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Chapter 2

Traditional Advanced Control

Approaches Feedforward, Cascadeand Selected Control

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2-1 Feed Forward Control (FFC)

Block Diagram

Design of FFC controllers

Examples

Applications

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Why Feedforward ?

Advantages of Feedback Control Corrective action is independent of sources of

disturbances

No knowledge of process (process model) is required

Versatile and robust

Disadvantages No corrective action until disturbance has affected the

output. Perfect control is impossible.

Nothing can be done about known process disturbance

If disturbances occur at a frequency comparable to thesettling time of the process. Then process may neversettle down.

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Feedforward Control

FeedforwardController Disturbance

Process

Output

ManipulatedVariable

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Feedforward Control

Advantages Corrective action is taken as soon as disturbances

arrives.

Controlled variable need not be measured.

Does not affect the stability of the processes

Disadvantages Load variable must be measured

A process model is required

Errors in modeling can result in poor control

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LI

FFC

steam

FI

LI

steam

FI

FFCFB

Feedback control

Feedforward control

Combined feedforward-feedback control

LI

FB

BoilerFeed control

steam

FI

EXAMPLES

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Design Procedures (Block diagram

Method)

GL(s)

Load transfer function

GF(s)

Load

ManipulatedVariable

Gp(s)

Process

X2

C

Output

L

M

FF

Controller

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Derivation

functiontransferprocess,(2)

functiontransferload),()1(:need

or

0)(Hence).(allfor0)(wantWe

)()(

)()()()()(

)()()()()(

sG

sG

sG

sGsG

sGsGsG

sLsC

sLsGsGsG

sLsGsGsLsG

sMsGsLsGsC

P

L

P

L

F

FPL

FPL

FPL

PL

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Examples

Example 1 Let Gp(s)=Kp/ps+1, GL(s)=KL/Ls+1

Then, GF(s)=-(KL/Kp)(ps+1)/(Ls+1)

Therefore,feedforward controller is a lead-lag unit.

Example 2 Let Gp(s)=Kpe

-Dps/ps+1, GL(s)=KLe-DLs/Ls+1

Then, GF(s)=-(KL/Kp)(ps+1)/(Ls+1)e(-DL+DP)s

If -DL+DPis positive, then this controller is unrealizable.However, an approximation would be to neglect thedelay terms, and readjusting the time constants. In thiscase, perfect FF compensation is impossible.

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Tuning feedforward controllers

Let

This has three adjustable constants, K, 1, 2

Tuning K, K is selected so that for a persistent

disturbance, there is no steady state error inoutput.

Adjusting1, 2 can be obtained from transferfunctions. Fine tune 1, 2 such that for a step

disturbance, the response is somewhatsymmetrical about the set point.

11)(

2

1

ssKsGF

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Example: A simulated disturbed plant

Waste watertreatment

Disturbedflow rate

BOD

Chemicals

(CV)

DV

MV

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Simulated Block Disgram

1

1 2 3s s s Disturbed flowrate

+

3

1

1s

Chemicals

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Feedforward v.s. Feedback Control

0 5 10 15 20 25 30-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

FB

FF

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Example: Distillation Column

Example: Distillation Column Mass Balance: F=D+B

Fz=Dy+Bx

D=F(z-x)/(y-x)

In practice

For example: If light key increase in feed, increasedistillate rate.

setset

set

xy

xzFD

)(

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Design of Feedforward Control Using

Material and Energy Balances Consider the hear exchanger

Energy Balance yields Q=WC(T2-T1)=Ws

Where =hear of vaporization Ws=WC(T2-T1)/

This equation tells us the current stream demand based on (1)current flow rate, W, (2) current inlet temperature, T1, (3) desiredvalue of outlet temperature T2.

Steam

T2w, T1

Condensate

Ws

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Control Law and Design

Implementation:

Note no dynamics are incorporated

K

X

measured Tset

Gain

measured Ws

w

T1- +

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When to use Feedforward ?

Feedback control is unsatisfactory

Disturbance can be measured andcompensated for

Frequency of disturbance variations arecomparable to frequency of oscillation of thesystem

Output variable cannot be measured. There are large time delays in the system

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2-2 Cascade Control

Block Diagram

Design Considerations

Applications

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Illustrative Example : Steam Jacket

PCPT

TC

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Illustrative Example: Steam Jacket -

Continued

Energy Balance of the Tank:

Energy Balance of Jacket:

Material Balance of the Jacket

LossHeat TThAdt

dTV J

dt

nPd

R

V

Rn

VP

dt

d

dt

dT sJJ

s

JJJ /

condensatendt

dnin

s

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Illustrative Example: Steam Jacket -

Continued

Assume:

Where X=valve position

21110

113130

1

)(

sssX

sPsssP

sT

J

J

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Block Diagram

Feed backController

SteamValve

StirredTank

Tset

Steamsupply

pressure

Valve

position

Jacket

steampressure primary

Tank

Temp.

secondary

PrimaryController

JacketPressureController

SteamValve

StirredTank

Tset secondary

Jacketpressure

supplypressure

TankTemp.

