f 2 (t )

1 set

x6

CALC

SP

f 1 (t ) AC

FC FC

FT

Figure 7-5.2 Nonlinear feedforward control.

165

CLOSING COMMENTS ON FEEDFORWARD CONTROLLER DESIGN

Figure 7-5.3 Control performance of x6(t) to a decrease of 500 gpm in f2(t) and a decrease

of 0.2 in x2(t).

steady-state feedforward controller, depending on the signi¬cance given to the

feedback signal. The designer has complete freedom to make this decision. In the

¬rst case the feedback controller biased the feedforward calculation. This is a simple

and valid choice and the one most commonly used. The second choice is also a

set

simple choice. Please note that the actual desired value of x6 is the set point to the

set set

feedback controller. The feedback controller changes the term 1/x6 , or x6 , in the

feedforward equation to keep its own set point.

Sometimes the development of a nonlinear steady-state compensator from ¬rst

principles may be just dif¬cult to obtain. Fortunately, process engineering tools

provide yet another way to develop this compensator. Processes are usually

designed either by steady-state ¬‚owsheet simulators or any other steady-state sim-

ulation. These simulators, together with regression analysis tools, provide another

avenue to design the steady-state compensator. The simulation can be run at dif-

set

ferent conditions [i.e., different f2(t), x2(t), and x6 ] and the required manipulated

variable f1(t) can be calculated to keep the controlled variable at set point. This

information can then be fed to a multiple regression program to develop an equa-

tion relating the manipulated variables to the disturbances and set point.

7-6 CLOSING COMMENTS ON FEEDFORWARD CONTROLLER DESIGN

There are some comments about the process and example presented in this section,

and about feedforward control in general, that should be discussed before pro-

ceeding with more examples.

The ¬rst comment refers to the process itself. Figure 7-2.10 shows the response

of the control system when f2(t) changes from 1000 gpm to 2000 gpm. The composi-

166 FEEDFORWARD CONTROL

tion of this stream is quite high (0.99), and thus this change in f2(t) tends to increase

x6(t). However, the response shown in Fig. 7-2.10 shows that initially the composi-

tion x6(t) tends to decrease and then increase. This behavior is an inverse response,

and of course there is an explanation for this behavior. Because the tanks are at

constant volume, an increase in f2(t) results in an immediate increase in f4(t). The

composition of stream 4, which enters the third tank, is less than the composition

of stream 6, which exits the third tank. Thus this increase in f4(t) tends initially to

dilute (decrease) the composition x6(t). Eventually, the increase in f2(t) results in an

increase in the composition entering the third tank and a corresponding increase in

x6(t). Figure 7-2.10 shows that the response under feedforward control exhibits a

more pronounced inverse response. What occurs is that when f2(t) increases, f1(t) is

also increased by the feedforward controller. Thus the total ¬‚ow to the third tank

increases even more, and the dilution effect in that tank is more pronounced. Could

the reader explain why the inverse response is more pronounced under dynamic

feedforward than under steady-state feedforward?

The second comment refers to the lead/lag term. The lead/lag is a simple algo-

rithm used to implement the dynamic compensation in feedforward controllers. We

showed how to tune the lead/lag, or adjust tld and tlg, based on step-testing the

process. This method gives an initial tuning for the algorithm. But what if the step

testing cannot be done? How do we go about tuning the algorithm? Following are

some tuning guidelines.

If we need to lag the input signal (slow down the effect of the manipulated vari-

•

able), set the lead to zero and select a lag.

If we need to lead the input signal (speed up the effect of the manipulated

•

variable), concentrate on the lead term; however, you must also choose a lag.

Obviously, do not use a dead time.

From the response of the lead/lag algorithm to a step change in input, it is clear

•

that if tld > tlg, it ampli¬es the input signal. For noisy signals (e.g., ¬‚ow) do not

use ratios greater than 2.

Because the dead time just adds to the lag, a negative dead time would effec-

•

tively decrease the net lag if it could be implemented. Thus we could decrease

the lag in the lead/lag unit by the positive dead time. That is,

t lg to be used = t lg calculated + (t oD - t o M )

Alternatively, we could increase the lead in the lead/lag unit by the negative of

the dead time. That is,

t ld to be used = t ld calculated - (t oD - t oM )

If signi¬cant dead time is needed, use a lag, with no lead, and a dead time. It

•

would not make sense to delay the signal and then lead it, even if the transfer

functions calls for it.

The third comment also refers to the lead/lag unit, speci¬cally to the location

of the unit when multiple disturbances are measured and used in the feedforward

167

ADDITIONAL DESIGN EXAMPLES

controller. If linear compensators are implemented, all that is needed is a single

lead/lag unit with adjustable gain for each input. The outputs from the units are then

added in the summer, as shown in Fig. 7-4.2. When dynamic compensation

is required with nonlinear steady-state compensators, the individual lead/lag

units should be installed just after each transmitter, that is, on the inputs to the

steady-state compensator. This permits the dynamic compensation for each distur-

bance to be implemented individually. It would be impossible to provide different

dynamic compensations after the measurements are combined in the steady-state

compensator.

The fourth comment refers to the steady-state portion of the feedforward

controller. This section has shown the development of a linear and a nonlinear

compensator. The nonlinear compensator has been shown to provide better

performance. Often, it is easy to develop this nonlinear compensator using ¬rst prin-

ciples or a steady-state simulation. If the development of a nonlinear compensator

is possible, this is the preferred method. However, if this development is not possi-

ble, a linear compensator can be set for each input, and a summer. The decision as

to which method to use depends on the process.

The ¬fth and ¬nal comment refers to the comparison of feedforward control to

cascade, and ratio control. Feedforward and cascade control take corrective action

before the controlled variable deviates from the set point. Feedforward control

takes corrective action before, or at the same time as, the disturbance enters the

process. Cascade control takes corrective action before the primary controlled

variable is affected but after the disturbance has entered the process. Figure 7-2.6

shows the implementation of feedforward control only, that is, with no feedback

compensation. Interestingly, this scheme is similar to the ratio control scheme shown

in Fig. 5-2.2. The ratio control scheme does not have dynamic compensation;

however, the ratio unit in Fig. 5-2.2 provides the same function as the gain unit

shown in Fig. 5-2.6. Thus, we can say that ratio control is the simplest form of feed-

forward control.