12019 lines
508 KiB
Org Mode
12019 lines
508 KiB
Org Mode
#+TITLE: Sensor Fusion Paper - Tikz Figures
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:DRAWER:
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#+HTML_LINK_HOME: ../index.html
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#+HTML_LINK_UP: ../index.html
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/>
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/>
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#+HTML_HEAD: <script src="../js/jquery.min.js"></script>
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#+HTML_HEAD: <script src="../js/bootstrap.min.js"></script>
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#+HTML_HEAD: <script src="../js/jquery.stickytableheaders.min.js"></script>
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#+HTML_HEAD: <script src="../js/readtheorg.js"></script>
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#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{/home/thomas/Cloud/thesis/papers/dehaeze20_virtu_senso_fusio/tikz}{config.tex}")
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#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
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#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
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#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
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#+PROPERTY: header-args:latex+ :results raw replace :buffer no
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#+PROPERTY: header-args:latex+ :eval no-export
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#+PROPERTY: header-args:latex+ :exports both
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#+PROPERTY: header-args:latex+ :mkdirp yes
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#+PROPERTY: header-args:latex+ :noweb yes
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#+PROPERTY: header-args:latex+ :output-dir figs
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#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
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:END:
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Configuration file is accessible [[file:config.org][here]].
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* Change some default
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#+NAME: tikz_default
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#+begin_src latex
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#+end_src
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* Data :ignore:noexport:
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:PROPERTY: header-args:latex+ :eval no
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#+end_src
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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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#+end_src
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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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#+RESULTS:
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[[file:figs/sf_arch.png]]
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* Equivalent configuration
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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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\node[block, below right=0.5 and -0.2 of K] (Gm){$G$};
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\node[block, below left =0.5 and -0.2 of K] (Hh){$H_H$};
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\node[block, below=1.5 of G] (Hl) {$H_L$};
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\node[addb={+}{}{}{}{}, right=1 of Hl] (addn) {};
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\draw[->] (addfb.east) -- (addK.west);
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\draw[->] (addK.east) -- (K.west);
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\draw[->] (K.east) -- (G.west) node[above left]{$u$};
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\draw[->] (G.east) -- (adddy.west);
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\draw[->] ($(G.west)+(-0.8, 0)$) node[branch](sffb){} |- (Gm.east);
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\draw[->] (Gm.west) -- (Hh.east);
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\draw[->] (Hh.west) -| (addK.south);
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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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\draw[->] (Hl.west) -| (addfb.south) node[below right]{};
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\begin{scope}[on background layer]
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\node[fit={($(addK.west|-Hh.south)+(-0.1, 0)$) (K.north-|sffb)}, inner sep=5pt, draw, fill=black!20!white, dashed, label={$K$}] (Kfb) {};
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\end{scope}
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\end{tikzpicture}
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#+end_src
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#+name: fig:sf_arch_eq
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#+caption: Equivalent configuration ([[./figs/sf_arch_eq.png][png]], [[./figs/sf_arch_eq.pdf][pdf]], [[./figs/sf_arch_eq.tex][tex]]).
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#+RESULTS:
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[[file:figs/sf_arch_eq.png]]
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* Equivalent configuration - classical Feedback
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#+begin_src latex :file sf_arch_class.pdf :tangle figs/sf_arch_class.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[block, right=of addfb] (K){$K$};
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\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\\
|
|
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1000 -329.745759958342\\
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};
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\addplot [color=black, line width=1.5pt, forget plot]
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table[row sep=crcr]{%
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1000 -179.954404899517\\
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};
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|
\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
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|
0.1 43470401.5635197\\
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|
275.067600790807 59592410.0067978\\
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|
359.381366380463 101766885.625809\\
|
|
#+end_src
|
|
|
|
#+NAME: data:bode_Kfb_phase
|
|
#+begin_src latex :exports none
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|
0.1 -155.364714507098\\
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|
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28.2130767593954 165.113720376764\\
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29.8177229001969 166.161840342236\\
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31.5136348486643 167.068888278142\\
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33.3060034362469 167.846326749679\\
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38.2456972246693 169.291252815606\\
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41.5545533471895 169.862433154403\\
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43.1156199031825 170.054192980089\\
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44.7353305449843 170.210701908133\\
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46.4158883361268 170.333854209\\
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47.7176094893859 170.40538524839\\
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50.4315948717143 170.497813484418\\
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51.3701354335138 170.514297645932\\
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52.3261423948667 170.523904524208\\
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54.794723369002 170.518858182568\\
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56.8531791387359 170.486111558014\\
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|
64.0924401935642 170.215762940957\\
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|
66.50018030431 170.085099181676\\
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|
69.6374473062844 169.891975079658\\
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|
72.9227205872842 169.666607449389\\
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|
