Automated Continuous Process Control Part 9 ppt

150 FEEDFORWARD CONTROL

Dividing both sides by Df2 and solving for FFC yields

(7-2.1)

Equation (7-2.1) is the design formula for the feedforward controller. We understand

that at this moment, this design formula does not say much; furthermore, you

wonder what is it all about. Don’t despair, let us give it a try.

As learned in earlier chapters, first-order-plus-dead-time transfer functions are

commonly used as an approximation to describe processes; Chapter 2 showed how

to evaluate this transfer function from step inputs. Using this type of approxima￾tion for this process,

(7-2.2)

(7-2.3)

and assuming that the flow transmitter is very fast, HD is only a gain:

(7-2.4)

Substituting Eqs. (7-2.2), (7-2.3), and (7-2.4) into (7-2.1) yields

(7-2.5)

We next explain in detail each term of this feedforward controller.

The first element of the feedforward controller, -KD/KTDKM, contains only gain

terms. This term is the part of the feedforward controller that compensates for the

steady-state differences between the GD and GM paths. The units of this term help

in understanding its significance:

Thus the units show that the term indicates how much the feedforward con￾troller output, mFF(t) in %CO, changes per unit change in transmitter’s output, D in

%TOD.

Note the minus sign in front of the gain term. This sign helps to decide the

“action” of the controller. In the process at hand, KD is positive, because as f2(t)

increases, the outlet concentration x6(t) also increases because stream 2 is more

concentrated than the outlet stream. KM is negative, because as the signal to the

K

K K

D

TM D D

[ ] = ( ) ( ) = %TO gpm

%TO gpm %TO %CO

%CO

D %TO

FFC = - +

+

K - - ( )

K K

s

s

e D

T M

M

D

tts

D

oD oM t

t

1

1

H K D T = D

%TO

gpm

D

G K e

s M

M

t s

M

oM

= +

-

t 1

%TO

%CO

G K e

s D

D

t s

D

oD

= +

-

t 1

%TO

gpm

FFC = - G

H G

D

D M

c07.qxd 7/3/2003 8:26 PM Page 150

valve increases, the valve opens, more water flow enters, and the outlet concentra￾tion decreases. Finally, KTD is positive, because as f2(t) increases, the signal from the

transmitter also increases. Thus the sign of the gain term is negative:

A negative sign means that as %TOD increases, indicating an increase in f2(t), the

feedforward controller output mFF(t) should decrease, closing the valve. This action

does not make sense. As f2(t) increases, tending to increase the concentration of the

output stream, the water flow should also increase, to dilute the outlet concentra￾tion, thus negating the effect of f2(t). Therefore, the sign of the gain term should be

positive. Notice that when the negative sign in front of the gain term is multiplied

by the sign of this term, it results in the correct feedforward action. Thus the nega￾tive sign is an important part of the controller.

The second term of the feedforward controller includes only the time constants

of the GD and GM paths. This term, referred to as lead/lag, compensates for the dif￾ferences in time constants between the two paths. In Section 7-3 we discuss this term

in detail.

The last term of the feedforward controller contains only the dead-time terms of

the GD and GM paths. This term compensates for the differences in dead time

between the two paths and is referred to as a dead-time compensator. Sometimes

the term toD - toM may be negative, yielding a positive exponent. As we learned in

Chapter 2, the Laplace representation of dead time includes a negative sign in the

exponent. When the sign is positive, it is definitely not a dead time and cannot be

implemented. A negative sign in the exponential is interpreted as “delaying” an

input; a positive sign may indicate a “forecasting.” That is, the controller requires

taking action before the disturbance happens. This is not possible. When this occurs,

quite often there is a physical explanation, as the present example shows.

Thus it can be said that the first term of the feedforward controller is a steady￾state compensator, while the last two terms are dynamic compensators. All these

terms are easily implemented using computer control software; Fig. 7-2.7 shows the

implementation of Eq. (7-2.5). Years ago, when analog instrumentation was solely

used, the dead-time compensator was either extremely difficult or impossible to

implement. At that time, the state of the art was to implement only the steady-state

and lead/lag compensators. Figure 7-2.6 shows a component for each calculation

needed for the feedforward controller, that is, one component for the dead time,

one for the lead/lag, and one for the gain. Very often, however, lead/lags have

adjustable gains, and in this case we can combine the lead/lag and gain into only

one component.

Well, enough for this bit of theory, and let us see what results out of all of this.

Returning to the mixing system, under open-loop conditions, a step change of 5%

in the signal to the valve provides a process response form where the following first￾order-plus-dead-time approximation is obtained:

G (7-2.6) e

s M

s

= -

+

- 1 095

3 50 1

0 9 .

.

. %TO

%CO

K

K K

D

T M D

Æ

+

+ - = -

BLOCK DIAGRAM DESIGN OF LINEAR FEEDFORWARD CONTROLLERS 151

c07.qxd 7/3/2003 8:26 PM Page 151