2 Intro Automatique

 

Nmtrhkuotnhm å b„guth`gtnquj

7 Kr. L. BGIGKN

Ohurs k„Guth`gtnquj k„Guth`gtnquj 9551/9 9551/955> 55> (7árj gmmîj Nmcîmnjur)

 

Ubgm 

Kîdnmntnhm kj b„guth`gtnquj

 

Iut kj b„guth`gtnquj Kh`gnmjs k„gppbnogtnhm



Jxj`pbjs k„gppbnogtnhm

9

 

Kîdnmntnhm kj b„guth`gtnquj Jmsj`ibj kj taîhrnjs, kj tjoamnqujs, k„hutnbs ... utnbnsîs phur rjmkrj bjs systá`js guthmh`js, nmkîpjmkgmts kj b„nmtjrvjmtnhm au`gnmj, gdnm kj rîkunrj bg drîqujmoj jt bg knddnoubtî kjs téoajs au`gnmjs.

?

 

Kîdnmntnhm kj b„guth`gtnquj B„guth`gtnquj jst b„grt kj `hkîbnsjr, k„gmgbysjr puns kj oh``gmkjr bjs systá`js. O„jst gussn ojbun kj trgntjr b„nmdhr`gtnhm jt kj prjmkrj kjs kîonsnhms.

;

 

Kîdnmntnhm kj b„guth`gtnquj B„guth`gtnquj dgnt pgrtnj kjs sonjmojs kj b„nmcîmnjur. Jbbj trgntj kj bg 6 @hkîbnsgtnhm

Gmgbysj

Oh``gmkj

Yîcubgtnhm

…

kjs systá`js kymg`nqujs Jbbj g phur dhmkj`jmts taîhrnqujs 6 bjs `gtaî`gtnqujs bg taîhrnj ku sncmgb

b„nmdhr`gtnquj b„îbjotrhmnquj

…

:

 

Iut kj b„guth`gtnquj 



B„guth`gtnquj g phur hifjt bj ohmtrûbj guth`gtnquj kj  prhoîkîjs nmkustrnjbs hu k„gppgrjnbbgcj knvjrs kgms bj iut kj supprn`jr hu kj dgonbntjr b„nmtjrvjmtnhm au`gnmj. Ansthrnquj  71;5

6 Yîcubgtjur Yîcubgtjur kj Sgtt (I (Ijshnm jshnmss kj b„nmku b„nmkustrnj strnj å vgpju vgpjur). r).

 7>;:

6 Kjuxná`j cujrrj `hmkngbj (kîvjbhppj`jmt kj b„guth`gtnquj kgms b„gvngtnhm).

 7>45

6 Gppgrntnhm kj b„nmdhr`gtnquj (ohs`hs, trgntj`jmt rgpnkj

kj b„n b„nmd mdhr hr`g `gtn tnhm hm,, phss phssni ninbn nbntî tî kj rrîs îshb hbut utnh nhmm kkjs js sy syst stá` á`js js oh`pbjxjs jto.) 4

 

Kh`gnmjs k„gppbnogtnhm Kjux kh`gnmjs k„nmtjrvjmtnhm kj b„guth`gtnquj 6 _ystá`js _ystá` js å Îvîmj` Îvîmj`jmts jmts Knsorjt Knsorjtss

_ystá`js Ohmtnmus

(_JK)

(_O)

îtgts

îtgts

tj`ps

GZ[H@G[N_@J

tj`ps

GZ[H@G[NWZJ OHM[NMZJ

3

 

Kh`gnmjs k„gppbnogtnhm • Kgms bjs systá`js å îvîmj`jmts knsorjts knsorjts,, hm pgrbj k„guth`gtns`j k„guth`gtns`j (sîqujmoj k„gotnhms kgms bj tj`ps). • Jxj`p j`pbjs k„ k„gpp gppbnog nogtnh tnhms 6 Bjs knstrniutjurs guth`gtnqujs, bjs gsojmsjurs, bj `hmtgcj guth`gtnquj kgms bj `nbnju nmkustrnjb, bjs djux kj orhnsj`jmt, bjs pgssgcjs å mnvjgux. 1

 

Kh`gnmjs k„gppbnogtnhm • Kgms bjs systá`js ohmtnmus phur gssjrvnr jt/hu oh``gmkjr kjs crgmkjurs paysnqujs kj dgãhm prîonsj jt sgms gnkj jxtîrnjurj.

