Relatório_Exp2_Funções Básicas de Tempo Discreto_Processadores Digitais Em Controle e Automação_Quad5.2

7/21/2019 Relatrio_Exp2_Funes Bsicas de Tempo Discreto_Processadores Digitais Em Controle e Automao_Quad5.2

1/11

_MGQOPSGDHDO AODOPHE DB H@C

AOPMHMDB FOMPGX_O LBIOS [_CHTOEEG

AOPMHMDH SGEQH L_G[G

Zrbcosshdbros Dglgthgs oi Cbmtrbeo o Hutbihchb;

Eh`brhtbrgb 0; Aumcbos @hsgchs do Toipb Dgscrotb

SHMTB HMDPO

81 DO B_T_@PB DO 0:84


2/11

8

8 Gmtrbduchb

Bs b`kotgvbs dosto trh`hefb shb b`tor bs lrhcbs dhs aumcbos `hsgchs mb trhthdb do

sgmhgs cbib b gipuesb o b dolrhu umgthrgbs o sous dosebchiomtbs> vorgchr hs chushs do

sgmhgs dgscrotbs porgbdgcbs o hporgbdgcbs> omtomdor cbib h aumchb do cbrroehchb porigto

cbiphrhr sgmhgs gmceusgvo dghmto dh prosomch do rudb ibdoehdb cbib db tgpb `rhmcb

lhussghmb.

Hs oquhcbos utgegzhdhs shb; b gipuesb umgthrgb dgscrotb oi (8)> b dolrhu umgthrgb

dgscrotb (0)> h aumchb do cbrroehchb cruzhdh (3) mh quhe v o b cbipeoxb cbmkulhdb do v

o oeh so tbrmh h aumchb do hutbcbrroehchb quhmdb u9 v > (4) o h aumchb do prb`h`gegdhdo

`hsohdh mh dgstrg`ugchb lhussghmh> (?) o h Trhmsabrihdh do Aburgor do Toipb Dgscrotb

(DTAT; Dgscroto Tgio Aburgor Trhmsabri)> o (1) shb roehcbos dhs aumcbos trglbmbiotrgchs

cbi h oxpbmomcghe cbipeoxh.

^m m:Y 9

8, m9 m:

:, m9m:(8)

u ^m m:Y 9

8, m m:

:, c.c.(0)

Puv() 9

u(t+)v()d > Puu() 9Pu() 9

u(t+)u()d (3)

Z() 9 8

00

o(x)0

00 dx (4)

DTA T{x ^mY}9 V() 9

m9

x ^mY okm (?)

0cbs() 9ok +ok > 0ksgm () 9ok ok (1)

Cgtoibs hgmdh heluihs prbprgodhdos dh aumchb do hutbcbrroehchb.

8. Pu() 9Pu() ; h aumchb do hutbcbrroehchb o phr.

0. Pu(:) 90u ; h aumchb do hutbcbrroehchb phrh 9 : oqugvheo h vhrghmcgh do u.

3.|Pu()| Pu(:) ; b ihxgib dh aumchb do hutbcbrroehchb bcbrro phrh 9 :.

0 Posuethdbs dh Sgiuehchb

Zrgiogrhiomto abg gipeoiomthdb b dosebchiomtb toipbrhe oi duhs umgdhdos h dgrogth

dhs aumcbos gipuesb o dolrhu umgthrgb dgscrotgzhdh. Oi solugdh b prbcodgiomtb abg ropo-

tgdb phrh b dosebchiomtb dhs iosihs aumcbos oi tros umgdhdos jh osquordh.


3/11

0

Mh Aglurh 8 toibs b gipuesb umgthrgb oi zorb o cbi dosebchiomtbs jh dgrogth o jh

osquordh, hi`hs crghdhs cbi b helbrgtib dh sochb4.8.

(h) Sgmhgs `hso o cbi dosebchiomtb jh dgrogth (`) Sgmhgs dosebchdbs jh osquordh

Aglurh 8; Sgmhgs dosebchdbs `hsohdbs (8) o (0)

Mh solumdh phrto, abg rohegzhdh h hmhegso dh porgbdgcgdhdo do aumcbos sombgdhgs dgscro-

tgzhdhs. H Aglurh0hprosomth sgmhgs porgbdgcbs o hporgbdgcbs crghdbs h phrtgr db helbrgtib

dh sochb4.0.

