12019 lines
508 KiB
Org Mode
12019 lines
508 KiB
Org Mode
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#+TITLE: Sensor Fusion Paper - Tikz Figures
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* Sensor Fusion with complementary filters
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#+begin_src latex :file sf_arch.pdf :tangle figs/sf_arch.tex :exports both
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<<tikz_default>>
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\begin{tikzpicture}
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\node[addb={+}{}{}{}{-}] (addfb) at (0, 0){};
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\node[block, right=of addfb] (K){$k$};
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\node[block, right=1.2 of K] (G){$G^\prime$};
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\node[addb={+}{}{}{}{}, right=of G] (adddy){};
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\coordinate[] (KG) at ($0.5*(K.east)+0.5*(G.west)$);
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\node[block, below=of KG] (Gm){$G$};
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\node[block, below=of Gm] (Hh){$H_H$};
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\node[addb={+}{}{}{}{}, below=of Hh] (addsf){};
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\node[block] (Hl) at (addsf-|G) {$H_L$};
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\node[addb={+}{}{}{}{}, right=1.2 of Hl] (addn) {};
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\draw[->] (addfb.east) -- (K.west) node[above left]{};
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\draw[->] (K.east) -- (G.west) node[above left]{$u$};
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\draw[->] (KG) node[branch]{} -- (Gm.north);
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\draw[->] (Gm.south) -- (Hh.north);
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\draw[->] (Hh.south) -- (addsf.north) node[above left]{};
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\draw[->] (Hl.west) -- (addsf.east);
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\draw[->] (addsf.west) -| (addfb.south) node[below right]{};
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\draw[->] (G.east) -- (adddy.west);
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\draw[<-] (addn.east) -- ++(\cdist, 0) coordinate[](endpos) node[above left]{$n$};
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\draw[->] (adddy.east) -- (G-|endpos) node[above left]{$y$};
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\draw[->] (adddy-|addn) node[branch]{} -- (addn.north);
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\draw[<-] (addfb.west) -- ++(-\cdist, 0) node[above right]{$r$};
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\draw[->] (addn.west) -- (Hl.east) node[above right]{$y_m$};
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\draw[<-] (adddy.north) -- ++(0, \cdist) node[below right]{$d_y$};
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\end{tikzpicture}
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||
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#+end_src
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||
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#+name: fig:sf_arch
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#+caption: Sensor Fusion with complementary filters ([[./figs/sf_arch.png][png]], [[./figs/sf_arch.pdf][pdf]], [[./figs/sf_arch.tex][tex]]).
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||
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#+RESULTS:
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||
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[[file:figs/sf_arch.png]]
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* Equivalent configuration
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||
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#+begin_src latex :file sf_arch_eq.pdf :tangle figs/sf_arch_eq.tex
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<<tikz_default>>
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\begin{tikzpicture}
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\node[addb={+}{}{}{}{-}] (addfb) at (0, 0){};
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\node[addb={+}{}{}{}{-}, right=of addfb] (addK){};
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\node[block, right=of addK] (K){$k$};
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\node[block, right=1.8 of K] (G){$G^\prime$};
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\node[addb={+}{}{}{}{}, right=of G] (adddy){};
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||
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\node[block, below right=0.5 and -0.2 of K] (Gm){$G$};
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||
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\node[block, below left =0.5 and -0.2 of K] (Hh){$H_H$};
|
||
|
\node[block, below=1.5 of G] (Hl) {$H_L$};
|
||
|
\node[addb={+}{}{}{}{}, right=1 of Hl] (addn) {};
|
||
|
|
||
|
\draw[->] (addfb.east) -- (addK.west);
|
||
|
\draw[->] (addK.east) -- (K.west);
|
||
|
\draw[->] (K.east) -- (G.west) node[above left]{$u$};
|
||
|
\draw[->] (G.east) -- (adddy.west);
|
||
|
\draw[->] ($(G.west)+(-0.8, 0)$) node[branch](sffb){} |- (Gm.east);
|
||
|
\draw[->] (Gm.west) -- (Hh.east);
|
||
|
\draw[->] (Hh.west) -| (addK.south);
|
||
|
\draw[<-] (addn.east) -- ++(\cdist, 0) coordinate[](endpos) node[above left]{$n$};
|
||
|
\draw[->] (adddy.east) -- (G-|endpos) node[above left]{$y$};
|
||
|
\draw[->] (adddy-|addn) node[branch]{} -- (addn.north);
|
||
|
\draw[<-] (addfb.west) -- ++(-\cdist, 0) node[above right]{$r$};
|
||
|
\draw[->] (addn.west) -- (Hl.east) node[above right]{$y_m$};
|
||
|
\draw[<-] (adddy.north) -- ++(0, \cdist) node[below right]{$d_y$};
|
||
|
\draw[->] (Hl.west) -| (addfb.south) node[below right]{};
|
||
|
|
||
|
\begin{scope}[on background layer]
|
||
|
\node[fit={($(addK.west|-Hh.south)+(-0.1, 0)$) (K.north-|sffb)}, inner sep=5pt, draw, fill=black!20!white, dashed, label={$K$}] (Kfb) {};
|
||
|
\end{scope}
|
||
|
\end{tikzpicture}
|
||
|
#+end_src
|
||
|
|
||
|
#+name: fig:sf_arch_eq
|
||
|
#+caption: Equivalent configuration ([[./figs/sf_arch_eq.png][png]], [[./figs/sf_arch_eq.pdf][pdf]], [[./figs/sf_arch_eq.tex][tex]]).
|
||
|
#+RESULTS:
|
||
|
[[file:figs/sf_arch_eq.png]]
|
||
|
|
||
|
* Equivalent configuration - classical Feedback
|
||
|
#+begin_src latex :file sf_arch_class.pdf :tangle figs/sf_arch_class.tex
|
||
|
<<tikz_default>>
|
||
|
\begin{tikzpicture}
|
||
|
\node[addb={+}{}{}{}{-}] (addfb) at (0, 0){};
|
||
|
\node[block, right=of addfb] (K){$K$};
|
||
|
\node[block, right=of K] (G){$G^\prime$};
|
||
|
\node[addb={+}{}{}{}{}, right=of G] (adddy){};
|
||
|
\node[addb={+}{}{}{}{}, below right=and 0.5 of adddy] (addn) {};
|
||
|
\node[block] (Hh) at (G|-addn) {$H_L$};
|
||
|
|
||
|
\draw[->] (addfb.east) -- (K.west) node[above left]{};
|
||
|
\draw[->] (K.east) -- (G.west) node[above left]{$u$};
|
||
|
\draw[->] (G.east) -- (adddy.west);
|
||
|
\draw[<-] (addn.east) -- ++(\cdist, 0) coordinate[](endpos) node[above left]{$n$};
|
||
|
\draw[->] (G-|addn)node[branch]{} -- (addn.north);
|
||
|
\draw[->] (adddy.east) -- (G-|endpos) node[above left]{$y$};
|
||
|
\draw[<-] (addfb.west) -- ++(-\cdist, 0) node[above right]{$r$};
|
||
|
\draw[->] (addn.west) -- (Hh.east);
|
||
|
\draw[->] (Hh.west) -| (addfb.south);
|
||
|
\draw[<-] (adddy.north) -- ++(0, \cdist) node[below right]{$d_y$};
|
||
|
\end{tikzpicture}
|
||
|
#+end_src
|
||
|
|
||
|
#+RESULTS:
|
||
|
#+name: fig:sf_arch_class
|
||
|
#+caption: Equivalent configuration - classical Feedback ([[./figs/sf_arch_class.png][png]], [[./figs/sf_arch_class.pdf][pdf]], [[./figs/sf_arch_class.tex][tex]]).
|
||
|
[[file:figs/sf_arch_class.png]]
|
||
|
|
||
|
* Equivalent configuration - classical Feedback with pre-filter
|
||
|
#+begin_src latex :file sf_arch_class_prefilter.pdf :tangle figs/sf_arch_class_prefilter.tex
|
||
|
<<tikz_default>>
|
||
|
\begin{tikzpicture}
|
||
|
\node[addb={+}{}{}{}{-}] (addfb) at (0, 0){};
|
||
|
\node[block, left=of addfb] (Kr){$K_r$};
|
||
|
\node[block, right=of addfb] (K){$K$};
|
||
|
\node[block, right=of K] (G){$G^\prime$};
|
||
|
\node[addb={+}{}{}{}{}, right=of G] (adddy){};
|
||
|
\node[addb={+}{}{}{}{}, below right=0.7 and 0.3 of adddy] (addn) {};
|
||
|
\node[block, left=of addn] (Hh) {$H_H$};
|
||
|
|
||
|
\draw[->] (addfb.east) -- (K.west) node[above left]{};
|
||
|
\draw[->] (K.east) -- (G.west) node[above left]{$u$};
|
||
|
\draw[->] (G.east) -- (adddy.west);
|
||
|
\draw[<-] (addn.east) -- ++(\cdist, 0) coordinate[](endpos) node[above left]{$n$};
|
||
|
\draw[->] (G-|addn)node[branch]{} -- (addn.north);
|
||
|
\draw[->] (adddy.east) -- (G-|endpos) node[above left]{$y$};
|
||
|
\draw[<-] (Kr.west) -- ++(-\cdist, 0) node[above right]{$r$};
|
||
|
\draw[->] (Kr.east) -- (addfb.west);
|
||
|
\draw[->] (addn.west) -- (Hh.east);
|
||
|
\draw[->] (Hh.west) -| (addfb.south);
|
||
|
\draw[<-] (adddy.north) -- ++(0, \cdist) node[below right]{$d_y$};
|
||
|
\end{tikzpicture}
|
||
|
#+end_src
|
||
|
|
||
|
#+name: fig:sf_arch_class_prefilter
|
||
|
#+caption: Equivalent configuration - classical Feedback with pre-filter ([[./figs/sf_arch_class_prefilter.png][png]], [[./figs/sf_arch_class_prefilter.pdf][pdf]], [[./figs/sf_arch_class_prefilter.tex][tex]]).
|
||
|
#+RESULTS:
|
||
|
[[file:figs/sf_arch_class_prefilter.png]]
|
||
|
|
||
|
* Equivalent configuration - bis
|
||
|
#+begin_src latex :file sf_arch_class_bis.pdf :tangle figs/sf_arch_class_bis.tex
|
||
|
<<tikz_default>>
|
||
|
\begin{tikzpicture}
|
||
|
\node[addb={+}{}{}{}{-}] (addfb) at (0, 0){};
|
||
|
\node[block, left=of addfb] (Kr){${H_L}^{-1}$};
|
||
|
\node[block, right=of addfb] (K){$G^{-1} {H_H}^{-1} H_L$};
|
||
|
\node[block, right=of K] (G){$G^\prime$};
|
||
|
\node[addb={+}{}{}{}{}, right=of G] (adddy){};
|
||
|
\node[addb={+}{}{}{}{}, below right=0.7 and 0.3 of adddy] (addn) {};
|
||
|
|
||
|
\draw[->] (addfb.east) -- (K.west) node[above left]{};
|
||
|
\draw[->] (K.east) -- (G.west) node[above left]{$u$};
|
||
|
\draw[->] (G.east) -- (adddy.west);
|
||
|
\draw[<-] (addn.east) -- ++(\cdist, 0) coordinate[](endpos) node[above left]{$n$};
|
||
|
\draw[->] (G-|addn)node[branch]{} -- (addn.north);
|
||
|
\draw[->] (adddy.east) -- (G-|endpos) node[above left]{$y$};
|
||
|
\draw[<-] (Kr.west) -- ++(-\cdist, 0) node[above right]{$r$};
|
||
|
\draw[->] (Kr.east) -- (addfb.west);
|
||
|
\draw[->] (addn.west) -| (addfb.south);
|
||
|
\draw[<-] (adddy.north) -- ++(0, \cdist) node[below right]{$d_y$};
|
||
|
\end{tikzpicture}
|
||
|
#+end_src
|
||
|
|
||
|
#+name: fig:sf_arch_class_bis
|
||
|
#+caption: Equivalent configuration - bis ([[./figs/sf_arch_class_bis.png][png]], [[./figs/sf_arch_class_bis.pdf][pdf]], [[./figs/sf_arch_class_bis.tex][tex]]).
|
||
|
#+RESULTS:
|
||
|
[[file:figs/sf_arch_class_bis.png]]
|
||
|
|
||
|
* H-Infinity - Complementary filters - Generalized plant
|
||
|
#+begin_src latex :file sf_hinf_filters_plant_b.pdf :tangle figs/sf_hinf_filters_plant_b.tex
|
||
|
<<tikz_default>>
|
||
|
\begin{tikzpicture}
|
||
|
\node[block={4.0cm}{3.0cm}, draw, dashed, fill=black!20!white] (P) {};
|
||
|
\node[above] at (P.north) {$P$};
|
||
|
|
||
|
\coordinate[] (inputw) at ($(P.south west)!0.8!(P.north west) + (-\cdist, 0)$);
|
||
|
\coordinate[] (inputu) at ($(P.south west)!0.4!(P.north west) + (-\cdist, 0)$);
|
||
|
|
||
|
\coordinate[] (outputh) at ($(P.south east)!0.8!(P.north east) + ( \cdist, 0)$);
|
||
|
\coordinate[] (outputl) at ($(P.south east)!0.4!(P.north east) + ( \cdist, 0)$);
|
||
|
\coordinate[] (outputv) at ($(P.south east)!0.1!(P.north east) + ( \cdist, 0)$);
|
||
|
|
||
|
\node[block, left=2*\cdist of outputl] (WL){$w_L$};
|
||
|
\node[block, left=2*\cdist of outputh] (WH){$w_H$};
|
||
|
\node[addb={+}{}{}{}{-}, left=of WH] (sub) {};
|
||
|
|
||
|
\draw[->] (inputw) node[above right]{$w$} -- (sub.west);
|
||
|
\draw[->] (inputu) node[above right]{$u$} -- (WL.west);
|
||
|
\draw[->] (inputu-|sub) node[branch]{} -- (sub.south);
|
||
|
\draw[->] (sub.east) -- (WH.west);
|
||
|
\draw[->] ($(inputw)+(2*\cdist, 0)$) node[branch]{} |- (outputv) node[above left]{$v$};
|
||
|
\draw[->] (WH.east) -- (outputh)node[above left]{$z_H$};
|
||
|
\draw[->] (WL.east) -- (outputl)node[above left]{$z_L$};
|
||
|
\end{tikzpicture}
|
||
|
#+end_src
|
||
|
|
||
|
#+name: fig:sf_hinf_filters_plant_b
|
||
|
#+caption: H-Infinity - Complementary filters - Generalized plant ([[./figs/sf_hinf_filters_plant_b.png][png]], [[./figs/sf_hinf_filters_plant_b.pdf][pdf]], [[./figs/sf_hinf_filters_plant_b.tex][tex]]).
|
||
|
#+RESULTS:
|
||
|
[[file:figs/sf_hinf_filters_plant_b.png]]
|
||
|
|
||
|
* H-Infinity - Complementary filters
|
||
|
#+begin_src latex :file sf_hinf_filters_b.pdf :tangle figs/sf_hinf_filters_b.tex
|
||
|
<<tikz_default>>
|
||
|
\begin{tikzpicture}
|
||
|
\node[block={4.0cm}{3.0cm}, draw, dashed, fill=black!20!white] (P) {};
|
||
|
\node[above] at (P.north) {$P$};
|
||
|
|
||
|
\coordinate[] (inputw) at ($(P.south west)!0.8!(P.north west) + (-\cdist, 0)$);
|
||
|
\coordinate[] (inputu) at ($(P.south west)!0.4!(P.north west) + (-\cdist, 0)$);
|
||
|
|
||
|
\coordinate[] (outputh) at ($(P.south east)!0.8!(P.north east) + ( \cdist, 0)$);
|
||
|
\coordinate[] (outputl) at ($(P.south east)!0.4!(P.north east) + ( \cdist, 0)$);
|
||
|
\coordinate[] (outputv) at ($(P.south east)!0.1!(P.north east) + ( \cdist, 0)$);
|
||
|
|
||
|
\node[block, left=2*\cdist of outputl] (WL){$w_L$};
|
||
|
\node[block, left=2*\cdist of outputh] (WH){$w_H$};
|
||
|
\node[addb={+}{}{}{}{-}, left=of WH] (sub) {};
|
||
|
|
||
|
\node[block, below=\cdist of P] (HL) {$H_L$};
|
||
|
|
||
|
\draw[->] (inputw) node[above right]{$w$} -- (sub.west);
|
||
|
\draw[->] (HL.west) -| ($(inputu)+(0.5*\cdist, 0)$) -- (WL.west);
|
||
|
\draw[->] (inputu-|sub) node[branch]{} -- (sub.south);
|
||
|
\draw[->] (sub.east) -- (WH.west);
|
||
|
\draw[->] ($(inputw)+(2*\cdist, 0)$) node[branch]{} |- ($(outputv)+(-0.5*\cdist, 0)$) |- (HL.east);
|
||
|
\draw[->] (WH.east) -- (outputh)node[above left]{$z_H$};
|
||
|
\draw[->] (WL.east) -- (outputl)node[above left]{$z_L$};
|
||
|
\end{tikzpicture}
|
||
|
#+end_src
|
||
|
|
||
|
#+name: fig:sf_hinf_filters_b
|
||
|
#+caption: H-Infinity - Complementary filters ([[./figs/sf_hinf_filters_b.png][png]], [[./figs/sf_hinf_filters_b.pdf][pdf]], [[./figs/sf_hinf_filters_b.tex][tex]]).
