#+TITLE: Active Damping of Rotating Platforms using Integral Force Feedback - Tikz Figures
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#+PROPERTY: header-args:latex  :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{/home/thomas/Cloud/thesis/papers/dehaeze20_contr_stewa_platf/tikz/}{config.tex}")
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Configuration file is accessible [[file:config.org][here]].

* X-Y Rotating Positioning Platform
#+begin_src latex :file system.pdf
  \begin{tikzpicture}
    % Angle
    \def\thetau{25}

    % Rotational Stage
    \draw[fill=black!60!white] (0, 0) circle (4.3);
    \draw[fill=black!40!white] (0, 0) circle (3.8);

    % Label
    \node[anchor=north west, rotate=\thetau] at (-2.5, 2.5) {\small Rotating Stage};

    % Rotating Scope
    \begin{scope}[rotate=\thetau]
      % Rotating Frame
      \draw[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6);
      % Label
      \node[anchor=north west, rotate=\thetau] at (-2.6, 2.6) {\small Suspended Platform};

      % Mass
      \draw[fill=white] (-1, -1) rectangle (1, 1);
      % Label
      \node[anchor=south west, rotate=\thetau] at (-1, -1) {\small Payload};

      % Attached Points
      \node[] at (-1, 0){$\bullet$};
      \draw[] (-1, 0) -- ++(-0.2, 0) coordinate(cu);
      \draw[] ($(cu) + (0, -0.8)$) coordinate(actu) -- ($(cu) + (0, 0.8)$) coordinate(ku);
      \node[] at (0, -1){$\bullet$};
      \draw[] (0, -1) -- ++(0, -0.2) coordinate(cv);
      \draw[] ($(cv) + (-0.8, 0)$)coordinate(kv) -- ($(cv) + (0.8, 0)$) coordinate(actv);

      % Spring and Actuator for U
      \draw[actuator={0.6}{0.2}] (actu) -- node[above=0.1, rotate=\thetau]{$F_u$} (actu-|-2.6,0);
      \draw[spring=0.2] (ku) -- node[above=0.1, rotate=\thetau]{$k$} (ku-|-2.6,0);
      \draw[damper={8}{8}] (cu) -- node[above left=0.2 and -0.1, rotate=\thetau]{$c$} (cu-|-2.6,0);

      \draw[actuator={0.6}{0.2}] (actv) -- node[left, rotate=\thetau]{$F_v$} (actv|-0,-2.6);
      \draw[spring=0.2] (kv) -- node[left, rotate=\thetau]{$k$} (kv|-0,-2.6);
      \draw[damper={8}{8}] (cv) -- node[left=0.1, rotate=\thetau]{$c$} (cv|-0,-2.6);
    \end{scope}

    % Inertial Frame
    \draw[->] (-4, -4) -- ++(2, 0) node[below]{$\vec{i}_x$};
    \draw[->] (-4, -4) -- ++(0, 2) node[left]{$\vec{i}_y$};
    \draw[fill, color=black] (-4, -4) circle (0.06);
    \node[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:$\vec{i}_z$] at (-4, -4){};

    \draw[->] (0, 0) node[above left, rotate=\thetau]{$\vec{i}_w$} -- ++(\thetau:2) node[above, rotate=\thetau]{$\vec{i}_u$};
    \draw[->] (0, 0) -- ++(\thetau+90:2) node[left, rotate=\thetau]{$\vec{i}_v$};
    \draw[fill, color=black] (0,0) circle (0.06);
    \node[draw, circle, inner sep=0pt, minimum size=0.3cm] at (0, 0){};
    \draw[dashed] (0, 0) -- ++(2, 0);
    \draw[] (1.5, 0) arc (0:\thetau:1.5) node[midway, right]{$\theta$};

    \draw[->] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$};
  \end{tikzpicture}
#+end_src

#+RESULTS:
[[file:figs/system.png]]

* X-Y Rotating Positioning Platform
#+begin_src latex :file control_diagram_iff.pdf
  \tikzset{block/.default={0.8cm}{0.8cm}}
  \tikzset{addb/.append style={scale=0.7}}
  \tikzset{node distance=0.6}

  \begin{tikzpicture}
    \node[block={1.8cm}{2.2cm}] (G) {$\bm{G}_f$};

    % Inputs of the controllers
    \coordinate[] (output1) at ($(G.south east)!0.75!(G.north east)$);
    \coordinate[] (output2) at ($(G.south east)!0.25!(G.north east)$);
    \coordinate[] (input1)  at ($(G.south west)!0.75!(G.north west)$);
    \coordinate[] (input2)  at ($(G.south west)!0.25!(G.north west)$);

    \node[block, left=1.8 of input1] (K1) {$K_F$};
    \node[block] (K2) at ($(K1.east|-input2)+(0.6, 0)$) {$K_F$};

    % Connections and labels
    \draw[->] (K1.east) -- (input1)node[above left]{$F_u$}node[below left]{$-$};
    \draw[->] (K2.east) -- (input2)node[above left]{$F_v$}node[below left]{$-$};