• Jxj`p j`pbjs k„gp „gppbn pbnog ogttnhm nhm 6 B„gmcbj k„umj dusîj, bg phsntnhm ku irgs k„um rhiht, bj pnbhtgcj guth`gtnquj k„um gvnhm.

>

 

Jxj`pbjs k„gppbnogtnhm 

Gîrhmgutnquj

@goanmjs-hutnbs

 pnbhtjs guth`gtnqujs< guth`gtnqujs< oh``gmkjs kj vhb, cunkgcj kj dusîjs, phsntnhmmj`jmt kj sgtjbbntjs, oh``gmkjs mu`îrnqujs phur b'usnmgcj<

Îbjotrhtjoamnquj

oh``gmkjs kj `htjurs, …

_pgtngb

  

Guth`hinbj



ohmtrûbj kjs `htjurs, rîcubgtjurs kj vntjssj, ohmtrûbj k„îqunpj`jmts, 75

 

C î m î r g b n t î s s su u r b bj j s _y s t á` js B n m îgn r js

77 Kr. L. BGIGKN

Ohurs k„Guth`gtnquj k„Guth`gtnquj 9551/9 9551/955> 55> (7árj gmmîj Nmcîmnjur)

 

Ubgm   Mhtnhm

kj systá`j



_ystá`js bnmîgnrjs



Urnmonpgbjs prhprnîtîs

79

 

Mhtnhm kj systá`j 



Hm soaî`gtnsj um systá`j pgr um ibho  phssîkgmt umj hu  pbusnjurs jmtrîjs jt umj hu pbusnjurs shrtnjs. Bjs gutrjs crgmkjurs umj gotnhm mhm kîsnrîj shmt kjs pjrturigtnhms (jmtrîjsgygmt pgrgsntjs).

pjrturigtnhms jmtrîjs

_^_[J@J

shrtnjs

7?

 

Mhtnhm kj systá`j _ystá`j `hmhvgrngibj 6 Zm systá`j `hmhvgrngibj phssákj `hmhvgrngibj phssákj umj sjubj jmtrîj j(t) jt umj sjubj shrtnj s(t). j(t)

_^_[J@J

s(t)

_ystá`j `ubtnvgrngibj 6 Zm systá`j phssîkgmt pbusnjurs crgmkjurs k„jmtrîj jt/hu kj shrtnj jst knt `ubtnvgrngibj 7;

 

_ystá`js bnmîgnrjs _ystá`j bnmîgnrj 6 Zm systá`j jst knt bnmîgnrj bhrsquj sjs crgmkjurs k'jmtrîj jt kj shrtnj pjuvjmt sj `jttrj shus bg dhr`j k'um jmsj`ibj k'îqugtnhms knddîrjmtnjbbjs å ohjddnonjmts ohmstgmts. Y  j(t)

O

s(t) 0 To(t)

j(t)0YO

kTo (t) kt

+T (t) o 7:

 

Urhprnîtîs 

Urhp Ur hphr hrtn tnhm hmmg mgbn bntî tî 6

Q(t)

Jmtrîj

_^_[J@J

B„jddjt B„jd djt jst jst prhphrt prhphrtnhmmj nhmmjbb å bg ogusj ogusj ^(t)

 Ó Q(t)

 

_hrtnj

Jmtrîj

_^_[J@J

Ó ^(t)

_hrtnj

74

 

Urhprnîtîs 

Gkkntn Gkk ntnvnt vntîî (su (supjr pjrphs phsntn ntnhm) hm) 6

Q7(t)

_^_[J@J

^7(t) Q7(t)+ +Q9(t) Q7(t)

Q9(t)

_^_[J@J

_^_[J@J

^7(t)+ ^7(t) +^9(t)

^9(t)

73

 

Urhprnîtîs j(t) /bnmîgnrj Bg shrtnj s(t)B„jmtrîj k„um systá`j jst umj krhntj. 



Bg mgturj sncmgb kj shrtnj jst kj ku `æ`j mgturj quj bj sncmgb k„jmtrîj.



