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

This difficulty can be avoided by observing that the

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Unformatted text preview: resistor of 100 kO and input resistors of 50 kO and 20 kO respectively. The op a mp realization in Fig. 6.32 is not necessarily the one t hat uses the fewest op amps. I t is possible to avoid the two inverting op amps (with gain - 1) in Fig. 6.32 by adding signal s X(s) to the input and output summers directly, using the noninverting amplifier configuration in Fig. 6.16. There are also circuits (such as Sallen-Key) which realize a first- or second-order transfer function using only one op amp. • Exercise E6.11 Show that the transfer functions of the op amp circuits in Figs. 6 .33a and 6.33b are HI(S) and H2(S), respectively, where 6, 6.7 Application t o F eedback a nd C ontrol S tate E quations 427 A possible solution t o t his problem is t o a pply a n i nput t hat is not a predetermined function o f t ime, b ut which will change t o c ounteract t he effects of changing system characteristics a nd t he e nvironment. I n s hort, we m ust provide a correction· a t t he s ystem i nput t o a ccount for t he u ndesired changes mentioned above. B ut t hese c~anges a re ? enerally u npredictable, a nd i t is difficult t o p rogram a ppropriate cor:ectlOns t o t he m put. However, t he difference between t he a ctual o utput a nd t he ~eslred o utput c learly indicates t he s uitable c orrection t o b e a pplied t o t he system m put. Hence, we could make t he i nput f (t) p roportional t o t he desired o utput, a nd feed back t he a ctual o utput yet) t o t he i nput for comparison. T he difference a cts a s t he c orrected i nput t o t he s ystem. T he i nput t o t he s ystem is therefore continuously a djusted t o o btain t he d esired response. Such s ystems (Fig. 6.34b) a re called f eedback o r c losed-loop s ystems for obvious reasons. We observe t housands o f e xamples o f feedback systems a round u s in everyday life. Most social, economical, educational, a nd p olitical processes are, in fact, feedback processes. T he h uman b ody i tself is a fine example of a feedback system; a lmost all of o ur a ctions are t he p roduct o f feedback mechanism. T he h uman s ensors such as eyes, ears, nose, tongue, a nd t ouch are continuously monitoring t he s tate o f o ur s ystem. T his information is fed back t o t he b rain, which acts as a controller t o a pply corrected i nputs t hrough o ur m otor m echanisms a nd t hus a ccomplish t he d esired objective. f (t) • ~ k y (t) ( J ( 8) (a) y ( I) (J ( 8) I (b) F ig. 6 .34 Open-loop and closed-loop (feedback) systems. - Rf H I(S)=- ( -a- ) R s +a C H 2(S)=-Cf 6.7 (S+b) -s +a b= ~ RC 'V Application to Feedback and Controls Generally, systems are designed t o p roduce a desired o utput yet) for a given i nput f (t). U sing t he given performance criteria, we c an design a system shown in Fig. 6.34a. Ideally, such a n o pen-loop s ystem s hould yield t he desired o utput. I n p ractice, however, t he s ystem characteristics change w ith t ime, as a result of aging D r r eplacement of some components, or bec...
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This note was uploaded on 04/14/2013 for the course ENG 350 taught by Professor Bayliss during the Spring '13 term at Northwestern.

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