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8.1 OAATE AECTBA 8.1.1 pe oaae Haoee pacpocpae p oaae pep aeca, pee cceax ypae, c:

1 Caeca oa peypoa yc, opeeea a paoc ey ycaoc aee peypyeo epeeo ee aa aee (pc. 8.1), .e. yc = yyc - ya.

2 aeca oa peypoa y, opeeea a aoee ooee epexoo poecce peypyeo epe-eo o ee ycaoeoc ae (pc.

8.2).

3 Bpe peypoa Tp - pe, a oopoe paoc ey ey aee peypyeo epeeo ee aa aee ( ycaoc) caoc ee (pc. 8.1, 8.2), |ya(t) - y(t)| <.

4 epepeypoae, epeoe % paoe ooe epoo acaoo ooe peypyeo epeeo o ee ycaoeoc ae oy ycaoeyc ae (pc. 8.3):

. (8.1) aeco peypoa caec yoeope, ec epepeypoae e peae 30 - 40 %.

5 Cee ayxa, epea %, cy oeceo oeo ecoc ayxa oeaex poecco opeeec a ooee paoc epo pee ay epo aye (pc. 8.4):

. (8.2) ecoc ayxa oea ccee caec yoeopeo, ec cee ayxa cocae 75 % e, eoopx cyax oycaec opa 60 %.

oo, o ccea aoaecoo peypoa yoeopa peyeoy aecy eoxoo, o pe oaae aeca peypoa o cce ee pa aa, .e.

.

oa peoa o aecy peypoa oy oee ece, apep, epexo poecc oe ooo ooo e epeo.

pe oaae aeca yoo cooa ex cyax, oa eec pa epexooo poecca y(t), oop oe oye cepeao peao ccee peypoa ye oepoa a BM. Ec e ao oooc e, .e. e yaec a opao oy py epexooo poecca, o oyc oce oaae aeca, oope cc e ocpoe paa epexooo poecca o oea ypa-e o aco xapaepca.

8.1.2 ocee oaae aeca Ocoy pyy cpe ocex oaaee aeca coca opee oaae aeca peypoa, oop oocc cee ycooc cee oeaeoc. oaae ye cooa opeee oe aaca ycooc (. 7.3, e o ao x opeeee). Co pe aeca peypoa oo cea ceye o.

1 Cee ycooc, opeeea o opye (7.7), xapaepye ecoc ayxa aoee eeo ayxae eoeaeo cocae epexooo poecca, oopa opeeec a y(t) = Ce-t. yc paccapaea ccea ocaec epea ypaee opoo opa, xapaepcecoe ypaee oopoo ee a ecex pax op s1 = 1, s2 = 2 < 2 (pc. 8.5, a). oce cooecy e eeape cocae coooo e cce (pc. 8.5, ):

a o pao epexox poecco, e ee acooe aee op xapaepcecoo ypae, e eeee ayxae cooecya ey cocaa. Peypy epexo poecc y(t) = yi(t). Eo ayxae opeeec aoee eeo ayxae cocae, .e. ae o acooy ae ope xapaepcecoo ypae.

Pc. 8.5 Opeeee aeca ooox epexox poecco o cee ycooc:

a - pacooee ope xapaepcecoo ypae;

- cocae epexooo poecca Pc. 8.6 Opeeee aeca oeaex epexox poecco o cee ycooc:

a - pacooee ope xapaepcecoo ypae;

- epexoe poecc Ec e xapaepcecoe ypaee cce ee oece copee op, o cocaa epexooo poecca yi(t) ye e oeae xapaep yi(t) = Cie-tcost, ecea ac op, a aec cee ycooc, a a =, xapaepye oay (pc. 8.6).

a o pc. 8.6, a oeaex epexox poecca pao aco e oaoe oae, .e. yo = e-t. Ho p oaoo cee ycooc aeco x epexox poecco cyeceo oaec py o pya. Ceoaeo, a cee ycooc oe aeca oeaex epexox poecco eocaoo.

Cee ycooc oe cooaa oe pee peypoa ooox epexox poecco. acaea = e-t oe t = 0 oceae a oc accc opeo (pc. 8.5, ). Bpe peypoa o cyae opeeec a Tp <. (8.3) Ec peyec ye pe peypoa, o, a ceye (8.3), cee ycooc ao yea. p oee pee peypoa acoa e yaec.

