TikZ: Robust and automated creation of signal-flow graph (parallel form)

Question

Following up on my previous question, I would like to know how I can automatically and robustly create the parallel form of a signal-flow diagram for the following without manual drawing of the lines/nodes:

Consider a transfer function without repeated poles

Each term is a first-order subsystem with R(s) as the input, and the output C(s) can be considered the sum of the three terms

Therefore, this leads to the following desired parallel form of the signal-flow diagram

My questions about my code below are:

1- why doesn't foreach work in my code?

2- How to fine-tune the position of amark labels to make them move away a bit from the curved lines?

3- How can I robustly automate the process of drawing the diagram without the manual drawing of lines/nodes?

4- Is there a more simplified code of the code below using tikz-cd, matrix of nodes, or chains?

\documentclass[tikz,border=5mm]{standalone}
\usetikzlibrary{calc,decorations.markings,positioning,arrows.meta,matrix}
\newif\iflabrev
\begin{document}
    \begin{tikzpicture}[
        node distance = 15mm and 15mm, 
        relative = false,
        label revd/.is if = labrev,
        label revd/.default = true,
        amark/.style = {
            decoration={             
                markings,   
                mark=at position {0.5} with { 
                    \arrow{stealth},
                    \iflabrev \node[below] {#1};\else \node[above] {#1};\fi
                }
            },
            postaction={decorate}
        },
    terminal/.style 2 args={draw,alias=ln,circle,inner sep=2pt,label={#1:#2}},
        ]
        \path
        node[terminal={left}{$R(s)$}] (R) {}
        node[above right=of R, terminal={}{}] (sX-1) {}
        node[right=of sX-1, terminal={}{}] (X-1) {}
        node[right=of R, terminal={}{}] (sX-2) {}
        node[right=of sX-2, terminal={}{}] (X-2) {}
        node[right=of X-2, terminal={right}{$C(s)$}] (C) {}
        node[below right=of R, terminal={}{}] (sX-3) {}
        node[right=of sX-3, terminal={}{}] (X-3) {}
        ;
        %
        \foreach \X in {1,...,3}{
            (sX-\X) edge[amark=1/s] (X-\X)
        };
    \path (R) edge[out=90,in=180,amark=12] (sX-1) (X-1) edge[out=-90,in=-90,amark=-2] (sX-1) edge[out=0,in=90,amark=1] (C);
    \path (R) edge[amark=-24] (sX-2) (X-2) edge[out=-90,in=-90,amark=-3] (sX-2) edge[amark=1] (C);
    \path (R) edge[out=-90,in=180,amark=12,label revd] (sX-3) (X-3) edge[out=-90,in=-90,amark=-4] (sX-3) edge[out=0,in=-90,amark=1,label revd] (C);
    \end{tikzpicture}
\end{document}

Answer 1

These are just some quick fixes.

1. foreach does not work because there is no \path command.
2. You can use an edge label to achieve an arguably better positioning.

Items 3 and 4 would require more thought. But this would make more sense if it was clear what the overall structure of these diagrams is. This would allow one to gauge which strategy may be the most appropriate one.

\documentclass[tikz,border=5mm]{standalone}
\usetikzlibrary{calc,decorations.markings,positioning,arrows.meta,matrix}
\makeatletter
\pgfmathdeclarefunction{Dim}{1}{%
  \begingroup%
    \pgfmath@count=0\relax
    \edef\pgfutil@tmpb{#1}%
    \pgfutil@for\pgfutil@tmpa:={\pgfutil@tmpb}\do{%
      \advance\pgfmath@count by1\relax}%
    \edef\pgfmathresult{\the\pgfmath@count}% 
    \pgfmath@smuggleone\pgfmathresult% 
  \endgroup}  
\makeatother
\begin{document}
    \begin{tikzpicture}[
        node distance = 15mm and 15mm, 
        relative = false,
        amark/.style = {
            decoration={             
                markings,   
                mark=at position {0.5} with { 
                    \arrow{stealth},
                }
            },
            postaction={decorate},
            edge label={#1}
        },
        amark'/.style = {
            decoration={             
                markings,   
                mark=at position {0.5} with { 
                    \arrow{stealth},
                }
            },
            postaction={decorate},
            edge label'={#1}
        },
    terminal/.style 2 args={draw,alias=ln,circle,inner sep=2pt},
        ]
        % input
        \def\GraphInput{12/-2,-24/-3,12/-4}
        %\def\GraphInput{12/-2,-24/-3,12/-4,5/-7}
        %\def\GraphInput{12/-2,-24/-3,12/-4,5/-7,3/-3}
        % number of insertion
        \pgfmathtruncatemacro{\mydim}{Dim("\GraphInput")}
        % local bounding box is a trick that all distances derive from node distance
        \path[local bounding box=graph] 
         foreach \X/\Y [count=\Z] in \GraphInput {
         % draw the inner nodes in a loop
          \ifnum\Z=1
          node[terminal] (sX-\Z){} node[right=of sX-\Z,terminal] (X-\Z){}
          \else
          node[terminal,below=of sX-\the\numexpr\Z-1] (sX-\Z){} 
          node[right=of sX-\Z,terminal] (X-\Z){}
          \fi
        }
        % draw R and S nodes
        node[left=of graph,terminal,label=left:{$R(s)$}] (R){}
        node[right=of graph,terminal,label=right:{$C(s)$}] (C){}
        % loop for connections
        foreach \X/\Y [count=\Z] in \GraphInput {
        % bug in pgf, out does not get parsed properly
        [/utils/exec=\pgfmathsetmacro{\myout}{90-(\Z-1)*180/(\mydim-1)}]
        (sX-\Z) edge[amark={$1/s$}] (X-\Z)
        (X-\Z) edge[amark'={$\Y$},out=-90,in=-90] (sX-\Z)
        \ifnum\Z>\numexpr\mydim/2
         (R) edge[amark'={$\X$},out=\myout,in=180] (sX-\Z)
         (X-\Z) edge[amark'={$1$},out=0,in=180-\myout] (C)
        \else
         (R) edge[amark={$\X$},out=\myout,in=180] (sX-\Z)
         (X-\Z) edge[amark={$1$},out=0,in=180-\myout] (C)
        \fi
        };
 \end{tikzpicture}
\end{document}