    \draw[->] (output1) -- ++(0.8, 0) node[above left]{$f_u$};
    \draw[->] (output2) -- ++(0.8, 0) node[above left]{$f_v$};

    \draw[->] ($(output1)+(0.2, 0)$)node[branch]{} -- ++(0,  1.2) -| ($(K1.west) + (-0.8, 0)$)coordinate(start) -- (K1.west);
    \draw[->] ($(output2)+(0.2, 0)$)node[branch]{} -- ++(0, -1.2) -| (start|-K2) -- (K2.west);

    \begin{scope}[on background layer]
      \node[fit={(K1.north west) (K2.south east)}, inner sep=6pt, draw, dashed, fill=black!20!white] (K) {};
      \node[below left] at (K.north east) {$\bm{K}_F$};
    \end{scope}
  \end{tikzpicture}
#+end_src

#+RESULTS:
[[file:figs/control_diagram_iff.png]]

* Decentralized Integral Force Feedback
#+begin_src latex :file system_iff.pdf
  \begin{tikzpicture}
    % Angle
    \def\thetau{25}

    % Rotational Stage
    \draw[fill=black!60!white] (0, 0) circle (4.3);
    \draw[fill=black!40!white] (0, 0) circle (3.8);

    % Label
    \node[anchor=north west, rotate=\thetau] at (-2.5, 2.5) {\small Rotating Stage};

    % Rotating Scope
    \begin{scope}[rotate=\thetau]
      % Rotating Frame
      \draw[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6);
      % Label
      \node[anchor=north west, rotate=\thetau] at (-2.6, 2.6) {\small Suspended Platform};

      % Mass
      \draw[fill=white] (-1, -1) rectangle (1, 1);
      % Label
      \node[anchor=south west, rotate=\thetau] at (-1, -1) {\small Payload};

      % Attached Points
      \node[] at (-1, 0){$\bullet$};
      \draw[] (-1, 0) -- ++(-0.2, 0) coordinate(au);
      \node[] at (0, -1){$\bullet$};
      \draw[] (0, -1) -- ++(0, -0.2) coordinate(av);

      % Force Sensors
      \draw[fill=white] ($(au) + (-0.2, -0.5)$) rectangle ($(au) + (0, 0.5)$);
      \draw[] ($(au) + (-0.2, -0.5)$)coordinate(actu) -- ($(au) + (0,  0.5)$);
      \draw[] ($(au) + (-0.2,  0.5)$)coordinate(ku)   -- ($(au) + (0, -0.5)$);

      \draw[fill=white] ($(av) + (-0.5, -0.2)$) rectangle ($(av) + (0.5, 0)$);
      \draw[] ($(av) + ( 0.5, -0.2)$)coordinate(actv) -- ($(av) + (-0.5,  0)$);
      \draw[] ($(av) + (-0.5, -0.2)$)coordinate(kv)   -- ($(av) + ( 0.5,  0)$);

      % Spring and Actuator for U
      \draw[actuator={0.6}{0.2}] (actu) -- coordinate[midway](actumid) (actu-|-2.6,0);
      \draw[spring=0.2] (ku) -- node[above=0.1, rotate=\thetau]{$k$} (ku-|-2.6,0);

      % \draw[actuator={0.6}{0.2}] (actv) -- node[right, rotate=\thetau]{$F_v$} (actv|-0,-2.6);
      \draw[actuator={0.6}{0.2}] (actv) -- coordinate[midway](actvmid) (actv|-0,-2.6);
      \draw[spring=0.2] (kv) -- node[left, rotate=\thetau]{$k$} (kv|-0,-2.6);

      \node[block={0.8cm}{0.6cm}, rotate=\thetau] (Ku) at ($(actumid) + (0, -1.2)$) {$K_{F}$};
      \draw[->] ($(au) + (-0.1, -0.5)$) |- (Ku.east) node[below right, rotate=\thetau]{$f_{u}$};
      \draw[->] (Ku.north) -- ($(actumid) + (0, -0.1)$) node[below left, rotate=\thetau]{$F_u$} node[below right, rotate=\thetau]{$-$};

      \node[block={0.8cm}{0.6cm}, rotate=\thetau] (Kv) at ($(actvmid) + (1.2, 0)$) {$K_{F}$};
      \draw[->] ($(av) + (0.5, -0.1)$) -| (Kv.north) node[above right, rotate=\thetau]{$f_{v}$};
      \draw[->] (Kv.west) -- ($(actvmid) + (0.1, 0)$) node[below right, rotate=\thetau]{$F_v$} node[above right, rotate=\thetau]{$-$};
    \end{scope}

    % Inertial Frame
    \draw[->] (-4, -4) -- ++(2, 0) node[below]{$\vec{i}_x$};
    \draw[->] (-4, -4) -- ++(0, 2) node[left]{$\vec{i}_y$};
    \draw[fill, color=black] (-4, -4) circle (0.06);
    \node[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:$\vec{i}_z$] at (-4, -4){};