Ujmtj 0 Cgnm ku systá`j

71

 

Urhprnîtîs 

Zm systá`j jst knt nmvgrngmt sn bg rîphmsj rîphmsj ku sys systá`j tá`j å um snc sncmgb mgb  x(t) kn kndd ddîr îrîî k„ k„um um tj`p tj`pss ϋ jst bg `æ`j quj bg rîphmsj  y(t) ku systá`j `gns knddîrîj kj ϋ. shrtnj

jmtrîj _^_[J@J

t

t

shrtnj

jmtrîj

_^_[J@J t

t  

 

7>

 

Urhprnîtîs 

Ogus Og usgb gbnt ntîî 6 Uhur um systá`j ogusgb, bg ogusj prîoákj thufhurs b„jddjt, bg rîphmsj n`pubsnhmmjbbj mj oh``jmoj pgs gvgmt b„n`pubsnhm. b„ n`pubsnhm. Zm systá`j  um jmsj`ibj kj rjbgtnhms ogusgbjs jmtrj • kjs crg crgmkj mkjurs urs k„jmt k„jmtrîj rîj 6 OGZ_ OGZ_J_ J_ • kjs cr crgmkjurs gmkjurs kj shr shrtnj tnj 6 JDDJ[ JDDJ[_ _ Uhur um sncmgb, ojbg sncmndnj qu„nb jst mub phur t 2 5 95

 

Cîmîrgbntîs sur bjs _ystá`js kj Oh``gmkj

97 Kr. L. BGIGKN

Ohurs k„Guth`gtnquj k„Guth`gtnquj 9551/9 9551/955> 55> (7árj gmmîj Nmcîmnjur)

 

Ubgm 

Oh``gmkj guth`gtnquj



_ystá`j kj oh``gmkj



Ugrg`átrjs k„um systá`j kj oh``gmkj



_ystá`j jm ihuobj huvjrtj / djr`îj

 

 Mîojssntî k„um systá`j jm ihuobj djr`îj Dhmotnhms k„um systá`j kj oh``gmkj - Gssjrvn Gssjrvnssj ssj`jm `jmtt

- Yîcu Yîcubg bgtn tnhm hm 

Ohmstntugmts k„um systá`j kj oh``gmkj



Urhprnîtîs k„um systá`j kj oh``gmkj 99

 

Oh``gmkj guth`gtnquj Oh``gmkj guth`gtnquj 

Jbbjj ohm Jbb ohmsns snstj tj å rj` rj`pbg pbgojr ojr bb„nm „nmtjr tjrvjm vjmtnh tnhmm au au`gn `gnmj mj ppgr gr oj ojbbj bbj k„um k„um knsphsntnd gpprhprnî.



Nb kjvrg å pgrtnr kjs nmd nmdhr`gtn hr`gtnhms hms qu„n qu„nbb rjãhnt pnbh pnbhtjr tjr bj prhojss prhojssus us jm vuj k„g`jmjr k„g`jm jr bg shrtnj å sunvr sunvrjj umj trgfjo trgfjothnrj thnrj n`p n`phsîj. hsîj.

Nmtîræts kj bg oh``gmkj 

Unbhtjr gvjo rîcubgrntî rîcubgrntî kjs téoajs pîmn pîmnibjs, ibjs, rîpît rîpîtntnvjs ntnvjs hu `hm `hmhthmjs hthmjs..



Unbhtjr gvjo prîon Unbhtjr prîonsnhm snhm jt jm tthutj hutj sî sîourntî ourntî kjs syst systá`js á`js rgpn rgpnkjs, kjs, pju stgibj hu oh`pbjxj. 9?

 

_ystá`j kj oh``gmkj Zm systá`jjt ku oh` ` gá`j mkjî å joh st``gm ohgmkj `pkjr. hsr.î k„um systá`j kj oh``gmkj syst sy stá` oh`` 

Oh``gmkjr 6 O„jst hrcgmnsjr um systá`j kgms um iut dnxî.

Bj systá`j å oh``gmkjr js jstt bj sy syst stá` á`jj sufjt ufjt å bg oh``gmkj (dhur, `htjur, rîgotjur ...)