|
||
|
#+RESULTS:
|
||
|
[[file:figs/sf_hinf_filters_b.png]]
|
||
|
|
||
|
* H-Infinity - 3 Complementary filters
|
||
|
#+begin_src latex :file comp_filter_three_hinf.pdf :tangle figs/comp_filter_three_hinf.tex
|
||
|
<<tikz_default>>
|
||
|
\begin{tikzpicture}
|
||
|
\node[block={5.0cm}{4.0cm}, dashed] (P) {};
|
||
|
\node[above] at (P.north) {$P$};
|
||
|
|
||
|
\coordinate[] (inputw) at ($(P.south west)!0.8!(P.north west) + (-\cdist, 0)$);
|
||
|
\coordinate[] (inputu) at ($(P.south west)!0.4!(P.north west) + (-\cdist, 0)$);
|
||
|
|
||
|
\coordinate[] (output3) at ($(P.south east)!0.8!(P.north east) + ( \cdist, 0)$);
|
||
|
\coordinate[] (output2) at ($(P.south east)!0.6!(P.north east) + ( \cdist, 0)$);
|
||
|
\coordinate[] (output1) at ($(P.south east)!0.4!(P.north east) + ( \cdist, 0)$);
|
||
|
\coordinate[] (outputv) at ($(P.south east)!0.1!(P.north east) + ( \cdist, 0)$);
|
||
|
|
||
|
\node[block, left=2*\cdist of output1] (W1){$w_1$};
|
||
|
\node[block, left=2*\cdist of output2] (W2){$w_2$};
|
||
|
\node[block, left=2*\cdist of output3] (W3){$w_3$};
|
||
|
\node[addb={+}{}{}{}{-}, left=of W3] (sub1) {};
|
||
|
\node[addb={+}{}{}{}{-}, left=of sub1] (sub2) {};
|
||
|
|
||
|
\node[block, below=\cdist of P] (H) {$\begin{bmatrix}H_1 \\ H_2\end{bmatrix}$};
|
||
|
|
||
|
\draw[->] (inputw) node[above right]{$w$} -- (sub2.west);
|
||
|
\draw[->] (W1-|sub1)node[branch]{} -- (sub1.south);
|
||
|
\draw[->] (W2-|sub2)node[branch]{} -- (sub2.south);
|
||
|
\draw[->] ($(sub2.west)+(-0.5, 0)$) node[branch]{} |- (outputv) |- (H.east);
|
||
|
\draw[->] ($(H.south west)!0.7!(H.north west)$) -| ($(inputu|-W1)+(0.4, 0)$) -- (W1.west);
|
||
|
\draw[->] ($(H.south west)!0.3!(H.north west)$) -| (inputu|-W2) -- (W2.west);
|
||
|
|
||
|
\draw[->] (sub2.east) -- (sub1.west);
|
||
|
\draw[->] (sub1.east) -- (W3.west);
|
||
|
\draw[->] (W1.east) -- (output1)node[above left]{$z_1$};
|
||
|
\draw[->] (W2.east) -- (output2)node[above left]{$z_2$};
|
||
|
\draw[->] (W3.east) -- (output3)node[above left]{$z_3$};
|
||
|
\end{tikzpicture}
|
||
|
#+end_src
|
||
|
|
||
|
#+name: fig:comp_filter_three_hinf
|
||
|
#+caption: H-Infinity - Complementary filters ([[./figs/comp_filter_three_hinf.png][png]], [[./figs/comp_filter_three_hinf.pdf][pdf]], [[./figs/comp_filter_three_hinf.tex][tex]]).
|
||
|
#+RESULTS:
|
||
|
[[file:figs/comp_filter_three_hinf.png]]
|
||
|
|
||
|
* Input Multiplicative Uncertainty
|
||
|
#+begin_src latex :file input_uncertainty.pdf :tangle figs/input_uncertainty.tex
|
||
|
<<tikz_default>>
|
||
|
\begin{tikzpicture}
|
||
|
% Blocs
|
||
|
\node[block] (G) {$G$};
|
||
|
|
||
|
\node[addb, left= of G] (addi) {};
|
||
|
\node[block, above left=0.3 and 0.3 of addi] (deltai) {$\Delta_I$};
|
||
|
\node[block, left= of deltai] (wi) {$w_I$};
|
||
|
\node[branch] (branch) at ($(wi.west|-addi)+(-0.4, 0)$) {};
|
||
|
|
||
|
% Connections and labels
|
||
|
\draw[->] (branch.center) |- (wi.west);
|
||
|
\draw[->] ($(branch)+(-0.6, 0)$) -- (addi.west);
|
||
|
\draw[->] (wi.east) -- (deltai.west);
|
||
|
\draw[->] (deltai.east) -| (addi.north);
|
||
|
\draw[->] (addi.east) -- (G.west);
|
||
|
\draw[->] (G.east) -- ++(0.6, 0);
|
||
|
|
||
|
\begin{scope}[on background layer]
|
||
|
\node[fit={(branch|-wi.north) (G.south east)}, inner sep=6pt, draw, dashed, fill=black!20!white] (Gp) {};
|
||
|
\node[below left] at (Gp.north east) {$G\prime$};
|
||
|
\end{scope}
|
||
|
\end{tikzpicture}
|
||
|
#+end_src
|
||
|
|
||
|
#+name: fig:input_uncertainty
|
||
|
#+caption: Input Multiplicative Uncertainty ([[./figs/input_uncertainty.png][png]], [[./figs/input_uncertainty.pdf][pdf]], [[./figs/input_uncertainty.tex][tex]]).
|
||
|
#+RESULTS:
|
||
|
[[file:figs/input_uncertainty.png]]
|
||
|
|
||
|
* One mass
|
||
|
#+begin_src latex :file mech_sys_alone.pdf :tangle figs/mech_sys_alone.tex
|
||
|
<<tikz_default>>
|
||
|
\begin{tikzpicture}
|
||
|
% ====================
|
||
|
% Parameters
|
||
|
% ====================
|
||
|
\def\massw{2.2} % Width of the masses
|
||
|
\def\massh{0.8} % Height of the masses
|
||
|
\def\spaceh{1.2} % Height of the springs/dampers
|
||
|
\def\dispw{0.3} % Width of the dashed line for the displacement
|
||
|
\def\disph{0.5} % Height of the arrow for the displacements
|
||
|
\def\bracs{0.05} % Brace spacing vertically
|
||
|
\def\brach{-10pt} % Brace shift horizontaly
|
||
|
% ====================
|
||
|
|
||
|
|
||
|
% ====================
|
||
|
% Ground
|
||
|
% ====================
|
||
|
\draw (-0.5*\massw, 0) -- (0.5*\massw, 0);
|
||
|
\draw[dashed] (0.5*\massw, 0) -- ++(\dispw, 0);
|
||
|
\draw[->] (0.5*\massw+0.5*\dispw, 0) -- ++(0, \disph) node[right]{$w$};
|
||
|
% ====================
|
||
|
|
||
|
\begin{scope}[shift={(0, 0)}]
|
||
|
% Mass
|
||
|
\draw[fill=white] (-0.5*\massw, \spaceh) rectangle (0.5*\massw, \spaceh+\massh) node[pos=0.5]{$m$};
|
||
|
|
||
|
% Spring, Damper, and Actuator
|
||
|
\draw[spring] (-0.4*\massw, 0) -- (-0.4*\massw, \spaceh) node[midway, left=0.1]{$k$};
|
||
|
\draw[damper] (0, 0) -- ( 0, \spaceh) node[midway, left=0.2]{$c$};
|
||
|
\draw[actuator] ( 0.4*\massw, 0) -- ( 0.4*\massw, \spaceh) node[midway, left=0.1](F){$F$};
|
||
|
|
||
|
% Displacements
|
||
|
\draw[dashed] (0.5*\massw, \spaceh) -- ++(\dispw, 0);
|
||
|
\draw[->] (0.5*\massw+0.5*\dispw, \spaceh) -- ++(0, \disph) node[right]{$x$};
|
||
|
|
||
|
% Legend
|
||
|
% \draw[decorate, decoration={brace, amplitude=8pt}, xshift=\brach] %
|
||
|
% (-0.5*\massw, \bracs) -- (-0.5*\massw, \spaceh+\massh-\bracs) %
|
||
|
% node[midway,rotate=90,anchor=south,yshift=10pt]{};
|
||
|
\end{scope}
|
||
|
\end{tikzpicture}
|
||
|
#+end_src
|
||
|
|
||
|
#+name: fig:mech_sys_alone
|
||
|
#+caption: One mass ([[./figs/mech_sys_alone.png][png]], [[./figs/mech_sys_alone.pdf][pdf]], [[./figs/mech_sys_alone.tex][tex]]).
|
||
|
#+RESULTS:
|
||
|
[[file:figs/mech_sys_alone.png]]
|
||
|
|
||
|
* One mass - Control
|
||
|
#+begin_src latex :file mech_sys_alone_ctrl.pdf :tangle figs/mech_sys_alone_ctrl.tex
|
||
|
<<tikz_default>>
|
||
|
\begin{tikzpicture}
|
||
|
% ====================
|
||
|
% Parameters
|
||
|
% ====================
|
||
|
\def\massw{2.2} % Width of the masses
|
||
|
\def\massh{0.8} % Height of the masses
|
||
|
\def\spaceh{1.2} % Height of the springs/dampers
|
||
|
\def\dispw{0.3} % Width of the dashed line for the displacement
|
||
|
\def\disph{0.5} % Height of the arrow for the displacements
|
||
|
\def\bracs{0.05} % Brace spacing vertically
|
||
|
\def\brach{-10pt} % Brace shift horizontaly
|
||
|
% ====================
|
||
|
|
||
|
|
||
|
% ====================
|
||
|
% Ground
|
||
|
% ====================
|
||
|
\draw (-0.5*\massw, 0) -- (0.5*\massw, 0);
|
||
|
\draw[dashed] (0.5*\massw, 0) -- ++(\dispw, 0);
|
||
|
\draw[->] (0.5*\massw+0.5*\dispw, 0) -- ++(0, \disph) node[below right]{$w$};
|
||
|
% ====================
|
||
|
|
||
|
\begin{scope}[shift={(0, 0)}]
|
||
|
% Mass
|
||
|
\draw[fill=white] (-0.5*\massw, \spaceh) rectangle (0.5*\massw, \spaceh+\massh) node[pos=0.5]{$m$};
|
||
|
|
||
|
% Spring, Damper, and Actuator
|
||
|
\draw[spring] (-0.4*\massw, 0) -- (-0.4*\massw, \spaceh) node[midway, left=0.1]{$k$};
|
||
|
\draw[damper] (0, 0) -- ( 0, \spaceh) node[midway, left=0.2]{$c$};
|
||
|
\draw[actuator] ( 0.4*\massw, 0) -- ( 0.4*\massw, \spaceh) coordinate[midway, right=0.15](F);
|
||
|
|
||
|
% Displacements
|
||
|
\draw[dashed] (0.5*\massw, \spaceh) -- ++(\dispw, 0);
|
||
|
\draw[->] (0.5*\massw+0.5*\dispw, \spaceh) -- ++(0, \disph) node[right](x){$x$};
|
||
|
\end{scope}
|
||
|
|
||
|
\node[block, right=1 of F] (Kfb) {$K$};
|
||
|
\node[addb={+}{}{-}{}{}, right=2*\cdist of Kfb] (add) {};
|
||
|
\node[addb] (addn) at (x-|Kfb) {};
|
||
|
\node[block, right=of addn] (Hl) {$H_L$};
|
||
|
|
||
|
\draw[->] (x) -- (addn.west);
|
||
|
\draw[->] (addn.east) -- (Hl.west);
|
||
|
\draw[->] (Hl.east) -| (add.north);
|
||
|
\draw[->] (add.west) -- (Kfb.east);
|
||
|
\draw[->] (Kfb.west) -- (F) node[above right]{$F$};
|
||
|
\draw[<-] (addn.north) -- ++(0,\cdist) node[below right]{$n$};
|
||
|
\draw[<-] (add.east) -- ++(\cdist,0) node[above left]{$r$};
|
||
|
\end{tikzpicture}
|
||
|
#+end_src
|
||
|
|
||
|
#+name: fig:mech_sys_alone_ctrl
|
||
|
#+caption: One mass - Control ([[./figs/mech_sys_alone_ctrl.png][png]], [[./figs/mech_sys_alone_ctrl.pdf][pdf]], [[./figs/mech_sys_alone_ctrl.tex][tex]]).
|
||
|
#+RESULTS:
|
||
|
[[file:figs/mech_sys_alone_ctrl.png]]
|
||
|
|
||
|
* Piezoelectric Actuator
|
||
|
#+begin_src latex :file 1dof_isolation_piezo.pdf :tangle figs/1dof_isolation_piezo.tex
|
||
|
<<tikz_default>>
|
||
|
\begin{tikzpicture}
|
||
|
\node[piezo={2}{3}{10}] (piezo) at (0, 0){};
|
||
|
\node[draw, fill=white, anchor=south, minimum width=3cm, minimum height=1.5cm] (mass) at ($(piezo.north)+(0, 0.5)$) {Mass};
|
||
|
\draw[] ($(piezo.south)+(-1.5, -0.5)$) -- ++(3, 0);
|
||
|
\draw ($0.8*(piezo.north west)+0.2*(piezo.north east)$) -- ++(0, 0.5);
|
||
|
\draw ($0.2*(piezo.north west)+0.8*(piezo.north east)$) -- ++(0, 0.5);
|
||
|
\draw ($0.8*(piezo.south west)+0.2*(piezo.south east)$) -- ++(0, -0.5);
|
||
|
\draw ($0.2*(piezo.south west)+0.8*(piezo.south east)$) -- ++(0, -0.5);
|
||
|
\end{tikzpicture}
|
||
|
#+end_src
|
||
|
|
||
|
#+name: fig:1dof_isolation_piezo
|
||
|
#+caption: Piezoelectric Actuator ([[./figs/1dof_isolation_piezo.png][png]], [[./figs/1dof_isolation_piezo.pdf][pdf]], [[./figs/1dof_isolation_piezo.tex][tex]]).
