If a Block diagram which consists of a forward path having one block, a feed back path having one bl

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ME 55 Control Engineering
CANNONICAL FORM OF CLOSED LOOP SYSTEM
If a Block diagram which consists of a forward
path having one block, a feed back path having
one block, a take off point and a summing point,
it represents a Cannonical form of a closed loop
system
_
Dr.D.V.Girish, Professor Head (Mechanical)
MCE, Hassan
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ME 55 Control Engineering
R(s) Laplace Transform of Reference Input
?(t) C(s) Laplace Transform of Controlled
Output c(t) E(s) Laplace Transform of
Error signal e(t) B(s) Laplace
Transform of Feed back signal b(t) G
(S) Equivalent forward path Transform function
(c(s)/E(s)) H (S) Equivalent feedback path
Transform function (c(s)/E(s))
Dr.D.V.Girish, Professor Head (Mechanical)
MCE, Hassan
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ME 55 Control Engineering
BLOCK DIAGRAM ALGEBRA
Block diagrams of some of the control systems
turn out to be very complex such that the
evaluation of their performance requires
simplification (or reduction) of block diagrams
which is carried out by block diagram
rearrangements, using the rules of BLOCK DIAGRAM
ALGEBRA Some of the important Block diagram
rearrangements are discussed here
Dr.D.V.Girish, Professor Head (Mechanical)
MCE, Hassan
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ME 55 Control Engineering
Block diagram Reduction (i) Block diagram of
a closed loop system
In the above figure, we can write E (S) R (S)
B (S) B (S) C (S) . H (S) C (S) G
(S) . E (S) C (S) G (S) . R (S) B (S)
Dr.D.V.Girish, Professor Head (Mechanical)
MCE, Hassan
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ME 55 Control Engineering
C (S) G (S) . R (S) - G (S) H (S) . C (S) ?C
(S) G (S) . H (S) . C (S) G (S) . R (S) C
(S) 1 G (S) H (S) G (S) . R (S) ? C (S)
/ R (S) G (S) / 1 G (S) H (S)
Dr.D.V.Girish, Professor Head (Mechanical)
MCE, Hassan
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ME 55 Control Engineering
Similarly it can be shown for a positive feed
back C (S) / R (S) G (S) / 1 G(S) H (S)
?In General we can write C (S) / R (S) G
(S) / 1 G (S) H (S) In Block diagram
representation we can write
Dr.D.V.Girish, Professor Head (Mechanical)
MCE, Hassan
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ME 55 Control Engineering
RULES OF BLOCK DIAGRAM ALGEBRA (Fourteen)
Original Block Diagram
Equivalent Block Diagram
Transformation
Rearranging Summing Points
(1)
C
Splitting the Summing Points
(2)
Dr.D.V.Girish, Professor Head (Mechanical)
MCE, Hassan
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ME 55 Control Engineering
Original Block Diagram
Equivalent Block Diagram
Transformation
(3)
Interchanging the Blocks
(4)
Combining the Blocks in Cascade
Combining the Blocks in Parallel OR Eliminating
a Forward Loop
(5)
Dr.D.V.Girish, Professor Head (Mechanical)
MCE, Hassan
9
ME 55 Control Engineering
Original Block Diagram
Equivalent Block Diagram
Transformation
Moving a Summing Point head of a Block
(6)
Moving a Summing Point Beyond a Block
(7)
Dr.D.V.Girish, Professor Head (Mechanical)
MCE, Hassan
10
ME 55 Control Engineering
Equivalent Block Diagram
Original Block Diagram
Transformation
(8)
Moving a take off point ahead of a Block
A
Moving a take off point beyond a Block
(9)
Dr.D.V.Girish, Professor Head (Mechanical)
MCE, Hassan
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ME 55 Control Engineering
(10)
Moving a take off point before (ahead of) a
summing Block
Moving a take off point after (beyond) a Summing
block
(11)
A -B
Dr.D.V.Girish, Professor Head (Mechanical)
MCE, Hassan
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ME 55 Control Engineering
(12)
Removing a Block from a Forward Path
Dr.D.V.Girish, Professor Head (Mechanical)
MCE, Hassan
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ME 55 Control Engineering
(13)
Removing a Block from a Feed Back Loop
( No. 10, 11, 12 13 to be used very carefully
or better to be avoided )
Dr.D.V.Girish, Professor Head (Mechanical)
MCE, Hassan
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ME 55 Control Engineering
(14)
Eliminating a Feedback Loop
( No. 6, 7, 8, 9 14, are very Important / to be
used frequently )
Dr.D.V.Girish, Professor Head (Mechanical)
MCE, Hassan
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ME 55 Control Engineering
Procedure for reduction of Block Diagram Step.
1 Reduce the Cascade BlocksStep. 2 Reduce
the parallel BlocksStep. 3 Reduce the
internal Feed back loopsStep. 4 It is
advisable to shift take off points towards right
and summing points towards left.
It is always better to avoid
rules - - - - and -- - - - i.e.
shafting take off point before a summing block
and shifting of take off point
after summing block
11
10
Dr.D.V.Girish, Professor Head (Mechanical)
MCE, Hassan
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ME 55 Control Engineering
Step. 5 Repeat steps 1 to step 4 until the
simple form is obtainedStep. 6
Find transfer function of the over all system
using the formula Cs / R (S) Any
complicated system can be brought into simple
form by reduction of block diagram using block
diagram Algebra, discussed earlier.
Dr.D.V.Girish, Professor Head (Mechanical)
MCE, Hassan