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).