|
||
|
#+RESULTS:
|
||
|
[[file:figs/1dof_isolation_piezo.png]]
|
||
|
|
||
|
* Upper bounds
|
||
|
#+begin_src latex :file spec_S_T.pdf :tangle figs/spec_S_T.tex
|
||
|
<<tikz_default>>
|
||
|
\setlength\fwidth{7cm}
|
||
|
\setlength\fheight{5cm}
|
||
|
|
||
|
\begin{tikzpicture}
|
||
|
\begin{axis}[%
|
||
|
name=axis,
|
||
|
width=\fwidth,
|
||
|
height=\fheight,
|
||
|
at={(0, 0)},
|
||
|
scale only axis,
|
||
|
separate axis lines,
|
||
|
every outer x axis line/.append style={black},
|
||
|
every x tick label/.append style={font=\color{black}},
|
||
|
every x tick/.append style={black},
|
||
|
xmode=log,
|
||
|
xmin=0.1,
|
||
|
xmax=1000,
|
||
|
xminorticks=true,
|
||
|
xlabel={Frequency [Hz]},
|
||
|
every outer y axis line/.append style={black},
|
||
|
every y tick label/.append style={font=\color{black}},
|
||
|
every y tick/.append style={black},
|
||
|
ymode=log,
|
||
|
ymin=0.001,
|
||
|
ymax=10,
|
||
|
yminorticks=true,
|
||
|
ylabel={Magnitude},
|
||
|
axis background/.style={fill=white},
|
||
|
xmajorgrids,
|
||
|
xminorgrids,
|
||
|
ymajorgrids,
|
||
|
yminorgrids
|
||
|
]
|
||
|
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-robust-stability>>
|
||
|
};
|
||
|
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-bandwidth>>
|
||
|
};
|
||
|
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-noise-attenuation-1>>
|
||
|
};
|
||
|
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-noise-attenuation-2>>
|
||
|
};
|
||
|
\addplot [color=S, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-dist-rejection>>
|
||
|
};
|
||
|
|
||
|
\node[draw, fill=white, align=center, anchor=west] (noise) at (20, 0.01){Noise\\Attenuation};
|
||
|
\draw[->] (noise.north) -- (100, 0.1-|noise.north);
|
||
|
\draw[->] (noise.east) -- (500, 0.01);
|
||
|
|
||
|
\node[draw, fill=white, align=center, anchor=north east] (bandwidth) at (900, 8) {Bandwidth\\Limitation};
|
||
|
\draw[->] (bandwidth.west) -- (20, 0.7);
|
||
|
|
||
|
\node[draw, fill=white, align=center, anchor=south west] (robust) at (0.2, 1) {Robust\\Stability};
|
||
|
\draw[->] (robust.east) -- (8,2|-robust.east);
|
||
|
|
||
|
\node[draw, fill=white, align=center, anchor=south west] (dist) at (0.11, 0.1) {Disturbance\\Rejection};
|
||
|
\draw[->] (dist.south) -- (1, 0.025);
|
||
|
\end{axis}
|
||
|
|
||
|
% \begin{customlegend}[legend cell align=left, %<= to align cells
|
||
|
% legend entries={ % <= in the following there are the entries
|
||
|
% $S$,
|
||
|
% $T$
|
||
|
% },
|
||
|
% legend style={at={(axis.north east)}, outer sep=5pt, font=\footnotesize}]
|
||
|
% \addlegendimage{upperbound, S}
|
||
|
% \addlegendimage{upperbound, T}
|
||
|
% \end{customlegend}
|
||
|
|
||
|
\end{tikzpicture}
|
||
|
#+end_src
|
||
|
|
||
|
#+name: fig:spec_S_T
|
||
|
#+caption: Upper bounds ([[./figs/spec_S_T.png][png]], [[./figs/spec_S_T.pdf][pdf]], [[./figs/spec_S_T.tex][tex]]).
|
||
|
#+RESULTS:
|
||
|
[[file:figs/spec_S_T.png]]
|
||
|
|
||
|
* Bode plot of the mechanical system
|
||
|
#+NAME: data:bode_plot_mech_sys_magnitude
|
||
|
#+begin_src latex :exports none
|
||
|
0.1 0.000100077040681054\\
|
||
|
0.272543253128103 0.000100575030023101\\
|
||
|
0.43314832233764 0.000101464934759738\\
|
||
|
0.587176639073325 0.000102724574034075\\
|
||
|
0.737679760252773 0.000104367175122706\\
|
||
|
0.882969995549408 0.000106373827767982\\
|
||
|
1.02804473209331 0.000108834566992957\\
|
||
|
1.1723818032866 0.000111792586344107\\
|
||
|
1.30953502048267 0.000115140426960708\\
|
||
|
1.44264395121816 0.000118966190620297\\
|
||
|
1.57833140565212 0.00012354732835445\\
|
||
|
1.70306502925285 0.00012847169721901\\
|
||
|
1.82499324481615 0.000134067470279222\\
|
||
|
1.95565071586595 0.000141092091396706\\
|
||
|
2.08122156998634 0.000149060642425566\\
|
||
|
2.19959306803007 0.000157914155457765\\
|
||
|
2.32469705998565 0.000169028899516352\\
|
||
|
2.43998629725955 0.000181271551082471\\
|
||
|
2.56099310025846 0.000196738235618899\\
|
||
|
2.68800102153761 0.000216674296189979\\
|
||
|
2.82130767593947 0.000242927525096564\\
|
||
|
2.96122543798804 0.000278143152215355\\
|
||
|
3.10808217386906 0.000325419446839597\\
|
||
|
3.35371015200293 0.000419096223177928\\
|
||
|
3.42400613797143 0.000439341276461064\\
|
||
|
3.47168681892656 0.000447567844417553\\
|
||
|
3.52003147279668 0.000449984807083431\\
|
||
|
3.54445567397044 0.000448731850351484\\
|
||
|
3.59381366380463 0.000441170960941456\\
|
||
|
3.64385898376355 0.000427344400826069\\
|
||
|
3.72023668141307 0.00039763388652928\\
|
||
|
3.824569722467 0.000349750691805404\\
|
||
|
4.09838367175726 0.000240611931259811\\
|
||
|
4.39180089259609 0.000169131547428242\\
|
||
|
4.67379510799246 0.000127877923720101\\
|
||
|
4.97389595879007 9.967307801278e-05\\
|
||
|
5.32999408084409 7.76763468688566e-05\\
|
||
|
5.75121707184161 6.05462047310449e-05\\
|
||
|
6.29214610961035 4.62441646969631e-05\\
|
||
|
6.9317172761554 3.53667028681261e-05\\
|
||
|
7.74263682681128 2.65611239929399e-05\\
|
||
|
8.8296999554941 1.9284460658412e-05\\
|
||
|
10.2804473209331 1.35628028157818e-05\\
|
||
|
12.3906215694792 8.96920494033127e-06\\
|
||
|
15.5665435927106 5.5069217658656e-06\\
|
||
|
20.9566239948044 2.96718273940607e-06\\
|
||
|
31.9524750575921 1.25569563497959e-06\\
|
||
|
64.2403365939419 3.07819423434704e-07\\
|
||
|
100 1.26808063706741e-07\\
|
||
|
#+end_src
|
||
|
|
||
|
#+NAME: data:bode_plot_mech_sys_phase
|
||
|
#+begin_src latex :exports none
|
||
|
0.1 -0.360279720677909\\
|
||
|
0.110928986489522 -0.399726239508823\\
|
||
|
0.122204468663152 -0.440446767977335\\
|
||
|
0.13462605792989 -0.485336746925839\\
|
||
|
0.148310251433614 -0.534830252917459\\
|
||
|
0.162259528707813 -0.585330760453786\\
|
||
|
0.177520801171768 -0.640642308219981\\
|
||
|
0.194217468148908 -0.701236456999254\\
|
||
|
0.212484535249894 -0.767635080810521\\
|
||
|
0.232469705998571 -0.840416979069801\\
|
||
|
0.252582002696278 -0.91382126433902\\
|
||
|
0.274434330322828 -0.9937740634835\\
|
||
|
0.298177229001969 -1.0808986125088\\
|
||
|
0.323974262952812 -1.17588848183723\\
|
||
|
0.352003147279672 -1.27951850633903\\
|
||
|
0.382456972246693 -1.39265813896972\\
|
||
|
0.415545533471895 -1.51628791363001\\
|
||
|
0.451496777203605 -1.65151992855328\\
|
||
|
0.490558370636517 -1.79962357173105\\
|
||
|
0.529326605836072 -1.94793502196421\\
|
||
|
0.571158647812626 -2.10957933285724\\
|
||
|
0.616296625513279 -2.28604784742126\\
|
||
|
0.6650018030431 -2.47907386285402\\
|
||
|
0.717556091893683 -2.69068950564727\\
|
||
|
0.774263682681121 -2.92329985625085\\
|
||
|
0.829695852083464 -3.15539135978239\\
|
||
|
0.889096598952924 -3.40978953925455\\
|
||
|
0.952750047242714 -3.68959754515299\\
|
||
|
1.02096066230607 -3.9985784472124\\
|
||
|
1.09405470720574 -4.34134801105651\\
|
||
|
1.16430313292089 -4.68343908636479\\
|
||
|
1.23906215694794 -5.06271309073682\\
|
||
|
1.31862140139471 -5.48563013111718\\
|
||
|
1.40328908478584 -5.96033793666024\\
|
||
|
1.48310251433614 -6.43414310335521\\
|
||
|
1.5674554102056 -6.96642431057373\\
|
||
|
1.65660595894989 -7.56917034593727\\
|
||
|
1.75082703173578 -8.25798483497323\\
|
||
|
1.83765620038813 -8.94739205623571\\
|
||
|
1.92879150802077 -9.73672637995722\\
|
||
|
2.02444650997683 -10.6502453305039\\
|
||
|
2.11020342856859 -11.5566518641599\\
|
||
|
2.19959306803003 -12.6059438949727\\
|
||
|
2.29276931286572 -13.8354493380888\\
|
||
|
2.38989256623109 -15.2964499277763\\
|
||
|
2.47396410088675 -16.7419892536468\\
|
||
|
2.56099310025844 -18.455940403627\\
|
||
|
2.65108360190857 -20.5188442655184\\
|
||
|
2.74434330322828 -23.0448181567426\\
|
||
|
2.84088369018327 -26.1991511292148\\
|
||
|
2.92055551218269 -29.3354738213304\\
|
||
|
3.00246170908546 -33.2060093347327\\
|
||
|
3.08666494333735 -38.0554185709144\\
|
||
|
3.17322963473503 -44.2102992203773\\
|
||
|
3.26222200971169 -52.0707471833003\\
|
||
|
3.35371015200292 -62.0209044940134\\
|
||
|
3.47168681892662 -77.4986746832345\\
|
||
|
3.7982153061908 -120.230303267244\\
|
||
|
3.90473523688559 -129.722782020331\\
|
||
|
4.01424249049931 -137.194379975395\\
|
||
|
4.1268208457029 -143.04709416857\\
|
||
|
4.24255643071768 -147.66917780573\\
|
||
|
4.39180089259608 -152.179051563568\\
|
||
|
4.54629546953248 -155.675990585521\\
|
||
|
4.70622484984116 -158.450422486142\\
|
||
|
4.8717802187946 -160.697705094482\\
|
||
|
5.04315948717143 -162.551498658356\\
|
||
|
5.25679112201842 -164.386209456898\\
|
||
|
5.4794723369002 -165.899912200972\\
|
||
|
5.71158647812626 -167.169971678082\\
|
||
|
5.95353313081449 -168.251091455024\\
|
||
|
6.24878807200671 -169.325881490414\\
|
||
|
6.55868565957134 -170.242767336282\\
|
||
|
6.88395206964551 -171.034789262572\\
|
||
|
7.2754835291961 -171.818109931866\\
|
||
|
7.68928372075853 -172.497125933675\\
|
||
|
8.12661920009201 -173.091900053792\\
|
||
|
8.58882855954615 -173.617602567035\\
|
||
|
9.14031074875622 -174.1408898981\\
|
||
|
9.72720319245064 -174.604302165229\\
|
||
|
10.351779556302 -175.017743351308\\
|
||
|
11.0164594963369 -175.388976689248\\
|
||
|
11.8051652856881 -175.759420020454\\
|
||
|
12.6503372039588 -176.09209734734\\
|
||
|
13.556017853294 -176.392392885436\\
|
||
|
14.5265392594678 -176.66465781875\\
|
||
|
15.674554102056 -176.936002663135\\
|
||
|
16.9132951702966 -177.18161128073\\
|
||
|
18.2499324481618 -177.404677801875\\
|
||
|
19.6922025547921 -177.6078573887\\
|
||
|
21.2484535249894 -177.793380869149\\
|
||
|
22.9276931286572 -177.96314114721\\
|
||
|
24.911300260678 -178.132254818644\\
|
||
|
27.0665207003317 -178.286340385618\\
|
||
|
29.4082017058709 -178.426951191446\\
|
||
|
31.9524750575915 -178.555433956644\\
|
||
|
34.7168681892662 -178.672965021387\\
|
||
|
37.7204249341695 -178.780578807612\\
|
||
|
40.9838367175735 -178.879190388815\\
|
||
|
44.5295850994262 -178.96961355724\\
|
||
|
48.717802187946 -179.05917305424\\
|
||
|
53.2999408084406 -179.140800582232\\
|
||
|
58.313051135262 -179.215233540711\\
|
||
|
63.7976680860626 -179.283132632794\\
|
||
|
69.7981390783064 -179.345091670682\\
|
||
|
76.3629826128223 -179.40164575426\\
|
||
|
84.1249704973636 -179.457058846282\\
|
||
|
92.6759330114683 -179.507307463976\\
|
||
|
100 -179.543486140468\\
|
||
|
#+end_src
|
||
|
|
||
|
#+begin_src latex :file bode_plot_mech_sys.pdf :tangle figs/bode_plot_mech_sys.tex :exports results
|
||
|
<<tikz_default>>
|
||
|
\setlength\fwidth{7cm}
|
||
|
\setlength\fheight{5cm}
|
||
|
|
||
|
\begin{tikzpicture}
|
||
|
\begin{axis}[%
|
||
|
width=\fwidth,
|
||
|
height=0.45\fheight,
|
||
|
at={(0,0.55\fheight)},
|
||
|
xmode=log,
|
||
|
xmin=0.1,
|
||
|
xmax=100,
|
||
|
xtick={0.1,1,10,100},
|
||
|
xticklabels={{}},
|
||
|
xminorticks=true,
|
||
|
ymode=log,
|
||
|
ymin=2e-07,
|
||
|
ymax=0.001,
|
||
|
yminorticks=true,
|
||
|
ylabel={Magnitude [$\si{\meter/\newton}$]},
|
||
|
xminorgrids,
|
||
|
yminorgrids
|
||
|
]
|
||
|
\addplot [color=mycolor1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:bode_plot_mech_sys_magnitude>>
|
||
|
};
|
||
|
\end{axis}
|
||
|
|
||
|
\begin{axis}[%
|
||
|
width=\fwidth,
|
||
|
height=0.45\fheight,
|
||
|
at={(0,0.05\fheight)},
|
||
|
xmode=log,
|
||
|
xmin=0.1,
|
||
|
xmax=100,
|
||
|
xminorticks=true,
|
||
|
xlabel={Frequency [$\si{\hertz}$]},
|
||
|
ymin=-180,
|
||
|
ymax=180,
|
||
|
ytick={-180, -90, 0, 90, 180},
|
||
|
ylabel={Phase [deg]},
|
||
|
xminorgrids
|
||
|
]
|
||
|
\addplot [color=mycolor1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:bode_plot_mech_sys_phase>>
|
||
|
};
|
||
|
\end{axis}
|
||
|
\end{tikzpicture}
|
||
|
#+end_src
|
||
|
|
||
|
#+name: fig:bode_plot_mech_sys
|
||
|
#+caption: Bode plot of the mechanical system ([[./figs/bode_plot_mech_sys.png][png]], [[./figs/bode_plot_mech_sys.pdf][pdf]], [[./figs/bode_plot_mech_sys.tex][tex]]).
