19 feed-forward control

8/12/2019 19 Feed-Forward Control

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Chen CL 1

A Process Heater with Feedback Control


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Chen CL 2

A Simple Pure Feedforward ControlConsidering Inlet Temperature As Main Disturbance

EB: Q Cp (To Ti) = FHv EffTi = MAIN disturbance

To = desired outlet temp

F = QCpHv

Eff(To Ti)


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Chen CL 3

Pure FF Control for Multiple DisturbancesConsidering Variation of Inlet Temperature,

Process Flow Rate, and Fuel Heating Value

Disturbance 1: variations of inlet temperature F = QCpHvEffTo Ti

Disturbance 2: variations of process flow rate

Disturbance 3: variations in fuel heating value


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Chen CL 4






C C


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Chen CL 5






Ch CL 6


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Chen CL 6

Dynamic Adjustment for FF Control Action

Fo(s)Fi(s)

= ds + 1gs + 1

eds

=

dg

+1 d/ggs + 1

eds

Ch CL 7


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Chen CL 7

FF Control withAdditive/Multiplicative FB Trim

Ch CL 8


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Chen CL 8

FF Control with Additive FB Trim

Most important disturbances are compensated by FF

Why feedback trim ?

Error in process model Un-measurable disturbances

FB signal should be scaled so that when it is in the center of its

range it represent zero correction to the FF signal

Process gain of the FB loop may vary inversely withprocess flow rate

Kp = measurement

controller output =

outlet temperature

fuel

To = Ti+Hv EffQ Cp

F

Kp = To

F = Hv

Eff

Q Cp 1

Fp

Ch CL 9


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Chen CL 9

FF Control with Multiplicative FB Trim

FB signal: a multiplying factor, K

If FF controller is exact

no correction is necessary K= 1

Temperature controller output should be scaled so that 0 100%of signal range represents a limited range of correction

Example: K= 0.75 1.25 FB can correct FF results by a factor25%


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Chen CL 12


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Chen CL 12

Experimental Approach for FF Control

Dynamic Effect of Manipulated Variable to Controlled Variable

TpdTo(t)

dt + To(t) = KpF(t dp)

Gp(s) = To(s)

F(s) =

Kpedps

Tps + 1

Chen CL 13


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Chen CL 13


Desired: No Response of Controlled Variable to Load Change

without FF: To(s) = G(s)Q(s)use of FF: To(s) = G(s)Q(s) + Gp(s)F(s)

= G(s)Q(s) + Gp(s)GF(s)Q(s)

= [G(s) + Gp(s)GF(s)]

=0Q(s) = 0

Chen CL 14


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Chen CL 14


Desired: No Response of Controlled Variable to Load Change

= GF(s) = G(s)

Gp(s) =

Keds

Ts+1

Kpedps

Tps+1

=

KKp

Tps + 1

Ts + 1

e(ddp)s

Chen CL 15


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Chen CL 15

Dynamic Compensation

Possible barriers to implementing perfect FF control: Other disturbances might exist

Process model may be incorrect

There had been no consideration of process dynamics

Abstract view of the

process:

two external influences

Load (disturbance)

Control effort


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Chen CL 18


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Chen CL 18

Implementation of Feedforward Control

Test each of the process paths:loadand processdynamics by FOPDT models

Take the ratio of the two TFs

Add feedback to compensate for un-measured disturbances or errorsin process models

Relax FB controller from the tuning if FB were used alone

(lower gain, longer reset, no D) No D action in FB (load upset is taken by FF)

Primary purpose of FB is to correct for steady-state errors in FF

controller

Responsibility of FB controller is not as great as if it werecontrolling the process alone

Chen CL 19


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Chen CL 19

Step Response of Lead-lag(with/without Dead Time) Function

Lead/Lag Only with Dead Time

Chen CL 20


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Chen CL 20

Fine Tuning The FF Controller

A FF control system by itself will rarely provide perfectcompensation for the measured disturbance

combined with FB

FB control acts only after the fact

(it must see an error to make a correction) the closer to perfect compensation the FF makes

the less correction required by FB controller


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Chen CL 23


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Incremental Effect of Various Adjustments:Summary

A change in only dead time will result in an incremental processresponse relatively soon after load change

A change in only lead-lag ratio will result in an incremental process

response that is somewhat father out in time from the time of load

change

A change in lag time (constant lead-lag ratio) will result in an

incremental process response that is the fastest away in time

Chen CL 24


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Effect of Composite Adjustments

Fine Tuning:

Observe initial response to a load change of the FF control

system

Determine the direction and relative time scale of the required

incremental corrective process response Adjust dynamic compensating terms accordingly

Example: Composite Adjustments

Decrease dead time to start the increased fuel response sooner Decrease lead-lag ratio to give less fuel increment once its

response is begun

Decrease lag time (maintaining a constant lead/lag ratio) to

cause a faster approach of the fuel to final equilibrium

Chen CL 25


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Chen CL 26


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Feed-forward: Balance Equation ApproachEX: A Mixing Process with Simple FB Control

