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# Tikz Figures

## Table of Contents

- 1. X-Y Rotating Positioning Platform
- 2. X-Y Rotating Positioning Platform with Force Sensors
- 3. Decentralized Integral Force Feedback
- 4. Decentralized Direct Velocity Feedback
- 5. Springs in parallel

Configuration file is accessible here.

## 1 X-Y Rotating Positioning Platform

    \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 X-Y Stage};

        % 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);

        % % Displacement measurement
        % \draw[<->, dashed] (-2.6, -0.8) --node[midway, below, rotate=\thetau]{$d_u$} (-1  , -0.8);
        % \draw[<->, dashed] ( 0.8, -2.6) --node[midway, right, rotate=\thetau]{$d_v$} ( 0.8, -1);
      \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) -- ++(\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) {$\bullet$};
      \node[left] at (0,0) {$(x, y)$};

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

## 2 X-Y Rotating Positioning Platform with Force Sensors

    \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 X-Y Stage};

        % 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) node[above=0.1, rotate=\thetau]{$f_{u}$}   -- ($(au) + (0, -0.5)$);

        \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) node[left=0.1, rotate=\thetau]{$f_{v}$} -- ($(av) + ( 0.5,  0)$);

        % 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[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);
      \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) -- ++(\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) {$\bullet$};
      \node[left] at (0,0) {$(x, y)$};

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

## 3 Decentralized Integral Force Feedback

    \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 X-Y Stage};

        % 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) node[above=0.1, rotate=\thetau]{$f_{u}$}   -- ($(au) + (0, -0.5)$);
        \node[above, rotate=\thetau] at ($(av) + (-0.1, 0.5)$) {$f_{u}$};

        \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[left, rotate=\thetau] at ($(av) + (-0.5, -0.1)$) {$f_{v}$};

        % 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);
        \draw[->] (Ku.north) -- ($(actumid) + (0, -0.1)$) node[below left, rotate=\thetau]{$F_u$};

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

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

## 4 Decentralized Direct Velocity Feedback

    \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 X-Y Stage};

        % 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);

        % Attached Points
        \node[] at (-1, 0){$\bullet$};
        \draw[] (-1, 0) -- ++(-0.2, 0) coordinate(cu);
        \draw[] ($(cu) + (0, -0.5)$) coordinate(actu) -- ($(cu) + (0, 0.5)$) coordinate(ku);
        \node[] at (0, -1){$\bullet$};
        \draw[] (0, -1) -- ++(0, -0.2) coordinate(cv);
        \draw[] ($(cv) + (-0.5, 0)$)coordinate(kv) -- ($(cv) + (0.5, 0)$) coordinate(actv);

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

        % Displacement measurement
        \draw[<->, dashed] (-2.6, -0.8) -- (-1  , -0.8) coordinate(dutop);
        \draw[<->, dashed] ( 0.8, -2.6) -- ( 0.8, -1) coordinate(dvtop);

        % Controllers
        \node[block={0.6cm}{0.6cm}, rotate=\thetau] (Ku) at ($(actumid) + (0, -1.2)$) {$K_{V}$};
        \draw[->] ($(dutop) + (-0.1, 0)$) node[below left, rotate=\thetau]{$v_u$} |- (Ku.east);
        \draw[->] (Ku.north) -- ($(actumid) + (0, -0.1)$);

        \node[block={0.6cm}{0.6cm}, rotate=\thetau] (Kv) at ($(actvmid) + (1.2, 0)$) {$K_{V}$};
        \draw[->] ($(dvtop) + (0, -0.1)$) node[below right, rotate=\thetau]{$v_v$} -| (Kv.north);
        \draw[->] (Kv.west) -- ($(actvmid) + (0.1, 0)$);

        \node[above=0.1, rotate=\thetau] at (actumid) {$F_u$};
        \node[left=0.1, rotate=\thetau] at (actvmid) {$F_v$};
      \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) -- ++(\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) {$\bullet$};
      \node[left] at (0,0) {$(x, y)$};

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

## 5 Springs in parallel

    \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 X-Y Stage};

        % 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]{$k$} (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]{$k$} (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){};

      \draw[->] (0, 0) -- ++(\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) {$\bullet$};
      \node[left] at (0,0) {$(x, y)$};

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

Author: Thomas Dehaeze

Created: 2020-06-22 lun. 14:45