|
||
|
#+RESULTS:
|
||
|
[[file:figs/bode_plot_mech_sys.png]]
|
||
|
|
||
|
* Bode plot of the mechanical system - Uncertainty
|
||
|
#+begin_src latex :file bode_plot_mech_sys_uncertainty.pdf :tangle figs/bode_plot_mech_sys_uncertainty.tex :exports results
|
||
|
<<tikz_default>>
|
||
|
\setlength\fwidth{7cm}
|
||
|
\setlength\fheight{5cm}
|
||
|
|
||
|
\begin{tikzpicture}
|
||
|
\begin{axis}[%
|
||
|
width=\fwidth,
|
||
|
height=0.45\fheight,
|
||
|
at={(0,0.55\fheight)},
|
||
|
xmode=log,
|
||
|
xmin=0.1,
|
||
|
xmax=1000,
|
||
|
xtick={0.1,1,10,100,1000},
|
||
|
xticklabels={{}},
|
||
|
xminorticks=true,
|
||
|
ymode=log,
|
||
|
ymin=1e-09,
|
||
|
ymax=1e-3,
|
||
|
ytick={1e-9, 1e-6, 1e-3},
|
||
|
yminorticks=true,
|
||
|
ylabel={Magnitude [$\si{\meter/\newton}$]},
|
||
|
xminorgrids,
|
||
|
yminorgrids
|
||
|
]
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
0.1 0.000108498472276567\\
|
||
|
0.302329468440578 0.000109188544929584\\
|
||
|
0.483820966492596 0.000110418604153911\\
|
||
|
0.661943345877439 0.000112224979618964\\
|
||
|
0.833529396509819 0.000114578199252702\\
|
||
|
1.00230754828387 0.000117548894744437\\
|
||
|
1.1616226326085 0.00012103243176088\\
|
||
|
1.32166418394661 0.000125301574693943\\
|
||
|
1.47628147190939 0.000130287836635005\\
|
||
|
1.63385387780986 0.00013641328669452\\
|
||
|
1.77520801171764 0.000142993715765725\\
|
||
|
1.92879150802078 0.000151577506079878\\
|
||
|
2.07643010725577 0.000161588535712108\\
|
||
|
2.21485523372636 0.00017296483238895\\
|
||
|
2.36250846547795 0.000187840273024438\\
|
||
|
2.49687842888433 0.00020458381426681\\
|
||
|
2.63889081445751 0.000226691873020851\\
|
||
|
2.78898029238044 0.000256696230431381\\
|
||
|
2.94760625512486 0.000298488589789484\\
|
||
|
3.11525422355549 0.000357022114315742\\
|
||
|
3.35371015200293 0.000456376292189216\\
|
||
|
3.44776405473446 0.000483697154807179\\
|
||
|
3.51192753045073 0.000490210174062816\\
|
||
|
3.54445567397044 0.000488828287718365\\
|
||
|
3.57728509936788 0.000484170922063144\\
|
||
|
3.64385898376355 0.000465620308132517\\
|
||
|
3.746050032749 0.000420826502193084\\
|
||
|
3.88677669089267 0.00035034481560035\\
|
||
|
4.4222739805059 0.000178619450603848\\
|
||
|
4.76077523022637 0.000129345222527601\\
|
||
|
5.12518692705333 9.74788316252629e-05\\
|
||
|
5.56859644428641 7.3426682653119e-05\\
|
||
|
6.10640754223204 5.52840526279009e-05\\
|
||
|
6.82077673286569 4.0539956498055e-05\\
|
||
|
7.76050333513357 2.90635654349117e-05\\
|
||
|
8.99402217409205 2.03989054111842e-05\\
|
||
|
10.7159339982267 1.37364782200262e-05\\
|
||
|
13.1255683577184 8.89639047515701e-06\\
|
||
|
16.527920614649 5.55296106586516e-06\\
|
||
|
21.0049824165392 3.47331689714748e-06\\
|
||
|
26.4498018242772 2.25625963624715e-06\\
|
||
|
32.6974974451177 1.54589958453738e-06\\
|
||
|
40.0500075787361 1.09729365615611e-06\\
|
||
|
48.1595791019235 8.17610486996005e-07\\
|
||
|
57.9112264764176 6.19633126975516e-07\\
|
||
|
69.6374473062822 4.77291436823566e-07\\
|
||
|
84.5136633068472 3.68563192568884e-07\\
|
||
|
105.444279352617 2.78587091692968e-07\\
|
||
|
140.328908478587 1.97169505427614e-07\\
|
||
|
255.509709035251 9.59282113283662e-08\\
|
||
|
318.789129267765 7.22976682432238e-08\\
|
||
|
386.890073932798 5.56483026764306e-08\\
|
||
|
465.229952396019 4.27238324167138e-08\\
|
||
|
559.432570616938 3.22804273547493e-08\\
|
||
|
678.940681269611 2.36368639820181e-08\\
|
||
|
831.610415323096 1.67526925333487e-08\\
|
||
|
1000 1.20843331770768e-08\\
|
||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
0.1 0.000106710688259385\\
|
||
|
0.273172159844137 0.000108505716453839\\
|
||
|
0.488302208687788 0.000110327745905599\\
|
||
|
0.674262224177834 0.000112349994976854\\
|
||
|
0.849041520408875 0.000114839034008563\\
|
||
|
1.02096066230605 0.000117951638371099\\
|
||
|
1.18324062745838 0.000121594304795896\\
|
||
|
1.34626057929891 0.000126062184614937\\
|
||
|
1.50375532129974 0.000131292426353532\\
|
||
|
1.64898694447106 0.00013707033631946\\
|
||
|
1.7916503273639 0.000143825761912395\\
|
||
|
1.92879150802078 0.000151549647975981\\
|
||
|
2.07643010725577 0.000161538054161382\\
|
||
|
2.21485523372636 0.000172889306053977\\
|
||
|
2.36250846547795 0.000187732962669881\\
|
||
|
2.49687842888433 0.000204441733121838\\
|
||
|
2.63889081445751 0.000226504973620545\\
|
||
|
2.78898029238044 0.000256449602851223\\
|
||
|
2.94760625512486 0.000298159363577881\\
|
||
|
3.11525422355549 0.000356575611377486\\
|
||
|
3.35371015200293 0.000455712137230615\\
|
||
|
3.44776405473446 0.000482955087060811\\
|
||
|
3.51192753045073 0.00048943203417931\\
|
||
|
3.54445567397044 0.000488039249457236\\
|
||
|
3.57728509936788 0.000483376376434566\\
|
||
|
3.64385898376355 0.000464830987883892\\
|
||
|
3.746050032749 0.000420078562126635\\
|
||
|
3.88677669089267 0.000349683224650799\\
|
||
|
4.4222739805059 0.000178210117898908\\
|
||
|
4.76077523022637 0.000129017619374156\\
|
||
|
5.12518692705333 9.72075551516816e-05\\
|
||
|
5.56859644428641 7.32007325840928e-05\\
|
||
|
6.10640754223204 5.50947496535982e-05\\
|
||
|
6.82077673286569 4.03827908269195e-05\\
|
||
|
7.76050333513357 2.89335750279168e-05\\
|
||
|
8.99402217409205 2.0291241681051e-05\\
|
||
|
10.7159339982267 1.36474872366887e-05\\
|
||
|
13.1255683577184 8.82216731861334e-06\\
|
||
|
16.6810053720006 5.3889167397356e-06\\
|
||
|
21.3958887134342 3.29848798482441e-06\\
|
||
|
27.1915794303602 2.09662958652095e-06\\
|
||
|
33.9258338274099 1.4062384162666e-06\\
|
||
|
41.5545533471888 9.93020250542147e-07\\
|
||
|
50.4315948717136 7.25348050270024e-07\\
|
||
|
60.6432939540806 5.47088218516539e-07\\
|
||
|
72.9227205872831 4.1941743859224e-07\\
|
||
|
88.5007491447344 3.22365233230992e-07\\
|
||
|
110.418805085416 2.42510384874621e-07\\
|
||
|
145.600599502065 1.72639960611931e-07\\
|
||
|
270.042071883778 8.1234821873906e-08\\
|
||
|
336.920570598027 6.09037642599898e-08\\
|
||
|
408.894822629486 4.66371438210421e-08\\
|
||
|
491.690357762803 3.56191637519681e-08\\
|
||
|
591.250841383188 2.67719953843374e-08\\
|
||
|
717.556091893694 1.95023782021269e-08\\
|
||
|
887.04968896544 1.35353849708511e-08\\
|
||
|
1000 1.09303865227853e-08\\
|
||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
0.1 0.000106161777540379\\
|
||
|
0.302329468440578 0.00010683260431838\\
|
||
|
0.488302208687789 0.000108065416285876\\
|
||
|
0.668074391569561 0.000109856317880892\\
|
||
|
0.841249704973612 0.000112191462399587\\
|
||
|
1.01159111222383 0.00011514260303287\\
|
||
|
1.1723818032866 0.000118607695657118\\
|
||
|
1.33390569003906 0.000122860612639371\\
|
||
|
1.48995507285286 0.000127836510573029\\
|
||
|
1.63385387780986 0.000133326857657485\\
|
||
|
1.77520801171764 0.000139735603133973\\
|
||
|
1.92879150802078 0.000148096943313887\\
|
||
|
2.07643010725578 0.000157850123821692\\
|
||
|
2.21485523372636 0.000168934893316964\\
|
||
|
2.36250846547795 0.000183430778610122\\
|
||
|
2.49687842888433 0.000199748558984006\\
|
||
|
2.63889081445751 0.000221295858503897\\
|
||
|
2.78898029238044 0.00025054041914577\\
|
||
|
2.94760625512486 0.000291274843672557\\
|
||
|
3.11525422355549 0.00034832382088498\\
|
||
|
3.35371015200293 0.000445131433358172\\
|
||
|
3.44776405473447 0.000471726874493622\\
|
||
|
3.51192753045073 0.000478042713610977\\
|
||
|
3.54445567397044 0.000476676965625263\\
|
||
|
3.57728509936788 0.000472117242644679\\
|
||
|
3.64385898376354 0.000453993168246729\\
|
||
|
3.746050032749 0.000410269121228143\\
|
||
|
3.88677669089267 0.000341499907122307\\
|
||
|
4.4222739805059 0.000174002660822199\\
|
||
|
4.76077523022638 0.000125953002750396\\
|
||
|
5.12518692705333 9.48823336523521e-05\\
|
||
|
5.56859644428641 7.14336614941324e-05\\
|
||
|
6.10640754223204 5.3748626198339e-05\\
|
||
|
6.82077673286569 3.93785608284397e-05\\
|
||
|
7.76050333513357 2.819510114619e-05\\
|
||
|
8.99402217409205 1.9752848137873e-05\\
|
||
|
10.7159339982267 1.32620620305653e-05\\
|
||
|
13.2471398786612 8.38116592420399e-06\\
|
||
|
17.1488196987054 4.90497803070839e-06\\
|
||
|
23.0336287314214 2.71833736054597e-06\\
|
||
|
30.9378757173014 1.53780955978773e-06\\
|
||
|
40.420958397963 9.36082958712216e-07\\
|
||
|
50.8987019351967 6.21757614287542e-07\\
|
||
|
62.9214610961035 4.34707187758727e-07\\
|
||
|
76.3629826128226 3.19026297454473e-07\\
|
||
|
92.675933011469 2.3815169935653e-07\\
|
||
|
113.5154708921 1.78341563804994e-07\\
|
||
|
141.62866162992 1.32236047921706e-07\\
|
||
|
191.992066559329 8.91662569794807e-08\\
|
||
|
301.63343472592 4.96594928948551e-08\\
|
||
|
376.335836228653 3.66896574963568e-08\\
|
||
|
460.960448682844 2.73597185123051e-08\\
|
||
|
559.432570616939 2.0334592700151e-08\\
|
||
|
678.94068126961 1.48604462541444e-08\\
|
||
|
839.312949816637 1.03497545109271e-08\\
|
||
|
1000 7.58020925787276e-09\\
|
||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
0.1 0.000103988639710109\\
|
||
|
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1.48995507285286 0.000125200773153017\\
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||
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1.92879150802078 0.000145028662910928\\
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||
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2.21485523372636 0.000165421582656967\\
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||
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||
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||
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3.57728509936788 0.000462053653092282\\
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||
|
3.64385898376354 0.000444301690076666\\
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||
|
3.746050032749 0.000401490871474381\\
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||
|
3.88677669089267 0.000334169249530451\\
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||
|
4.4222739805059 0.000170217550409949\\
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||
|
4.76077523022638 0.000123188070662285\\
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||
|
5.12518692705333 9.27777533357391e-05\\
|
||
|
5.56859644428641 6.98278697413765e-05\\
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||
|
6.16296625513294 5.11162937166974e-05\\
|
||
|
6.88395206964551 3.7513061090711e-05\\
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||
|
7.8323825991792 2.68852794191347e-05\\
|
||
|
9.1614024571385 1.8436550945132e-05\\
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||
|
11.0164594963366 1.21307391875382e-05\\
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||
|
13.8720978054162 7.36682588683564e-06\\
|
||
|
18.292045048463 4.14167608426048e-06\\
|
||
|
25.4921465445142 2.12067998722584e-06\\
|
||
|
35.5263467657814 1.10792633200102e-06\\
|
||
|
47.7176094893875 6.34489282312018e-07\\
|
||
|
61.2049837247669 4.04041114929701e-07\\
|
||
|
76.3629826128226 2.75570769584807e-07\\
|
||
|
93.5343152029238 1.9749031946549e-07\\
|
||
|
114.566872863487 1.4405160838562e-07\\
|
||
|
141.62866162992 1.05418967420129e-07\\
|
||
|
179.992850678248 7.53481826964073e-08\\
|
||
|
412.682084570295 2.39567109625622e-08\\
|
||
|
505.479682119125 1.76488572213197e-08\\
|
||
|
619.144175597783 1.27818871387609e-08\\
|
||
|
758.367791499719 9.09889874401779e-09\\
|
||
|
946.184819472199 6.16881240263898e-09\\
|
||
|
1000 5.58332412998932e-09\\
|
||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
0.1 0.000110009306716853\\
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||
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||
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0.483820966492596 0.000111949037246895\\
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||
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0.661943345877439 0.000113774215714888\\
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||
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0.833529396509819 0.000116152401693014\\
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||
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||
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||
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1.32166418394661 0.000126994727442428\\
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
|
28.4743916646725 1.95267568213506e-06\\
|
||
|
35.8553985745982 1.28639395351798e-06\\
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||
|
44.324785912404 8.92962204769872e-07\\
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||
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53.7936150398071 6.51385876043374e-07\\
|
||
|
64.6860766154633 4.90512072076758e-07\\
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||
|
78.5045620020451 3.70523124977448e-07\\
|
||
|
96.157460014321 2.80945472495585e-07\\
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||
|
119.971773543589 2.11082394144838e-07\\
|
||
|
161.141427725302 1.46525392325845e-07\\
|
||
|
270.042071883778 7.74587223010911e-08\\
|
||
|
336.920570598027 5.79979202186438e-08\\
|
||
|
408.894822629486 4.43781129048905e-08\\
|
||
|
491.690357762803 3.38766916726025e-08\\
|
||
|
591.250841383188 2.54533236907731e-08\\
|
||
|
717.556091893694 1.85370225900837e-08\\
|
||
|
887.04968896544 1.28629676477814e-08\\
|
||
|
1000 1.03865891492337e-08\\
|
||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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3.11525422355549 0.000323578617601768\\
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||
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||
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||
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||
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3.57728509936788 0.000438422806790848\\
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||
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||
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||
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||
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||
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||
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||
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||
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|
||
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||
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||
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||
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||
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13.8720978054162 6.93457334522411e-06\\
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||
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18.8050405512858 3.65852134023875e-06\\
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||
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29.2729483504281 1.47714537226285e-06\\
|
||
|
85.2964449974102 1.698983972787e-07\\
|
||
|
151.070330448666 5.2752604976401e-08\\
|
||
|
218.443607114943 2.43042153739535e-08\\
|
||
|
293.404970921579 1.28044837198679e-08\\
|
||
|
383.33951017666 7.00855038877425e-09\\
|
||
|
500.840798984821 3.74821669541637e-09\\
|
||
|
685.229159528406 1.75473935348186e-09\\
|
||
|
1000 6.92454023447087e-10\\
|
||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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6.88395206964551 3.72553323208468e-05\\
|
||
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7.8323825991792 2.66964261972561e-05\\
|
||
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|
||
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11.0164594963366 1.20376100563483e-05\\
|
||
|
13.8720978054162 7.30469440287283e-06\\
|
||
|
18.4614694632455 4.02368740763619e-06\\
|
||
|
26.2070669648386 1.98056450736137e-06\\
|
||
|
37.5469422407334 9.76561820818653e-07\\
|
||
|
51.3701354335134 5.3758995557945e-07\\
|
||
|
67.1161176749627 3.29488869603869e-07\\
|
||
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84.5136633068474 2.20174486545317e-07\\
|
||
|
104.476597156081 1.54740840362616e-07\\
|
||
|
129.154966501488 1.10770538168833e-07\\
|
||
|
161.141427725302 7.95800386113291e-08\\
|
||
|
208.60240892485 5.50603633652723e-08\\
|
||
|
397.740302405804 2.21149334943059e-08\\
|
||
|
496.244487762891 1.58273931141042e-08\\
|
||
|
607.832312829724 1.14555388518188e-08\\
|
||
|
751.408106111696 8.02671587032835e-09\\
|
||
|
946.184819472199 5.35054626821901e-09\\
|
||
|
1000 4.84173808160309e-09\\
|
||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
0.1 9.2452141056678e-05\\
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
|
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||
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||
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||
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||
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|
||
|
69.6374473062824 3.38542269740303e-07\\
|
||
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|
||
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103.517795563018 1.91565448931411e-07\\
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||
|
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|
||
|
173.475935923393 9.85070900979107e-08\\
|
||
|
285.400976982924 5.25581499957518e-08\\
|
||
|
356.083255262927 3.91073830697976e-08\\
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||
|
432.151112778976 2.97511686596322e-08\\
|
||
|
524.468874949512 2.22661377188654e-08\\
|
||
|
636.507908129558 1.63787041836836e-08\\
|
||
|
779.636013040525 1.16625339421993e-08\\
|
||
|
972.720319245056 7.90457261366343e-09\\
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||
|
1000 7.5205644695094e-09\\
|
||
|
};
|
||
|
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||
|
table[row sep=crcr]{%
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||
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92.675933011469 2.84122122489313e-07\\
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||
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||
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152.469572701758 1.50846290450406e-07\\
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||
|
280.18665564592 7.10664614579381e-08\\
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||
|
349.577557436328 5.30684479499532e-08\\
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||
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424.255643071779 4.04857185710475e-08\\
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||
|
510.161531474984 3.08082484217316e-08\\
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||
|
619.144175597783 2.27330683218922e-08\\
|
||
|
758.367791499719 1.62337266836564e-08\\
|
||
|
946.184819472199 1.1031088716475e-08\\
|
||
|
1000 9.98841221082439e-09\\
|
||
|
};
|
||
|
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||
|
table[row sep=crcr]{%
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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280.18665564592 5.66834157176371e-08\\
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||
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349.577557436328 4.22784441511828e-08\\
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||
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||
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||
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624.878807200689 1.78160733018793e-08\\
|
||
|
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|
||
|
954.948563979197 8.6281052200465e-09\\
|
||
|
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|
||
|
};
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||
|
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||
|
table[row sep=crcr]{%
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||
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||
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||
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||
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||
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||
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||
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||
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146.949180062482 1.41066382638699e-07\\
|
||
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272.543253128103 6.62403032069316e-08\\
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||
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340.04119327037 4.96165029069407e-08\\
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||
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412.682084570295 3.79602368827775e-08\\
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||
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||
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||
|
724.202233460732 1.58325599410297e-08\\
|
||
|
895.265712599642 1.0979560009191e-08\\
|
||
|
1000 9.011753147682e-09\\
|
||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
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||
|
table[row sep=crcr]{%
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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28.7381269185107 1.83037878970775e-06\\
|
||
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36.1874981241128 1.20202325951004e-06\\
|
||
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44.7353305449846 8.31622056079418e-07\\
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||
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54.2918617761894 6.04624819635483e-07\\
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||
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65.8898955079996 4.47536250405451e-07\\
|
||
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79.9655452589236 3.37200660026265e-07\\
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||
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||
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|
||
|
161.141427725302 1.3536373031865e-07\\
|
||
|
277.61532944368 6.88252159882456e-08\\
|
||
|
346.369417737173 5.13952672001915e-08\\
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||
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||
|
505.479682119125 2.98629537916601e-08\\
