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0

Dtdi`tnjJdbtrdl XnzmVb`v 75.?5.7?05

V-0)@j mvrni tr`bshmr hdbjsnydbu0

K(s)s 0

dl`r`j vmrnlmb snstmi, `yrj z`i`b s`ys`l jdbtrdlf nlm jdbtrdl

menlimj nstmbimjtmenr.

n) Jdbtrdlf E(z) dli`j zmrm j`p`l mvrni jdbtrdl gldj eny`kr`ib kmrmjln mvrm gnrnilmrn nlm gnrlnjtm nznbnz.nn) E(z)90 dli`j zmrm, `yrj-z`i`b j`p`l mvrni tr`bshmr hdbjsnydbubu mlem menbnz. (rbmjlmim z`i`b U9?.0s)

V-7) ^`be` vmrnlmb sv smvnym snstminbn t`bil`y`blnbmmr dli`y`b enhmr`bsnyml embjlmi

0 k 7

eC(t)j X j 7kC(t)

et

dl`r`j vmrnlimjtmenr.

`)? k ?vm X (tC(t) C ) X

`li` bdjt`l`r nnb snstmin lnbmmrlmtnrnbnz vm eurui embjlminbn vmjtr i`trns hdriu

* *k

C(t)@ C(t) G X (t)

t

y`zbz vm tr`bshmr hdbjsnydbubu mlem menbnz.

g) Jdbtrdlf Kf(s) dli`j zmrm j`p`l mvrni gldj eny`kr`ib nznbnz.

V-6) Xmrnlmb mjnlem r(t) 9 7u(t), J9?.=, L90C vm WL90dli`j zmrm, llmb `ji U9?.0s rbmjlmim z`i`b nlmrbmjlmbimjtmenr.

`) Kmrmjln embjlmilmrn t-edimbnbem y`zbz.g) N(z) vm n(j) y mlem menbnz.

f) j90? nnb n(0?) `ji emmrnbn cms`p menbnz.

V-5) ^`be` vmrnlmb snstmi nnb

`) 70.=z ?.6=

K (z)z ?.=

,

f

8.?8z =.6K (z)

z 0

hK (z) 0 vm s

?.?5K (z)

z ?.>=

dl`r`j vmrnlimjtmenr.F(z) 9 4 nh`emsnbn s 7 h fK (z), K (z), K (z) vm K (z) g`l dl`r`j mlem menbnz.

g) W z ? vm gdzufu knrn z

E z

z 0

dli`j zmrm EF ( ) F( ) 4 emmrnbn cms`pl`ybz.

f)

---------------------------------------------------------------------------------------------------------------------------------0

0

00

0( ) ( ) ( )

( 0)! n

ibi j

ni z zn

ex j z z S z z

i ez

0

00

0( ) ( ) ( )

( 0)!n

ibi

ni sUn s s

e zS z s s S s

i es z m

? ?

* 0

,( )

C X

h@

C t

,

? ?

* 0

,( )

k C X

hG

X t

z 0

F( ) lni(z 0)F(z)

Pn

C

XkJn

pdip`

qd

Vrm0??ej, G``rl`r

_rdh.Er.@yc`bQEMIW

^re.Ed.Er.rh`b^@QNFN

7/26/2019 Otomatik Kontrol Sistemleri - Sakarya niversitesi 2014 Vize Sorular

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7

Fmv`p01`)

g)F(z) E(z)K(z)

U(z)W(z) 0 E(z)K(z)

sU0 m

K(z) Q K(s) Qs(s 0)

zebiuykul`br.

sU

sU0 mK(z) Q K(s) Q 0 m s

s(s 0)

0

ssU

s ?

z(s 0)

z m(s 0)

0

s (s 0)

sU

s 0

z

z m

z 0 z z z 0 z0

z z 0 z ?.>?53 z ?.>?53

?.>?53 z 0

z ?.>?53

?.?>=7K(z)

z ?.>?53

vm E(z) 0 vmrnlintnr.U(z) nh`emsnbemymrlmrnbm jdyulur.

?.?>=7

z ?.>?53U(z)

?.?>=70z ?.>?53

ezmblmbnrnsm

?.?>=7

z ?.>?53U(z)

?.?>=70z ?.>?53

?.?>=7U(z)

z ?.3?>8

dl`r`jmlemmenlnr.

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6

Fmv`p71 Vvsmvnymjdbtdlsnstminbnt`bil`y`bLnbmmrdli`y`benhmr`bsnymlembjlmi

0 0 k 7

eC(t)h j X j 7kC(t)

et dl`r`jvmrnlintnr. Euruiembjlminbn

* *

k

C(t)@ C(t) G X (t)

t

vmjtri`trnshdriube`y`z`gnlimjnnb *@ vm *G i`trnslmrnbnbmlemmenlimsnkmrmjnr.

