[Luyben] Process Mod.. - Student subdomain for University of Bath

FIGURE 16.5
Multivariable INA
(- 1, 0) point, the system may be closedloop unstable (Fig. 16.6b). The INA plots
for the Wood and Berry column are shown in Fig. 16.6~.
Usually the INA is a very conservative measure of stability. Compensators
are found by trial and error to reshape the INA plots so that the circles are small
and the system is “diagonally dominant.” The INA method strives for the elimination
of interaction among the loops and therefore has limited usefulness in
process control where load rejection is the most important question.
16.3.3 Decoupling
Some of the earliest work in multivariable control involved the use of decouplers
to remove the interaction between the loops. Figure 16.7 gives the basic structure
of the system. The decoupling matrix Qt9, is chosen such that each loop does not
affect the others. Figure 16.8 shows the details of a 2 x 2 system. The decoupling
element D, can be selected in a number of ways. One of the most straightforward
is to set D,, = D,, = 1 and design the D,, and D,, elements so that they cancel