76.3629826128223 169.409719163214\\
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|
80.7062014114933 169.060571856472\\
|
|
85.2964449974123 168.66733699213\\
|
|
90.9827289445557 168.153086563827\\
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|
97.0480887738009 167.578826478813\\
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|
103.51779556302 166.943723901156\\
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|
111.441525146678 166.141606661108\\
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|
119.971773543585 165.255344346467\\
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|
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|
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|
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|
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|
173.475935923388 159.403205311421\\
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|
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|
202.911801804663 156.066120624088\\
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|
220.466873523944 154.050554173503\\
|
|
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|
|
260.264788196906 149.420577135854\\
|
|
280.186655645918 147.072566796613\\
|
|
301.63343472593 144.521878314074\\
|
|
324.721849207315 141.74828535307\\
|
|
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|
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|
|
405.142317111462 131.837387817798\\
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|
436.153778920815 127.897493655173\\
|
|
469.539001068009 123.572179690684\\
|
|
505.479682119114 118.810514287571\\
|
|
544.1714286866 113.553525472907\\
|
|
585.82482001525 107.734558232872\\
|
|
630.666554056761 101.281715619792\\
|
|
678.940681269615 94.1241711336394\\
|
|
730.909932860277 86.2047189454912\\
|
|
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|
|
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
|
|
0.1 4351.30066559668\\
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|
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|
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|
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|
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|
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|
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|
903.557834613893 0.00100057295410498\\
|
|
963.793479961579 0.000899050671300346\\
|
|
1000 0.000839826664244425\\
|
|
#+end_src
|
|
|
|
#+NAME: data:bode_plot_loop_gain_phase
|
|
#+begin_src latex :exports none
|
|
0.1 -155.730410010604\\
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|
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|
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|
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0.540421642070586 -170.01417571457\\
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0.555577622239876 -169.976838587048\\
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0.598104096238105 -169.840841797148\\
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0.620572880677654 -169.752879660892\\
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|
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|
|
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|
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|
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|
6.82077673286572 -138.170971035104\\
|
|
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|
|
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|
|
7.97814457207674 -136.640412323733\\
|
|
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|
|
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|
|
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|
|
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|
|
9.68246611930323 -135.609591102768\\
|
|
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|
|
10.1392540755881 -135.512471769439\\
|
|
10.3279473191894 -135.489842692645\\
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|
10.5201521761614 -135.476485339516\\
|
|
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\\
|
|
67.7377599751758 -157.205218929792\\
|
|
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|
|
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|
|
79.2316862486613 -158.155977357457\\
|
|
82.9695852083464 -158.356297712351\\
|
|
86.0864769614942 -158.490412787294\\
|
|
89.3204599858103 -158.601273293247\\
|
|
92.6759330114683 -158.688893907112\\
|
|
95.2750047242714 -158.739383322341\\
|
|
97.9469667069515 -158.776853269827\\
|
|
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\\
|
|
114.566872863485 -158.745653454244\\
|
|
117.779870119709 -158.697781347301\\
|
|
121.082975023208 -158.637443831784\\
|
|
125.631660247414 -158.537817197554\\
|
|
130.351224468151 -158.416579908374\\
|
|
135.248087041786 -158.274111715337\\
|
|
141.628661629916 -158.066837891998\\
|
|
148.310251433614 -157.828056926875\\
|
|
156.74554102056 -157.501564384406\\
|
|
165.660595894989 -157.133726658968\\
|
|
176.704352608899 -156.656116134062\\
|
|
190.230118866895 -156.053077922383\\
|
|
206.688024962902 -155.313799873592\\
|
|
230.867799418716 -154.258437163579\\
|
|
285.40097698292 -152.21981175333\\
|
|
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_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\\
|
|
-0.0182877989612005 -0.0341876256850084\\
|
|
-0.00949586865416374 -0.022925836151285\\
|
|
-0.00479910770039127 -0.014741544921457\\
|
|
-0.00363324610547067 -0.0100681058133638\\
|
|
-0.00435743584879122 -0.00733261309976729\\
|
|
-0.00563324611328664 -0.00348377749065309\\
|
|
-0.00514088000326818 -0.000941016041339227\\
|
|
-0.00351299106432434 0.000772349409272843\\
|
|
-0.00127640949395635 0.00110843534418881\\
|
|
4.5667588106646e-06 6.23927080400932e-06\\
|
|
2.72330119810427e-06 2.90272460934382e-06\\
|
|
};
|
|
\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
|
|
table[row sep=crcr]{%
|
|
-1.56 -1.43933230012855\\
|
|
-1.39014801728604 -1.33497194103752\\
|
|
-1.19460034247808 -1.20338328527939\\
|
|
-1.03106667895463 -1.08298283611798\\
|
|
-0.893937910245688 -0.972733738271957\\
|
|
-0.778545397576963 -0.871729976747991\\
|
|
-0.681005749260745 -0.779184580275941\\
|
|
-0.598093858100534 -0.694419087896208\\
|
|
-0.527139466729534 -0.616853286290956\\
|
|
-0.465943040238388 -0.545994296038062\\
|
|
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};
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\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>>
|
|
\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={{}, {$10^{-2}$}, {}, {$10^0$}, {}, {$10^2$}, {}},
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|
yminorticks=true,
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|
ylabel={Magnitude [m/N]},
|
|
xminorgrids,
|
|
yminorgrids
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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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\addplot [color=black, opacity=0.1, line width=1.5pt, forget plot]
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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}},
|
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|
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|
|
table[row sep=crcr]{%
|
|
<<data:upperbound-bandwidth>>
|
|
};
|
|
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|
table[row sep=crcr]{%
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<<data:upperbound-noise-attenuation-1>>
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|
};
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|
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|
table[row sep=crcr]{%
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<<data:upperbound-noise-attenuation-2>>
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};
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|
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|
table[row sep=crcr]{%
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<<data:upperbound-dist-rejection>>
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};
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\end{axis}
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\end{tikzpicture}
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#+end_src
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#+name: fig:robust_perf
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#+caption: Robust performance ([[./figs/robust_perf.png][png]], [[./figs/robust_perf.pdf][pdf]], [[./figs/robust_perf.tex][tex]]).
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#+RESULTS:
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[[file:figs/robust_perf.png]]
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