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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

2

SCK

3

K = -0.15

K = -1.09

K = -0.69

K = -0.26

K = 0.-45K = -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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7

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

spMT

steam

% moisture

VG TK

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Separate Gp into 2 blocks

Heat Exchger

T

airblower

MC

spMT

steam

% moisture

sp

TTTC

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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13

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 outat the

set point

T2 out

Objective:

Keep TP

outat 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

BFT

FT

FY

FCBsp

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 ControlSuppose 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 ExchangerTTFT

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 ExchangerTTFT

TY

)(tTi)(tqi

steamTC

FF?

TYP

I)(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

GKGFFCD

TO%

TO%

Feed Forward Control: FFC Identification

Set by traditional means:

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DTKMT

D

GKGFFCD

Model fit to FOPDT equation: MD GG &

1

seKG

D

stD

D

Do

1

seKG

M

stM

M

Mo

gpmTO%

COTO

%%

gpmTOD%

stt

D

M

MT

D oMDo

D

ess

KKKFFC

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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

GKGFFCD

With Gc disconnected:• Step change COFB, say 5%• Fit C(s) response to FOPDT

MD GG &

1

seKG

D

stD

D

Do

1

seKG

M

stM

M

Mo

gpmTO%

COTO

%%

Still in open loop:• Step change Q, say 5 gpm• Fit C(s) response to FOPDT

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ss

KKKFFC

Lg

Ld

MT

D

D

Ldm lead timeLgD lag time

Lead/Lag or Dynamic CompensatorLook 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 ControlRule 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 FCCTune 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