Transcript Chapter 15 Control Case Studies

Chapter 18
Control Case Studies
Control Systems Considered
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•
•
•
Temperature control for a heat exchanger
Temperature control of a CSTR
Composition control of a distillation column
pH control
Temperature Control for Heat
Exchangers
Heat Exchangers
• Exhibit process deadtime and process
nonlinearity.
• Deadtime and gain both increase as tubeside
flow decreases.
• Major disturbances are feed flow and
enthalpy changes and changes in the
enthalpy of the heating or cooling medium.
Inferior Configuration for a
Steam Heated Heat Exchanger
TC
RS P
S te am
FC
FT
TT
Fe e d
C on de n sate
Analysis of Inferior
Configuration
• This configuration must wait until the outlet
product temperature changes before taking
any corrective action for the disturbances
listed.
Preferred Configuration for a
Steam Heated Heat Exchanger
TC
RS P
S te am
PC
PT
TT
Fe e d
C on de n sate
Analysis of Preferred
Configuration
• For the changes in the steam enthalpy and
changes in the feed flow or feed enthalpy,
they will cause a change in the heat transfer
rate which will in turn change the steam
pressure and the steam pressure controller
will take corrective action.
• There this configuration will respond to the
major process disturbances before their
effect shows up in the product temperature.
Modfication to Perferred
Configuration
TC
RS P
PC
PT
S te am
TT
Fe e d
C on de nsate
Analysis Modfication to
Perferred Configuration
• A smaller less expensive valve can be used
for this approach, i.e., less capital to
implement.
• This configuration should be slower
responding than the previous one since the
MV depends on changing the level inside
the heat exchanger in order to affect the
process.
Scheduling of PI Controller
Settings
2
 F 
K c    K c 0
 F0 
 F 
 I     I 0
 F0 
Inferior Configuration for a
Liquid/Liquid Heat Exchanger
TC
C ool ant
Inl e t
TT
Fe e d
C ool ant
O utl e t
Preferred Configuration for a
Liquid/Liquid Heat Exchanger
TC
TT
C ool ant
Inl e t
Fe e d
C ool ant
O utl e t
Comparison of Configurations for
Liquid/Liquid Heat Exchangers
• For the inferior configuration, the process
responds slowly to MV changes with
significant process deadtime. Moreover,
process gain and deadtime change
significantly with the process feed rate.
• For the preferred configuration, the system
responds quickly with very small process
deadtime. Process deadtime and gain
changes appear as disturbances.
Temperature Control for CSTRs
CSTR Temperature Control
• Severe nonlinearity with variations in
temperature.
• Effective gain and time constant vary with
temperature.
• Disturbances include feed flow, composition,
and enthalpy upsets, changes in the enthalpy
of the heating or cooling mediums, and
fouling of the heat transfer surfaces.
Preferred Configuration for
Endothermic CSTR
Fe e d
S te am
PC
PT
C on de n sate
Produ ct
TC
TT
Exothermic CSTR’s
• Open loop unstable
• Minimum and maximum controller gain for
stability
• Normal levels of integral action lead to
unstable operation
• PD controller required
• Must keep qp/p less than 0.1
Deadtime for an Exothermic CSTR
q p   mix   ht   coolant   s
• mix- Vr divided by feed flow rate, pumping rate
of agitator, and recirculation rate.
• ht- MCp/UA
• coolant- Vcoolant divided by coolant recirculation
rate
• s- sensor system time constant (6-20 s)
Exothermic CSTR Temperature
Control
Fe e d
TT
TC
C ool ant
Make u p
TT
RS P
TC
Produ ct
Exothermic CSTR Temperature
Control
Fe e d
C ool ant
Make u p
TT
TC
Produ ct
RS P
TC
TT
Maximizing Production Rate
Fe e d
TT
VPC
TC
C ool ant
Make u p
TT
RS P
TC
Produ ct
Using Boiling Coolant
Fe e d
LC
PT
LT
PC
RS P
Hot
C on de nsate
TT
TC
Produ ct
Distillation Control
Distillation Control
• Distillation control affects– Product quality
– Process production rate
– Utility usage
• Bottom line- Distillation control is
economically important
The Challenges Associated with
Distillation Control
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Process nonlinearity
Coupling
Severe disturbances
Nonstationary behavior
Material Balance Effects
D zx

F
yx
PT
LC
L
D
y
AT
zx
yx
D/F
F
z
V
LC
AT
B
x
Effect of D/F and Energy Input on
Product Purities [Thin line larger V]
1
y
Mole Fraction
0.8
0.6
z = 0.5
0.4
0.2
x
0
0
0.2
0.4
0.6
D/F
0.8
1
Combined Material and Energy
Balance Effects
• Energy input to a column generally
determines the degree of separation that is
afforded by the column while the material
balance (i.e., D/F) determines how the
separation will be allocated between the two
products.
Vapor and Liquid Dynamics
• Boilup rate changes reach the overhead in a
few seconds.
• Reflux changes take several minutes to
reach the reboiler.
• This difference in dynamic response can
cause interesting composition dynamics.