UJY[ZYIG[NHM_ HYKYJ_

KJ OH@@GMKJ _^_[J@J

GO[NHM KJ OH@@GMKJ

_^_[J@J G

_HY[NJ

OH@@GMKJY 9;

 

Ugrg`átrjs HYKYJ_



sncmgb k„jmtrîj, ohmsncmj 6 Jxj`pbj dnxjr umj tj`pîrgturj å ?3 µo hu dnxjr umj trgfjothnrj kk„um „um gvnhm.

GO[NHM KJ OH@@GMKJ



gotnhm susojptnibj kj oagmcjr b„îtgt ku systá`j å oh``gmkjr. Jbbj jst îbgihrîj jm dhmotnhm kjs hrkrjs.

UJY[ZYIG[NHM_ _HY[NJ



vgrngibjs gbîgthnrjs khmt hm mj ohmmgít pgs b„hrncnmj



sncmgbb kj shrtnj sncmg shrtnj,, vgrngi vgrngibj bj å ohmt ohmtrûbj rûbjr  r 

Gotnhm kj oh``gmkj Kîint ku cgz oh`iustnibj

Hrkrjs [ 0 7;5µO _^_[J@J KJ YJCBGCJ

Ujrturigtnhms 6 [j`p. jxtîrnjurj, jxtîrnjurj, …

DHZY

_hrtnj9: [ s

 

Ihuobj huvjrtj / djr`îj Hm knstnmcuj kjux obgssjs kj systá`js kj oh``gmkj6 



_ystá`j jm ihuobj huvjrtj 6 Bj sncmgb kj oh``gmkj jst nmkîpjmkgmt ku sncmgb kj shrtnj.

j(t) 0 Oh``gmkj

_^_[J@J

s(t)

_ystá`j jm ihuobj djr`îj 6 Bj sncmgb kj oh``gmkj jst bnî gu sncmgb kj shrtnj.

j(t) 0 Ohmsncmj

ÎBGIHYG[NHM Oh``gmkj KJ BG

_^_[J@J

_hrtnj

OH@@GMKJ Yjthur (ihuobgcj) 94

 

Jxj`pbj 7 Oaguddgcj îbjotrnquj k„umj sgbbj _ystá`j _hrtnj Oh``gmkj Ujrturigtnhms

0 sgbbj + jmsj`ibj oaguddgcj. 0 tj`pîrgturj kj bg sgbbj. 0 phsntnhm kj b„nmtjrruptjur  0 huvjrturj k„umj djmætrj, kj bg phrtj hu bjs rgyhms ku shbjnb

Jm ihuobj huvjrtj 6 bg oh``gmkj oh``gmkj jst nm nmsjmsni sjmsnibj bj å bg sh shrtnj rtnj Jm ihuobj djr`îj 6 utnbnsgtnhm k„um tajr`hstgt. Bg oh``gmkj jst îbgihrîj jm dhmotnhm kj bg ohmsncmj (tj`pîrgturj shuagntîj) jt kj bg shrtnj (tj`pîrgturj kj bg pnáoj). _hrtnj 0 Ohmsncmj 0 [j`pîrgturj

[AJY@H_[G[

Oh``gmkj

YGKNG[JZY [j`pîrgturj + _GBBJ 93

 

Jxj`pbj 9 Oh`phrtj`jmt au`gnm

91

 

Mîojssntî k„umj ihuobj djr`îj Bj systá`j kj oh``gmkj pjut hpîrjr jm ihuobj huvjrtj å  pgrtnr ku sjub sncmgb kj ohmsncmj.

@gnsbgstginbnsjr ihuobj djr`îj (ohmtrj rîgotnhm) jst ogpgibj kj6 um systá`j nmstgibj jm IH  oh`pjmsjr

bjs pjrturigtnhms jxtjrmjs (vjmt, ahubj, …)

 oh`pjmsjr

bjs nmojrtntukjs nmtjrmjs (`hkábj n`pgrdgnt)

9>

 

Dhmotnhms k„umj oh``gmkj Kjux dhmotnhms shmt phssnibjs kgms bg oh``gmkj 6



Gssjrvnssj`jmt Zm systá`j gssjrvn jst um systá`j knt sunvjur, o„jst bg ohmsncmj qun vgrnj. Jxj`pbj6 oh``gmkjr um `nssnbj qun phursunt umj onibj.



