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PROCESS CONTROL 4CLOSED-LOOP TRANSFER FUNCTIONS
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STANDARD BLOCK DIAGRAM SYMBOLS
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Gc, G1 andG2is referred to as the forward path and is usually
lumped togetheras G
H is referred to as the feedback path
The product of GH is known as the open-loop transfer
function
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OVERALL TRANSFER FUNCTION FOR
SINGLE-LOOP SYSTEMS
Overall Transfer function for change in Set Point. i.e.
U=0
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OVERALL TRANSFER FUNCTION FOR
CHANGE IN LOAD
( )
HCB
B
GGM
MUGC
C
=
=
=
+=
1
2
Solving
Simultaneously( )( )HCGGUGC C += 12
Rearrange to
transfer function
form
GH
G
U
C
+
=
1
2
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METHODS TO SOLVE OVERALL TRANSFER
FUNCTION
STARTING AT THE LEFT AND WORKING ACROSS BLOCK DIAGRAM
( )[ ]
UGH
GR
GH
GC
CforSolving
CGUGGCHR C
+
+
+
=
=+
11
2
21
N i f db k
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loop
forward
X
Y
+
=
1
Product of transfer functions in forward path between
locations of X and Y
Product of transfer functions in loop
forward
loop
loop
forward
X
Y
=
1
Negative feedback
Positive feedback
Product of transfer functions in forward path between
locations of X and Y
Product of transfer functions in loop
forward
loop
NOTE: IF TWO INPUT CHANGES OCCURS AT THE SAME
TIME, THEN PROCEED AS PER SINGLE INPUT CHANGE
AND SUM THE CHANGES
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Example
Determine the transfer functions C/R, C/U1and B/U2for the system
shown
below. Also determine C if R and U1change simultaneously
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SMALL RECAP
ALWAYS START FROM INNERLOOP AND WORK OUTWARDS
