Post on 20-Jan-2016
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CBE 491 / CBE 433
26 Nov 12Process Linearity, Integral Windup, PID Controllers
Linearity, Windup, & PID
Process LinearityTest the Heat Exchanger process linearity by:• Starting Loop Pro trainer• Set %CO to 80%• Make steps down (say 10% down) to the %CO• Measure the response • Calculate the process gain
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SCK
3
K = -0.15
K = -1.09
K = -0.69
K = -0.26
K = 0.-45
K = -0.33
Adaptive Control ?
Integral (Reset) Windup
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• “Windup” can occur if integral action present• Most modern controllers have anti-windup protection• If doesn’t have windup protection, set to manual when reach point
of saturation, then switch back to auto, when drops below sat. level
• IE: LoopPro Trainer, select Heat Exchanger• Set %CO to 90%; SP to 126; Kc to 1 %/deg C; Tau I to 1.0 min• Set Integral with Anti-Reset Windup ON• Change Set Point to 120 deg. C. (~10 min); then change back to
126 deg. C• Repeat with controller at ON: (Integral with Windup)
Integral (Reset) Windup
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In-Class PID Controller Exercise
Tune the Heat Exchanger for a PID Controller:• Use the built in IMC, and choose Moderately Aggressive• Start Loop Pro trainer• Tune at the initial %CO and exit temperature• Compare PI with PID• Compare PID with PID with filter
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26 Nov 12Cascade Control: Ch
9
Advanced control schemesCBE 491 / CBE 433
Improve Feedback Control
Feedback control:• Disturbance must be measured before action taken• ~ 80% of control strategies are simple FB control• Reacts to disturbances that were not expected
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We’ll look at:• Cascade Control (Master – Slave)• Ratio Control• Feed Forward
Cascade Control
• Control w/ multiple loops• Used to better reject specific disturbances
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Take slow process:
PGcG-
sE+ sR sC)(sM
??PG
Split into 2 “processes” that can measure intermediate variable?
2PGcG-
sE+ sR sC
A-
+1PG
2TK
2CG
Gp2 must be quicker responding than GP1. • Inner (2nd-dary) loop faster
than primary loop• Outer loop is primary loop
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Material Dryer Example
PGcG-
sE+ sR sCmoisture%
Heat Exchger
T
airblower
MC
sp
MT
steam
% moisture
VG TK
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Separate Gp into 2 blocks
Heat Exchger
T
airblower
MC
sp
MT
steam
% moisture
sp
TT
TC
TPG1cG
-
sE+ sR sC
A-
+MPG
TTK
2CG VGMTK
primaryset point Secondary
Controller
secondary process variable
primary process variable
Final ControlElement
SecondaryProcess
PrimaryController
Primary Process
secondaryset point
DisturbanceProcess I
–+ ++–+
DisturbanceProcess II
secondaryprocessvariable
++
primaryprocessvariable
disturbancevariable I
disturbancevariable II
cascade control can improve rejection of this disturbance
but can not help rejection of this disturbance
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Problem Solving Exercise: Heat
Exchanger
Heat Exchger
T
Hot water
TC
sp
TTsteam
Single feedback loop.Suppose known there will be steam
pressure fluctuations…
Design cascade system that measures (uses) the steam pressure in the HX shell.
Heat Exchger
T
Hot water
TTsteamPT
Temperature Control of a Well-Mixed Reactor (CSTR)
Responds quicker to Tichanges than coolant temperature changes.
Ti
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Temperature Control of a Well-Mixed Reactor (CSTR)
Ti
If Tout (jacket) changes it is sensed and controlled before “seen” by primary T sensor.
Use Cascade Control to improve control.
Secondary Loop• Measures Tout (jacket)• Faster loop• SP by output primary loop
Primary Loop:• Measures controlled var.• SP by operator
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Cascade Control
• Disturbances in secondary loop corrected by 2ndary loop controller
• Flowrate loops are frequently cascaded with another control loop
• Improves regulatory control, but doesn’t affect set point tracking
• Can address different disturbances, as long as they impact the secondary loop before it significantly impacts the primary (outer loop).