Yîcubgtnhm

Kgms oj ogs, bg ohmsncmj jst dnxîj jt bj systá`j khnt oh`pjmsjr b„jddjt kjs pjrturigtnhms. Jxj`pbj6 bj rîcbgcj kj bg tj`pîrgturj kgms um dhur  ?5

 

Urhprnîtîs Bj rûbj k„um guth`gtnonjm jst kj ohmojvhnr um systá`j guth`gtnquj qun shnt 6 

_tgibj



Urîons



Ygpnkj

Bg crgmkjur kj shrtnj khnt ohmvjrcjr vjrs umj vgbjur dnmnj sn bj sncmgb k„jmtrîj jst gussn bn`ntî Bg crgmk crgmkjur jur å `js `jsurj urjrr khn khntt ætrj bbgg pbus pprho rhoaj aj kj oj ojbbj bbj kîsnrî kîs nrîjj å b„î b„îtgt tgt st stgtn gtnquj quj Nb khnt rîphmkr rîphmkrjj rgpnkj rgpnkj`jmt `jmt å umj jxon jxontgtnhm tgtnhm.. _hrtnj

Jmtrîj (ohmsncmj)

j(t) t

_ystá`j kj oh``gmkj

s(t)

n    m  s  t    g  i   b    j  

s  t    g  i   b    j  

t

U  r   î     o   s  n     n      h m

?7

Ygpnkntî  

Oh`phsgmts

?9

 

Oh`phsgmts OGU[JZY 



KJ[JO[JZY K„JOGY[

hrcgmj kj trgmsdh hrcgmj trgmsdhr`gt r`gtnhm nhm k„ k„umj umj crg crgmkj mkjur ur pays paysnqu nqujj å umj crgmkjur kj typj îbjotrnquj hu pmju`gtnquj (ogptjur kj tj`pîrgturj, kj phsntnhm, kj vntjssj, …)



GO[NHMMJZY 



oh`pgrgtjur, oh`pgrgt jur, prhphrt sy systá`j stá`jnhmmjbbj å kjux mtrîjs shrtnjs kjs ogp ogptjurs) tjurs) jt umj shrtnj prhphrtnhmmjbb j åjjmtrîjs b„jrrjur((shrtnjs hu bb„îogrt „îogrt jjmtrj mtrj bj bjss kjux jmtrîjs. îbî`jmt qun oh``gmkj oh``gmkj bj systá`j å gssjrvn gssjrvnr. r. _g dhmotnh dhmotnhmm

 prnmonpgbj jst khmo b„jxîoutnhm. NNbb trgvgnbbj shuvjmt å kj trás agutjs punssgmojs. G@UBNDNOG[JZY   Nb sj sntuj jmtrj bj kîtjotjur k„îogrt jt b„gotnhmmjur. O„jst bun qun khmmj khmmj qun kîbnvrj bg puns punssgmoj sgmoj k„ k„jmtrîj jmtrîj mmîojssgnrj îojssgnrj å oj kjrmnjr. OHYYJO[JZY   nb sj pbgoj jmtrj bj kîtjotjur k„îogrt jt b„g`pbndnogtjur. Nb  pjr`jt k„g`îbnhrjr bjs pjrdhr`gmojs pjrd hr`gmojs ku systá`j å gssjrvnr. ??

 

Bjs snc Bjs s ncmg mgux ux kj oh oh`` ``g gmk mkj j

?; Kr. L. BGIGKN

Ohurs k„Guth`gtnquj k„Guth`gtnquj 9551/9 9551/955> 55> (7árj gmmîj Nmcîmnjur)

 

Ubgm 

Kîdnmntnhms



[ypj kj sncmgux 

Yg`pj  Îoajbhm N`pubsnhm

kj Knrgo ?:

 

_ncmgux 

_ncmgb 6 Crgmkjur paysnquj cîmîrîj pgr um gppgrjnb hu trgkuntj pgr um ogptjur (tjmsnhm, tj`pîrgturj, kîint, jto.) s(t)

j(t)