|
||
|
613.462171799252 2.20497921359692e-08\\
|
||
|
751.408106111696 1.57565556892409e-08\\
|
||
|
937.501501514531 1.07139708514884e-08\\
|
||
|
1000 9.54277383513251e-09\\
|
||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
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||
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||
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8.99402217409205 1.99642110663454e-05\\
|
||
|
10.7159339982267 1.34032039464609e-05\\
|
||
|
13.2471398786612 8.47161646994992e-06\\
|
||
|
16.9914417203463 5.05607161712883e-06\\
|
||
|
22.4052786930002 2.91112279843684e-06\\
|
||
|
29.2729483504281 1.74163767171847e-06\\
|
||
|
37.5469422407334 1.10120925498642e-06\\
|
||
|
46.8458011587305 7.46948555878386e-07\\
|
||
|
57.3797641421414 5.33112345002567e-07\\
|
||
|
69.6374473062824 3.93374149330558e-07\\
|
||
|
84.5136633068474 2.95417927327583e-07\\
|
||
|
103.517795563018 2.22669423509006e-07\\
|
||
|
129.154966501488 1.66278594485007e-07\\
|
||
|
173.475935923393 1.14537928127025e-07\\
|
||
|
285.400976982924 6.11206785820795e-08\\
|
||
|
356.083255262927 4.54802022576636e-08\\
|
||
|
432.151112778976 3.46000651124471e-08\\
|
||
|
524.468874949512 2.58954932515578e-08\\
|
||
|
636.507908129558 1.90486081940581e-08\\
|
||
|
779.636013040525 1.3563749870387e-08\\
|
||
|
972.720319245056 9.19321688434344e-09\\
|
||
|
1000 8.74661016440386e-09\\
|
||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
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||
|
0.1 9.69823629889104e-05\\
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||
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0.506646100892127 9.90610698391231e-05\\
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||
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||
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1.34626057929891 0.000112789533922455\\
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3.44776405473447 0.000431341553125306\\
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||
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3.57728509936788 0.0004316576347069\\
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||
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||
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||
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||
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6.16296625513294 4.77085939148161e-05\\
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||
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6.88395206964551 3.49999150721356e-05\\
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||
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7.8323825991792 2.50710658675659e-05\\
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||
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9.1614024571385 1.71780136518707e-05\\
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||
|
11.0164594963366 1.12869997524151e-05\\
|
||
|
13.8720978054162 6.83655762817621e-06\\
|
||
|
18.8050405512858 3.61095983473549e-06\\
|
||
|
28.4743916646725 1.54727756578968e-06\\
|
||
|
49.0558370636505 5.20372343211911e-07\\
|
||
|
81.4537176628074 1.9214020445582e-07\\
|
||
|
118.87076977119 9.32312735412384e-08\\
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||
|
161.141427725302 5.30951351375537e-08\\
|
||
|
214.452607597167 3.1894376377903e-08\\
|
||
|
293.404970921579 1.860236274033e-08\\
|
||
|
648.353428605471 4.80848253662481e-09\\
|
||
|
862.851256636689 2.87581835410995e-09\\
|
||
|
1000 2.18974291441358e-09\\
|
||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
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||
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0.520854855057766 0.00010124662570021\\
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||
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||
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||
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||
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||
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||
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||
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||
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||
|
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||
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||
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29.2729483504281 1.48310914169164e-06\\
|
||
|
170.306502925284 4.09673419247559e-08\\
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||
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||
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301.63343472592 1.18103267937682e-08\\
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||
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||
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473.887960971765 4.05570585059275e-09\\
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||
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591.250841383187 2.31797054878541e-09\\
|
||
|
744.512291079513 1.26223545984491e-09\\
|
||
|
963.79347996158 6.22196033020179e-10\\
|
||
|
1000 5.61288719318092e-10\\
|
||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
|
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||
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||
|
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|
||
|
10.7159339982267 1.310161134422e-05\\
|
||
|
13.2471398786612 8.2735012219088e-06\\
|
||
|
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|
||
|
22.822244741869 2.72755663960327e-06\\
|
||
|
30.3726357970332 1.56967005572315e-06\\
|
||
|
39.3182875570577 9.72029592857116e-07\\
|
||
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49.5102015955635 6.46160034044481e-07\\
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||
|
60.6432939540807 4.59350568377994e-07\\
|
||
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73.5981447526576 3.37494357356692e-07\\
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||
|
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|
||
|
109.405470720574 1.892777525113e-07\\
|
||
|
136.500780654601 1.40642893059921e-07\\
|
||
|
183.342548256229 9.62646511270318e-08\\
|
||
|
296.122543798803 5.20357226013982e-08\\
|
||
|
369.460120519931 3.854054892539e-08\\
|
||
|
452.538627817017 2.88049019788423e-08\\
|
||
|
549.211648388779 2.14533234080418e-08\\
|
||
|
666.536326812492 1.570813913445e-08\\
|
||
|
816.416760492149 1.11370868723883e-08\\
|
||
|
1000 7.77436184850145e-09\\
|
||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
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||
|
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||
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||
|
0.421332174384729 9.27934623704146e-05\\
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||
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0.598104096238093 9.40901529296489e-05\\
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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|
||
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4.4222739805059 0.000150107378667092\\
|
||
|
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|
||
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5.12518692705333 8.18663291769054e-05\\
|
||
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|
||
|
6.10640754223204 4.63888378128404e-05\\
|
||
|
6.82077673286569 3.39950665671626e-05\\
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||
|
7.76050333513357 2.43500135571208e-05\\
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||
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|
||
|
10.7159339982267 1.14729422303671e-05\\
|
||
|
13.2471398786612 7.26567694206746e-06\\
|
||
|
16.835508029612 4.43299192031026e-06\\
|
||
|
21.7940698430296 2.65895926067324e-06\\
|
||
|
27.9541599906785 1.65665330710599e-06\\
|
||
|
35.2003147279668 1.08982542124e-06\\
|
||
|
43.5149650092505 7.55649709135941e-07\\
|
||
|
52.8107971193434 5.50705069747892e-07\\
|
||
|
63.5042516859598 4.14367343684538e-07\\
|
||
|
76.3629826128226 3.16879850300103e-07\\
|
||
|
92.675933011469 2.42928590579215e-07\\
|
||
|
115.628013120738 1.82236215101026e-07\\
|
||
|
153.881775003835 1.27836989854711e-07\\
|
||
|
275.067600790807 6.24491830609934e-08\\
|
||
|
343.190719745904 4.67068614698865e-08\\
|
||
|
416.504424854519 3.56902251713913e-08\\
|
||
|
500.840798984821 2.72041425367968e-08\\
|
||
|
602.254120146193 2.04082289593092e-08\\
|
||
|
730.909932860292 1.48396803805134e-08\\
|
||
|
903.557834613892 1.02819506619376e-08\\
|
||
|
1000 8.57749894484449e-09\\
|
||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
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||
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||
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0.488302208687789 9.83954287053046e-05\\
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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5.12518692705333 8.61611336978476e-05\\
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||
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5.56859644428641 6.4836993756402e-05\\
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||
|
6.16296625513294 4.7451062621475e-05\\
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||
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6.88395206964551 3.48116856894877e-05\\
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||
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||
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||
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11.0164594963366 1.12286231936817e-05\\
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||
|
13.8720978054162 6.80287675388796e-06\\
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||
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18.6324631193156 3.66459678894313e-06\\
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||
|
27.697619350369 1.63218445265623e-06\\
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||
|
44.7353305449846 6.26822304412387e-07\\
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||
|
68.3651600451024 2.74080488879543e-07\\
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||
|
95.275004724273 1.462457250407e-07\\
|
||
|
125.631660247412 8.83232481756404e-08\\
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||
|
161.141427725302 5.71595521684842e-08\\
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||
|
206.688024962908 3.7683805729868e-08\\
|
||
|
277.61532944368 2.34437234939699e-08\\
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||
|
514.886745013749 8.73199301217271e-09\\
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||
|
660.419396233031 5.73973512231102e-09\\
|
||
|
847.086826655742 3.70359445063856e-09\\
|
||
|
1000 2.73875241060332e-09\\
|
||
|
};
|
||
|
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||
|
table[row sep=crcr]{%
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||
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||
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||
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||
|
};
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||
|
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||
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table[row sep=crcr]{%
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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xmode=log,
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||
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||
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xmax=1000,
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||
|
xminorticks=true,
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||
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xlabel={Frequency [$\si{\hertz}$]},
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||
|
ymin=-380,
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||
|
ymax=0,
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||
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||
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ylabel={Phase [deg]},
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||
|
xminorgrids
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||
|
]
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};
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table[row sep=crcr]{%
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||
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};
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||
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||
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table[row sep=crcr]{%
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};
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||
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||
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};
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||
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};
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||
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||
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table[row sep=crcr]{%
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||
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||
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1000 -329.399839682371\\
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||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
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||
|
table[row sep=crcr]{%
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||
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||
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||
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||
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1000 -156.902998696731\\
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||
|
};
|
||
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\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
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||
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table[row sep=crcr]{%
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||
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||
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||
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||
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||
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||
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1000 -157.371821836267\\
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};
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||
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||
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table[row sep=crcr]{%
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||
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};
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||
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||
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table[row sep=crcr]{%
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||
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||
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};
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||
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||
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table[row sep=crcr]{%
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};
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||
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||
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table[row sep=crcr]{%
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};
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};
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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|
||
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|
||
|
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|
||
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|
||
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233.006141069691 -179.804275570755\\
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||
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272.543253128104 -179.83267911444\\
|
||
|
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||
|
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|
||
|
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|
||
|
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|
||
|
730.909932860277 -179.937618038116\\
|
||
|
954.948563979212 -179.952253810262\\
|
||
|
1000 -179.954404899517\\
|
||
|
};
|
||
|
\end{axis}
|
||
|
\end{tikzpicture}
|
||
|
#+end_src
|
||
|
|
||
|
#+name: fig:bode_plot_mech_sys_uncertainty
|
||
|
#+caption: Bode plot of the mechanical system - Uncertainty ([[./figs/bode_plot_mech_sys_uncertainty.png][png]], [[./figs/bode_plot_mech_sys_uncertainty.pdf][pdf]], [[./figs/bode_plot_mech_sys_uncertainty.tex][tex]]).
|
||
|
#+RESULTS:
|
||
|
[[file:figs/bode_plot_mech_sys_uncertainty.png]]
|
||
|
|
||
|
* Bode plot of the controller
|
||
|
#+NAME: data:bode_Kfb_magnitude
|
||
|
#+begin_src latex :exports none
|
||
|
0.1 43470401.5635197\\
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||
|
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||
|
0.225088005209546 8841324.97190729\\
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||
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||
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||
|
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|
||
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||
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|
||
|
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|
||
|
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|
||
|
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||
|
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||
|
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||
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||
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||
|
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|
||
|
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|
||
|
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|
||
|
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|
||
|
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|
||
|
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|
||
|
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||
|
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||
|
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||
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||
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||
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||
|
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||
|
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|
||
|
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|
||
|
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|
||
|
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|
||
|
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||
|
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||
|
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||
|
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||
|
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||
|
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||
|
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|
||
|
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|
||
|
12.0804213467733 76239.9049999386\\
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||
|
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|
||
|
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||
|
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||
|
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||
|
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||
|
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||
|
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||
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||
|
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|
||
|
359.381366380463 101766885.625809\\
|
||
|
#+end_src
|
||
|
|
||
|
#+NAME: data:bode_Kfb_phase
|
||
|
#+begin_src latex :exports none
|
||
|
0.1 -155.364714507098\\
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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|
||
|
730.909932860277 86.2047189454912\\
|
||
|
786.8571506937 77.500553662828\\
|
||
|
854.93270662683 66.8230752479042\\
|
||
|
946.184819472219 52.7908656572718\\
|
||
|
1000 44.8958338224281\\
|
||
|
#+end_src
|
||
|
|
||
|
#+begin_src latex :file bode_Kfb.pdf :tangle figs/bode_Kfb.tex :exports results
|
||
|
<<tikz_default>>
|
||
|
\setlength\fwidth{7cm}
|
||
|
\setlength\fheight{5cm}
|
||
|
|
||
|
\begin{tikzpicture}
|
||
|
\begin{axis}[%
|
||
|
width=\fwidth,
|
||
|
height=0.55\fheight,
|
||
|
at={(0,0.45\fheight)},
|
||
|
xmode=log,
|
||
|
xmin=0.1,
|
||
|
xmax=1000,
|
||
|
xminorticks=true,
|
||
|
xticklabels={{}},
|
||
|
xminorticks=true,
|
||
|
ymode=log,
|
||
|
ymin=5e3,
|
||
|
ymax=1e8,
|
||
|
yminorticks=true,
|
||
|
ylabel={Magnitude [m/N]},
|
||
|
xminorgrids,
|
||
|
yminorgrids
|
||
|
]
|
||
|
\addplot [color=mycolor1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:bode_Kfb_magnitude>>
|
||
|
};
|
||
|
\end{axis}
|
||
|
|
||
|
\begin{axis}[%
|
||
|
width=\fwidth,
|
||
|
height=0.4\fheight,
|
||
|
at={(0,0)},
|
||
|
xmode=log,
|
||
|
xmin=0.1,
|
||
|
xmax=1000,
|
||
|
xminorticks=true,
|
||
|
xlabel={Frequency [$\si{\hertz}$]},
|
||
|
ymin=-180,
|
||
|
ymax=180,
|
||
|
ytick={-180, -90, 0, 90, 180},
|
||
|
ylabel={Phase [deg]},
|
||
|
xminorgrids
|
||
|
]
|
||
|
\addplot [color=mycolor1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:bode_Kfb_phase>>
|
||
|
};
|
||
|
\end{axis}
|
||
|
\end{tikzpicture}
|
||
|
#+end_src
|
||
|
|
||
|
#+name: fig:bode_Kfb
|
||
|
#+caption: Bode plot of the controller ([[./figs/bode_Kfb.png][png]], [[./figs/bode_Kfb.pdf][pdf]], [[./figs/bode_Kfb.tex][tex]]).
