Drawing a block diagram with TiKz

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Fixes:

1. Added a node Measurement positioning it halfway between the nodes System and Model using this syntax: \node ... at ($(system)!.5!(model)$) {};. This requires calc to be added to the Tikz libraries.
2. Changed your diagonal path to \draw [->] (outfork) -| (sum.north) node [very near end] {\(t\)}; so that the node stops exactly at the north point of sum.
3. The [very near end] above ensures that the node appears very close to the arrow tip.
4. Removed minimal size for your nodes that makes them look square (it's a bit ugly), and replaced it with inner sep which adds space inside the node consistently so that the rectangle borders are equally far from the node text.
5. For the node u (the path on the left), I added the key [anchor=south west] so that it moves it right and up a bit and appears next to the path.
6. Used labels for the - and + symbols. Originally they were nodes but it looks better like this and the code is cleaner and shorter.

\documentclass{standalone}

\usepackage{tikz}       
\usetikzlibrary{arrows,positioning,patterns,decorations.pathmorphing,calc}

\begin{document}

\tikzstyle{block} = [draw, rectangle, inner sep=6pt]
\tikzstyle{joint} = [draw, circle,minimum size=1em]

\begin{tikzpicture}[>=stealth, auto, node distance=2cm]
    % Place nodes
    \node [block] (system) {System};
    \node [coordinate, left=of system] (infork) {};
    \node [coordinate, left=of infork] (input) {};
    \node [coordinate, right=of system] (outfork) {};
    \node [coordinate, right=of outfork] (output) {};
    \node [coordinate, above=of system] (disturbances) {};
    \node [block, below=of system] (model) {Model};
    \node [joint, right=of model, anchor=center,label={[shift={(2mm,-1mm)}]-},label={[shift={(-3mm,-5.5mm)}]\tiny +}] (sum) {};

    \node [coordinate, right=of sum] (error) {};
    \node [block, dashed, fill=gray, anchor=center, text width=7cm, align=center] at ($(system)!.5!(model)$) {\textsc{Measurement}};

    % Connect nodes
    \draw [->, decorate, decoration={snake, post length=1mm}] (disturbances) -- node {\(d'\)} (system);
    \draw [->] (input) -- node {\(u'\)} (system);
    \draw [->] (system) -- node {\(t'\)} (output);
    \draw [->] (model) -- node {\(y\)} (sum);
    \draw [->] (sum) -- node {\(\epsilon\)} (error);
    \draw [->] (infork) |- node [anchor=south west] {\(u\)} (model);
    \draw [->] (outfork) -| (sum.north) node [very near end] {\(t\)};
\end{tikzpicture}

\end{document}

None of the answers here capture the hand drawn look of the original. Here is a Metapost solution that uses mp-sketch to get the hand drawn look. I also use Comic Neue and Euler fonts. Here is the result:

    \usetypescriptfile[euler]
\definetypeface[mainfont][rm][specserif][ComicNeue][default]
\definetypeface[mainfont][mm][math] [pagellaovereuler][default]
\setupbodyfont[mainfont,12pt]

% Set upright style for Euler Math
\appendtoks \rm \to \everymathematics
\setupmathematics
  [lcgreek=normal, ucgreek=normal]

\startMPinclusions
  input rboxes;
  input mp-sketch;
\stopMPinclusions

\defineframed
  [labelframe]
  [
    background=color,
    backgroundcolor=gray,
    frame=off,
  ]