_ystá`j

Uhur um systá`j khmmîj, hm knstnmcuj 6 _ncmgb k„jmtrîj 6 nmkîpjmkgmt ku systá`j, nb sj kîoh`phsj jm oh``gmkgibj jt mhm oh``gmkgibj (pjrturigtnhms) _ncmgb kj shrtnj 6 kîpjmkgmt ku systá`j jt kj sncmgb k„jmtrîj. Hm knstnmcuj shrtnj hisjrvgibj jt mhm hisjrvgibj ?4

 

_ncmgux kj oh``gmkj 

Uhur gmgbysjr bj oh`phrtj`jmt k„um systá`j, hm utnbnsj um jmsj`ibj kj sncmgux k„jmtrîj (sncmgux typj). _hrtnj6 s(t)

Jmtrîj6 j(t) _^_[Á@J



B„îvhbut B„îv hbutnhm nhm kj bg shrtnj shrtnj ku systá`j systá`j shu`ns shu`ns å ojs sncmgux sncmgux typj typj  pjr`jttrg bj systá`j, jt dgonbntjrg bg oh`pgrgnshmkjkjsogrgotîrnsjr rîsubtgts hitjmus. ?3

 

_ncmgux typj _ncmgb jm Îoajbhm

j(t) 0 J 5³u(t) Gvjo Z(t) dhmotnhm kj Ajgvnsnkj 5

sn t 2 5

7

sn t =5

u(t)0

Ojttj dhmotnhm dhmotnhm pjr`jt kj kj shu`jttr shu`jttrjj um systá`j å umj jmtrîj ohm ohmstgmtj stgmtj

?1

 

_ncmgux typj _ncmgb jm Yg`pj

j(tt) 0 g³t j( ³t³³ u(t)

Oj sncmgb pjr`jt k„gmgbysjr bg rîphmsj k„um systá`j jm  phursuntj

?>

 

_ncmgux typj _ncmgb snmushèkgb

j(t)0L³snm(ώ .t)³u(t) .t)³u(t)

Oj sncmgb pjr`jt k„gmgbysjr bg rîphmsj drîqujmtnjbbj k„um systá`j

;5

 

_ncmgux typj N`pubsnhm kj Knrgo ∅t  ≥  5,

λ (t)

+∝

0 5 jt ∬ λ  (t) ⋊ kt 0 7 -∝

λ

t Oj sncmgb pjr`jt kj sn`ubjr b„jddjt k„umj gotnhm s„jxjrãgmt kurgmt um tj`ps

;7

trás irjd (n`pubsnhm, oaho)  

« b„ b„j jss ssj jmoj kj kjs s ihm ihmmj mjs s `goanmjs j jst st kj k j sj chu vjrmjrr pg chuvjrmj pgrr jbb bbj js-`æ s-`æ`js, `js, gut utg gmt qu qu„n „nbb jst phssn phs snibj ibj jt sg sgms ms bj sj sjohu ohurs rs kj b„nmtjbbncj b„nmtj bbncjmoj moj au`g au`gnmj nmj ¼

F.T. Uhmojbjt (7194), jxtrgnt ku prj`njr (8) Ohurs k„Guth`gtnquj (k„gprás ‑Îbî`jmts k„Guth`gtnquj„, Dgurrj, Yhinm, Kumhk)

;9

 

 G  Gm m m jx jxj j6

;?

 

Bj rîcubgtjur å ihubjs kj Sgtt soaî`gtnsî on-gprás jst b„um kjs `ubtnpbjs `ubtnp bjs `îog `îogmns`js mns`js nnmcîmnju mcîmnjuxx kîvjbh kîvjbhppîs ppîs gu 71á` 71á`j j snáobj snáobj kurgmt bg rîvhbutnhm nmkustrnjbbj. trnmcbjrnj

Bjs ihubjs s„îogrtjmt hu sj rgpprhoajmt

phnmtjgu

Nb s„gcnt kj stginbnsjr bg vntjssj kj rhtgtnhm ku `htjur å vgpjur, jm rîcubgmt bg prjssnhm kj bg vgpjur kgms bg oaguknárj. _nmhm, oj prhojssus nmstgibj. O„jst khmo umjgmcbh-sgxhms gppbnogtnhm kuoh``j prnmonpj ohmtrj rîgotnhm, jtjst Sgtt jst prîsjmtî pgr bjs bj kj párj kjs guth`gtns`js. ;;