2. A graphical tool can help us to visualize the model of
a system and evaluate the mathematical
relationships between their elements, using their
transfer functions.
Using block diagram, we can solve the equations by
graphical simplification, which is often easier and
more informative than algebraic manipulation, even
though the methods are in every way equivalent
Introduction
4. Block Diagram
• It represents the mathematical relationships between the
elements of the system.
• The transfer function of each component is placed in box,
and the input-output relationships between components
are indicated by lines and arrows.
)
(
)
(
)
( 1
1
1 s
Y
s
G
s
U
9. Single loop negative
feedback
1
1 2
( )
( ) 1
G
Y s
R s G G
2 1
( ) ( ) ( )
Y s R s Y s G G
1 1 2
( ) ( ) ( )
Y s G R s GG Y s
1 2 1
( ) 1 ( )
Y s GG G R s
1
1 2
( )
( ) 1
G
Y s
R s G G
What about single loop with
positive feedback? ?
Negative
feedback
19. 1 2 5 1 6
1 3 1 2 4
1
G G G G G
G G G G G
1 2
1 3
1 2 4
1 3
1 6
5
2
1
( )
( )
( ) 1
G G
G G
G G G
G G
G
Y s
T s G
R s G
Transfer Function from Block
Diagram
21. 1 2 5 1 6
1 3 1 2 4
1
G G G G G
G G G G G
1 2
1 3
1 2 4
1 3
1 6
5
2
1
( )
( )
( ) 1
G G
G G
G G G
G G
G
Y s
T s G
R s G
Transfer Function from Block
Diagram
23. ?
1 2
1 2
( )
( ) 1
R
Y s G G
R s G G H
When D(s) 0,
When R(s) 0,
2 2
1 2 1 2
( )
( ) 1 ( ) 1
D
Y s G G
D s G G H G G H
Example: MISO
Find the response of the system Y(s) to simultaneous application of
the reference input R(s) and disturbance D(s).
24. Example MISO
( ) ( ) ( )
R D
Y s Y s Y s
1 2 2
1 2 1 2
( ) ( ) ( )
1 1
G G G
Y s R s D s
G G H G G H
2
1
1 2
( ) ( ) ( )
1
G
Y s G R s D s
G G H