Wiley signals and systems e book TLFe BO 411

16. Stabilitv avid Fkcdback Svsteins

396

Figure lfi.4: Structure of the system G ( s ) with ftdback loop

S

~

~the ~

t

~

i

~

~

Wheii c ~ n ~ t i i i ~an
t ,electronic
ii~~
iiiiqAifier, for cxample, for audio usc, the principle
o f riegativc. feedbacl<(illnstrated in Figizrr 16.5) is very uscful. An anip1ific.r with a

K
Figure 16.5: Sniootliing the fieyuency rcqmise with fredbacli

very high factor of a n ~ ~ l i ~ { /F(jd)/
: ~ ~ i o>~> i1can he built eabily, it' strong variations
in the freqiieiry rcsponse F ( j w ) can 1x2 tolcratcd. Some of the amplification is
t h w sacrificed, by conuectir-rgthc nirtpul Itack to the input with a gaiu fwtor K ,
The rcsinlt iiig freqixency respame

is nearly constant. It is important, of coiu'w, that J F ( j u ) is
J large enough ihat the
ineqiialit~y/ K F ( ~ J >>
) / 1 is also true for small valixes of I<, so that the negative
feedback systteriihas L: siifficicntly high amplification l/li-.

.3.3 Using Feedback t o Stabilise a System
In many control system applications, thc fofor.cvard path (the 'plant') i s a large teclrnical iustdlation that! clrtiinot IP c.lr;.tnged by siinplcl mcans. The system behaviour
iizodified by couplizig a second
m to i f , wiially as it bnckwarcis
ng a closed f ~ ~ b a cloop.
lr
This
d system i s also called the cmis ronstructcd so thtxt, its propcrtieu can be changed without too much
effort. We ill now he coalsidering whet h ~ an
r nn, ble plant can he coupled with
a feedback system, to yield a coinplete system that is stable.