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T

Condensate

return

Figure 6-2.2 Heat exchanger showing new transmitter location.

generates a dead time due to transportation. That is, it takes some time to п¬‚ow from

the exchanger to the new transmitter location. Assume that this dead time is only

4 sec. Figure 6-2.3 is a block diagram showing the dead time. The characteristic equa-

tion is now

900 s3 + 420 s 2 + 43s + (1 + 0.8 KC e -4 s ) = 0

The new ultimate gain and ultimate period are

%CO

KCU = 9 and TU = 47.8 sec

%TO

Note the drastic effect of the dead time on KCU. A 4-sec dead time has reduced KCU

by 62.2%. TU was also drastically affected. This proves our comment in Chapter 2

that dead time drastically affects the stability of control loops and therefore the

aggressiveness of the controller tunings.

6-2.4 Effect of Integral Action in the Controller

All of the presentation above has been done assuming the controller to be propor-

tional only. A valid question is: How does integration affect KCU and TU? Even

though ZieglerвЂ“Nichols deп¬Ѓned the meaning of KCU for a P controller only, we will

still use it because it still is the maximum gain. The transfer function of a PI con-

troller is given by Eq. (3-2.11):

tIs +1

GC = KC

tIs

140 BLOCK DIAGRAMS AND STABILITY

Ti Pu

Fp

o

F psig

gpm

G2 G3 G4

Heat

Controller Valve

exchanger

m

c set + e T, oF

F

GV

GC G1

lb/

% CO

% TO

% TO - min

c , % TO

e- 4 s

H

Sensor/

Dead time

transmitter

Figure 6-2.3 Block diagram showing dead time.

and the characteristic equation becomes

t I s + 1Л†

ГЉ

900 s 3 + 420 s 2 + 43 s + 1 + 0.8 KC =0

Г‹ tIs ВЇ

Using tI = 30 sec, the ultimate gain and period are

%CO

KCU = 16.2 and TU = 34.4 sec

%TO

Thus the addition of integration removes the offset, but it reduces KCU. Integration

adds instability to the loop. It also increases TU, resulting in a slower loop. You may

ask yourself: What is the effect of decreasing tI? That is, what would happen to KCU

if tI = 20 sec?

6-2.5 Effect of Derivative Action in the Controller

Now that the effect of integration on the loop stability has been studied, what is the

effect of the derivative? Let us look at using a PD controller. The transfer function

for a PD controller is given by Eq. (3-2.15):

GC = KC (t D s + 1)

and the characteristic equation becomes

900 s3 + 420 s 2 + 43s + [1 + 0.8 KC (t D s + 1)] = 0

Using tD = 1 sec, the ultimate gain and period are

141

REFERENCE

%CO

KCU = 36.2 and TU = 28.2 sec

%TO

Thus the addition of derivative increases the KCU value, adding stability to the loop!

From a stability point of view, derivative is desirable because it adds stability and

therefore makes it possible to tune a controller more aggressively. However, as dis-

cussed in Chapter 3, if noise is present, derivative will amplify it and will be detri-

mental to the operation.

In this section we have discussed brieп¬‚y how to calculate the ultimate gain of a

loop. However, we have discussed in more detail how the various gains, time con-

stants, and dead time of a loop affect this ultimate gain. We presented these effects

by changing transmitters, process unit (exchanger) design, and so on. What occurs

most commonly, however, is that the process unit itself changes, due to its nonlin-

ear characteristics.

6-3 SUMMARY

In this chapter we have presented the development of block diagrams and discussed

the important subject of stability of control loops. These subjects are used in all sub-

sequent chapters.

REFERENCE

1. C. A. Smith and A. B. Corripio, Principles and Practice of Automatic Process Control, 2nd

ed., Wiley, New York, 1997.

Automated Continuous Process Control. Carlos A. Smith

Copyright 2002 John Wiley & Sons, Inc. ISBN: 0-471-21578-3

CHAPTER 7

FEEDFORWARD CONTROL

In this chapter we present the principles and application of feedforward control,

quite often a most proп¬Ѓtable control strategy. Feedforward is not a new strategy;

the п¬Ѓrst reports date back to the early 1960s [1,2]. However, the use of computers

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