|
||
|
#+RESULTS:
|
||
|
[[file:figs/bode_Kfb.png]]
|
||
|
|
||
|
* Bode plot of the loop gain
|
||
|
#+NAME: data:bode_plot_loop_gain_magnitude
|
||
|
#+begin_src latex :exports none
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||
|
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||
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||
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||
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||
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||
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||
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||
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||
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||
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|
||
|
#+end_src
|
||
|
|
||
|
#+NAME: data:bode_plot_loop_gain_phase
|
||
|
#+begin_src latex :exports none
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
|
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||
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||
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||
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||
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||
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||
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||
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||
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||
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|
||
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||
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|
||
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||
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||
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||
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||
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||
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||
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|
||
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||
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||
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|
||
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|
||
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|
||
|
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|
||
|
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|
||
|
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|
||
|
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|
||
|
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|
||
|
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|
||
|
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|
||
|
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|
||
|
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|
||
|
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|
||
|
1000 -194.454742635627\\
|
||
|
#+end_src
|
||
|
|
||
|
#+begin_src latex :file bode_plot_loop_gain.pdf :tangle figs/bode_plot_loop_gain.tex :exports results
|
||
|
<<tikz_default>>
|
||
|
\setlength\fwidth{7cm}
|
||
|
\setlength\fheight{5cm}
|
||
|
|
||
|
\begin{tikzpicture}
|
||
|
\begin{axis}[%
|
||
|
width=\fwidth,
|
||
|
height=0.55\fheight,
|
||
|
at={(0,0.45\fheight)},
|
||
|
xmode=log,
|
||
|
xmin=0.1,
|
||
|
xmax=1000,
|
||
|
xminorticks=true,
|
||
|
xticklabels={{}},
|
||
|
xminorticks=true,
|
||
|
ymode=log,
|
||
|
ymin=1e-3,
|
||
|
ymax=1e3,
|
||
|
ytick={1e-3, 1e-2, 1e-1, 1, 1e1, 1e2, 1e3},
|
||
|
yticklabels={{}, {$10^{-2}$}, {}, {$10^0$}, {}, {$10^2$}, {}},
|
||
|
yminorticks=true,
|
||
|
ylabel={Magnitude [m/N]},
|
||
|
xminorgrids,
|
||
|
yminorgrids
|
||
|
]
|
||
|
\addplot [color=mycolor1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:bode_plot_loop_gain_magnitude>>
|
||
|
};
|
||
|
\end{axis}
|
||
|
|
||
|
\begin{axis}[%
|
||
|
width=\fwidth,
|
||
|
height=0.4\fheight,
|
||
|
at={(0,0)},
|
||
|
xmode=log,
|
||
|
xmin=0.1,
|
||
|
xmax=1000,
|
||
|
xminorticks=true,
|
||
|
xlabel={Frequency [$\si{\hertz}$]},
|
||
|
ymin=-270,
|
||
|
ymax=0,
|
||
|
ytick={-270, -180, -90, 0},
|
||
|
ylabel={Phase [deg]},
|
||
|
xminorgrids
|
||
|
]
|
||
|
\addplot [color=mycolor1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:bode_plot_loop_gain_phase>>
|
||
|
};
|
||
|
\end{axis}
|
||
|
\end{tikzpicture}
|
||
|
#+end_src
|
||
|
|
||
|
#+name: fig:bode_plot_loop_gain
|
||
|
#+caption: Bode plot of the loop gain ([[./figs/bode_plot_loop_gain.png][png]], [[./figs/bode_plot_loop_gain.pdf][pdf]], [[./figs/bode_plot_loop_gain.tex][tex]]).
|
||
|
#+RESULTS:
|
||
|
[[file:figs/bode_plot_loop_gain.png]]
|
||
|
|
||
|
* Upper bounds with weights
|
||
|
#+begin_src latex :file spec_S_T_weights.pdf :tangle figs/spec_S_T_weights.tex :exports results
|
||
|
<<tikz_default>>
|
||
|
\setlength\fwidth{7cm}
|
||
|
\setlength\fheight{4cm}
|
||
|
|
||
|
\begin{tikzpicture}
|
||
|
\begin{axis}[%
|
||
|
name=axis,
|
||
|
width=\fwidth,
|
||
|
height=\fheight,
|
||
|
at={(0, 0)},
|
||
|
xmode=log,
|
||
|
xmin=0.1,
|
||
|
xmax=1000,
|
||
|
xminorticks=true,
|
||
|
xlabel={Frequency [Hz]},
|
||
|
ymode=log,
|
||
|
ymin=0.001,
|
||
|
ymax=10,
|
||
|
yminorticks=true,
|
||
|
ylabel={Magnitude},
|
||
|
axis background/.style={fill=white},
|
||
|
xminorgrids,
|
||
|
yminorgrids
|
||
|
]
|
||
|
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-robust-stability>>
|
||
|
};
|
||
|
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-bandwidth>>
|
||
|
};
|
||
|
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-noise-attenuation-1>>
|
||
|
};
|
||
|
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-noise-attenuation-2>>
|
||
|
};
|
||
|
\addplot [color=S, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-dist-rejection>>
|
||
|
};
|
||
|
\addplot [color=T, dashed, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:weight-hl>>
|
||
|
};
|
||
|
\addplot [color=S, dashed, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:weight-hh>>
|
||
|
};
|
||
|
\end{axis}
|
||
|
\begin{customlegend}[legend cell align=left, %<= to align cells
|
||
|
legend entries={ % <= in the following there are the entries
|
||
|
${w_L}^{-1}$,
|
||
|
${w_H}^{-1}$,
|
||
|
},
|
||
|
legend style={at={(axis.north east)}, anchor=north east, outer sep=5pt, font=\footnotesize}]
|
||
|
\addlegendimage{dashed, S}
|
||
|
\addlegendimage{dashed, T}
|
||
|
\end{customlegend}
|
||
|
\end{tikzpicture}
|
||
|
#+end_src
|
||
|
|
||
|
#+name: fig:spec_S_T_weights
|
||
|
#+caption: Upper bounds with weights ([[./figs/spec_S_T_weights.png][png]], [[./figs/spec_S_T_weights.pdf][pdf]], [[./figs/spec_S_T_weights.tex][tex]]).
|
||
|
#+RESULTS:
|
||
|
[[file:figs/spec_S_T_weights.png]]
|
||
|
|
||
|
* Upper bounds with Complementary Filters
|
||
|
#+begin_src latex :file hinf_filters_result_tikz.pdf :tangle figs/hinf_filters_result_tikz.tex :exports results
|
||
|
<<tikz_default>>
|
||
|
\setlength\fwidth{7cm}
|
||
|
\setlength\fheight{4cm}
|
||
|
|
||
|
\begin{tikzpicture}
|
||
|
\begin{axis}[%
|
||
|
name=axis,
|
||
|
width=\fwidth,
|
||
|
height=\fheight,
|
||
|
at={(0, 0)},
|
||
|
scale only axis,
|
||
|
separate axis lines,
|
||
|
every outer x axis line/.append style={black},
|
||
|
every x tick label/.append style={font=\color{black}},
|
||
|
every x tick/.append style={black},
|
||
|
xmode=log,
|
||
|
xmin=0.1,
|
||
|
xmax=1000,
|
||
|
xminorticks=true,
|
||
|
xlabel={Frequency [Hz]},
|
||
|
every outer y axis line/.append style={black},
|
||
|
every y tick label/.append style={font=\color{black}},
|
||
|
every y tick/.append style={black},
|
||
|
ymode=log,
|
||
|
ymin=0.001,
|
||
|
ymax=10,
|
||
|
yminorticks=true,
|
||
|
ylabel={Magnitude},
|
||
|
axis background/.style={fill=white},
|
||
|
xmajorgrids,
|
||
|
xminorgrids,
|
||
|
ymajorgrids,
|
||
|
yminorgrids
|
||
|
]
|
||
|
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-robust-stability>>
|
||
|
};
|
||
|
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-bandwidth>>
|
||
|
};
|
||
|
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-noise-attenuation-1>>
|
||
|
};
|
||
|
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-noise-attenuation-2>>
|
||
|
};
|
||
|
\addplot [color=S, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-dist-rejection>>
|
||
|
};
|
||
|
\addplot [color=T, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:hl>>
|
||
|
};
|
||
|
\addplot [color=S, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:hh>>
|
||
|
};
|
||
|
\end{axis}
|
||
|
\end{tikzpicture}
|
||
|
#+end_src
|
||
|
|
||
|
#+name: fig:hinf_filters_result_tikz
|
||
|
#+caption: Upper bounds with Complementary Filters ([[./figs/hinf_filters_result_tikz.png][png]], [[./figs/hinf_filters_result_tikz.pdf][pdf]], [[./figs/hinf_filters_result_tikz.tex][tex]]).
|
||
|
#+RESULTS:
|
||
|
[[file:figs/hinf_filters_result_tikz.png]]
|
||
|
|
||
|
* Upper bounds with weights and Complementary Filters
|
||
|
#+begin_src latex :file hinf_filters_result_weights.pdf :tangle figs/hinf_filters_result_weights.tex :exports results
|
||
|
<<tikz_default>>
|
||
|
\setlength\fwidth{7cm}
|
||
|
\setlength\fheight{4cm}
|
||
|
|
||
|
\begin{tikzpicture}
|
||
|
\begin{axis}[%
|
||
|
name=axis,
|
||
|
width=\fwidth,
|
||
|
height=\fheight,
|
||
|
at={(0, 0)},
|
||
|
scale only axis,
|
||
|
separate axis lines,
|
||
|
every outer x axis line/.append style={black},
|
||
|
every x tick label/.append style={font=\color{black}},
|
||
|
every x tick/.append style={black},
|
||
|
xmode=log,
|
||
|
xmin=0.1,
|
||
|
xmax=1000,
|
||
|
xminorticks=true,
|
||
|
xlabel={Frequency [Hz]},
|
||
|
every outer y axis line/.append style={black},
|
||
|
every y tick label/.append style={font=\color{black}},
|
||
|
every y tick/.append style={black},
|
||
|
ymode=log,
|
||
|
ymin=0.001,
|
||
|
ymax=10,
|
||
|
yminorticks=true,
|
||
|
ylabel={Magnitude},
|
||
|
axis background/.style={fill=white},
|
||
|
xmajorgrids,
|
||
|
xminorgrids,
|
||
|
ymajorgrids,
|
||
|
yminorgrids
|
||
|
]
|
||
|
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-robust-stability>>
|
||
|
};
|
||
|
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-bandwidth>>
|
||
|
};
|
||
|
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-noise-attenuation-1>>
|
||
|
};
|
||
|
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-noise-attenuation-2>>
|
||
|
};
|
||
|
\addplot [color=S, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-dist-rejection>>
|
||
|
};
|
||
|
\addplot [color=T, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:hl>>
|
||
|
};
|
||
|
\addplot [color=S, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:hh>>
|
||
|
};
|
||
|
\addplot [color=T, dashed, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:weight-hl>>
|
||
|
};
|
||
|
\addplot [color=S, dashed, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:weight-hh>>
|
||
|
};
|
||
|
\end{axis}
|
||
|
|
||
|
\begin{customlegend}[legend cell align=left, %<= to align cells
|
||
|
legend entries={ % <= in the following there are the entries
|
||
|
${w_L}^{-1}$,
|
||
|
${w_H}^{-1}$,
|
||
|
$H_L$,
|
||
|
$H_H$
|
||
|
},
|
||
|
legend style={at={(axis.north east)}, anchor=north east, outer sep=5pt, font=\footnotesize}]
|
||
|
\addlegendimage{dashed, S}
|
||
|
\addlegendimage{dashed, T}
|
||
|
\addlegendimage{S}
|
||
|
\addlegendimage{T}
|
||
|
\end{customlegend}
|
||
|
|
||
|
\end{tikzpicture}
|
||
|
#+end_src
|
||
|
|
||
|
#+name: fig:hinf_filters_result_weights
|
||
|
#+caption: Upper bounds with weights and Complementary Filters ([[./figs/hinf_filters_result_weights.png][png]], [[./figs/hinf_filters_result_weights.pdf][pdf]], [[./figs/hinf_filters_result_weights.tex][tex]]).
|
||
|
#+RESULTS:
|
||
|
[[file:figs/hinf_filters_result_weights.png]]
|
||
|
|
||
|
* Robustness - Nyquist
|
||
|
#+begin_src latex :file nyquist_robustness.pdf :tangle figs/nyquist_robustness.tex :exports results
|
||
|
<<tikz_default>>
|
||
|
\setlength\fwidth{4cm}
|
||
|
\setlength\fheight{4cm}
|
||
|
|
||
|
\begin{tikzpicture}
|
||
|
\begin{axis}[%
|
||
|
width=\fwidth,
|
||
|
height=\fheight,
|
||
|
at={(0,0)},
|
||
|
xmin=-1.4,
|
||
|
xmax=0.2,
|
||
|
xtick={-1.4, -1.2, -1, -0.8, -0.6, -0.4, -0.2, 0, 0.2},
|
||
|
xticklabels={{}, {-1.2}, {}, {-0.8}, {}, {-0.4}, {},{0}, {}},
|
||
|
xlabel={Real Part},
|
||
|
ymin=-1.4,
|
||
|
ymax=0.2,
|
||
|
ytick={-1.4, -1.2, -1, -0.8, -0.6, -0.4, -0.2, 0, 0.2},
|
||
|
yticklabels={{}, {-1.2}, {}, {-0.8}, {}, {-0.4}, {},{0}, {}},
|
||
|
ylabel={Imaginary Part}
|
||
|
]
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
-1.36797893526011 -1.50001862303624\\
|
||
|
-1.16498995424946 -1.35696621231185\\
|
||
|
-0.99559961025809 -1.22636638984475\\
|
||
|
-0.853981047113767 -1.10705800080225\\
|
||
|
-0.735287602107294 -0.998016431478695\\
|
||
|
-0.635489695862679 -0.898340115021801\\
|
||
|
-0.551240783141879 -0.807238670583468\\
|
||
|
-0.479767470373703 -0.724021826265133\\
|
||
|
-0.418779528703161 -0.648088368331652\\
|
||
|
-0.366395990332399 -0.578914495116748\\
|
||
|
-0.321083862027054 -0.516041206974297\\
|
||
|
-0.281606321007443 -0.459060726222526\\
|
||
|
-0.216422889520012 -0.361318857422488\\
|
||
|
-0.0929771380261113 -0.173362161727646\\
|
||
|
-0.035769159430413 -0.087189343521481\\
|
||
|
-0.0217254152011825 -0.0637445100449405\\
|
||
|
-0.0132966735281785 -0.0474701710373959\\
|
||
|
-0.00732897645877051 -0.0328869515231414\\
|
||
|
-0.00480426849737592 -0.0235190250988806\\
|
||
|
-0.00437071071015693 -0.0174407071898124\\
|
||
|
-0.0051960505234796 -0.0141102837331601\\
|
||
|
-0.0087652414789805 -0.00586854263157233\\
|
||
|
-0.00814604208714309 -0.00174554484874134\\
|
||
|
-0.00563245364328702 0.00109158594302494\\
|
||
|
-0.00301516687412939 0.00183036879614207\\
|
||
|
-0.000566779138372553 0.00101175288654698\\
|
||
|
4.33619439887956e-06 4.64928740351311e-06\\
|
||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
-1.38182288726253 -1.47720407548674\\
|
||
|
-1.17870593604476 -1.33548392815947\\
|
||
|
-1.00915187892965 -1.20606472916479\\
|
||
|
-0.867327929571845 -1.08779627251356\\
|
||
|
-0.748382296263 -0.979666505553309\\
|
||
|
-0.6482811237289 -0.880787680121524\\
|
||
|
-0.563674588518503 -0.790384251379557\\
|
||
|
-0.491787249016289 -0.707781595808656\\
|
||
|
-0.430328358296008 -0.632394720384497\\
|
||
|
-0.377418281951746 -0.563716288696618\\
|
||
|
-0.331527494429166 -0.501303563132216\\
|
||
|
-0.291424947147702 -0.444764255017566\\
|
||
|
-0.224886811689192 -0.347900707876285\\
|
||
|
-0.130461816785873 -0.209758784622679\\
|
||
|
-0.0836704578794285 -0.144049177057663\\
|
||
|
-0.0317717903308949 -0.0719651343124343\\
|
||
|
-0.0192568735770182 -0.0526247411250802\\
|
||
|
-0.0101062808148391 -0.0357399886459873\\
|
||
|
-0.00584629385641566 -0.0250681751717676\\
|
||
|
-0.00427760097148022 -0.01821958147713\\
|
||
|
-0.00452284243741552 -0.0136749557973785\\
|
||
|
-0.00641101232382146 -0.00970837892099996\\
|
||
|
-0.00796341091244956 -0.00525775051172261\\
|
||
|
-0.00737661196267081 -0.00153941521146583\\
|
||
|
-0.00508976562629626 0.00100992422232382\\
|
||
|
-0.00272072529591427 0.0016654180204112\\
|
||
|
-0.000312287827330282 0.000721997291961651\\
|
||
|
3.9232421120694e-06 4.20209650453529e-06\\
|
||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
-1.56 -1.50535724900931\\
|
||
|
-1.390562472599 -1.39960601016154\\
|
||
|
-1.1914736871022 -1.26351068856521\\
|
||
|
-1.02514489104354 -1.13907720422495\\
|
||
|
-0.885858919182712 -1.0252185865401\\
|
||
|
-0.768857657453007 -0.920980627146513\\
|
||
|
-0.670182863069839 -0.825529617702031\\
|
||
|
-0.586545725763649 -0.738141612238793\\
|
||
|
-0.515220401554461 -0.658192268771019\\
|
||
|
-0.453957319695559 -0.585146379755512\\
|
||
|
-0.400912442964713 -0.518546331952047\\
|
||
|
-0.354588922046141 -0.457998997818767\\
|
||
|
-0.277564988204617 -0.353722680740706\\
|
||
|
-0.189930939976545 -0.234891112679668\\
|
||
|
-0.145100605685094 -0.177205309134045\\
|
||
|
-0.10905479740875 -0.13363228930125\\
|
||
|
-0.0806420898717188 -0.10134999526768\\
|
||
|
-0.0423866839328368 -0.0603668217745521\\
|
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||
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||
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||
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||
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||
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||
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-0.761477058582718 -0.517783666403887\\
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||
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-0.683336337961622 -0.447526722719317\\
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||
|
-0.615134118399525 -0.382948527517328\\
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||
|
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||
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||
|
-0.367090219292119 -0.138057433763396\\
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||
|
-0.329166941575128 -0.103785330195134\\
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||
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-0.293940766806355 -0.0741180024682204\\
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||
|
-0.261229470104432 -0.0488567157546642\\
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||
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-0.230943106475923 -0.0277455467526784\\
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||
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||
|
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||
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||
|
-0.0983993593063619 0.0317169157826898\\
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||
|
-0.0839280864788496 0.0340747496054825\\
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||
|
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||
|
-0.0509786257210472 0.0349725707112813\\
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||
|
-0.0360500595328743 0.0326664369615024\\
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||
|
-0.0252685860724196 0.0294335011496369\\
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||
|
-0.01459745471866 0.024255342899735\\
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||
|
-0.00820035003830211 0.0196078479908413\\
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||
|
-0.00167687341249545 0.0129776939262345\\
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||
|
0.00531391165394179 0.00476727820035538\\
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||
|
0.00533507067131156 0.00181798054013926\\
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||
|
0.00386350850104411 -0.000364179936283016\\
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||
|
0.00148241424171869 -0.00106372436853164\\
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||
|
-7.39728816356866e-06 -1.41275226703819e-05\\
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||
|
-2.89520000129606e-06 -3.17656691461998e-06\\
|
||
|
};
|
||
|
\addplot [color=black, line width=1.5pt, forget plot]
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||
|
table[row sep=crcr]{%
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||
|
-1.56 -1.31536039739137\\
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||
|
-1.39519165658224 -1.21724884641018\\
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||
|
-1.20616502526331 -1.09396735605765\\
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||
|
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||
|
-0.914759853882887 -0.87734512797337\\
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||
|
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||
|
-0.707157724167183 -0.694928230836314\\
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||
|
-0.625751468555272 -0.61483992088067\\
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||
|
-0.555656599458786 -0.541459970051376\\
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||
|
-0.494752271168762 -0.474369768813685\\
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||
|
-0.441311590551505 -0.413223939395889\\
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||
|
-0.278628849762548 -0.222835428366151\\
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||
|
-0.246990641943052 -0.187634884080071\\
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||
|
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||
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||
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||
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||
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||
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||
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||
|
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||
|
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||
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||
|
-0.00134565449189261 -0.000447481226480972\\
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||
|
-9.33014288835299e-05 0.000176897816299038\\
|
||
|
4.26700953015668e-07 4.18235178711868e-07\\
|
||
|
};
|
||
|
\end{axis}
|
||
|
\end{tikzpicture}
|
||
|
#+end_src
|
||
|
|
||
|
#+name: fig:nyquist_robustness
|
||
|
#+caption: Robustness - Nyquist ([[./figs/nyquist_robustness.png][png]], [[./figs/nyquist_robustness.pdf][pdf]], [[./figs/nyquist_robustness.tex][tex]]).