\starttext
\startMPpage[offset=3mm]
  sketchypaths;

  defaultdx := 16bp;
  defaultdy := 16bp;
  circmargin := 5bp;
  sketch_amount := 2bp;

  u := 1cm;
  drawoptions(withpen pencircle scaled 1bp);

  boxit.system("SYSTEM");
  boxit.model ("MODEL");
  circleit.adder("$\cdot$");

  system.c = origin;
  system.s - model.n = (0, 3u);

  z.0 = system.w - (2u, 0);
  z.1 = 0.5[  z.0, system.w ];
  z.2 = (x.1, ypart model.w);
  z.3 = system.e + (u, 0);
  z.4 = system.e + (2u, 0);
  z.5 = (x.4, y.2);

  adder.c = (x.3, ypart model.c);

  drawboxed(system, model, adder);

  z.6 = 0.5[system.s, model.n];
  stripe_path_n
    (withpen pencircle scaled 2 withcolor 0.5white)
    (draw)
    fullsquare xyscaled(x.3 - x.1 + u, 2*LineHeight) 
    shifted z.6 dashed evenly;

  label("\labelframe{Measurement}", z.6);


  % Reduce the amount of randomness for the lines
  sketch_amount := bp;

  drawarrow z.0 -- lft system.w;
  drawarrow z.1 -- z.2 -- lft model.w;
  drawarrow system.e -- z.4 ;
  drawarrow model.e -- lft adder.w ;
  drawarrow z.3 -- top adder.n ;
  drawarrow adder.e -- z.5 ;

  label.urt("$-$", adder.n);
  label.llft("$+$", adder.w);

  label.top("$u'$", z.1);
  label.top("$t'$", z.3);
  label.top("$ε$", 0.5[adder.e, z.5]);

  dx := 12bp;
  label.urt("$t$", adder.n + (0, dx));
  label.urt("$u$", z.2 + (0, dx));

\stopMPpage
\stoptext

For whom it may interest, here is a solution with MetaPost and the MetaObj package, inside a LuaLaTeX program. It is based on the s and m parameters which allow to locate the “System” and “Model” boxes, respectively centered at points (s,0) and (s, m).

\documentclass[border=2mm]{standalone}
\usepackage{luamplib}
  \mplibtextextlabel{enable}
\begin{document}
  \begin{mplibcode}
    input metaobj
    s := 4.5cm; m := -3cm; % locates upper and lower boxes
    beginfig(1);
      % Central box
      newBox.msrmt("Measurement") "filled(true)", "fillcolor(.8white)", 
        "dx(.6s)", "framestyle(dashed evenly)";
      msrmt.c = (s, .5m); drawObj(msrmt);
      % Upper and lower boxes
      newBox.syst("System") "dx(2mm)", "dy(3mm)"; 
      newBox.model("Model") "dx(2mm)", "dy(3mm)";
      syst.c = (s, 0); model.c = (s, m);
      drawObj(syst); drawBox(model);
      % Empty circle
      ep := .5(xpart syst.w); t := xpart syst.e + ep; u := xpart syst.w - ep;
      newCircle.circ("") "circmargin(1.5mm)";
      circ.c = (t, m);
      drawObj(circ);
      % Connections
      drawarrow origin -- syst.w;
      drawarrow (u, 0) -- (u, m) -- model.w;
      drawarrow syst.e -- (t+ep, 0);
      drawarrow (t, 0) -- circ.n;
      drawarrow model.e -- circ.w;
      drawarrow circ.e -- (t+ep, m);
      % The spring (and its label)
      newEmptyBox.upper(0, 0); upper.c = (s, -.75m);
      picture lab; lab = textext("$d'$");
      nczigzag(upper)(syst) "coilwidth(2.5mm)", "coilarmA(0mm)", 
        "coilarmB(3mm)", "linearc(.4mm)", "labpic(lab)", "labdir(rt)";
      % Other labels  
      label.top("$u'$", (u, 0)); label.urt("$u$", (u, m));
      label.top("$t'$", (t, 0));
      label.top("$y$", .5(model.e+circ.w));
      label.rt("$t$", (t, ypart(.5(msrmt.s+circ.n))));
      label.top("$\epsilon$", .5[(t,m), (t+ep, m)]);
      labeloffset := .5bp;
      label.llft("\tiny$+$", circ.sw);
      label.urt("\tiny$-$", circ.ne);
      labeloffset := 3bp;
    endfig; 
  \end{mplibcode}
\end{document}