Effect of Liquid and Vapor
Dynamics [(D,V) configuration]
• Consider +DV
• L/V decrease causes
impurity to increase
initially
• After DV reaches
F
z
accumulator, L will
increase which will
reduce the impurity
level.
• Result: inverse action
PT
LC
L
D
y
AT
V
LC
AT
B
x
Disturbances
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Feed composition upsets
Feed flow rate upsets
Feed enthalpy upsets
Subcooled reflux
Loss of reboiler steam pressure
Column pressure swings
Regulatory Control
• Flow controllers. Standard flow
controllers on all controlled flow rates.
• Level controllers. Standard level
controllers applied to reboiler,
accumulators, and internal accumulators
• Pressure controllers. Examples follow
Minimum Pressure Operation
PT
C .W .
Manipulating Refrigerant Flow
PC
Re frige ran t
PT
Flooded Condenser
PC
LT
CW
LC
PT
Venting for Pressure Control
PC
Ve n t
PT
C .W .
Venting/Inert Injection
S
PC
PT
C .W .
Ve n t
Ine rt
Gas
Inferential Temperature Control
• Use pressure corrected temperature
• Use CAD model to ID best tray temperature
to use
Single Composition Control - y
PT
LC
L
D
y
AT
F
z
V
AC
LC
AT
B
x
• L is fast responding
and least sensitive to
Dz.
• No coupling present.
• Manipulate L to
control y with V fixed.
Single Composition Control - x
PT
LC
L
D
y
AT
F
z
V
AC
LC
AT
B
x
• V is fast responding
and least sensitive to
Dz.
• No coupling present.
• Manipulate V to
control x with L fixed
Dual Composition Control
Low L/D Columns
• For columns with L/D < 5, use energy
balance configurations:
–
–
–
–
(L,V)
(L,V/B)
(L/D,V)
(L/D,V/D)
Dual Composition Control
High L/D Columns
• For columns with L/D > 8, use material
balance configurations:
–
–
–
–
–
(D,B)
(D,V)
(D,V/B)
(L,B)
(L/D,B
When One Product is More
Important than the Other
• When x is important, use V as manipulated
variable.
• When y is important, use L as manipulated
variable.
• When L/D is low, use L, L/D, V, or V/B to
control the less important product.
• When L/D is high, use D, L/D, B, or V/B to
control the less important product
Configuration Selection Examples
• Consider C3 splitter: high L/D and overhead
propylene product is most important: Use
(L,B) or (L,V/B)
• Consider low L/D column where the
bottoms product is most important: Use
(L,V) or (L/D,V).
When One Product is More
Important than the Other
• Tune the less important composition control
loop loosely (e.g., critically damped) first.
• Then tune the important composition
control loop tightly (i.e., 1/6 decay ratio)
• Provides dynamic decoupling
Typical Column Constraints
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Maximum reboiler duty
Maximum condenser duty
Flooding
Weeping
Maximum reboiler temperature
Max T Constraint - y Important
PT
LC
L
D
y
AT
F
z
V
LC
AC
TT
TC
LS
AC
AT
B
x
Max T Constraint - x Important
PT
LC
L
AT
F
z
V
LC
TC
D
y
AC
TT
AT
B
x
Keys to Effective Distillation Control
• Ensure that regulatory controls are
functioning properly.
• Check analyzer deadtime, accuracy, and
reliability.
• For inferential temperature control use
RTD, pressure compensation, correct tray.
• Use internal reflux control.
• Ratio L, D, V, B to F.
• Choose a good control configuration.
• Implement proper tuning.
pH Control
pH Control
• pH control is important to any process
involving aqueous solutions, e.g.,
wastewater neutralization and pH control
for a bio-reactor.
• pH control can be highly nonlinear and
highly nonstationary.
• Titration curves are useful because they
indicate the change in process gain with
changes in the system pH or base-to-acid
ratio.
14
14
12
12
10
10
8
8
pH
pH
Strong Acid and Weak Acid Titration
Cures for a Weak Base
Which is an easier control problem?
6
6
4
4
2
2
0
0
0
1
2
Base/Acid Ratio
0
1
2
Base/Acid Ratio
14
14
12
12
10
10
8
pH
pH
Effect of pKa on the Titration
Curves for a Strong and Weak Base
pK a = 6
6
pK a = 3
4
2
0
1
Base/Acid Ratio
pK a = 6
6
pK a = 3
4
2
pK a = 1
0
8
pK a = 1
0
2
0
1
Base/Acid Ratio
2
Titration Curves
• The shape of a titration curve is determined
from the pKa and pKb of the acid and the
base, respectively.
Degree of Difficulty for pH Control
Problems
• Easiest: relatively uniform feed rate, influent
concentration and influent titration curve with
a low to moderate process gain at neutrality.
(Fixed gain PI controller or manual control)
• Relatively easy: variable feed rate with
relatively uniform influent concentration and
influent titration curve. (PI ratio control)
Degree of Difficulty for pH Control
Problems
• More Difficult: variable feed rate and influent
concentration, but relatively uniform titration
curve. (A ratio controller that allows the user
to enter the titration curve)
• MOST DIFFICULT: variable feed rate,
influent concentration and titration curve.
Truly a challenging problem. (An adaptive
controller, see text for discussion of inline pH
controllers).