In this presentation I've discussed about "Signal Flow Graph",one of the widely used block reduction techniques in CONTROL SYSTEM.

1. SIGNAL FLOW GRAPH &
BLOCK DIAGRAM REDUCTION
Gourab Chandra Ghosh
Surendra Institute of Engineering &
Management

2. CONTENTS:
1. What is Transfer function ?
2. Types of Transfer function
3. Block Diagram Reduction Technique
4. Example
5. Reference
6. Q & A
2

3. Transfer Function:
 Transfer function is defined as the ratio of Laplace
transform of output to the of Laplace transform of input
(with all initial conditions being zero)
r(t) c(t)g
R(s) G C(s)
T.F.= £{c(t)}/£{r(t)}
C(S) / R(s)
3

4. Open & Close Loop Transfer
Function:
4
R(s) G(s) C(s)
R(s) G(s) C(s)
H(s)
G(s)=C(S) / R(s)
C(S) / R(s)= G(s)/(1±G(s)
H(s))

5. Block Diagram Reduction :
 Blocks in series:
5
G1 G2 G3
G1 x G2 x G3

6. Block Diagram Reduction :
 Blocks in parallel:
6
G1
G2
G3
G1+G2+G3

7. Block Diagram Reduction :
 Shifting of a summing point behind a block:
7
G G
1/G

8. Block Diagram Reduction :
 Shifting of a summing point beyond a block:
8
G G
G

9. Block Diagram Reduction :
 Shifting of a take-off point beyond a block:
9
G G
G

10. Block Diagram Reduction :
 Shifting of a take-off point beyond a block:
10
G G
1/G

11. Example:
11
G1
H1
G2
H2
C(s)
R(s)
H3
+
-
++
--
We know for C.L.T.F.C(S) / R(s)= G(s)/(1±G(s) H(s))

12. Example:
12
-
G1
(1+ G1.H1)
H3
G2
(1+ G2.H2)
R(s) C(s)

13. Example:
13
G1.G2
(1+ G1.H1) (1+ G2.H2)
H3
-
R(s) C(s)

14. Example:
14
G1.G2
(1+ G1.H1) (1+ G2.H2)+ G1.G2.H3-
R(s) C(s)

15. Reference:
 Automatic Control Systems- B.C.KUO
 Modern Control Engineering- K. OGATA
15

16. Question &
Answer Session
16