Signal Processing and Linear Systems-B.P.Lathi copy

630b t hen z js 1 gs zs r a nd 6 424 c ontinuous time

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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 ~ O 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 G 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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