CBE / MET 433
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1 CBE / MET 433 15 Feb 12 (Chapter 3: Process Modeling) Models of Process Dynamics • Empirical Dynamic Models: can frequently describe process dynamics, but are “data fits” over a specific range of operation. • Theoretical Dynamic Models: are based on theory and might be useful for extrapolating. Also can be useful for determining controller tuning. Accuracy depends upon model details.
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CBE / MET 433. 15 Feb 12 (Chapter 3: Process Modeling). Models of Process Dynamics Empirical Dynamic Models: can frequently describe process dynamics, but are “data fits” over a specific range of operation. - PowerPoint PPT Presentation
Transcript of CBE / MET 433
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CBE / MET 433
15 Feb 12(Chapter 3: Process Modeling)
Models of Process Dynamics• Empirical Dynamic Models: can frequently describe
process dynamics, but are “data fits” over a specific range of operation.
• Theoretical Dynamic Models: are based on theory and might be useful for extrapolating. Also can be useful for determining controller tuning. Accuracy depends upon model details.
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Process Modeling: Stirred Tank Heater
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Process Modeling: Stirred Tank Heater
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5
6
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8
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Develop Block Diagram
Develop Block Diagram
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T Sensor
Transducer
.var.var..
inputindeviationoutputindeviationFT
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Develop System Block DiagramTransmitter
http://www.omega.com/thermocouples.html
TE selection guide
Type T TC
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Develop System Block DiagramTransmitter
Transducer
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Develop System Block DiagramTransmitter
Transducer
Valve
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Develop System Block DiagramTransmitter
Transducer
Valve
Energy Transfer
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Develop System Block DiagramTransmitter
Transducer
Valve
Energy Transfer Controller
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Develop System Block DiagramTransmitter
Transducer
Valve
Energy Transfer Controller
Process
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Feedback Block DiagramTransmitter
Transducer
Valve
Energy Transfer Controller
Process
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Feedback Block Diagram
11s
11
sK
s+
+
si
sQ
sWVK
sMcK sM y-
sE+ sR
TK sC
sMor T
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Feedback Block Diagram (simplified)
11s
1
sK
s+
+
si
sWVK
sMcK
-
sE+ sR
TK sC
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Closed Loop Transfer Function (let R(s)=0)
11s
1
sK
s+
+
si
sWVK
sMcK
-
sE+ sR
TK sC
sKKKsKs
ss TcVi
11
1
TcVi KKK
sKs
ss
11
11
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Closed Loop Transfer Function (let R(s)=0)
11s
1
sK
s+
+
si
sWVK
sMcK
-
sE+ sR
TK sC
TcV
i KKKsKs
ss
11
11
looptheinblocksallouputtoinputfrompathdirectonblocksall
ss
input
output
1
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Open Loop vs Closed Loop
Transfer Function (R(s)=0)
11s
1
sK
s
++
si
sWVK
sMcK
-
sE+ sR
TK sC
TcVi KKK
sKs
ss
11
11
Open Loop:
Closed Loop:
11ss
s
i
TcV KKKKs
11
11
11
sKKKK
KKKK
TcV
TcV
1*
*
sK
*
* 1K tt
evse *
t
eAt 1
*1*
teAKt
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0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 1 2 3 4 5
time (t)
Y(t)
Open - loop
Closed - loop
t
time
AK *
A
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Transfer Functions (Chap 3-5)
11s
1
sK
s
++
si
sWVK
sMcK
-
sE+ sR
TK sC
11
s
GL
Define:
For heated, stirred tank:
..FTG
)()(ss
i
VV KG
1
sKGP
cc KG
TT KG
11s
1
sK
s
++
si
sWVK
sMcK
-
sE+ sR
TK sC
LG
PGVGcG
TG
)()(sRs
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11s
skgsW C
LG sTo
11s
skg
s sW C
sG sTo
11s
CsTi
C
iTG sTo
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LG
sG sTo+
+
sW
sWsVG
sMcG
-
sE+ sR
TG sC
iTG
sTi
+
sRSPG
sT seto
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LG
sG sTo+
+
sW
sWsVG
sMcG
-
sE+ sR
TG sC
iTG
sTi
+
)(sWsTo
)(sTsT
i
o
)(sT
sTseto
o
