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puep 5.3 aca epeaoy y cce (pc. 5.50) o aay (x y).

y x W1(s) W2(s) W3(s) W4(s) Pc. 5.50 Cpyypa cxea exooecoo oea B cpyypo cxee oea o aay (x y) eec o po y (r = 1) c epeaoo ye Wp1(s) = W1(s) W2(s) a ayx oypa (b = 2) c epeao y paoyx ee c opae opa c:

Wp 1 (s) = W1(s)W2(s)W3(s)W4 (s) ;

Wp 2 (s) = W1(s)W4(s).

oca oyeoe paee (5.90), oya:

W1(s)W2(s)(1+W1(s)W4(s)) (1+W1(s)W2(s)W3(s)W4(s)) Wx-y (s)=.

(1+W1(s)W4(s))(1+W1(s)W2(s)W3(s)W4(s)) Pacpa co ca e, coepae epeaoe y ox ee, ooaeo oya:

W1(s)W2(s) Wx-y (s) =.

1+W1(s)W2(s) +W1(s)W2 (s)W3(s)W4(s) 5.4 TOBE AOH PEPOBAH aoo peypoa aaec ypaee, ocaee acoc ey xoo peyopa y(t) = y(t) - ya eo xoo xp(t).

Bce ao peypoa opaec a pocee: poopoa (), epa (), epea () poee: poopoaoepa (), poopoao-epea (), poopoaoepao-epea ().

He poc xapaepca cex aoo peypoa c o pe x aecx coc.

5.4.1 poopoa ao peypoa poopoa ao peypoa ocaec ypaee xp (t) = -S1y(t), (5.91) e S1 apaep acpo.

a () opaae o a, o peyop aec ccey o py opaeo opao c.

poopoa peyopo oe cy ooe yceoe eo c ee oeo yce, eoe opaey opay c o ooe oey. B c c aece xapaepc -peyopa ocoo coaa c xapaepca yceoo ea e :

- epeaoa y W (s) = -S1; (5.92) - acoe xapaepc, pa oopx opae a pc. 5.51:

AX W (i) = -S1 = S1ei ; (5.93) AX M () = S1; (5.94) X () =. (5.95) a) ) ) M Im s -s0 0 Re Pc. 5.51 acoe xapaepc -peyopa:

a AX; X; AX epexoa y (pc. 5.52, a):

h(t) = xp(t) = -S11(t) (5.96) Becoa y (pc. 5.52, ):

w(t) = -S1(t) (5.97) y y a) ) (t) 0 t t w -h ss1 (t) 0 t t Pc. 5.52 epexoe xapaepc -peyopa:

a epexoa y; ecoa y oo, o c eoca ococa oo oo aoa peypoa, eoxoo paccope epexo poecc ayo cce.

epexo poecc ACP c -peyopo, opae a pc. 5.53, xapaepyec e, o eec caeca oa pey poa, paa yyc ya. eceo, o eopee o oeo ae y oo aca:

y yyc ya t Pc. 5.53 epexo poecc ACP c -peyopo lim y(t) = lim sy(s) = lim sx(s)Wc (s), t s0 s1 Wo (s) Wo (s) a a x(s) = ; Wc(s) = =, s 1+Wo (s)Wp(s) 1+Wo (s)So Wo (s) ko s lim y(t) = = =, (5.98) t s 1+Wo (s)S1 1+ ko Sec limWo (s) = ko.

sTa opao, caeca oa peypoa ac o oea yce oea apaepa acpo peyopa. pe caeca oa e ee, e oe aee apaepa acpo S1. oo, o a oa ocycoaa, .e. yyc = 0 p ko 0, eoxoo, o S1. Ceoaeo, auue cmamueco ouu peyupoau emc opauecu eocmamo ACP c nponopuoa peymopo.

5.4.2 epa ao peypoa epa ao peypoa ocaec ypaee t xp (t) = -S0 y()d, (5.99) xp (t) = -S0y(t) (5.99) e S0 - apaep acpo peyopa.

epa peyopo oe cy eppyee eo c epee epeao oeo, eoe opaey opay c oey.

aece xapaepc -peyopa e :

- epeaoa y SW(s) = ; (5.100) s - acoe xapaepc, opaee a pc. 5.54:

-SAX W (i) = = (S0 / )ei(- / 2) = (S0 / )ei / 2 ; (5.101) i SAX M () = ; (5.102) X () =. (5.103) a) ) Im M ) / 0 Re Pc. 5.54 acoe xapaepc -aoa peypoa:

a AX; X; AX y y a) ) 0 t t -h -w st t Pc. 5.55 epexoe xapaepc -aoa peypoa:

a epexoa y; ecoa y epexoe xapaepc, pa oopx pecae a pc. 5.55:

epexoa y h(t) = S0t; (5.104) ecoa y w(t) = S0 (5.105) y ya t Pc. 5.56 epexo poecc APC c -peyopo epexoo poecc ACP c -peyopo, opae a pc. 5.56, xapaepyec ocyce caeco o peypoa, ao aee ooe peypyeo e o ycaoeoc ae o cpae c py aoa peypoa, ao peee peypoa.

