#+TITLE: Sensor Fusion Paper - Tikz Figures
:DRAWER:
#+HTML_LINK_HOME: ../index.html
#+HTML_LINK_UP: ../index.html
#+HTML_HEAD:
#+HTML_HEAD:
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{/home/thomas/Cloud/thesis/papers/dehaeze20_virtu_senso_fusio/tikz}{config.tex}")
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
#+PROPERTY: header-args:latex+ :results raw replace :buffer no
#+PROPERTY: header-args:latex+ :eval no-export
#+PROPERTY: header-args:latex+ :exports both
#+PROPERTY: header-args:latex+ :mkdirp yes
#+PROPERTY: header-args:latex+ :noweb yes
#+PROPERTY: header-args:latex+ :output-dir figs
#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
:END:
Configuration file is accessible [[file:config.org][here]].
* Change some default
#+NAME: tikz_default
#+begin_src latex
\tikzset{block/.default={0.8cm}{0.6cm}}
\tikzset{addb/.append style={scale=0.7}}
\tikzset{node distance=0.6}
\def\cdist{0.7}
\definecolor{T}{rgb}{0.230, 0.299, 0.754}%
\definecolor{S}{rgb}{0.706, 0.016, 0.150}%
#+end_src
* Data :ignore:noexport:
:PROPERTIES:
:PROPERTY: header-args:latex+ :eval no
:END:
#+NAME: data:upperbound-robust-stability
#+begin_src latex
0.1 4.7609074288834\\
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#+NAME: data:upperbound-bandwidth
#+begin_src latex
20 0.7\\
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#+NAME: data:upperbound-noise-attenuation-1
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50 0.1\\
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500 0.01\\
1000 0.01\\
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#+NAME: data:upperbound-dist-rejection
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0.02 1e-05\\
2 0.1\\
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1000 0.00125323629492883\\
#+end_src
#+NAME: data:weight-hh
#+begin_src latex
0.203380030584698 0.000989777819887578\\
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5.12518692705333 0.622210572704616\\
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#+end_src
#+NAME: data:hl
#+begin_src latex
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596.727119597332 0.00162874587725399\\
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808.924348680594 0.00131717393449145\\
895.26571259964 0.00124828640279652\\
1000 0.00118697716847575\\
#+end_src
#+NAME: data:hh
#+begin_src latex
0.211020342856859 0.000991355164946403\\
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2.42876438246045 0.128327524780232\\
3.54445567397044 0.267992154829373\\
4.4632339267104 0.413805848676621\\
5.26892142135068 0.557587736797486\\
5.99484250318941 0.693160496305138\\
6.63470812109235 0.81193792953703\\
7.27548352919623 0.925424392834698\\
7.90492762269643 1.02770565894096\\
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9.07732652521023 1.18510732855918\\
9.68246611930312 1.24761337860369\\
10.3279473191895 1.30053311262914\\
11.0164594963366 1.34273501848344\\
11.7508713090481 1.37382109949711\\
12.534242654614 1.39409360664554\\
13.3698374182495 1.4044213762404\\
14.3932264471941 1.40566001105301\\
15.6384675830225 1.39616695613207\\
17.1488196987054 1.37570643727067\\
19.3324228755505 1.33943394453979\\
23.6796006783308 1.26895368211008\\
31.2244282309286 1.18029446890997\\
37.5469422407334 1.13328156575089\\
44.7353305449847 1.09818850827496\\
53.793615039807 1.07013138018377\\
65.8898955079995 1.04777741305257\\
82.9695852083491 1.03046080493667\\
110.418805085416 1.01711094138512\\
159.662602210143 1.00783805748313\\
275.067600790807 1.00210387254234\\
794.145171902934 0.999522245381891\\
1000 0.999396233385764\\
#+end_src
* Sensor Fusion with complementary filters
#+begin_src latex :file sf_arch.pdf :tangle figs/sf_arch.tex :exports both
<>
\begin{tikzpicture}
\node[addb={+}{}{}{}{-}] (addfb) at (0, 0){};
\node[block, right=of addfb] (K){$k$};
\node[block, right=1.2 of K] (G){$G^\prime$};
\node[addb={+}{}{}{}{}, right=of G] (adddy){};
\coordinate[] (KG) at ($0.5*(K.east)+0.5*(G.west)$);
\node[block, below=of KG] (Gm){$G$};
\node[block, below=of Gm] (Hh){$H_H$};
\node[addb={+}{}{}{}{}, below=of Hh] (addsf){};
\node[block] (Hl) at (addsf-|G) {$H_L$};
\node[addb={+}{}{}{}{}, right=1.2 of Hl] (addn) {};
\draw[->] (addfb.east) -- (K.west) node[above left]{};
\draw[->] (K.east) -- (G.west) node[above left]{$u$};
\draw[->] (KG) node[branch]{} -- (Gm.north);
\draw[->] (Gm.south) -- (Hh.north);
\draw[->] (Hh.south) -- (addsf.north) node[above left]{};
\draw[->] (Hl.west) -- (addsf.east);
\draw[->] (addsf.west) -| (addfb.south) node[below right]{};
\draw[->] (G.east) -- (adddy.west);
\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]{$d_y$};
\end{tikzpicture}
#+end_src
#+name: fig:sf_arch
#+caption: Sensor Fusion with complementary filters ([[./figs/sf_arch.png][png]], [[./figs/sf_arch.pdf][pdf]], [[./figs/sf_arch.tex][tex]]).