2 Cee oeaeoc a e, a cee ycooc, coyec oe aaca ycooc oe aeca peypoa. Cee oeaeoc, opeeea cooec c (7.8), xapaepye ayxae aoee eeo ayxae cocae, oopa opeeec a y(t) = Ae-mtsint, oya ceye, o eee aco ee eee ay oea.

Cee oeaeoc ooao caa co cee ayxa. eceo, oe pee t0 aya cooo cocae opeeec a y1=, a oe pee t0 + T, .e. epe epo, y3 =. B o cyae cee ayxa, coaco (8.2), aec:

, a a, o = 1 - e-2m. (8.4) Cee ayxa eec o 0 o 1, a cee oeaeoc - o 0 o.

Haoee aco coyc ceye x ae: m = 0,141 ( = 0,61); m = 0,221 ( = 0,75); m = 0,366 ( = 0,9); m = 0,478 ( = 0,95).

3 Oea caeco o oe oyea o peeo eopee:

yc =, (8.5) e W.c(s) - epeaoa y ayo cce o aay o; X(s) opaee aaeo oec, oce cyae x(t) = C = const oa X(s) =. Cyeo ecaaoo yc =.

Hapep, cce c epa peyopo caeca oa ocycye, a cce c poopoa peyopo paa.

Ec Wo(s) oe epea pae k, o.

oceeo coooe o, o cceax c -peyopo caeca oa yeaec c yeee ae apaepa acpo peyopa. B peax cceax epec acao oooe aee S1, cxo oecee aaca ycooc.

B aee ceye ae, o aeca oa ope eoa e oeaec.

8.1.3 epae pep aeca epae pep aeca peca coo opeeee epa o pee peeax o 0 o o eoopo y epexooo poecca y(t) o (t) cc eocpeceo, o o epexo y cce, o oea epeaoo y cce. e cooa x pepe ec oyee oe oe cpoec ooe peypyeo e o ycaoeoc ae. epa pep aeca pec a peoa: a) pocoa ce epaa; ) ecooc pae epe oe epeaoo ypae.

8.1.3.1 ue umepa pumepu (8.6) cy oe aeca eoeaex poecco. eoepec o pep xapaepye oa, aey ey po epexooo poecca oc accc (pc. 8.7, a), o yae a pe peypoa, a ey aecx ooe. Ec eeca pa epexooo poecca, o eca epeaoa y ayo cce W.c(s) xoa epeea x(t) = 1(t), o aee eoo epaoo pep opeeec c cooae eope o oeo ae y. eceo, opyy (8.6) oo aca ae:

oa e epa pep aeca oo c py eoa.

Hapep, ec a epeaoe ypaee aae yco:

(n-1) an y(n)(t) + an-1y (t) + +a0y(t) = 0, y(n - 1)(0), , y(0), y(0), o, poeppoa eo, oy ycox cce y(i)() = 0 i = 1, 2, , n.

(n - 2) Toa any(n - 1)(0) - an - 1 y (0) - a0J = 0, oya J =, a p yex aax ycox J =.

Cyecy oa eoo epaoo pep, oope pec ex cyax, oa aa yaco epexooo poecca ec eee oece, apep,..

Bee opyy, ooy c ao pep. oo poepepye o s y, ocyecy peopaoae o aacy y y(t):

.

Ec epe peey p s 0, o oy.

Ceye oe, o ce ax pepe e peyec ae epexooo poecca. e ee aee eoo epaoo pep, e ye aeco poecca peypoa. Oao cooae aoo a pepe aoepeex epexox poecco e ae oeo ap, a, apep, eayxae cyco J = 0. ooy oe aeca peypoa ax poecco coy -epae oe, aoepeeoc oepao y oopx ycpaea a-o cocoo.

pep 8.Tpeyec c J* cce c Peee.

Hae y(s):.

.