a ococo epaoo peyopa ec ocyce caeco o peypoa. eceo:

1 Wo (s) lim y(t) = lim sy(s) = lim s = 0.

t 0 s0 s0 Ss 1+ Wo (s) s 5.4.3 epea ao peypoa epea ao peypoa ocaec ypaee xp (t) = -S2y (t), (5.106) e S2 apaep acpo, oopoe ec ypaee eaoo epepyeo ea. Ha pae epea ao oe peaoa peo opeeeo epae aco. epeaa cocaa oc ao peypoa oo, o ye cpoece peyopa, a a o cyae peyop peapye e a acooe aee peypyeo e, a a copoc ee ee. epea peyop e peec peypoa, a a p o ocoo ae peypyeo e xoo ca aoo peyopa pae y.

aece xapaepc -aoa peypoa:

epeaoa y W (s) = -S2s ; (5.107) acoe xapaepc, opaee a pc. 5.57:

i AX W (i) = -S2i = S2e ; (5.108) AX M () = S2 ; (5.109) X () =. (5.110) Im a) ) ) M = Re Pc. 5.57 acoe xapaepc -aoa peypoa:

a AX; X; AX y h a) ) s2 (t) 0 t t Pc. 5.58 epexoa y -aoa peypoa:

a eoe oece, epexoa y epexoe xapaepc:

epexoa y h(t) = S2 (t); (5.111) ecoa y w(t) = S2(t), (5.112) pa oopx opae a pc. 5.58.

epeaa cocaa yacye oo cox aoax peypoa yye aeca epexooo poecca.

5.4.4 poopoao-epea ao peypoa poopoao-epea ao peypoa o-caec ypaee. (5.113) xp (t) = -[S1y(t) + S2y (t)] o peyop o cyecy coco yx apaeo ex cocax:

poopoao epepye.

aece xapaepc -peyopa:

epeaoa y ; (5.114) W (s) = -(S1 + S2 s) acoe xapaepc, pa oopx opae a pc. 5.59:

2 AX (5.115) W(i) = -(S1 + S2 i) = S1 + S2 2 ei(+arctg(S2/ S1));

2 AX ; (5.116) M () = S1 + S2 X. (5.117) () = arctg(S2/ S1) + a) ) ) M Im W(i ) ss = Re Pc. 5.59 acoe xapaepc -peyopa:

a AX; -- X; - AX epexoa y, pa oopo opae a pc. 5.60:

h(t) = -S11(t) - S2(t). (5.117') Becoa y:

. (5.118) w(t) = -S1(t) - S2 (t) h(t) st Pc. 5.60 epexoa y -peyopa C o pe aeca poecca peypoa ayo ACP poopoaoepea peyop oaae ocoeoc oox aoo peypoa (pc.

5.61). Hae oec o pooo o y(t) yeae cpoece peyopa, aoap ey yeaec aeca oa o cpae c poopoa peyopo.

B ycaoxc peax, oa y' = 0, peyop ee ce a o peyop. Bea caeco o ocaec ao e, a cyae pee peyopa, eceo:

1 Wo(s) Ko (5.119) lim y(t) = limsy(s) = lims = t s0 ss 1+Wo(s)(S1 + S2s) KoS1 +y yyc ya t Pc. 5.61 epexo poecc ACP c -peyopo 5.4.5 poopoao-epa ao peypoa poopoao-epa ao peypoa ocaec ypaee t (5.120) xp (t) = -(S1y (t ) + S y ()d) pecae coo apaeoe coeee poopoao epao cocax. aece xapaepc -pey-opa:

epeaoa y S W(s) = - S1 + ; (5.121) s acoe xapaepc (pc. 5.62):

S AX W(i) = - S1 + ; (5.122) i 2 S1 2 + SAX M()= ; (5.123) SX. (5.124) () = + arctg 2 S epexoa y (pc. 5.63, a):

h(t) = -(S1 1(t) + S0 t). (5.125) Becoa y (pc. 5.63, ):

w(t) = -(S1(t) + S0). (5.126) M a) ) ) Im W(i ) s s1 Re Pc. 5.62 acoe xapaepc -peyopa:

a - AX; - X; AX h a) w ) ss0 t t Pc. 5.63 epexoe xapaepc:

a epexoa y; ecoa y poopoao-epa peyop coeae cee ococa - -aoo peypoa, a eo: poopoaa cocaa oeceae ocaooe cpoece peyopa, a epaa cocaa pye caecy oy peypoa. epexo poecc ACP c peyopo opae a pc. 5.64.

