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Unformatted text preview: ause of changes in t he e nvironment in
which t he s ystem is o perating. Hence, for a given i nput, t he o utput o f t he s ystem
will also change w ith time. T his c ondition is clearly undesirable in precision systems. Consider t he p rocess of driving a n a utomobile. O ur senses are continuously
feeding t he i nformation t o t he b rain. Eyes r eport seeing a child on t he road. T he
b rain will immediately apply i nput t o t he a rms t o s teer t he c ar away from t he child.
T here is a red light ahead. Again t he b rain will a pply t he i nput t o t he legs t o b rake
t he c ar. S uddenly, e ars r eport a n a mbulance siren; t he b rain will apply corrective
i nput t o s teer t he c ar off t he s treet t emporarily. A foul smell is r eported by t he
nose. T he b rain will again take measures t o s peed away t he c ar from t he s pot. I n
t his example, t he child, t he red light, t he a mbulance siren, a nd t he foul smell a re
unpr~dictable changes in t he e nvironment (fed back t o t he i nput by o ur senses).
DespIte t hese u npredictable changes in t he e nvironment, t he p rocess of reaching
t he d estination is c ompleted because of feedback. T he foregoing is a n e xample of
multiple variable feedback.
A feedback system c an a ddress t he p roblems arising because of unwanted disturbances s uch as random-noise signals in electronic systems, a g ust of wind affecting 6 428 Continuous-Time System Analysis Using the Laplace Transform a tracking a ntenna, a meteorite hitting. a spacecr~ft, ~~~k~he;e~!i~:c::~~na~:oa~~
t iaircraft gun platforms mounted on ships or movillg .
( b d width)
used t o reduce nonlinearities in a system, or control ItS ns~ t~meb.ort" a n ithin ~
Feedback is used to achieve, with a given system, the deSire h Jec .Ive w t A
iven tolerance despite partial ignorance of the system and t e en:Tlro~men .
~ d b k te~ t hus has an ability for supervision and self-correctiOn I~ the face
d x t m al disturbances (change ill t he enlee ac sys
o~ change~ in~~:s~x:~et~e~::::~~r::n~~ifi:r i~ Fig. 6.35. Let t he forward amplifier
~~~n~: 000. One hundredth of t~e outP.ut is fed back to the input (H = 0.01).
T he gain T of t he feedback amplifier IS obtailled by [see Eq. «6.69)J lo, _ _ _ = 10,000 = 99.01
T - 1 + GH
1 + 100 f a ing or replacement of some transistors, t he gain G of
10 000 to 20 000. T he new gain of the feedback
Suppose t hat bec.ause h g f
the forward a mplifier c anges r om,
amplifier is given by 6.7 Application to Feedback and Control S tate E quations 429 W hat is t he difference between the two situations? Crudely speaking, the former case is called the n egative f eedback a nd the l atter is t he p ositive f eedback.
We shall later see t hat, generally, feedback system cannot be described in such black
and white terms. T he positive feedback increases gain, b ut t ends t o make the system more sensitive to parameter variations. I t could also lead to instability. In t he
above case, when G = 111,111, G H = 1, a nd T = 0 0. T he cause of instability is
t hat t he signal fed back in t...
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