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Chapter 18
Control Case Studies
Control Systems Considered
• 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
TT FT
FCTC
Condensate
SteamRSP
Feed
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
TT PT
PCTC
Condensate
SteamRSP
Feed
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
TT
PTPCTC
Condensate
Steam
RSP
Feed
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
00
0
2
0
II
cc
F
F
KF
FK
Inferior Configuration for a Liquid/Liquid Heat Exchanger
TT
TC
CoolantOutlet
CoolantInlet
Feed
Preferred Configuration for a Liquid/Liquid Heat Exchanger
TC
CoolantOutlet
CoolantInlet
Feed
TT
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
Feed
Product
PT
TC
PC
TT
Steam
Condensate
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 p/p less than 0.1
Deadtime for an Exothermic CSTR
• 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)
scoolanthtmixp
Exothermic CSTR Temperature Control
Feed
Product
TTCoolantMakeup
TC
TT
TC
RSP
Exothermic CSTR Temperature Control
CoolantMakeup
Feed
ProductTT
TC
TT
TCRSP
Maximizing Production Rate
Feed
Product
TTCoolantMakeup
TC
TT
TC
RSPVPC
Using Boiling Coolant
Feed
ProductTT
HotCondensate
PCPT
TC
RSP
LTLC
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
• Process nonlinearity
• Coupling
• Severe disturbances
• Nonstationary behavior
Material Balance Effects
AT
LC
LC
AT
Dy
L
Bx
VFz
PT
FD
xzxy
xy
xz
F
D
/
Effect of D/F and Energy Input on Product Purities [Thin line larger
V]
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1D/F
Mol
e F
ract
ion
x
y
z = 0.5
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 +V
• L/V decrease causes impurity to increase initially
• After V reaches accumulator, L will increase which will reduce the impurity level.
• Result: inverse action
LC
LC
AT
DyL
Bx
VFz
PT
AT
Disturbances
• 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
PT
PC
Refrigerant
Flooded Condenser
PT
PC
CW
LT
LC
Venting for Pressure Control
PT
PC
VentC.W.
Venting/Inert Injection
PT
PC
VentC.W. Inert
Gas
S
Inferential Temperature Control
• Use pressure corrected temperature
• Use CAD model to ID best tray temperature to use
Single Composition Control - y
AT
LC
LC
AT
Dy
L
Bx
VFz
PT
AC
• L is fast responding and least sensitive to z.
• No coupling present.• Manipulate L to
control y with V fixed.
Single Composition Control - x
AT
LC
LC
AT
Dy
L
Bx
VFz
PT
AC
• V is fast responding and least sensitive to z.
• No coupling present.• Manipulate V to
control x with L fixed
Dual Composition ControlLow 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 ControlHigh 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
• Maximum reboiler duty
• Maximum condenser duty
• Flooding
• Weeping
• Maximum reboiler temperature
Max T Constraint - y Important
AT
LC
LC
Dy
L
Bx
VFz
PT
AC
AT
TT TC ACLS
Max T Constraint - x Important
AT
LC
LC
Dy
L
Bx
VFz
PT
AC
AT
TT
TC
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.
Strong Acid and Weak Acid Titration Cures for a Weak Base
Which is an easier control problem?
0
2
4
6
8
10
12
14
0 1 2Base/Acid Ratio
pH
0
2
4
6
8
10
12
14
0 1 2Base/Acid Ratio
pH
Effect of pKa on the Titration Curves for a Strong and Weak Base
0
2
4
6
8
10
12
14
0 1 2Base/Acid Ratio
pH pK a = 6
pK a = 3
pK a = 10
2
4
6
8
10
12
14
0 1 2Base/Acid Ratio
pH pK a = 6
pK a = 3
pK a = 1
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).