Chen CL 27


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Chen CL 28


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Steady-State Feed-forward Scheme

Steady-state overall mass balance

0 = q5 + q1(t) + q2(t) + q7 q6(t)0 = q5+ q1(t) + q2(t) + q7 q6(t) (= const.)

q1(t) = q6(t) q2(t) 1000

Steady-state mass balance on component Aand the feed-forward relation:

0 = q5x5+ q2(t)x2+ q7x7 q6(t)x6(t)

q6(t) = 1

x6(t)[q5x5+ q7x7+ q2(t)x2]

= 1

x6(t)[850 + 0.99q2(t)]

q1(t) = 1xset6

[850 + 0.99q2(t)]

FY11Aq2(t) 1000

FY11B

Chen CL 29


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Steady-State Feed-forward Scheme

q1(t) =

1

xset6[850 + 0.99q

2(t)]

FY11A

q

2(t)

1000

FY11B

Chen CL 30


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FF Control with Dynamic Compensation

q1(t) =

1

xset6[850 + 0.99q

2(t)]

FY11A

q

2(t)

1000

FY11B


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Chen CL 32


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FF Control: Block Diagram Approach

Chen CL 33


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Pure Feed-forward Control

X6Q1

=G1X6Q2

=G2Q1M

=GFCM

TO=GF

TO

Q2=H2

X6=G2 Q2+ G1 Q1GFC M

GF TO

H2 Q2

Chen CL 34


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= [G2+ G1GFCGFH2] Q2 = 0 (desired)

GF(s) =

G2G1GFCH2

let G1GFC = KP1e

d1s

1s+1 (mf/%CO)

G2 = KP2ed

2s

2s+1 (mf/gpm)

H2(s) = KT2 (%TO/gpm)

GF =KP2KP1KT2

%CO/%TO

1s + 1

2s + 1

lead/lag

e(d2d1)s dead time

Chen CL 35


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Feed-forward Control with Feedback Trim

Chen CL 36


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Summer FY-11C: OUT = KxX+ KyY + KzZ+ B0FB signal: X; FF signal: Y; bias: B0 Kx= 1;Ky = 1;B0= (KP2/KT2KP1)40%

Steady-state value ofq2(t) 1000 gpm

Range of transmitter for q2 0 2500gpmSteady-state value of the flow 40%

Steady-state output from FF (KP2/KT2KP1)40%Bias to cancel SS FF signal (KP2/KT2KP1)40%Steady-state value ofq1(t) 1900 gpm

Range of transmitter for q1

0

3800gpm

Output from summer must be 50%

Output from FB is forced to be 50%

Ky = 0: FF is turned off

Chen CL 37

C


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FF Control for Boiler DrumSingle-Element Control


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Chen CL 40

FF f Di ill i C l


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FF for Distillation ColumnSimple Feedback Control

Chen CL 41

FF f Di ill i C l


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FF for Distillation ColumnFeed-forward Control Scheme

m

: lbm/hr;

: Btu/lbm

q

s = q

t q

1= q

t m

= q

t Kh

= f1(P)

= f2(P)

signalcharacterizers

Chen CL 42

FF C l A Di ill i C l


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FF Control on A Distillation Column

Chen CL 43

FF C t l f Di till ti F d


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FF Control for Distillation FeedFF Control Handles Two Upsets Simultaneously

Variables:

feed composition and flow-rate to a distillation column

excessive impurities to appear in bottoms product

Temperature of the two-component mixture in lower-bottoms

sump has a direct relationship to impurity concentration (sufficient

correlation often exists even for multi-component mixtures)

F, z, Fz: feed, fraction of light, flow of lighter component

Steam flow-rate should be nearly proportional to Fz temperature controller adjusts the ratio to compensate

for possible errors in measurement, model

Chen CL 44

M t diffi lt t d i ti


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Most difficult part: dynamic compensation


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Chen CL 47

FF C t l E t


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FF Control on Evaporator

Mass and Energy Balances:

(W: mass rate, kg/h; x: weight fraction;E: economy, kg vapor/kg steam)

1st effect: W0x0 = W1x1

W0 = W1+ V12st effect: W1x1 = W2x2

W1 = W2+ V2

W2 = (x0/x2)W0

W0 = W2+ V1+ V2

W00F0

1 x0x2

= V1+ V2

EWs

Ws =

1

E

0F0 1x0

x

2

Chen CL 48

Feed density and feed solids weight fraction is related


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Feed density and feed solids weight fraction is related

signal characterizer f(0) :x0 vs. 0

Feed flow signal (F0) is dynamically compensated with lead/lag

function

Product density does not respond with equal speed to changes

in feed-rate and steam flow

Changes in steam flow produce a slower response because of

thermal time lags associated with heat transfer surfaces apredominant lead function

Density normally does not vary as fast as feed flow

feed-density dynamic compensation is not included

FB trim is provided by density controller to provide desired setpoint,

x2, in feed-forward model

Chen CL 49



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19 feed-forward control

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