Benefits:
• Secondary loop must be faster than primary loop
• Bit more complex to tune
• Requires additional sensor and controller
Challenges:
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Cascade Control
Examples
Objective:
Regulate temperature (composition)
at top and bottom of
column
Distillation Columns
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Objective:
Keep T2 out
at the set point
T2 out
Objective:
Keep TP
out
at the set point
TP out
Heat Exchanger
Furnace
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In-Class Exercise: Cascade Control System Design
What affects flowrate?• Valve position• Height of liquid• P (delta P across valve)
Design a cascade system to control level (note overhead P can’t be controlled)
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In-Class Exercise: Cascade Control System Design
Does this design reject P changes in the overhead vapor space?
Tuning a Cascade System
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• Both controllers in manual
• Secondary controller set as P-only (could be PI, but this might slow sys)
• Tune secondary controller for set point tracking
• Check secondary loop for satisfactory set point tracking performance
• Leave secondary controller in Auto
• Tune primary controller for disturbance rejection (PI or PID)
• Both controllers in Auto now
• Verify acceptable performance
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In-Class Exercise: Tuning Cascade Controllers
• Select Jacketed Reactor• Set T cooling inlet at 46 oC (normal operation temperature; sometimes it drops to 40 oC)• Set output of controller at 50%.• Desired Tout set point is 86 oC (this is steady state temperature)
• Tune the single loop PI control• Criteria: IMC aggressive tuning• Use doublet test with +/- 5 %CO• Test your tuning with disturbance from 46 oC to 40 oC
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In-Class Exercise: Tuning Cascade Controllers
• Select Cascade Jacketed Reactor
• Set T cooling inlet at 46 oC (again)
• Set output of controller (secondary) at 50%.
• Desired Tout set point is 86 oC (as before)
• Note the secondary outlet temperature (69 oC) is the SP of the secondary controller
• Tune the secondary loop; use 5 %CO doublet open loop• Criteria: ITAE for set point tracking (P only)• Use doublet test with +/- 5 %CO• Test your tuning with 3 oC setpoint changes• Tune the primary loop for PI control; make 3 oC set point changes (2nd-dary controller)• Note: MV = sp signal; and PV = T out of reactor• Criteria: IAE for aggressive tuning (PI)• Implement and with both controllers in Auto… change disturbance from 46 to 40 oC.• How does response compare to single PI feedback loop?
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26 Nov 12Ratio Control: Ch 10
Advanced control schemesCBE 491 / CBE 433
Ratio Control
• Special type of feed forward control
• Blending/Reaction/Flocculation
• A and B must be in certain ratio to each other
A B
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Ratio ControlPossible control system:
• What if one stream could not be controlled?
• i.e., suppose stream A was “wild”; or it came from an upstream process and couldn’t be controlled.
A B
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FT
FC
sp
FY
FT
FC
sp
FY
Ratio ControlPossible cascade control systems:
“wild” stream
A
B
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FT
FT
FY FC
sp
A
B
AB
Desired Ratio
A
B
FT
FT
FY
FC
Bsp
A
B
AB
Desired RatioThis unit multiplies A by the desired ratio; so output = A
BA
“wild” stream
AB
Ratio Control Uses:
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• Constant ratio between feed flowrate and steam in reboiler of distillation column
• Constant reflux ratio
• Ratio of reactants entering reactor
• Ratio for blending two streams
• Flocculent addition dependent on feed stream
• Purge stream ratio
• Fuel/air ratio in burner
• Neutralization/pH
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In-Class Exercise: Furnace Air/Fuel Ratio• Furnace Air/Fuel Ratio model• disturbance: liquid flowrate• “wild” stream: air flowrate• ratioed stream: fuel flowrate
• Minimum Air/Fuel Ratio 10/1• Fuel-rich undesired (enviro, econ, safety)• If air fails; fuel is shut down
Independent MV
PV
Ratio set point
Dependent MV
Disturbance var.
TC
TC output
Desired 2 – 5% excess O2
Check TC tuning to disturbance & SP changes.
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26 Nov 12Feed Forward Control: Ch 11
Advanced control schemesCBE 491 / CBE 433
Feed Forward Control
Suppose qi is primary disturbance
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Heat Exchanger
TC
TT)(tqi
)(tTi
? What is a drawback to this feedback control loop?
? Is there a potentially better way?
