A feedback control system is shown in figure (a) Draw the signal-flow graph that represents the system.
(b) Find the total number of loops in the graph and determine the loop-gains of all the loops.
(c) Find the number of all possible combination of non-touching loops taken two at a time.
(d) Determine the transfer function of the system using the signal-flow graph.

Draw a signal flow graph for the following set of algebraic equations: $$$\begin{array}{l}y_2=ay_1-\;gy_3\\y_3=ey_2+\;cy_4\\y_4=by_2-dy_4\end{array}$$$ Hence, find the gains $$\frac{y_2}{y_1}$$ and $$\frac{y_3}{y_1}$$.

Reduce the signal flow graph shown in fig. below, to obtain another graph which does not contain the node e₅.Also, remove any self-loop from the resulting graph.