Post on 29-Jan-2016
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CBE 491 / 433
16 Oct 12Deadtime in a Process
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Dead Time in a Process
• Show how dead time might show up
• How it affects block diagrams• How it affects response
LT LC
)(1 tVp
)(tWv
)(2 tVp
)(th
steam
)(tWi
)(tQi )(
)(tW
tQ ii
)( ov ttW
3
2G
++
sQi
1GcG-
sE+ sR sH
Closed loop response: (no setpoint
change)
Level Loop (melt tank)
)(2 sVp
sH
Tc
stV
KGG
GeK o
1
2
12
TK
)(1 sVp
stV
oeK 2
sVp2
)()( 22 ovi ttVpKtQ
)()( 22 sVpeKsQ stvi
o
If: s
AsVp )(2
0t
)(2 tVp
)(tH
A
ot
11
11
1
s
KKG V
12
22
s
KG
4
2G
++
sQi
1GcG-
sE+ sR sH
Closed loop response: (setpoint change)
Level Loop (melt tank)
)(sR
sH
Tc
C
KGG
GG
1
1
1
TK
)(1 sVp
stV
oeK 2
sVp2
If: s
AsR )(
0t
)(tR
)(tH
A
)( otdeadtimeno
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Dead Time in a Process
Suppose change manipulated variable
LT
LC
)(1 tVp
)(tWv
)(2 tVp
)(th
steam
)(tQi
)(tR
FC FT
)(tRF
6
1G
++ sQi
2GcG-
sE+ sR sH
Level Loop (melt tank)
)(sR
sH
Tst
Vc
stVc
KGeKG
GeKGo
o
2
2
2
2
1
TK
)(1 sVp
stV
oeK 2
sVp2
)()( 22 sVpeKsQ stvi
o
• D(s) not a polynomial; can’t do P.F. expansion, so different procedure
needed.
• Dead time effect is to reduce the ultimate loop gain (will oscillate at lower
Kc values)
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11
1
s
KKG V
12
22
s
KG
Tst
Vc
stVc
KKeKKs
KeKKo
o
22
2
2
2
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Tuning: adjust controller parameters to obtain specified closed loop
response.
Feedback Controller Tuning
Values of parameters depend upon:
• Desired response
• Dynamic characteristics of other elements in the control
loop.
We’ll come back to general tuning approaches, but lets first explore
the solid feeder example that has some dead time….
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Tuning Introduction
Feeder with some dead time (to)
WC)(tWv
)(2 tVp
)(tW
)(tR
WY
WT
aT = aV = aP = aC =
+1 +1 +1 -1
)()( tEKtM C
LG
++
sL
PGcG-
sE+ sR sC)(sM
ststTP
oo eeKG
1 VL KG
1 CC KG
ot
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Tuning Example (w/ P-only Controller)
t
t
tWV
tWT
tM
0
sp
¼ Decay Ratio or Quarter Amplitude Damping:
QAD or ¼ Decay Ratio
• Convenient
• Relatively quick response
• Relatively high overshoot on setpoint changes
• Non-unique (theoretically infinite no. tuning parameters)
If dead time in loop:
• Makes closed loop closer to unstable
• Reduce Kc … but then more sluggish response
• Instead of pure feed back control … could implement
Dead-Time Compensation (Smith Predictor)
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Ziegler Nichols Tuning Method (I)
For our simple example with
WC)(tWv
)(2 tVp
)(tW
)(tR
WY
WT
1 CC KG
ot
CuK To achieve QAD we set
CuC KK 21
Ziegler Nichols Tuning Method I
• P-only control
• Find
• Set CuC KK 21
CuK
We’ll see another Ziegler Nichols: ZN II related to FOPDT fit
Empirical formula to get closed loop response close to QAD
UT
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Feedback Controller Tuning: (General Approaches)
1) Simple criteria; i.e QAD via ZN I, tr, etc• easy, simple, do on existing process• multiple solutions
2) Time integral performance criteria• ISE integral square error• IAE integral absolute value error• ITAE integral time weighted average error
3) Semi-empirical rules• FOPDT (ZN II)• Cohen-Coon
4) ATV, or Autotuning
5) Trial and error
6) Rules of thumb
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Questions ??