B aae poecca peypoa ocoy po pae poopoaa cocaa, a a epaa cocaa ac e oo o acooo ae, o o pee. C yeee pee opacae po epao cocae, oeceae ycpaee caeco o, .e.

1 Wo (s) y(t) = sy(s) = s = lim lim lim t -> s->0 s->0 s 1+ Wo (s)(S1 + S0 / s) (5.127) sWo (s) = = 0.

lim s->s + Wo (s)S1s + Soopo apaepo acpo S0 S1 oo e ye ec ao cocae. B acoc, p S0 = 0 oyaec -peyop, a p S1 = 0 - peyop.

y t Pc. 5.64 epexo poecc ACP c -, - -peyopa 5.4.6 poopoao-epao-epea ao peypoa poopoao-epao-epea ao peypoa ocaec ypaee t xp (t) = -(S1y(t) + Sy()d + S2y(t)). (5.128) aece xapaepc -peyopa:

epeaoa y SW(s) = (S1 + + S2s). (5.129) s acoe xapaepc (pc. 5.65):

S AX W(i) = (S1+ + S2s); (5.130) i S1 2 + (S0 - S22) AX ; (5.131) M ( ) = S X. (5.132) ( ) = + arctg S0 - S epexoe xapaepc:

epexoa y, p t > h(t) = (S1 + S0t + S2 (t)); (5.133) ecoa y w(t) = (S1 (t) + S0 + S2 '(t)). (5.134) a) ) ) M Im 3 / s s1 0 Re / s2 sPc. 5.65 acoe xapaepc -peyopa:

a AX; X; AX pa epexoo y -peyopa pecae a pc. 5.66.

h s0 t Pc. 5.66 epexoa y -peyopa -peyop coeae cee ococa cex pex pocex aoo peypoa: cooe cpoece aoap a yca o pooo o y(t) ocyce caeco o, oopoe oeceae epaa cocaa (pc. 5.67).

y t Pc. 5.67 epexoe poecc ACP c pa aoa peypoa Heoxoo oe, o peee peyopo c epea coca, ecop a x ococa, e cea eecoopao, a oa eoyco. Ta, oeo c o aaae o aay peypoa ecoeo o oece o pooo o peypyeo e, a a o yc ye ocya peyop o cee pee coo aaa oce pxoa oye, a oopoe oee oy aoc oe ooe. oee oo, ax cyax -peyop oe "pacaa" oe ccea oepe ycooc.

5.5 TPEHPOBOHE AAH 1 e aac oee ee cce, oopx pocxo peopaoae xox cao xoe. Ec epeaoa y ea ee poco po, o aoe eo oocc pye ox eeapx ee, ypae oopx oo oy epeaoo ypae a2 y (t) + a1 y (t) + a0 y(t) = b1 x (t) + b0 x(t), ppaa e e oe y.

Paa ceye e: yceoe, epaoe, eaoe peaoe epepye, coo aaa, aepoecoe epoo opa, aepoecoe opoo opa, oeaeoe. aoe epecex ee paccapaec c o aaa x aecx xapaepc.

A ae e ocac ooe epea ypae B oey eaoe epepyee eo ec e peayeo C Ha ae py ec oe e 2 p aae cee cce aoaecoo ypae poo coyec cpyyp aa. B o cpyypo cxee oy pcycoa oo p a coee: oceoaeoe, apaeoe, coeee c opao c. aee epeaox y oex ee ooe aca epeaoe y coee ocpo x acoe xapaepc.

Peae oe oaa coo cpyypo, x ec, a aaee, epepece c, oope eoxoo paa, coy paa peopaoa cpyypx cxe.

A ae epeaoe y oo aca oooypo cce aoaecoo peypoa B aa epeaoe y ee W1(s) = k; W2 (s) = 4. aca acoe Ts xapaepc oceoaeoo apaeoo coee.

C epeoc ax eeo p peopaoa cxe pooc e ooex peopaoa 3 eea oooypo cce aoaecoo peypoa c oe peyop. Bce ao peypoa opaec a pocee:

poopoa, epea, epa poee: poopoaoepa, poopoao-epea, poopoao-epao-epea. Bce ao peypoa paccapac c o pe x aecx coc.

A ao aoo peypoa ec e peayec B o ae eee ao peypoa epeao cocae C epeaoe y peyopo acac co ao "". ay opa ae o a 5.6 TECT 1 ae e oocc pye caecx ee A Caeca xapaepca oa o y.

B Caeca xapaepca e cyecye.

C Caeca xapaepca paa y.

2 epeaoa y aoo ea ee W (s) = T s A ceoo.

B Peaoo epepyeo.

C epaoo.

3 epeaoa y aepoecoo ea epoo o-pa Ks A W (s) =.

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