    \node[draw, circle, inner sep=0pt, minimum size=0.3cm] at (0, 0){};
    \draw[->] (0, 0) node[above left, rotate=\thetau]{$\vec{i}_w$} -- ++(\thetau:2) node[above, rotate=\thetau]{$\vec{i}_u$};
    \draw[->] (0, 0) -- ++(\thetau+90:2) node[left, rotate=\thetau]{$\vec{i}_v$};
    \draw[dashed] (0, 0) -- ++(2, 0);
    \draw[] (1.5, 0) arc (0:\thetau:1.5) node[midway, right]{$\theta$};
    \node[] at (0,0) {$\bullet$};

    \draw[->] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$};
  \end{tikzpicture}
#+end_src

#+RESULTS:
[[file:figs/system_iff.png]]

* Springs in parallel
#+begin_src latex :file system_parallel_springs.pdf
  \begin{tikzpicture}
    % Angle
    \def\thetau{25}

    % Rotational Stage
    \draw[fill=black!60!white] (0, 0) circle (4.3);
    \draw[fill=black!40!white] (0, 0) circle (3.8);

    % Label
    \node[anchor=north west, rotate=\thetau] at (-2.5, 2.5) {\small Rotating Stage};

    % Rotating Scope
    \begin{scope}[rotate=\thetau]
      % Rotating Frame
      \draw[fill=black!20!white] (-2.6, -2.6) rectangle (2.6, 2.6);
      % Label
      \node[anchor=north west, rotate=\thetau] at (-2.6, 2.6) {\small Suspended Platform};

      % Mass
      \draw[fill=white] (-1, -1) rectangle (1, 1);
      % Label
      \node[anchor=south west, rotate=\thetau] at (-1, -1) {\small Payload};

      % Attached Points
      \draw[] (-1, 0) -- ++(-0.2, 0) coordinate(au);
      \draw[] (0, -1) -- ++(0, -0.2) coordinate(av);

      % Force Sensors
      \draw[fill=white] ($(au) + (-0.2, -0.5)$) rectangle ($(au) + (0, 0.5)$);
      \draw[] ($(au) + (-0.2, -0.5)$)coordinate(actu) -- ($(au) + (0,  0.5)$);
      \draw[] ($(au) + (-0.2,  0.5)$)coordinate(ku)   -- ($(au) + (0, -0.5)$);
      \node[below=0.1, rotate=\thetau] at ($(au) + (-0.1, -0.5)$) {$f_{u}$}

      \draw[fill=white] ($(av) + (-0.5, -0.2)$) rectangle ($(av) + (0.5, 0)$);
      \draw[] ($(av) + ( 0.5, -0.2)$)coordinate(actv) -- ($(av) + (-0.5,  0)$);
      \draw[] ($(av) + (-0.5, -0.2)$)coordinate(kv)   -- ($(av) + ( 0.5,  0)$) ;
      \node[right=0.1, rotate=\thetau] at ($(av) + (0.5, -0.1)$) {$f_{v}$}

      % Spring and Actuator for U
      \draw[actuator={0.6}{0.2}] (actu) -- node[below=0.1, rotate=\thetau]{$F_u$} (actu-|-2.6,0);
      \draw[spring=0.2] (ku) -- node[below=0.1, rotate=\thetau]{$k_a$} (ku-|-2.6,0);
      \draw[spring=0.2] (-1, 0.8) -- node[above=0.1, rotate=\thetau]{$k_p$} (-1, 0.8-|-2.6,0);

      \draw[actuator={0.6}{0.2}] (actv) -- node[right=0.1, rotate=\thetau]{$F_v$} (actv|-0,-2.6);
      \draw[spring=0.2] (kv) -- node[right=0.1, rotate=\thetau]{$k_a$} (kv|-0,-2.6);
      \draw[spring=0.2] (-0.8, -1) -- node[left=0.1, rotate=\thetau]{$k_p$} (-0.8, -1|-0,-2.6);
    \end{scope}

    % Inertial Frame
    \draw[->] (-4, -4) -- ++(2, 0) node[below]{$\vec{i}_x$};
    \draw[->] (-4, -4) -- ++(0, 2) node[left]{$\vec{i}_y$};
    \draw[fill, color=black] (-4, -4) circle (0.06);
    \node[draw, circle, inner sep=0pt, minimum size=0.3cm, label=left:$\vec{i}_z$] at (-4, -4){};

    \node[draw, circle, inner sep=0pt, minimum size=0.3cm] at (0, 0){};
    \draw[->] (0, 0) node[above left, rotate=\thetau]{$\vec{i}_w$} -- ++(\thetau:2) node[above, rotate=\thetau]{$\vec{i}_u$};
    \draw[->] (0, 0) -- ++(\thetau+90:2) node[left, rotate=\thetau]{$\vec{i}_v$};
    \draw[dashed] (0, 0) -- ++(2, 0);
    \draw[] (1.5, 0) arc (0:\thetau:1.5) node[midway, right]{$\theta$};
    \node[] at (0,0) {$\bullet$};

    \draw[->] (3.5, 0) arc (0:40:3.5) node[midway, left]{$\Omega$};
  \end{tikzpicture}
#+end_src

#+RESULTS:
[[file:figs/system_parallel_springs.png]]
