Question

(SLO ... (6)Points) 3. Find the C(S)/R(S) for the signal flow diagram using Mason's Gain Rule

Answer 1

First, we need to convert the Block diagram into signal Flow Graph

Step 1:

that

fig 1.

For that consider the input as a node, Summing point as a node, Branching as a node and output as a node.

So Total there are 9 Nodes.

For the signal flow graph draw a Forward path with 9 nodes.

Step 2:

fig 2.

Then draw the feedback in these nodes.

Then we need to consider Gain in these nodes, If there is no gain take it as unit gain as Follows

As) | 46 | | ریا) ( (

ܨܠ + ܙܠ' _ ܕܠ:15 - (T ( s

There are only Two forward Path $P_{1}$ and $P_{2}$

$P_{1}$ is Taken as in the fig (2)

$P_{2}$ as Follows.

P = G1G2G3

P2 = G1G4

A1 = 1-0

-1= ܕܠ

Then consider How many loops are there in the diagram

There is a total of 5 loops.

Loop 1

Pu = -G1G2H1

LOOP 2

-HI - H

P12 = -G2G3H2

Loop 3

R(S) (6) 7 9 -Hi - H2

P13 = -G1G2G3

Loop 4

P14 = -G1GA

Loop 5

一个

P15 = -GAH

For all the Loops

Pu = -G1G2H1

P12 = -G2G3H2

P13 = -G1G2G3

P14 = -G1GA

P15 = -GAH

P = G1G2G3

P2 = G1G4

A1 = 1-0

-1= ܕܠ

ܨܠ + ܙܠ' _ ܕܠ:15 - (T ( s

(sum of all loops)

A =1–

ܕܠ%+ ܙܠ-(ne

By substituting all the values we get as

GG G3 +G2G4 1+(G1G2H + G G3H2 +G1G2G3 + G G4 + GAH)