Secondary loop

Primary loop

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Principal Advantages and Disadvantages

Advantages Disturbances in the secondary loop are corrected by

secondary controllers

Response of the secondary loop is improved, thusincreasing the speed of response of the primary loop

Gain variations in secondary loop are compensated bysecondary loop

Disadvantages Increased cost of instrumentation

Need to tune two loops instead of one Secondary variable must be measured

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Design Considerations

Secondary loop must be fast responding otherwisesystem will not settle

Time constant in the secondary loop must be smaller than primaryloop

Since secondary loop is fast, proportional actionalone is sufficient, offset is not a problem insecondary loop

Only disturbances within the secondary loop are

compensated by the secondary loop. Hence,cascading improves the response to thesedisturbances

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Applications: 1. Valve Position Control

Valve motion is affected by friction and pressuredrop in the line. Friction causes dead band. High

pressure drop also causes hysteresis in the valveresponse

Useful in most loops except flow and pressure

ControlValveMotor

Desired

position

Secondaryloop

Valveposition

Air Pressure to

Valve Motor

A li i 2 C d Fl L

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Application 2. Cascade Flow LoopOutput From

Primary Controller no cascade

Output From

Primary ControllerFC

FT

Fset

DP

cascade

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GC2 GC1 GP1 GP2

Primarycontroller

Secondarycontroller

Secondaryprocess

primaryprocess

cm2e2mset

Secondary loop

Primary loop

cset

2

11

112

1C

PC

PC

set

GGG

GGmm

GC2 GCL GP2 mset m2

ccset

22

22

1 PCLC

PCLC

set GGG

GGG

c

c

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Gc 12)110()1(

12 SS )13)(130(

1

SS

+

-

Primary

+

-

GC2

Secondary

G2(S) G3(S)

2

32

121

12

G

GG

c

For a cascade system

(open-loop)

Without cascade control

32GG

c

c

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Illustrative Example: Steam Jacket

Continued Cascade Case

Wu = 0.53

Mag = 20*log10(AR) = -30 (dB)

AR = 0.0316

6228.311

AR

Ku

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Illustrative Example: Steam Jacket

Continued No Cascade Case

Wu = 0.25

Mag = 20*log10(AR) = 0 (dB)

AR = 1

11

AR

Ku

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Illustrative Example: Steam Jacket

Continued No Cascade Case

Ku = 1;wu = 0.25;Pu = 2*Pi / wu = 25.1327

Kc = Ku/1.7 = 0.5882

Taui = Pu / 2 = 12.5664 Taud = Pu /8 = 3.1416

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Illustrative Example: Steam Jacket

Continued Cascade Case

Ku = 20;wu = 0.53;Pu = 2*Pi / wu = 12

Kc = Ku/1.7 = 11.8

Taui = Pu / 2 = 6

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2-3 Selective Control Systems

Override Control

Auctioneering Control

Ratio Control

Change from one controlled (CV) or manipulated variables

(MV) to another

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LT LC LSS

PC

Normalloop

water

steam

1. Override Control Example Boiler Control

LSS: Low Selective Switch Output a lower of two inputsPrevents: 1. Level from going too low, 2. Pressure fromexceeding limit (lower)

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motor

SC

HSS

PC FC

Gas out

Gas in

Normal loop

Example: Compressor Surge Control

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High Pressure Line

Low Pressure Line

PC

PC

HSS

Example: Steam Distribution System

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Length of reactor

Tem

perate

T1

T2

Hot spot

2. Auctioneering Control Systems

Temperature profiles in a tubular reactor

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TT TTTTTT

HSS

Cooling flow

Auctioneering Control Systems

TC

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Temperature Control

Steam

T2

Bypass

Exchanger

TC

Split Range Control: More than one manipulated variable is

adjusted by the controller

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Boiler 2 Steam Header

Boiler 2

Boiler 2

PC

Example: Steam Header: Pressure Control

3 Ratio Control Type of feedforward control

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FT

Driver

FT

A Wild stream

Controlled StreamB

FB

Gc

Desired

Ratio

FA

3. Ratio Control Type of feedforward control

However, one stream in proportion to another. Use if the ratio

must be measured and displayed

Disadvantage:Ratio may goTo erratic

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A Wild stream

FT

Desired Ratio

Multiplier

FC

FT

Controlled streamFB

FA

Another implementation of Ratio Control

+

-