#+RESULTS:
[[file:figs/sf_arch.png]]
* Equivalent configuration
#+begin_src latex :file sf_arch_eq.pdf :tangle figs/sf_arch_eq.tex
<>
\begin{tikzpicture}
\node[addb={+}{}{}{}{-}] (addfb) at (0, 0){};
\node[addb={+}{}{}{}{-}, right=of addfb] (addK){};
\node[block, right=of addK] (K){$k$};
\node[block, right=1.8 of K] (G){$G^\prime$};
\node[addb={+}{}{}{}{}, right=of G] (adddy){};
\node[block, below right=0.5 and -0.2 of K] (Gm){$G$};
\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
<>
\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
<>
\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
<>
\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
<>
\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
<>
\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
<>
\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
<>
\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
<>
\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
<>
\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
<>
\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
<>
\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]{%
<>
};
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
table[row sep=crcr]{%
<>
};
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
table[row sep=crcr]{%
<>
};
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
table[row sep=crcr]{%
<>
};
\addplot [color=S, line width=1.5pt, forget plot, upperbound]
table[row sep=crcr]{%
<>
};
\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\\
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#+end_src
#+begin_src latex :file bode_plot_mech_sys.pdf :tangle figs/bode_plot_mech_sys.tex :exports results
<>
\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]{%
<>
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\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]},
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\addplot [color=mycolor1, line width=1.5pt, forget plot]
table[row sep=crcr]{%
<>
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\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
<>
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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
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#+end_src
#+NAME: data:bode_Kfb_phase
#+begin_src latex :exports none
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#+end_src
#+begin_src latex :file bode_Kfb.pdf :tangle figs/bode_Kfb.tex :exports results
<>
\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]{%
<>
};
\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,
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ylabel={Phase [deg]},
xminorgrids
]
\addplot [color=mycolor1, line width=1.5pt, forget plot]
table[row sep=crcr]{%
<>
};
\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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#+end_src
#+NAME: data:bode_plot_loop_gain_phase
#+begin_src latex :exports none
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190.230118866895 -156.053077922383\\
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519.655724382751 -152.64888225052\\
539.177464038763 -153.423469450032\\
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580.448594276896 -155.421679482729\\
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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
<>
\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]{%
<>
};
\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]{%
<>
};
\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
<>
\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]{%
<>
};
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
table[row sep=crcr]{%
<>
};
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
table[row sep=crcr]{%
<>
};
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
table[row sep=crcr]{%
<>
};
\addplot [color=S, line width=1.5pt, forget plot, upperbound]
table[row sep=crcr]{%
<>
};
\addplot [color=T, dashed, line width=1.5pt, forget plot]
table[row sep=crcr]{%
<>
};
\addplot [color=S, dashed, line width=1.5pt, forget plot]
table[row sep=crcr]{%
<>
};
\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
<>
\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]{%
<>
};
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
table[row sep=crcr]{%
<>
};
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
table[row sep=crcr]{%
<>
};
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
table[row sep=crcr]{%
<>
};
\addplot [color=S, line width=1.5pt, forget plot, upperbound]
table[row sep=crcr]{%
<>
};
\addplot [color=T, line width=1.5pt, forget plot]
table[row sep=crcr]{%
<>
};
\addplot [color=S, line width=1.5pt, forget plot]
table[row sep=crcr]{%
<>
};
\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
<>
\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]{%
<>
};
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
table[row sep=crcr]{%
<>
};
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
table[row sep=crcr]{%
<>
};
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
table[row sep=crcr]{%
<>
};
\addplot [color=S, line width=1.5pt, forget plot, upperbound]
table[row sep=crcr]{%
<>
};
\addplot [color=T, line width=1.5pt, forget plot]
table[row sep=crcr]{%
<>
};
\addplot [color=S, line width=1.5pt, forget plot]
table[row sep=crcr]{%
<>
};
\addplot [color=T, dashed, line width=1.5pt, forget plot]
table[row sep=crcr]{%
<>
};
\addplot [color=S, dashed, line width=1.5pt, forget plot]
table[row sep=crcr]{%
<>
};
\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
<>
\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},
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#+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
<>
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#+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
<>
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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\\
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1.64898694447106 1.05659555246692\\
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2.52000499376409 1.1239507180103\\
3.05833803237844 1.17338880266678\\
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6.2776601058065 1.44057990425486\\
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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\\
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2.61467321180109 0.148407886961816\\
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10.2331657833025 1.32589651610798\\
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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\\
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\addplot [color=T, line width=1.5pt, forget plot, upperbound]
table[row sep=crcr]{%
<>
};
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
table[row sep=crcr]{%
<>
};
\addplot [color=T, line width=1.5pt, forget plot, upperbound]
table[row sep=crcr]{%
<>
};
\addplot [color=S, line width=1.5pt, forget plot, upperbound]
table[row sep=crcr]{%
<>
};
\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]]