion_old.tex][tex]]).
#+RESULTS:
[[file:figs/h_infinity_robust_fusion.png]]
[[file:figs/h_infinity_robust_fusion_old.png]]
* Fusion of two noisy sensors
#+begin_src latex :file fusion_two_noisy_sensors.pdf :tangle figs/fusion_two_noisy_sensors.tex
<<tikz_default>>
@ -761,3 +726,107 @@ Configuration file is accessible [[file:config.org][here]].
#+caption: Fusion of two noisy sensors_with_dyn ([[./figs/fusion_gain_mismatch.png][png]], [[./figs/fusion_gain_mismatch.pdf][pdf]], [[./figs/fusion_gain_mismatch.tex][tex]]).
#+RESULTS:
[[file:figs/fusion_gain_mismatch.png]]
* Architecture used for $\mathcal{H}_\infty$ synthesis of complementary filters
#+begin_src latex :file h_infinity_robust_fusion.pdf :tangle figs/h_infinity_robust_fusion.tex :exports both
<<tikz_default>>
\begin{tikzpicture}
\node[block={4.0cm}{2.5cm}, fill=black!20!white, dashed] (P) {};
\node[above] at (P.north) {$P(s)$};
\coordinate[] (inputw) at ($(P.south west)!0.75!(P.north west) + (-0.7, 0)$);
\coordinate[] (inputu) at ($(P.south west)!0.35!(P.north west) + (-0.7, 0)$);
\coordinate[] (output1) at ($(P.south east)!0.75!(P.north east) + ( 0.7, 0)$);
\coordinate[] (output2) at ($(P.south east)!0.35!(P.north east) + ( 0.7, 0)$);
\coordinate[] (outputv) at ($(P.south east)!0.1!(P.north east) + ( 0.7, 0)$);
\node[block, left=1.4 of output1] (W1){$W_1(s)$};
\node[block, left=1.4 of output2] (W2){$W_2(s)$};
\node[addb={+}{}{}{}{-}, left=of W1] (sub) {};
\node[block, below=0.3 of P] (H2) {$H_2(s)$};
\draw[->] (inputw) node[above right]{$w$} -- (sub.west);
\draw[->] (H2.west) -| ($(inputu)+(0.35, 0)$) node[above]{$u$} -- (W2.west);
\draw[->] (inputu-|sub) node[branch]{} -- (sub.south);
\draw[->] (sub.east) -- (W1.west);
\draw[->] ($(sub.west)+(-0.6, 0)$) node[branch]{} |- ($(outputv)+(-0.35, 0)$) node[above]{$v$} |- (H2.east);
\draw[->] (W1.east) -- (output1)node[above left]{$z_1$};
\draw[->] (W2.east) -- (output2)node[above left]{$z_2$};
\end{tikzpicture}
#+end_src
#+name: fig:h_infinity_robust_fusion
#+caption: Architecture used for $\mathcal{H}_\infty$ synthesis of complementary filters ([[./figs/h_infinity_robust_fusion.png][png]], [[./figs/h_infinity_robust_fusion.pdf][pdf]], [[./figs/h_infinity_robust_fusion.tex][tex]]).