B`sorvh-so quo phrh prgiogrh aumchb sombgdhe h aroquomcgh a mhb o iuetgpeh rhcgbmhe

do n, ? 9 9 0aa9 ?0 / X. Zbr gssb osth aumchb so chrhctorgzh cbib hporgbdgch.Kh phrh h solumdh aumchb cbssombgdhe,h aroquomcgha o iuetgpeh rhcgbmhe don, ?0

1 9 9

0a a9 ?1 X. Zbrthmtb oeh sorh porgbdgch. Shegomtoibs quo b ahtb dh porgbdgcgdhdo

osthr eglhdh cbi a X dovo-so hb ahtb do osthribs trh`hefhmdb cbi sgstoih do toipbdgscrotb, mb toipb cbmtmub osso aombiomb mhb bcbrro.

Agmheiomto toi-so h hibstrhloi do ui sgmhe porgbdgcb mb dbimgb db toipb cbmtmub

h quhe rosueth oi ui sgmhe dgscrotgzhdb hporgbdgcb. Osth chrhctorstgch dovo-so hb ahtb

vhebrT 9 80

dh hibstrhloi mhb sor iuetgpeb rhcgbmhe dh aroquomcgh db sgmhe cbmtmub.

Aglurh 0; Sombgdos porgbdgchs, hporgbdgchs o porgbdgch cbi hibstrhloi hporgbdgch


4/11

3

Hs Aglurhs do3h ? abrhi crghdhs h phrtgr db helbrgtib dh sochb4.3. Mosto helbrgtib

abrhi hmhegshdbs bs cbihmdbs do t, rhmdm o xcbrr.

Hmhegshmdb b cbdglb phrhzmh sochb4.3 voibs quo z o h sbih do y cbi poquomhs vh-

rghcbos heohtbrghs dombthdhs pbrmlorhdb cbi usb dh aumchb heohtbrghrhmd(), osth aumchbo ui lorhdbr do muiorb psoudb-heohtbrgb mbrihgs (soluo h lhussghmh (4)).B cbihmdba a t

dombth h Trhmsabrihdh do Aburgor do toipb Dgscrotb.

Zhrh h Aglurh4h dgaoromch omtro b sgmhe y o z9y+m bmdo m abg b`tgdb cbi usb dh

aumchbrhmd() db Ihteh` c quo lorh vhebros psoudbheohtbrgbs cbi dgstrg`ugchb lhussghmho hpomhs h phrto heohtbrgh sbihdh, tbdhvgh hb cbiphrhibs h Aglurh4(h) cbi h Aglurh

?(h) mbthibs quo h trhmsabrihdh do Aburgor do hi`hs shb gdomtgchs, gssb ibstrh b ahtb

do quo h sbih cbi ui sgmhe heohtbrgb mhb hetorh h aumchb do hutbcbrroehchb.

Mh Aglurh?mbthibs quo aumcbos mhb cbrroehths mhb lorhi sgmhgs phros (cbmsgdoro hpbssg`gegdhdo do dosebchr b zorb db ogxb dhs h`scgsshs phrh b chsb mh Aglurh?(h)).

Zbr mbthchb h aumchb do cbrroehchb cruzhdh mb Ihteh` c o xcbrr(h, `), chsb h9`, o haumchb do hutbcbrroehchb so h9 ` dombthdb pbr xcbrr(h) 9xcbrr(h, h).

(h) (t(y)-iodgh(y)) (`) (t(z)-iodgh(z))

Aglurh 3; Cbiphrhchb omtro y o zquo cbmtoi vhrghvoe heohtbrgh lhussghmhmsbihdh h y

(h) Cbrroehchb omtro y o z (`) Cbrroehchb omtro xo z

Aglurh 4; Dgaoromch omtro sgmhgs cbrroehtbs o mhb-cbrroehtbs


5/11

4

(h) Hutbcbrroehchb do y (`) Hutbcbrroehchb|t(y - iodgh(y))|

Aglurh ?; Hutbcbrroehchb do y o do suh trhmsabrihdh su`trhdh dh iodgh

H Aglurh1ibstrh h bmdh rothmluehr do -0 h 0 o duhs abrihs do checuehr suh trhmsabr-

ihdh do Aburgor. Oeh abg b`tgdh cbi b helbrgtib doscrgtb mh sochb4.4.