? ?

* 0

,( )

C X

h@

C t

,

? ?

* 0

,( )k C X

hG

X t

dleuukzbbm`lbrnsm,

? ?

00 77

7

, ?

77 ( )

( ) 7 7C X

h j kkj kC t

C t kC

nsm

? ?

* 00

,

( )k

C X

hG j

X t

* 7

?7

j k@

kC vm * 0G j mlemmenlnr.

* *k

C(t)@ C(t) G X (t)

t

nsmL`pl`fmebi`lbr,

* *ks C(s) @ C(s) G X (s) tr`bshmrhdbjsnydbu

*? 00

*7k ? 7

?

7kC j jC(s) Gj kX (s) s @ 7kC j ks7kC

dl`r`jmlemmenlnr.

(s)E jdbtrdlrdli`jzmrmsrmjlnz`i`b j`p`lmvrnijdbtrdlgldjeny`kr`ibnznbnz.

(s)K(s)X *

*@

G

s

(s)Cf

k

Vrmjlnz`i`bj`p`lmvrnijdbtrdlgldjeny`kr`ib

(s)K(s)X (s)C

f

k ? 0

? 7

7kC j

7kC j k

7/26/2019 Otomatik Kontrol Sistemleri - Sakarya niversitesi 2014 Vize Sorular

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5

Fmv`p61

tedimbnembjlmilmr Vedimbnembjlmilmr

0 drt] (t) J r(t) drt] (s) J W(s)

7 drt en(t)] (t) W n(t) L et drt] (s) W N(s) sLN(s) nsm

drt] (s)N(s)sL W

mlemmenlnr. drt] (s)

mntlnn N(s) nh`emsnbemymrnbmjdyulurnsm,J

N(s) W(s)sL W

dl`r`jmlemmenlnr.

r(t) 7u(t) nsm7

W(s)s

enr.J 7

N(s)sL W s

dlur. _`r`imtrmemmrlmrnymrlmnbmy`zlrnsm,

0N(s)

s(s 0)

dlur.Emvrmjbe`rbmjlmbin `jisdruleuube`b

*

* 0N(s)s(s 0)

y`bn

0N(z) Q z ebi uykul`br.

s(s 0)

0N(z) Q s

s(s 0)

0

s sU s ?

z(s 0)

z m(s 0)

0

s (s 0) sU s 0

z

z m

0

z zN(z)

z 0 z m

nsm

z zN(z)

z 0 z ?.>?53

dl`r`jmlemmenlnr.

n(j) nsm N(z) nh`emsnbnbtmrsQebinlmmlemmenlnr.

0n(j) Q N(z) (z 0) z

z 0j 0z

z 0

( z ?.>?53)

z

z ?.>?53j 0z

z ?.>?53

j jn(j) 0 ?.>?53 dl`r`jmlemmenlnr.

j 0? nnb 0? 0?N(0?) 0 ?.>?53 ?.8670 @ipmr dl`r`jcms`pmenlnr.

7/26/2019 Otomatik Kontrol Sistemleri - Sakarya niversitesi 2014 Vize Sorular

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=

Gnlkn`i`lkmbnlmtnlin sdruzi1

BDU1@ybsdrunnbsrmjlnz`i`bnnbziy`plr`jedrul`i`s``e`vmrnlintnr.

0N(s)

s(s 0)

nsm 0

0n(t) L s

s(s 0)

0

sst

s ?

m (s 0)(s 0)

0

s (s 0)st

s 0

m

tn(t) 0 m

srmjlnz`i`be``jinh`emsnmlemmenlnr.

j90?nnb t jU 0?*?.0 0sb dlur.Embjlmiemymrnbmjdyulurnsm, 0n(0) 0 m ?.8670@ipmr dl`r`jcms`p

menlnr.

?.8670

n(t) vmn(j) `ybkr`hnjmjr`bbe`nznin.

mjnlemsrmjlnz`i`b`ji n(t)vm U9?.0sbnlm

rbmjlmbin `ji*n(t) enr.N(j)mlemmenlintn.

@`

e`n(t)mlemmenlmfmjvmkr`hnjnznilmrnvmrnlmfmjtnr.

7/26/2019 Otomatik Kontrol Sistemleri - Sakarya niversitesi 2014 Vize Sorular

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8

Gnlkn`i`l jnbfn^dl1 z`i`bedimbnbemhdbjsnydbgnlnbnydrnsm Qebi , t jU y`zlrvm

7 0 7

0

0

, 00

b b bb

j b

q qq q

q

,mntlnnkzbbm`lb`r`j,U9?.0sbnnb,tmjt`r`hlzebi

?

( ) ( )j

j

j

H z h jU z

y`plr.

( ) 0 ( )t tN z Q m Q u t Q m

0 7 7 6 6 0 ?.0?

