Example 5.6 Show all steps to final result / solution Converting a Block Diagram to a Signal-Flow Graph PROBLEM: Convert the block diagram of Figure 5.11 to a signal-flow graph. SOLUTION: Begin by drawing the signal nodes, as shown in Figure 5.19(a). Next, interconnect the nodes, showing the direction of signal flow and identifying each transfer function. The result is shown in Figure 5.19(b). Notice that the negative signs at the summing junctions of the block diagram are represented by the negative transfer functions of the signal-flow graph. Finally, if desired, simplify the signal-flow graph to the one shown in Figure 5.19(c) by eliminating signals that have a single flow in and a single flow out, such as V₂(s), V6(s), V(s), and Vs(s). 0% R(s) O о V₁(0) о V₂la) о V(3) о 03 Vy(s) V(3) o O CIs) Vals) V(3) о V8(3) (a) G₁(8) 1 G₂(3) 1 G₁(3) Rs) O Cis) V₁(3) V₁(3) Vy(s) Vals) Ve(s) Hs) -14 Hyls) V-0) V8(3) Vis) H₁(3) (b) G₁(s) Gy(1) Gy(5) CU) R(3) V₁(s) Vs) Va(s) Vg(s) -H₂(s) -H3(3) -H(s) (c) FIGURE 5.19 Signal-flow graph development: a. signal nodes; b. signal-flow graph: c. simplified signal-flow graph R(s) + V₁(s) V₂(s)+ V3(s) V4(s) + V5(s) C(s) G₁(s) G₂(s) G3($) V₁(s) V8($) H2(8) H3(5) V6(s) H₁(s) Figure 5.11