Heat Exchanger
TTFT
FF
)(tTi
)(tqi
?What if Ti changes?
FF must be done with FB control!
steam
steam
Feed Forward and Feedback Control
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Heat Exchanger
TTFT
TY
)(tTi)(tqi
steamTC
FF
?
TY
PI
)(tM FF )(tM
)(tM
FFFF MtMtMtM )()()(
Block diagram:
TPGCG
sE sT++
FFG
TTK
VG
DTKLG
sQi
++
M
FFM
M-
+ sR
FFCGFF
Feed Forward Control
No change; perfect compensation!
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PGCG-
sE+ sR sT++
FFG
TTK
VG
DTKLG
sQi
++
M
FFM
M
t0
DT
PT
tT
PT
MFF
DT
tqi
Response to MFF
Feed Forward Control
Examine FFC T.F.
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MGCG-
sE+ sR sC++
FFC
DTKDG
sQi
++FFM
M
MG sC
FFC
DTKDG
sQi
++
FFM
gpm
TO%
DTO%
FFCO%
)()( sQKFFCGsQGsC iTMiD D
For “perfect” FF control: 0sC
)()(0 sQKFFCGsQG iTMiD D
MT
D
GK
GFFC
D
TO%
TO%
Feed Forward Control: FFC Identification
Set by traditional means:
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DTKMT
D
GK
GFFC
D
Model fit to FOPDT equation: MD GG &
1
s
eKG
D
st
DD
Do
1
s
eKG
M
st
MM
Mo
gpm
TO%
CO
TO
%
%
gpm
TOD%
stt
D
M
MT
D oMDo
D
es
s
KK
KFFC
1
1
FF Gain
Lead/lag unit
Dead time compensator
{ FFC ss }steady state FF control
{ FFC dyn }dynamic FF control
Accounts for time differences in 2 legs
Often ignored; if set term to 1
oMo ttD
Feed Forward Control: FFC IdentificationHow to determine FOPDT models :
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MG sC
FFC
DTKDG
sQi
++
FFM
gpm
TO%
DTO%
FBCO%
MT
D
GK
GFFC
D
With Gc disconnected:• Step change COFB, say 5%• Fit C(s) response to FOPDT
MD GG &
1
s
eKG
D
st
DD
Do
1
s
eKG
M
st
MM
Mo
gpm
TO%
CO
TO
%
%
Still in open loop:• Step change Q, say 5 gpm• Fit C(s) response to FOPDT
1
1
s
s
KK
KFFC
Lg
Ld
MT
D
D
Ldm lead time
LgD lag time
Lead/Lag or Dynamic Compensator
Look at effect of these two to step change in input
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Final Change from:• Magnitude of step change,• Initial response by the lead/lag, • Exponential decay from lag,
Lg
Ld
Time
c ff
ld/ lg = ½
ld/ lg = 1
ld/ lg = 2
Output or response )(tc
Lg
Ld
Lg
Feed Forward Control
Rule of Thumb: if lead-lag won’t help much; use FFCss
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3.165.0 Lg
Ld
(p 389)
In text: pp 393-395, useful comments if implementing FFC
+ -1. Compensates for disturbances
before they affect the process1. Requires measurement or
estimation of the disturbance
2. Can improve the reliability of the feedback controller by reducing the deviation from set point
2. Does not compensate for unmeasured disturbances
3. Offers advantages for slow processes or processes with large deadtime.
3. Linear based correction; only as good as the models; performance decreases with nonlinear processes.
No improvement using FFC with set point changes.
In-Class PS Exercise: Feed Forward Control
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What is the Gm, and what is the GD?
Determine FCC
Tune PI controller to aggressive IMC
• Test PI Controller
• Test PI + FFCss only
• Test PI + FFC full
For disturbance: Tjacket in
50oC – 60oC – 50oC
In-Class PS Exercise: Feed Forward Control
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PI only PI + FFCss only PI + full FFC
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CBE 491 / CBE 433
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Problem Solving Exercise: Heat Exchanger
Draw the block diagram: what is the primary and what is the secondary loop?
Heat Exchger
T
Hot water
TC
sp
TTsteamPT
PC
PPGTcG
-
sE+ sR sT
-
+TPG
PTK
PCG VG
TTK
sP