00

0 ?.>?53

jt jU j U U U

Uj

z zQ m m z m z m z m z

m z z m z

0 7?

( ) 00

jj

j

zQ u t z z z

z

( )0 ?.>?53

z zN z

z z

7/26/2019 Otomatik Kontrol Sistemleri - Sakarya niversitesi 2014 Vize Sorular

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;

Fmv`p51`)

mjnlemvmrnlmbsnstmimitdpl`is`lljzmllnnuykul`br.

n) Knrn ( ) ?zW , ( ) ?E z euruiunnbj ( ) ( )Wz zF F

nn)Knrn ( ) ?zE , ( ) ?zW euruiunnb j ( ) ( )Ez zF F

Cmrnjnknrn ( ) ?zW vm ( ) ?zB nnb j nh`emsn,cmrgnrknrn nnbmlemmenlmbjl`rbtdpl`i,

( ) ( ) ( )W Ez z zF F F nlmmlemmenlnr.

n) Knrn ( ) ?zW , ( ) ?zE nnb, j`p`lmvrnijdbtrdlgldjeny`kr`i,

fK(z)

sK(z)

W(z)

K(z)

W

F(z)

h

dl`r`jezmblmbmgnlnr.

( )( ) ( )

( )0 ( ) ( ) ( )

f sW

f s h

zK z K z

F W zK z K z K z

nn) Knrn ( ) ?zW , ( ) ?zE nnb, j`p`lmvrnijdbtrdlgldjeny`kr`i,

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3

fK(z)

sK(z)E(z)

K(z)h

7K(z)

WF(z)

7( )( ) ( )

( )0 ( ) ( ) ( )

sE

f s h

zK z K z

F E zK z K z K z

Cmrnjnknrn ( ) ?zW vm ( ) ?zB nnb j nh`emsn,cmrgnrknrn nnbmlemmenlmbjl`rbtdpl`i,

( ) ( ) ( )W Ez z zF F F

7( )( ) ( ) ( ) ( )

( ) ( )0 ( ) ( ) ( ) 0 ( ) ( ) ( )

f s s

f s h f s h

zK z K z K z K z

F W z E zK z K z K z K z K z K z

dl`r`j mlemmenlnr.

g)

z

E zz 0

vm 7( )( ) ( )

( )0 ( ) ( ) ( )

sE

f s h

zK z K z

F E zK z K z K z

dleuub`krm,

7 sE

z 0f s h

K (z) K (z)F ( ) F( ) lni(z 0) E(z)

0 K (z)K (z)K (z)

Ez 0

F ( ) F( ) lni (z 0)

0.=z ?.6= ?.?5

zz ?.= z ?.>=8.?8z =.6 ?.?5 z 0

0z 0 z ?.>=

E

z 0

0.=z ?.6= ?.?5 (z 0)(z ?.>=)F ( ) F( ) z ?.= z ?.>= (z 0)(z ?.>=) (8.?8z =.6)?.?5

p`y jsibe` (z 0) `rp`bbe`

z 0 vmrnlnrnsm?

s`y dluury`bn,

EF ( ) F( ) ? dlur.

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>

^DW]I1 lmrn ydle`jn fK (z) jdbtrdlfs ( )E z gdzufu knrn mtjnsnbm j`rlj kmlmb snstmi fmv`p EF ( ) jb

shrl`r,ydjmemr. Vnstmij fmv`gbe`s`emfm ( )W z knrn nnb ( )WF j`lr.

( )

0

W zW z

z

dli`snstmbsnb.

( )( ) ( )

( )0 ( ) ( ) ( )

f sW

f s h

zK z K z

F W zK z K z K z

f sW

z 0f s h

K (z)K (z)F ( ) F( ) lni(z 0) W(z)

0 K (z)K (z)K (z)

Wz 0

8.?8z =.6 ?.?5

W zz 0 z ?.>=F ( ) F( ) lni(z 0)

8.?8z =.6 ?.?5 z 00z 0 z ?.>=

WF ( ) F( ) (z 0) 8.?8z =.6

z 0

?.?5

z ?.>=

(z 0) (z ?.>=)

?

W z

(z 0)(z ?.>=) (8.?8z =.6)?.?5 z 0

z 0

W

(8.?8z =.6)?.?5F ( ) F( )

W z

( 8.?8z =.6)?.?5z 0

nh`emsnbem z 0 vmrnlnrnsm, WF ( ) F( ) W dl`r`jmlemmenlnr.

VDB]1( ) ( ) ( )

?W E

F F F

W

( )F W nlmrnydle`jnjdbtrdlf kmnfnrmanisdbube j fmv`gbe`jngdzufumtjnsnbnknemrnrvmjb

nstmbmbrmhmr`bsemmrWymkmlimsnbns`l`r.