|
||
|
#+RESULTS:
|
||
|
[[file:figs/nyquist_robustness.png]]
|
||
|
|
||
|
* Robustness - Loop Gain
|
||
|
#+begin_src latex :file bode_plot_loop_gain_robustness.pdf :tangle figs/bode_plot_loop_gain_robustness.tex :exports results
|
||
|
<<tikz_default>>
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||
|
\setlength\fwidth{7cm}
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||
|
\setlength\fheight{5cm}
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||
|
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||
|
\begin{tikzpicture}
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||
|
\begin{axis}[%
|
||
|
width=\fwidth,
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||
|
height=0.55\fheight,
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||
|
at={(0,0.45\fheight)},
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||
|
xmode=log,
|
||
|
xmin=0.1,
|
||
|
xmax=1000,
|
||
|
xminorticks=true,
|
||
|
xticklabels={{}},
|
||
|
xminorticks=true,
|
||
|
ymode=log,
|
||
|
ymin=1e-3,
|
||
|
ymax=1e3,
|
||
|
ytick={1e-3, 1e-2, 1e-1, 1, 1e1, 1e2, 1e3},
|
||
|
yticklabels={{}, {$10^{-2}$}, {}, {$10^0$}, {}, {$10^2$}, {}},
|
||
|
yminorticks=true,
|
||
|
ylabel={Magnitude [m/N]},
|
||
|
xminorgrids,
|
||
|
yminorgrids
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||
|
]
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||
|
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||
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||
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||
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||
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table[row sep=crcr]{%
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||
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||
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||
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||
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};
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||
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table[row sep=crcr]{%
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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table[row sep=crcr]{%
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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|
||
|
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||
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||
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||
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||
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||
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||
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||
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1000 -171.114165657579\\
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||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
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||
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table[row sep=crcr]{%
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||
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||
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||
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||
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||
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1000 -172.496839645079\\
|
||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
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||
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||
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||
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||
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1000 -173.941554924916\\
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||
|
};
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||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
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||
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table[row sep=crcr]{%
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||
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||
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||
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||
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||
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1000 -171.381286042618\\
|
||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
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||
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table[row sep=crcr]{%
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||
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||
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};
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||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
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||
|
table[row sep=crcr]{%
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};
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||
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||
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table[row sep=crcr]{%
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||
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};
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||
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||
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table[row sep=crcr]{%
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};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
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||
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table[row sep=crcr]{%
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||
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};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
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||
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table[row sep=crcr]{%
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275.067600790807 -104.448650949735\\
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282.781797962532 -104.522709232554\\
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||
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307.246884270909 -104.904652691143\\
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318.789129267769 -105.158194225658\\
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330.764978074424 -105.468265195542\\
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||
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||
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||
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||
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||
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887.04968896542 -156.994471416592\\
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||
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981.72984061889 -169.250305124494\\
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||
|
1000 -171.544521175135\\
|
||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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140.328908478584 -110.175178801276\\
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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255.509709035257 -105.574276090204\\
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||
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||
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||
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||
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267.563844455207 -105.557163721369\\
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||
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270.042071883779 -105.561583927846\\
|
||
|
275.067600790807 -105.578584544888\\
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||
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||
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285.40097698292 -105.646406787985\\
|
||
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293.404970921572 -105.728263310587\\
|
||
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301.63343472593 -105.838095355025\\
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||
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310.0926635932 -105.977260177756\\
|
||
|
318.789129267769 -106.147199237862\\
|
||
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330.764978074424 -106.424314634102\\
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||
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343.1907197459 -106.76276288728\\
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||
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356.083255262919 -107.166755741718\\
|
||
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369.46012051994 -107.640849248975\\
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||
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386.890073932801 -108.339585769886\\
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||
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|
||
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424.255643071768 -110.131857904331\\
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||
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||
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465.229952396024 -112.53319765298\\
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||
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487.17802187946 -113.997778271907\\
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||
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|
||
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539.177464038763 -117.939932019488\\
|
||
|
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|
||
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||
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|
||
|
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|
||
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710.970943231237 -135.17370975647\\
|
||
|
758.367791499744 -140.858094872203\\
|
||
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808.924348680602 -147.215582467729\\
|
||
|
870.843149769058 -155.244784872607\\
|
||
|
954.948563979212 -166.177782388948\\
|
||
|
1000 -171.872159572377\\
|
||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
0.1 -155.636346000086\\
|
||
|
0.108651577465251 -157.353782374141\\
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||
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0.118051652856874 -158.930380254901\\
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||
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||
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0.139361927422416 -161.692506702327\\
|
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||
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};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
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||
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table[row sep=crcr]{%
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||
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1000 -256.550678982586\\
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||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
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||
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table[row sep=crcr]{%
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1000 -172.279181231225\\
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||
|
};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
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||
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};
|
||
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
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||
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table[row sep=crcr]{%
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||
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};
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||
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table[row sep=crcr]{%
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||
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};
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||
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\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
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||
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table[row sep=crcr]{%
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||
|
8.58882855954615 -144.774620161222\\
|
||
|
8.8296999554939 -144.861154661988\\
|
||
|
9.07732652520994 -144.974520251574\\
|
||
|
9.33189771573286 -145.115059703511\\
|
||
|
9.6824661193026 -145.345245111981\\
|
||
|
10.0462042134688 -145.624922678504\\
|
||
|
10.4236067397645 -145.954621595262\\
|
||
|
10.9153593533143 -146.437717098176\\
|
||
|
11.430311291145 -147.000198028813\\
|
||
|
11.9695570235905 -147.642374300087\\
|
||
|
12.6503372039588 -148.518221541289\\
|
||
|
13.369837418249 -149.508431694137\\
|
||
|
14.2611370719404 -150.806856092002\\
|
||
|
15.2118551798618 -152.257027633563\\
|
||
|
16.2259528707813 -153.855415639561\\
|
||
|
17.4679621512724 -155.857824362758\\
|
||
|
18.9792164283904 -158.324646174581\\
|
||
|
20.6212180399902 -161.004831184814\\
|
||
|
22.6128006633736 -164.213776049563\\
|
||
|
25.0264009641792 -167.996508201912\\
|
||
|
27.9541599906775 -172.385696192116\\
|
||
|
31.8055201533307 -177.791202818151\\
|
||
|
37.2023668141304 -184.66151495032\\
|
||
|
47.2796959160057 -195.522851758987\\
|
||
|
64.0924401935684 -209.260322479074\\
|
||
|
75.6621850048106 -216.438818850657\\
|
||
|
86.8838263525077 -222.138960491558\\
|
||
|
98.8541702191994 -227.181223927243\\
|
||
|
111.441525146678 -231.601422438283\\
|
||
|
125.631660247406 -235.762899486069\\
|
||
|
141.628661629926 -239.672309347542\\
|
||
|
159.662602210142 -243.349147534466\\
|
||
|
181.659978837524 -247.086201751378\\
|
||
|
210.534524276677 -251.148236736065\\
|
||
|
304.427221206439 -261.185150269465\\
|
||
|
336.920570598025 -264.207855741295\\
|
||
|
366.069514759677 -266.879516038908\\
|
||
|
394.090164040321 -269.457051178812\\
|
||
|
401.424249049957 -270.137189611979\\
|
||
|
};
|
||
|
\addplot [color=black, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
0.1 -155.730410010604\\
|
||
|
0.108651577465251 -157.444329842179\\
|
||
|
0.118051652856881 -159.016305563146\\
|
||
|
0.128264983052803 -160.454312864014\\
|
||
|
0.139361927422416 -161.766002170186\\
|
||
|
0.151418932530433 -162.958631144936\\
|
||
|
0.163009236097978 -163.924315989144\\
|
||
|
0.175486714964814 -164.805798805554\\
|
||
|
0.188919277620761 -165.607251881691\\
|
||
|
0.2033800305847 -166.332537314949\\
|
||
|
0.218947676285658 -166.985205158253\\
|
||
|
0.233543813990654 -167.499274260959\\
|
||
|
0.24911300260678 -167.962206209181\\
|
||
|
0.265720110532445 -168.375798945693\\
|
||
|
0.283434330615137 -168.74167489725\\
|
||
|
0.299554933435982 -169.018407931952\\
|
||
|
0.316592411198347 -169.261965935831\\
|
||
|
0.334598912055007 -169.473073387997\\
|
||
|
0.350384224529072 -169.624669444468\\
|
||
|
0.366914237840248 -169.75449639023\\
|
||
|
0.384224084605498 -169.862835751751\\
|
||
|
0.398658107358057 -169.934199655476\\
|
||