Aglurh 1; Oxoipeb do checueb dh trhmsabrihdh do Aburgor phrh sgmhe dgscrotb oxocuthdb

do 0 abrihs dgaoromtos.

Qorgch-so quo hi`bs bs lrhcbs dh DAT db puesb rothmluehr dgscrotgzhdb roprosomthdbs

poeh lurh1 shb prhtgchiomto soioefhmto. Hs aumcbos do DAT (sbih do cbssombs o sgmc)

so chrhctorgzhi-so cbib phros o sgiotrgchs dovgdb hb puesb rothmluehr thi`oi sor uih

aumchb phr. Hs cbipbmomtos do aroquomcgh hprosomthi ui ihxgib porgbdgcb o b ospoctrb

db puesb rothmluehr so ostomdo hto gmmgtb (ehrlurh do `hmdh gmmgth).

H aumchb cbi cbssombs abg checuehdh cbmabrio gmdgchdb oi (


6/11

?

3 Cbmceushb

Htrhvos dosth htgvgdhdo abg pbssvoe b`sorvhr bs oaogtbs dh aroquomcgh do hibstrhloi

sb`ro h porgbdgcgdhdo do uih aumchb dgscrotgzhdh,cbmsththmdb quo osth prgiogrh dovo sorrhcgbmhe phrh quo fhkh ui sgmhe porgbdgcb dgscrotb.

H aumchb do cbrroehchb o h aumchb gdohe phrh so cbiphrhr b sgmhe rohe cbi rudb cbi

ui sgmhe gdohegzhdb pbgs b rudb oxgstomto mh aumchb rohe pbdomdb sor ibdoehdb cbib

`rhmcb lhussghmb mhb haoth b rosuethdb dh cbrroehchb cbi b sgmhe gdohegzhdb do roaoromcgh

o b rosuethdb sorh h hutbcbrroehchb db sgmhe do roaoromcgh.

Zbr i h utgegzhchb dh DTAT so ibstrbu uih aorrhiomth utge phrh h vgsuhegzhchb dh

h`rhmlomcgh oi aroquomcgh o ihlmgtudo ospoctrhe do sgmhgs.


7/11

1

4 Hmoxbs

4.8 Zrblrhih 8

n 9 -?;8:>

doeth 9 ( n =9 :) - (n =9 8)>

%999

agluro(8)

su`pebt(008)

stoi(n,doeth, ageeod)>xehòe(n)> yehòe(Udoeth(n))>

tgteo(Gipuesb _mgthrgb Dgscrotb)>

sfgatodRdoeth 9 ( n =9 0) - (n =9 3)>

su`pebt(000)>

stoi(n,sfgatodRdoeth,ageeod)>

xehòe(n)> yehòe(Udoeth^n-0Y)>

tgteo(Gipuesb Dosebchdb Dgscrotb)>

u 9 (n =9 :)> % Doagmgmdb o pebthmdb u^nY

su`pebt(003)>

stoi(n,u,ageeod)>

xehòe(n)> yehòe(u^nY)>

tgteo(Dolrhu Dgscrotb)>

sfgatodRu 9 (n =9 0)> % Doagmgmdb o pebthmdb u^n-0Y

su`pebt(004)>

stoi(n,sfgatodRu,ageeod)>

xehòe(n)> yehòe(u^n-0Y)>

tgteo(Dolrhu Dosebchdb Dgscrotb)>

agl 9 8>

aglmhio 9 âglR,mui0str(agl),.kplY>

shvohs(lca,aglmhio)>

%999

agluro(0)


8/11

su`pebt(088)>vgzuhegzhc~hb

stoi(n,sfgatodRdoeth,ageeod)>

xehòe(n)> yehòe(Udoeth^n+3Y)>

tgteo(Gipuesb Dosebchdb Dgscrotb)>

sfgatodRu 9 (n =9 -3)> % Doagmgmdb o pebthmdb u^n-0Y

su`pebt(080)>

stoi(n,sfgatodRu,ageeod)>

xehòe(n)> yehòe(u^n+3Y)>

tgteo(Dolrhu Dosebchdb Dgscrotb)>

agl 9 0>



%999

4.0 Zrblrhih 0

n 9 :;0:>x 9 sgm(?*n + :.8)>

%999

agluro(3)