#+RESULTS:
[[file:figs/h_infinity_robust_fusion.png]]
* H-Infinity - Optimal Complementary Filters
#+begin_src latex :file h_infinity_optimal_comp_filters.pdf :tangle figs/h_infinity_optimal_comp_filters.tex
<<tikz_default>>
\begin{tikzpicture}
\node[block={5.0cm}{3.0cm}, fill=black!20!white, dashed] (P) {};
\node[above] at (P.north) {$P$};
\coordinate[] (inputn1) at ($(P.south west)!0.8!(P.north west) + (-\cdist, 0)$);
\coordinate[] (inputn2) at ($(P.south west)!0.5!(P.north west) + (-\cdist, 0)$);
\coordinate[] (inputu) at ($(P.south west)!0.2!(P.north west) + (-\cdist, 0)$);
\coordinate[] (outputx) at ($(P.south east)!0.5!(P.north east) + ( \cdist, 0)$);
\coordinate[] (outputv) at ($(P.south east)!0.1!(P.north east) + ( \cdist, 0)$);
\node[block, right=1.5 of inputn1] (N1){$N_1$};
\node[block, right=1.5 of inputn2] (N2){$N_2$};
\node[addb={+}{}{}{}{-}, right=of N1] (sub) {};
\node[addb, right=2 of N2] (add) {};
\node[block, below=of P] (H1) {$H_1$};
\draw[->] (inputn1)node[above right]{$\tilde{n}_1$} -- (N1.west);
\draw[->] (inputn2)node[above right]{$\tilde{n}_2$} -- (N2.west);
\draw[->] (N1) -- (sub.west);
\draw[->] (N2) -| (sub.south);
\draw[->] (N2-|sub.south) node[branch]{} -- (add.west);
\draw[->] (sub.east) -- ++(0.5, 0) |- ($(outputv) + (-0.3, 0)$) |- (H1.east);
\draw[->] (H1.west) -| ($(inputu) + (0.3, 0)$) -| (add.south);
\draw[->] (add.east) -- (outputx) node[above left]{$\hat{x}$};
\end{tikzpicture}
#+end_src
#+name: fig:h_infinity_optimal_comp_filters
#+caption: H-Infinity - Optimal Complementary Filters ([[./figs/h_infinity_optimal_comp_filters.png][png]], [[./figs/h_infinity_optimal_comp_filters.pdf][pdf]], [[./figs/h_infinity_optimal_comp_filters.tex][tex]]).
#+RESULTS:
[[file:figs/h_infinity_optimal_comp_filters.png]]
* H-Infinity - Optimal Complementary Filters - Alternative
#+begin_src latex :file h_infinity_optimal_comp_filters_bis.pdf :tangle figs/h_infinity_optimal_comp_filters_bis.tex :exports both
<<tikz_default>>
\begin{tikzpicture}
\node[block={4.0cm}{2.5cm}, fill=black!20!white, dashed] (P) {};
\node[above] at (P.north) {$P(s)$};
\coordinate[] (inputw) at ($(P.south west)!0.75!(P.north west) + (-0.7, 0)$);
\coordinate[] (inputu) at ($(P.south west)!0.35!(P.north west) + (-0.7, 0)$);
\coordinate[] (output1) at ($(P.south east)!0.75!(P.north east) + ( 0.7, 0)$);
\coordinate[] (output2) at ($(P.south east)!0.35!(P.north east) + ( 0.7, 0)$);
\coordinate[] (outputv) at ($(P.south east)!0.1!(P.north east) + ( 0.7, 0)$);
\node[block, left=1.4 of output1] (N1){$N_1(s)$};
\node[block, left=1.4 of output2] (N2){$N_2(s)$};
\node[addb={+}{}{}{}{-}, left=of N1] (sub) {};
\node[block, below=0.3 of P] (H2) {$H_2(s)$};
\draw[->] (inputw) node[above right]{$w$} -- (sub.west);
\draw[->] (H2.west) -| ($(inputu)+(0.35, 0)$) node[above]{$u$} -- (N2.west);
\draw[->] (inputu-|sub) node[branch]{} -- (sub.south);
\draw[->] (sub.east) -- (N1.west);
\draw[->] ($(sub.west)+(-0.6, 0)$) node[branch]{} |- ($(outputv)+(-0.35, 0)$) node[above]{$v$} |- (H2.east);
\draw[->] (N1.east) -- (output1)node[above left]{$z_1$};
\draw[->] (N2.east) -- (output2)node[above left]{$z_2$};
\end{tikzpicture}
#+end_src
#+name: fig:h_infinity_optimal_comp_filters_bis
#+caption: Architecture used for $\mathcal{H}_\infty$ synthesis of complementary filters ([[./figs/h_infinity_optimal_comp_filters_bis.png][png]], [[./figs/h_infinity_optimal_comp_filters_bis.pdf][pdf]], [[./figs/h_infinity_optimal_comp_filters_bis.tex][tex]]).
#+RESULTS:
[[file:figs/h_infinity_optimal_comp_filters_bis.png]]