|
0.413634368406335 -169.992071969196\\
|
||
|
0.425234633452872 -170.026676678307\\
|
||
|
0.43716022482485 -170.053774811373\\
|
||
|
0.44942026621191 -170.073393329798\\
|
||
|
0.457784053837654 -170.082328116866\\
|
||
|
0.466303492974262 -170.087953921985\\
|
||
|
0.474981480322836 -170.090275173747\\
|
||
|
0.48382096649261 -170.089295371996\\
|
||
|
0.492824957004062 -170.085017096763\\
|
||
|
0.501996513311016 -170.077442017453\\
|
||
|
0.511338753841437 -170.066570902318\\
|
||
|
0.525679112201842 -170.044083651815\\
|
||
|
0.540421642070586 -170.01417571457\\
|
||
|
0.555577622239876 -169.976838587048\\
|
||
|
0.576448828292606 -169.915476501316\\
|
||
|
0.598104096238105 -169.840841797148\\
|
||
|
0.620572880677654 -169.752879660892\\
|
||
|
0.649849535446982 -169.624081686899\\
|
||
|
0.680507369673503 -169.474196167453\\
|
||
|
0.712611543011191 -169.303038112888\\
|
||
|
0.753142016597439 -169.069270441224\\
|
||
|
0.795977700231485 -168.804157497829\\
|
||
|
0.841249704973636 -168.507248325863\\
|
||
|
0.897331581458357 -168.120016590165\\
|
||
|
0.95715215389917 -167.688024548217\\
|
||
|
1.02096066230607 -167.21042358717\\
|
||
|
1.0991097009295 -166.60765156004\\
|
||
|
1.18324062745835 -165.942960546518\\
|
||
|
1.27381132318649 -165.215223922646\\
|
||
|
1.37131471775393 -164.423500101669\\
|
||
|
1.48995507285289 -163.455511153306\\
|
||
|
1.61885969017819 -162.405343463131\\
|
||
|
1.77520801171768 -161.14269719135\\
|
||
|
1.94665634334225 -159.781352889023\\
|
||
|
2.15443469003193 -158.174948885455\\
|
||
|
2.40647515001538 -156.302849606343\\
|
||
|
2.71289780037248 -154.153801679156\\
|
||
|
3.17322963473503 -151.205529431829\\
|
||
|
4.54629546953248 -144.377094173206\\
|
||
|
5.07815211232757 -142.4373419403\\
|
||
|
5.56859644428648 -140.941375845087\\
|
||
|
6.05036787939111 -139.712420666708\\
|
||
|
6.51349094627294 -138.728593464402\\
|
||
|
6.94771254846023 -137.960976922658\\
|
||
|
7.34287044716661 -137.377693322938\\
|
||
|
7.76050333513376 -136.867278165121\\
|
||
|
8.12661920009201 -136.499908582137\\
|
||
|
8.51000724712218 -136.186912800657\\
|
||
|
8.8296999554939 -135.976532727387\\
|
||
|
9.1614024571388 -135.802299878853\\
|
||
|
9.50556592010137 -135.664624007383\\
|
||
|
9.7721469697258 -135.585538330534\\
|
||
|
10.0462042134681 -135.5272635409\\
|
||
|
10.2331657833024 -135.499998082861\\
|
||
|
10.4236067397639 -135.482005348751\\
|
||
|
10.6175918348298 -135.47328149161\\
|
||
|
10.7159339982264 -135.472392170035\\
|
||
|
10.8151870255226 -135.473815278185\\
|
||
|
10.9153593533136 -135.477548257956\\
|
||
|
11.118496048193 -135.491931293482\\
|
||
|
11.3254131515284 -135.515511589385\\
|
||
|
11.5361810173649 -135.548252090693\\
|
||
|
11.8597101233768 -135.614439075708\\
|
||
|
12.192312516491 -135.700954071076\\
|
||
|
12.5342426546138 -135.807579299964\\
|
||
|
13.0051125217337 -135.980583697503\\
|
||
|
13.4936714058834 -136.188179011162\\
|
||
|
14.1302599059955 -136.49506046189\\
|
||
|
14.7968806268638 -136.852863183877\\
|
||
|
15.638467583022 -137.346459227106\\
|
||
|
16.5279206146492 -137.906215148844\\
|
||
|
17.629753752872 -138.636698197218\\
|
||
|
18.9792164283904 -139.56365114987\\
|
||
|
20.6212180399915 -140.707979086463\\
|
||
|
22.6128006633721 -142.081517225486\\
|
||
|
25.4921465445141 -143.980581035505\\
|
||
|
38.9574561577541 -150.818491561461\\
|
||
|
43.1156199031825 -152.292378930197\\
|
||
|
47.2796959160026 -153.530759774255\\
|
||
|
51.3701354335138 -154.550448738739\\
|
||
|
55.302242561928 -155.37441864889\\
|
||
|
59.5353313081449 -156.11600451482\\
|
||
|
63.5042516859595 -156.694462104983\\
|
||
|
67.1161176749614 -157.136456527192\\
|
||
|
70.9334120498816 -157.527799364309\\
|
||
|
74.9678187496691 -157.867803491394\\
|
||
|
78.5045620020441 -158.11156313327\\
|
||
|
82.2081575524031 -158.319136481398\\
|
||
|
85.2964449974123 -158.45906406804\\
|
||
|
88.5007491447353 -158.57573797581\\
|
||
|
91.8254283565626 -158.669165602539\\
|
||
|
94.4006478941749 -158.724001748113\\
|
||
|
97.0480887738009 -158.765807723025\\
|
||
|
99.7697764236289 -158.794618722137\\
|
||
|
101.626508939302 -158.806628236826\\
|
||
|
103.51779556302 -158.812897379575\\
|
||
|
105.444279352618 -158.813443658655\\
|
||
|
107.406615333344 -158.808286577014\\
|
||
|
109.405470720574 -158.797447692839\\
|
||
|
111.441525146678 -158.780950688716\\
|
||
|
113.515470892099 -158.758821449554\\
|
||
|
116.698981861712 -158.715129430179\\
|
||
|
119.971773543585 -158.658934092374\\
|
||
|
124.478714618793 -158.56476356672\\
|
||
|
129.154966501489 -158.448895352532\\
|
||
|
134.006889636394 -158.311696393338\\
|
||
|
140.328908478584 -158.110846970259\\
|
||
|
146.949180062486 -157.878281032746\\
|
||
|
155.307057393347 -157.558920005594\\
|
||
|
164.140297114445 -157.197790723965\\
|
||
|
175.082703173578 -156.727362305159\\
|
||
|
188.48434090338 -156.131494365148\\
|
||
|
204.791209666503 -155.398634109266\\
|
||
|
226.64980792737 -154.437974866883\\
|
||
|
288.044415339625 -152.137238996822\\
|
||
|
307.246884270909 -151.589904612471\\
|
||
|
324.721849207315 -151.176005010836\\
|
||
|
340.041193270368 -150.882498192212\\
|
||
|
352.81541153808 -150.688877511189\\
|
||
|
362.710025233077 -150.57150370737\\
|
||
|
372.882130718292 -150.480909180991\\
|
||
|
379.82153061908 -150.436755399541\\
|
||
|
386.890073932801 -150.406593243892\\
|
||
|
394.090164040346 -150.391310985555\\
|
||
|
397.740302405804 -150.389535648406\\
|
||
|
401.424249049931 -150.391827114438\\
|
||
|
405.142317111462 -150.398305018997\\
|
||
|
408.894822629482 -150.409090963391\\
|
||
|
416.504424854512 -150.444083317905\\
|
||
|
424.255643071768 -150.497817003391\\
|
||
|
432.151112778964 -150.571337440438\\
|
||
|
444.2706749607 -150.721086698389\\
|
||
|
456.730127016882 -150.921572700448\\
|
||
|
469.539001068009 -151.176749890355\\
|
||
|
482.707096560317 -151.490746493983\\
|
||
|
500.840798984813 -152.008364864025\\
|
||
|
519.655724382751 -152.64888225052\\
|
||
|
539.177464038763 -153.423469450032\\
|
||
|
559.432570616944 -154.343745369635\\
|
||
|
580.448594276896 -155.421679482729\\
|
||
|
607.832312829711 -157.009344358197\\
|
||
|
636.507908129576 -158.885996498353\\
|
||
|
666.5363268125 -161.074189606786\\
|
||
|
697.981390783064 -163.593949108199\\
|
||
|
730.909932860277 -166.460804534995\\
|
||
|
772.48114514036 -170.37056544538\\
|
||
|
816.416760492152 -174.787371383423\\
|
||
|
870.843149769058 -180.536564323253\\
|
||
|
937.50150151455 -187.757089622514\\
|
||
|
1000 -194.454742635627\\
|
||
|
};
|
||
|
\end{axis}
|
||
|
\end{tikzpicture}
|
||
|
#+end_src
|
||
|
|
||
|
#+name: fig:bode_plot_loop_gain_robustness
|
||
|
#+caption: Robustness - Loop Gain ([[./figs/sf_arch.png][png]], [[./figs/sf_arch.pdf][pdf]], [[./figs/sf_arch.tex][tex]]).
|
||
|
#+RESULTS:
|
||
|
[[file:figs/bode_plot_loop_gain_robustness.png]]
|
||
|
|
||
|
* Robust performance
|
||
|
#+begin_src latex :file robust_perf.pdf :exports results :tangle figs/robust_perf.tex :exports results
|
||
|
<<tikz_default>>
|
||
|
\setlength\fwidth{7cm}
|
||
|
\setlength\fheight{4cm}
|
||
|
|
||
|
\begin{tikzpicture}
|
||
|
\begin{axis}[%
|
||
|
name=axis,
|
||
|
width=\fwidth,
|
||
|
height=\fheight,
|
||
|
at={(0, 0)},
|
||
|
scale only axis,
|
||
|
separate axis lines,
|
||
|
every outer x axis line/.append style={black},
|
||
|
every x tick label/.append style={font=\color{black}},
|
||
|
every x tick/.append style={black},
|
||
|
xmode=log,
|
||
|
xmin=0.1,
|
||
|
xmax=1000,
|
||
|
xminorticks=true,
|
||
|
xlabel={Frequency [Hz]},
|
||
|
every outer y axis line/.append style={black},
|
||
|
every y tick label/.append style={font=\color{black}},
|
||
|
every y tick/.append style={black},
|
||
|
ymode=log,
|
||
|
ymin=0.001,
|
||
|
ymax=10,
|
||
|
yminorticks=true,
|
||
|
ylabel={Magnitude},
|
||
|
axis background/.style={fill=white},
|
||
|
xmajorgrids,
|
||
|
xminorgrids,
|
||
|
ymajorgrids,
|
||
|
yminorgrids
|
||
|
]
|
||
|
\addplot [color=T, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
0.1 1.0001931122177\\
|
||
|
0.535462089927361 1.00573493472724\\
|
||
|
0.922497005259217 1.01680236010719\\
|
||
|
1.32166418394661 1.03374858384494\\
|
||
|
1.74277467840892 1.05687817368458\\
|
||
|
2.21485523372636 1.08784873206357\\
|
||
|
2.76338529005317 1.12820099616263\\
|
||
|
3.51192753045073 1.18553946072086\\
|
||
|
5.22056752784697 1.28965685221731\\
|
||
|
5.93982669392036 1.31022397541787\\
|
||
|
6.57382014340959 1.31414440876117\\
|
||
|
7.20871503378214 1.30497065729765\\
|
||
|
7.8323825991792 1.28445066175576\\
|
||
|
8.51000724712225 1.25141598556613\\
|
||
|
9.24625711640574 1.20596156260807\\
|
||
|
10.0462042134681 1.14917565028267\\
|
||
|
10.9153593533139 1.08300042075559\\
|
||
|
11.9695570235904 1.00151443652005\\
|
||
|
13.2471398786612 0.906489000195522\\
|
||
|
14.796880626864 0.801614690150466\\
|
||
|
16.835508029612 0.683826841375039\\
|
||
|
19.5114834684662 0.561302789116589\\
|
||
|
23.6796006783308 0.42560963805056\\
|
||
|
33.0003479112529 0.259341011797121\\
|
||
|
45.9899209052244 0.159046987989402\\
|
||
|
57.3797641421413 0.116770448003281\\
|
||
|
70.2824426430835 0.0893928832098493\\
|
||
|
86.0864769614925 0.0695444840114252\\
|
||
|
105.444279352617 0.0549418589545345\\
|
||
|
130.351224468151 0.0435976465729145\\
|
||
|
161.141427725302 0.0350978183492074\\
|
||
|
197.376432630026 0.028904752452537\\
|
||
|
239.540735872088 0.0243262510672367\\
|
||
|
288.04441533963 0.0209107964333833\\
|
||
|
340.041193270371 0.0184689543209229\\
|
||
|
401.424249049932 0.0165108877066972\\
|
||
|
473.887960971766 0.0149335773074393\\
|
||
|
737.679760252773 0.0115264177379453\\
|
||
|
794.145171902934 0.0108525646870933\\
|
||
|
847.08682665574 0.0101810410947052\\
|
||
|
903.557834613893 0.00942356415046645\\
|
||
|
963.793479961579 0.00858500367514173\\
|
||
|
1000 0.00807691303004834\\
|
||
|
};
|
||
|
\addplot [color=S, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
0.218947676285662 0.000983633691377331\\
|
||
|
0.699592016543537 0.0099439702172477\\
|
||
|
2.00124979896904 0.0799937322915588\\
|
||
|
3.0302710828664 0.178577134330778\\
|
||
|
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
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||
|
937.501501514529 0.00597367066993419\\
|
||
|
1000 0.00539288850252799\\
|
||
|
};
|
||
|
\addplot [color=S, opacity=0.1, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
0.201513573381556 0.000991369565026902\\
|
||
|
0.550478980785497 0.00731880118015693\\
|
||
|
5.36697694554048 0.679839593590152\\
|
||
|
6.4537154016467 0.958477682381947\\
|
||
|
7.27548352919623 1.17696209521055\\
|
||
|
7.97814457207663 1.35512984917002\\
|
||
|
8.58882855954625 1.49417517168493\\
|
||
|
9.16140245713852 1.60534550339679\\
|
||
|
9.77214696972572 1.69980237718783\\
|
||
|
10.3279473191895 1.76324688565682\\
|
||
|
10.9153593533139 1.80822609146817\\
|
||
|
11.5361810173648 1.83421625412845\\
|
||
|
12.1923125164911 1.84223851847655\\
|
||
|
13.0051125217341 1.83187655378131\\
|
||
|
14.000583824681 1.79971564616347\\
|
||
|
15.211855179861 1.74612573305982\\
|
||
|
17.1488196987054 1.65270076885321\\
|
||
|
26.9420371368188 1.32921049267154\\
|
||
|
31.5136348486648 1.25102687383997\\
|
||
|
36.8609536217216 1.18953287215509\\
|
||
|
43.5149650092505 1.1395955040182\\
|
||
|
51.8459354389291 1.10036260736914\\
|
||
|
62.9214610961034 1.06923906517432\\
|
||
|
78.5045620020451 1.04501166315356\\
|
||
|
103.517795563018 1.02606896872531\\
|
||
|
148.31025143361 1.01260150224567\\
|
||
|
253.164847863136 1.0036921317713\\
|
||
|
972.720319245054 0.994672345758512\\
|
||
|
1000 0.994808613989335\\
|
||
|
};
|
||
|
\addplot [color=T, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
0.1 1.00020954496384\\
|
||
|
0.516074871038591 1.00579146307111\\
|
||
|
0.889096598952916 1.01703959463547\\
|
||
|
1.26212131452255 1.03383979653677\\
|
||
|
1.64898694447106 1.05659555246692\\
|
||
|
2.05737431343291 1.08574586815517\\
|
||
|
2.52000499376409 1.1239507180103\\
|
||
|
3.05833803237844 1.17338880266678\\
|
||
|
3.74605003274899 1.24045599701126\\
|
||
|
6.2776601058065 1.44057990425486\\
|
||
|
6.94771254846024 1.46116763418812\\
|
||
|
7.54879928165344 1.46382443377929\\
|
||
|
8.12661920009194 1.45223914241432\\
|
||
|
8.74866812047991 1.42539993442632\\
|
||
|
9.33189771573324 1.38858554667703\\
|
||
|
9.95400828762153 1.33949883455865\\
|
||
|
10.7159339982267 1.26977073990895\\
|
||
|
11.5361810173648 1.1882166195253\\
|
||
|
12.534242654614 1.0868667534867\\
|
||
|
13.7447909267754 0.968764216009991\\
|
||
|
15.211855179861 0.83985245355863\\
|
||
|
17.1488196987054 0.697328850279999\\
|
||
|
19.8745954958098 0.544449879386969\\
|
||
|
24.1202820761801 0.38544854739369\\
|
||
|
31.2244282309286 0.238078940532575\\
|
||
|
46.4158883361278 0.111034629018082\\
|
||
|
122.204468663149 0.0171162319914057\\
|
||
|
164.140297114447 0.00992430724437396\\
|
||
|
206.688024962908 0.00661436956912793\\
|
||
|
250.841505927754 0.00479772888002399\\
|
||
|
296.122543798803 0.00371157692757879\\
|
||
|
343.190719745904 0.00300548244364327\\
|
||
|
394.090164040345 0.002506686745748\\
|
||
|
452.538627817017 0.00212548895791761\\
|
||
|
519.655724382766 0.00183068994706429\\
|
||
|
613.462171799251 0.00155386932491147\\
|
||
|
744.512291079513 0.00128203494651237\\
|
||
|
816.416760492147 0.0011528522896618\\
|
||
|
878.909065341995 0.00104395024350009\\
|
||
|
911.92675984593 0.00098726789669818\\
|
||
|
};
|
||
|
\addplot [color=S, line width=1.5pt, forget plot]
|
||
|
table[row sep=crcr]{%
|
||
|
0.211020342856859 0.00099135526076278\\
|
||
|
0.598104096238094 0.00789341869276899\\
|
||
|
2.61467321180109 0.148407886961816\\
|
||
|
3.92277675892772 0.325690971355827\\
|
||
|
4.98537346387389 0.507889209498173\\
|
||
|
5.88531577519145 0.677513921741425\\
|
||
|
6.69616005485322 0.832012028793756\\
|
||
|
7.41088151564157 0.961752171130274\\
|
||
|
8.12661920009194 1.07959943238888\\
|
||
|
8.82969995549409 1.17955171767708\\
|
||
|
9.5055659201012 1.25893512355348\\
|
||
|
10.2331657833025 1.32589651610798\\
|
||
|
10.9153593533139 1.37244462231969\\
|
||
|
11.6430313292088 1.40699290954211\\
|
||
|
12.534242654614 1.4319795371025\\
|
||
|
13.4936714058831 1.44276985588542\\
|
||
|
14.6610868404698 1.44054164735945\\
|
||
|
16.0770442167382 1.42429827881865\\
|
||
|
18.1241754737424 1.38886050405382\\
|
||
|
21.5940615210357 1.32360151035419\\
|
||
|
32.1001089554317 1.18379119700084\\
|
||
|
39.3182875570577 1.13109190534588\\
|
||
|
48.1595791019235 1.09166733125577\\
|
||
|
60.0867589171969 1.06111065730019\\
|
||
|
77.070271142123 1.03827810402975\\
|
||
|
104.47659715608 1.02145049880974\\
|
||
|
156.74554102056 1.00995946517423\\
|
||
|
293.404970921579 1.00332016608336\\
|
||
|
1000 1.00081388192113\\
|
||
|
};
|
||
|
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-bandwidth>>
|
||
|
};
|
||
|
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-noise-attenuation-1>>
|
||
|
};
|
||
|
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-noise-attenuation-2>>
|
||
|
};
|
||
|
\addplot [color=S, line width=1.5pt, forget plot, upperbound]
|
||
|
table[row sep=crcr]{%
|
||
|
<<data:upperbound-dist-rejection>>
|
||
|
};
|
||
|
\end{axis}
|
||
|
\end{tikzpicture}
|
||
|
#+end_src
|
||
|
|
||
|
#+name: fig:robust_perf
|
||
|
#+caption: Robust performance ([[./figs/robust_perf.png][png]], [[./figs/robust_perf.pdf][pdf]], [[./figs/robust_perf.tex][tex]]).
|
||
|
#+RESULTS:
|
||
|
[[file:figs/robust_perf.png]]
|