Embed Size (px)
Citation preview
Control System Engineering
Kuntumal Sagar M.B.TECH (E.E)
UID-U41000000484Email: [email protected]
TOPIC BLOCK DIAGRAM EXAMPLES
Example 9
Find the transfer function of the following block diagrams
2G 3G1G
4G
1H
2H
)(sY)(sR
1. Moving pickoff point A ahead of block2G
2. Eliminate loop I & simplify
324 GGG B
1G
2H
)(sY4G
2G
1H
AB3G
2G
)(sR
I
Solution:
3. Moving pickoff point B behind block324 GGG
1GB
)(sR
21GH 2H
)(sY
)/(1 324 GGG
II
1GB
)(sRC
324 GGG
2H
)(sY
21GH
4G
2G A3G 324 GGG
4. Eliminate loop III
)(sR
)(1
)(
3242121
3241
GGGHHGG
GGGG
)(sY
)()(1
)(
)(
)()(
32413242121
3241
GGGGGGGHHGG
GGGG
sR
sYsT
)(sR
1GC
324
12
GGG
HG
)(sY324 GGG
2H
C
)(1 3242
324
GGGH
GGG
Using rule 6
2G1G
1H 2H
)(sR )(sY
3H
Example 10
Find the transfer function of the following block diagrams
Solution:
1. Eliminate loop I
2. Moving pickoff point A behind block
22
2
1 HG
G
1G
1H
)(sR )(sY
3H
BA
22
2
1 HG
G
2
221
G
HG
1G
1H
)(sR )(sY
3H
2G
2H
BA
II
I
22
2
1 HG
G
Not a feedback loop
)1
(2
2213
G
HGHH
3. Eliminate loop II
)(sR )(sY
22
21
1 HG
GG
2
2213
)1(
G
HGHH
21211132122
21
1)(
)()(
HHGGHGHGGHG
GG
sR
sYsT
Using rule 6
2G4G1G
4H
2H
3H
)(sY)(sR
3G
1H
Example 11
Find the transfer function of the following block diagrams
Solution:
2G4G1G
4H
)(sY
3G
1H
2H
)(sR
A B
3H4
1
G
4
1
G
I1. Moving pickoff point A behind block
4G
4
3
G
H
4
2
G
H
2. Eliminate loop I and Simplify
II
III
443
432
1 HGG
GGG
1G
)(sY
1H
B
4
2
G
H
)(sR
4
3
G
H
II
332443
432
1 HGGHGG
GGG
III
4
142
G
HGH
Not feedbackfeedback
)(sR )(sY
4
142
G
HGH
332443
4321
1 HGGHGG
GGGG
3. Eliminate loop II & IIII
143212321443332
4321
1)(
)()(
HGGGGHGGGHGGHGG
GGGG
sR
sYsT
Using rule 6
3G1G
1H
2H
)(sR )(sY
4G
2GA
B
Example 12
Find the transfer function of the following block diagrams
Solution:
1. Moving pickoff point A behind block3G
I
1H3
1
G
)(sY1G
1H
2H
)(sR
4G
2GA B
3
1
G
3G
2. Eliminate loop I & Simplify
3G
1H
2G B
3
1
G
2H
32GG B
2
3
1 HG
H
1G)(sR )(sY
4G
3
1
G
H
23212
32
1 HGGHG
GG
II
)(sR )(sY
12123212
321
1 HGGHGGHG
GGG
3. Eliminate loop II
12123212
3214
1)(
)()(
HGGHGGHG
GGGG
sR
sYsT
4G
Example-13: Simplify the Block Diagram.
Example-13: Continue.
Example-14: Reduce the Block Diagram.
Example-14: Continue.
Example-15: Reduce the Block Diagram. (from Nise: page-242)
Example-15: Continue.
Example-16: Reduce the system to a single transfer function. (from Nise:page-243).
Example-17: Simplify the block diagram then obtain the close-loop transfer function C(S)/R(S). (from Ogata: Page-47)
Example-18: Multiple Input System. Determine the output C due to inputs R and U using the Superposition Method.
Example-18: Continue.
Example-18: Continue.
Example-19: Multiple-Input System. Determine the output C due to inputs R, U1 and U2 using the Superposition Method.
Example-19: Continue.
Example-19: Continue.
Example-20: Multi-Input Multi-Output System. Determine C1 and C2 due to R1 and R2.
Example-20: Continue.
Example-20: Continue.
When R1 = 0,
When R2 = 0,
Block Diagram of Armature Controlled D.C Motor
Va
iaT
Ra La
J
c
eb
(s)IK(s)cJs
(s)V(s)K(s)IRsL
ama
abaaa
Block Diagram of Armature Controlled D.C Motor
(s)E(s)K(s)IRsL abaaa
Block Diagram of Armature Controlled D.C Motor
(s)IK(s)cJs ama
Block Diagram of Armature Controlled D.C Motor
Block Diagram of liquid level system
11
1 qqdt
dhC
1
211
R
hhq
212
2 qqdt
dhC
2
22
R
hq
Block Diagram of liquid level system
)()()( sQsQssHC 111
1
211
R
sHsHsQ
)()()(
2
22
R
sHsQ
)()( )()()( sQsQssHC 2122
11
1 qqdt
dhC
1
211
R
hhq
212
2 qqdt
dhC 2
22
R
hq
L
L
L
L
Block Diagram of liquid level system
)()()( sQsQssHC 111
1
211
R
sHsHsQ
)()()(
2
22
R
sHsQ
)()( )()()( sQsQssHC 2122
Block Diagram of liquid level system