su`pebt(008)>

stoi(n,x,ageeod)> lrgd>

xehòe(n)> yehòe(x^nY9sgm(?n+:.8))>

tgteo(Sgmhe m~hb Zorgbdgch Dgscroth mb Toipb)>

x 9 0*cbs(8:*pg*n/1 - :.00)>

su`pebt(000)>

stoi(n,x,ageeod)> lrgd>

xehòe(n)> yehòe(x^nY90cbs(8: Upg n/1-:.00))>

tgteo(Sgmhe Zorgbdgch Dgscroth mb Toipb)>

%999

t 9 :;:.:8;0:> % Qhebros cbmtumubs mb toipb

act 9 3*cbs(0*t+:.8?)> % Sgmhe cbmtgmub mb toipb

T 9 :.?> % Zorgbdb do hibstrhloi


9/11

6

n 9 :/T;0:/T> % Qhebros dgscrotbs mb toipb (t9nT)

adt 9 3*cbs(n+:.8?)> % Sgmhe dgscrotb mb toipb

%999

su`pebt(080)> % Zebthmdb bs dbgs sgmhgs oi ui ogxb cbmtgmub mb toipb

pebt(t,act)> % _tgegzhmdb t 9 nT phrh b sgmhe dgscrotb mb toipb

fbed bm>

stoi(n*T, adt, ageeod)>

fbed baa>

lrgd>

xeh`oe(t )> yeh`oe(a^nY,a(t))>

tgteo(Zorgbdgcb a(t)93cbs(0t+:.8?) Hibstrhdb cbi T9:.?s b`tomdb ui m~hb Zorgbdgcb aagl 9 3>



%999

4.3 Zrblrhih 3

agluro(4)pebt(xcbrr(h`s(aat(y-iohm(y)))))>lrgd>

tgteo(xcbrr(h`s(aat(y-iohm(y)))))>

agl 9 4>



agluro(?)

pebt(h`s(aat(y)-iohm(y)))> lrgd>

tgteo(| aat(y) - iohm(y)|)>

agl 9 ?>



%999

agluro(1)

pebt(h`s(aat(z)-iohm(z)))> lrgd>

tgteo(| aat(z) - iohm(z)|)>

agl 9 1>



10/11

7


agluro(

lrgd>

tgteo(xcbrr(y,z))>

agl 9



agluro(6)

pebt(xcbrr(x,z))> lrgd>tgteo(xcbrr(x,z))>

agl 9 6>



agluro(7)

pebt(xcbrr(y,y))> lrgd>

tgteo(xcbrr(y,y))>

agl 9 7>



agluro(8:)

pebt(xcbrr(h`s(aat(y-iohm(y)))))> lrgd>

tgteo(xcbrr(h`s(aat(y-iohm(y)))))>

agl 9 8:>



4.4 Zrblrhih 4

\ 9 -3*pg;:.:8;3*pg> % Doagmgmdb hs aroquomcghs DT

Ah 9 8 + 0*cbs(\) + 0*cbs(0*\)> % pebthmdb |A(\)| dbs cb-somb

agluro(88)

n 9 -?;?>

aRu 9 (n =9 -0) - (n =9 3)> % Doagmgmdb o pebthmdb u^nY


11/11

8:

su`pebt(388)>

stoi(n,aRu,ageeod)>

xehòe(n)> yehòe(aRu^nY)>

tgteo(Pot]hmlueb)>

su`pebt(380)>

pebt(\,h`s(Ah))>

xehòe(UBiolh )> yehòe(|A(UBiolh)|)>

tgteo(DTAT ba a^nY9u^n+0Y-u^n-3Y (dh sbih dbs cb-sombs))>

A` 9 sgm(0.?*\)./sgm(\/0)> % pebt |A(\)| sgmc-egno aumctgbm

su`pebt(383)>pebt(\,h`s(A`))>

xehòe(UBiolh )> yehòe(|A(UBiolh)|)>

tgteo(DTAT ba a^nY9u^n+0Y-u^n-3Y (dh aumc~hb sgmc))>

agl 9 88>



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Relatório_Exp2_Funções Básicas de Tempo Discreto_Processadores Digitais Em Controle e Automação_Quad5.2