Pc. 8.7 epae oe aeca peypoa:

a - ea; - oya; - apaa 8.1.3.2 Moy umepa pumepu (8.7) peec oe aeca oeaex poecco, a eoeaex poecco o coaae c e epa pepe. eo ce peyec ae epexooo poecca. Ha pae o pep coyec p ceo cceoa cce a oex c peee ceo ex, .e. a, e oepa oy e pecae pyoc. eoepec pep pae oa, aeo ey po y(t) oc accc (pc. 8.7, ). B eoopx cyax coy oa oyoo epaoo pep:

(8.8) oopa pae o ec ae epexooo poecca eo oe.

8.1.3.3 mepa apamu pumepu, (8.9) ec aoee pacpocpae pepe aeca pecae coo oa o po y2(t) (pc. 8.7, ). a o (8.9), pae o ee opa epexooo poecca xo pep c pa eco, o po oy, o aa yaco epexooo poecca popeae aoee aee, e eo "xoc", oop paec e e a apa pep. Cpec poa (8.9), aec py aoe ooe peypyeo e, ooy ae ae pep cea cooecy oeae poecca c a ayxae. Ce ycpae oo eocaa pe yyey apay oey:

, (8.10) oopa, poe cax ooe, yae c eco oeo x pooy.

Becoo oe paec pa eaeoy pee apaca peec peeax T, (8.11) e Tp - eaea eoc epexooo poecca.

apa pep, a e, oo c e ocpoe epexooo poecca o acoo xapaepce ayo cce peopaoa o ype o xooo caa.

coy opyy Pee, oya:

B aee ceye oe, o acoe ae o epao oe ca o cee e peca epeca. O cya coocae pax apao acpo oo o e cce, aae opeee apaepo acpo cce.

8.2 ACTOTHE METO AHAA AECTBA PEPOBAH B eepo pae poo coyc acoe eo cceoa cce ypae. B acoc, pya eoo, papaoaa B. B. Coooo, ooe oe aeco peypoa o eece aco xapaepca, ocpo epexoe poecc, aae cepoa oppepye ycpoca.

8.2.1 acoc ey epexoo aco xapaepca oe aeca peypoa eoxoo ycao c ey epexo aco xapaepca. B acoo oac epexoa xapaepca acaec epe peopaoae ype:

(8.12, a) epe AX cce opaee xoo epeeo o ype c pyo copo y(i) = W(i) X(i). (8.12, ) coy opaoe peopaoae ype ocee coooe, epexoo poecc (epexoa xapaepca) opeeec cey opao:

(8.13) p oec a xo eo cyeao ye x(t) = 1(t), opaee oopo x(i) = 1/(i), coooee (8.13) epexoo y aec a.

peca AX epe ecey y ac W(i) = Re() + iIm() paaa eit o opye epa, paee epexoo y peopayec oee yooy y c cooae BX - Re():

. (8.14) MX - Im():

. (8.15) Ha pae coyec opya (8.14), oopo BX pecae coo coy y eppoae ooo oo peo: ce eoa c peee BM o ye peapeo apoca coo xapaepc Re() ycoo-e y - cyo pae cyo peyoo, o ooe oy ocaoo yoe pae.

Ec a ccey ecye poooe oyee, o epexo poecc opeeec o ooe eeceo o xapaepca:

Reo() = Re[W(i)X(i)], Imo() = Im[W(i)X(i)], (8.16) p o eoxoo, o oc y W(s)X(s) pacoaac cea o o oc.

8.2.2 Coca eeceo-acox xapaepc cooecyx epexox poecco Ocoe coca BX epexox poecco cey (8.14).

1 Cocmo ueocmu: ec BX oo peca cyo (8.17, a) ao cocae cooecye epexo poecc, (8.17, ) o epexo poecc y(t) oe pecae cyo cocax. (8.17, ) Pc. 8.8 Cooece acao o oc opa:

a BX; nepexoe npoecc 2 Cooece acao o oc opa Re( ) u y(t).

Ec yo Re() a oco oe, o cooecyee aee y(t) oe yoaec a o oe (pc. 8.8).

3 Cooece acao o oc accc Re( ) u y(t).

Ec apye cooecye pae acoo xapaepc yo a ocooe co, o apye cooecye pae epexooo poecca ye ec a o co (pc. 8.9), .e.

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