стр. 60 
%CO
m
m FB
c
c set e GM
GC % CO % CO % TO
%
% TO +

Figure 74.1 Block diagram of feedforward control for two disturbances.
160 FEEDFORWARD CONTROL
Finally, substituting Eqs. (72.6), (74.5), and (74.6) into Eq. (74.4) yields
ГЉ 3.00 s + 1Л† (0.85 0.9 )s
FFC 2 = 0.293 (74.7)
e
Г‹ 2.50 s + 1 ВЇ
Because the dead time is again negative,
3.00 s + 1Л†
FFC 2 = 0.293 ГЉ (74.8)
Г‹ 2.50 s + 1ВЇ
Figure 74.2 shows the implementation of this new feedforward controller added
to the previous one and to the feedback controller. Figure 74.3 shows the response
of x6(t) to a change of 0.2 mf in x2(t) under feedback control, steadystate feed
forward, and dynamic feedforward control. The improvement provided by feedfor
ward control is certainly signiп¬Ѓcant. Most of the improvement in this case is
provided by the steadystate term; the addition of lead/lag provides an arguably
improvement. It is a judgment call in this case whether or not to implement lead/lag.
Note that the ratio of the leadtime constant to the lagtime constant is 1.20, which
is close to 1.0. Based on our discussion of the lead/lag term, the closer the ratio is
to 1.0, the less the need for lead/lag compensation. A rule of thumb that could be
used to decide whether or not to use lead/lag is: If tld/tlg is between 0.75 and 1.25,
f 6 (t ) x6 ( t )
AT
x3 ( t ) x4 ( t ) c( t ),%TO
f 3 (t ) f 4 (t )
x5 ( t ) x7 ( t )
AT
x2 ( t ) f 7 (t )
f 5 (t )
FT L/L L/L
f 2 (t )
K
K
SP
AC
FC
S
m , %CO m FB (t),%CO
f 1 (t )
Figure 74.2 Implementation of feedforward/feedback control for two disturbances.
161
DESIGN OF NONLINEAR FEEDFORWARD CONTROLLERS FROM BASIC PROCESS PRINCIPLES
Figure 74.3 Control performance of x6(t) to a disturbance in x2(t).
do not use lead/lag. The reason for this rule is because the added complexity hardly
affects the results. Outside these limits the use of lead/lag may signiп¬Ѓcantly improve
the control performance.
When more than one disturbance is compensated by feedforward, the algorithm
used to sum the feedforward and feedback signals must be expanded. Speciп¬Ѓcally,
Eq. (74.2) becomes
Г‚ [m (t ) + BFB ]
BFF =  (74.9)
FFi
and Eq. (74.3) becomes
Г‚ [m (t ) + BFF ]
BFB = (74.10)
FFi
75 DESIGN OF NONLINEAR FEEDFORWARD CONTROLLERS FROM
BASIC PROCESS PRINCIPLES
There are two important considerations of the feedforward controllers developed
thus far, Eqs. (72.9) and (74.8). First, both controllers are linear; they were devel
oped from linear models of the process which are valid only for small deviations
around the operating point where the step tests were performed. These controllers
are then used with the same constant parameters without consideration of the oper
ating conditions. As learned in Chapter 2, processes most often have nonlinear char
acteristics; consequently, as operating conditions change, the control performance
provided by linear controllers may degrade.
The second consideration is that step changes in the manipulated variable and
162 FEEDFORWARD CONTROL
in the disturbance(s) are required. Often, step changes in the disturbances are not
obtained easily. For example, how would you insert a step change in x2(t) to obtain
Eq. (74.5)? Certainly, this in not easy and may not be possible.
As discussed in Section 71, feedforward controllers are composed of steady
state and dynamic compensators. Very often, the steadystate compensator, which
we have called KD/KTDKM, can be obtained by other means, yielding a nonlinear
compensator and not requiring step changes in variables. The nonlinear compen
sator provides an improved control performance over a wide range of operating
conditions.
One method to obtain a nonlinear steadystate compensator consists of using п¬Ѓrst
principles, usually mass or energy balances. Using п¬Ѓrst principles, it is desired to
develop an equation that provides the manipulated variable as a function of the dis
turbances and the set point of the controlled variable. That is,
m(t ) = f [d1(t ), d2 (t ), . . . , dn (t ), setpoint]
For the process at hand,
f1 (t ) = f [ f5 (t ), x5 (t ), f2 (t ), x2 (t ), f7 (t ), x7 (t ), x6 (t )]
set
set
where x6 (t) is the set point of x6(t).
In Section 74 we decided that for this process the major disturbances are f2(t)
and x2(t) and that the other inlet п¬‚ows and compositions are minor disturbances.
стр. 60 