And this is a routine that draws the graph from some input like

\def\GraphInput{12/-2,-24/-3,12/-4}

I tried to add some explanations. Unfortunately there is also a pgf issue with the parsing of in and out in edges. This code also places the edge labels more tightly.

\documentclass[tikz,border=5mm]{standalone}
\usetikzlibrary{calc,decorations.markings,positioning,arrows.meta,matrix}
\makeatletter
\pgfmathdeclarefunction{Dim}{1}{%
  \begingroup%
    \pgfmath@count=0\relax
    \edef\pgfutil@tmpb{#1}%
    \pgfutil@for\pgfutil@tmpa:={\pgfutil@tmpb}\do{%
      \advance\pgfmath@count by1\relax}%
    \edef\pgfmathresult{\the\pgfmath@count}% 
    \pgfmath@smuggleone\pgfmathresult% 
  \endgroup}  
\makeatother
\begin{document}
    \begin{tikzpicture}[
        node distance = 15mm and 15mm, 
        relative = false,
        amark/.style = {
            decoration={             
                markings,   
                mark=at position {0.5} with { 
                    \arrow{stealth},
                }
            },
            postaction={decorate},
            nodes={inner xsep=0pt},
            edge label={#1}
        },
        amark'/.style = {
            decoration={             
                markings,   
                mark=at position {0.5} with { 
                    \arrow{stealth},
                }
            },
            postaction={decorate},
            nodes={inner xsep=0pt},
            edge label'={#1}
        },
    terminal/.style 2 args={draw,alias=ln,circle,inner sep=2pt},
        ]
        % input
        %\def\GraphInput{12/-2,-24/-3,12/-4}
        \def\GraphInput{12/-2,-24/-3,12/-4,5/-7}
        % number of insertions
        \pgfmathtruncatemacro{\mydim}{Dim("\GraphInput")}
        % local bounding box is a trick that all distances derive from node distance
        \path[local bounding box=graph] 
         foreach \X/\Y [count=\Z] in \GraphInput {
         % draw the inner nodes in a loop
          \ifnum\Z=1
          node[terminal] (sX-\Z){} node[right=of sX-\Z,terminal] (X-\Z){}
          \else
          node[terminal,below=of sX-\the\numexpr\Z-1] (sX-\Z){} 
          node[right=of sX-\Z,terminal] (X-\Z){}
          \fi
        }
        % draw R and S nodes
        node[left=of graph,terminal,label=left:{$R(s)$}] (R){}
        node[right=of graph,terminal,label=right:{$C(s)$}] (C){}
        % loop for connections
        foreach \X/\Y [count=\Z] in \GraphInput {
        % bug in pgf, out does not get parsed properly
        [/utils/exec=\pgfmathsetmacro{\myout}{90-(\Z-1)*180/(\mydim-1)}]
        (sX-\Z) edge[amark={$1/s$}] (X-\Z)
        (X-\Z) edge[amark'={$\Y$},out=-90,in=-90] (sX-\Z)
        \ifnum\Z>\numexpr\mydim/2
         (R) edge[amark'={$\X$},out=\myout,in=180] (sX-\Z)
         (X-\Z) edge[amark'={$1$},out=0,in=180-\myout] (C)
        \else
         (R) edge[amark={$\X$},out=\myout,in=180] (sX-\Z)
         (X-\Z) edge[amark={$1$},out=0,in=180-\myout] (C)
        \fi
        };
 \end{tikzpicture}
\end{document}

Answer 2

With use of the tiz-cd package (which is designed to draw such diagrams), you will avoid your problems. Code is relative simple and clear, and shorter:

\documentclass[border=5mm]{standalone}
\usepackage{tikz-cd}
\usetikzlibrary{arrows.meta,
                decorations.markings}
\newif\iflabrev
\begin{document}
\begin{tikzcd}[
    cells={nodes={circle, draw, inner sep=2pt}},
    every arrow/.append style = {decoration={markings, 
                                             mark=at position .5 with {\arrow{Straight Barb[scale=0.5]}}},
                                 postaction={decorate}, -
                                },
    every label/.append style = {font=\footnotesize}

                ]
    & \ar[r,"1/s"]
            & \ar[l,"-2",bend left=60]
              \ar[rd,"1",bend left]
                    &                       \
|[label=left:R(s)]| 
 \ar[ru,"12",bend left] 
 \ar[rd,"12",bend right]
 \ar[r,"-24"]

    & 
      \ar[r,"1/s"]
            & \ar[l,"-3", bend left=60]
              \ar[r,"1"]
                    & |[label=right:C(s)]|  \
    & \ar[r,"1/s"]
            & \ar[l,"-4",bend left=60]
              \ar[ru,"1",bend right]
                    &                       \
\end{tikzcd}
\end{document}

Note, if you like to change distances between node, than you only need to add to tikzcd options:

column sep=<desired distance between columns>,
row sep=<desired distance between rows>,