Otomatik Kontrol - Sakarya Üniversitesi Finaller
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Transcript of Otomatik Kontrol - Sakarya Üniversitesi Finaller
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FśfěĶgf guruo glěhśjlmblrh àĶjfrtĶboĶśtĶr.
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Xòzlyl sfehtblmohś O jòtblbh àlbhj tkp , yfy vl sþmòoblmghrhchglm kbuśfmglm`lgljh shstlo, lbljtrkoĶjmftĶs yfrgĶoĶ hbl òrlthblm N(t) juvvlth yfrgĶoĶ
hbl hstlmlm jkmuogf tutubofj hstlmoljtlghr. U,B lbljtrkoĶjmftĶs ghrlmch vllmgòjtfmsĶ, J juvvltblmghrhch jfzfmcĶ,j yfy sfehth, E vhsjkz sþmgòròcò
jftsfyĶsĶ kbofj òzlrl,
kbfrfj vlrhboljtlghr.
f) Shstlol fht t-gkolmh ghmfohj glmjbloblrh
()
() nkroumgf yfzĶmĶz.
e) Shstloh àfbĶśof mkjtfsĶ ltrfnĶmgf gkěrusfbbfśtĶrĶmĶz.
nkroumgf yfzĶmĶz.
c) FyrĶj -zfofm jfpfbĶ àlvrho jkmtrkb ebkj ghyf`rfoĶmĶ àhzhmhz.
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4 46 x t x set
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SĶrfsĶybf F* vl E* blmllr oftrhsblrh eubumfcfjtĶr.
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8/10/2019 Otomatik Kontrol - Sakarya Üniversitesi Finaller
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lěrhsh vlrhbohśthr.
f) FàĶj-àlvrho trfmsnlr nkmjshykmu, yfzĶmĶz.
e) , ‘h eubumuz.
c) hàhm ‘l fht ylr lěrhshmh àhzhmhz.
8/10/2019 Otomatik Kontrol - Sakarya Üniversitesi Finaller
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Iury jfrfrbĶbĶj yþmtloh jubbfmĶbfrfj jfrfrbĶbĶj hmclblmlcljthr.
6- @lrlj Jkśub
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6 4 N
ŝljhbgl vlrhblm fyrĶj -zfofm shstlohm ,
f- JfrfrbĶbĶěĶmĶ hmclblyhmhz.
e- JfpfbĶ-àlvrho jutupbfrĶmĶm kbfehbolsh hàhm
alsfp lghmhz.c-
Sòrljbh afb
aftfsĶ, lbgl lghmhz. lghmhz.
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f f śfrtĶ
sfěbfmofsĶ `lrljhr.
6 4.1610 4.83<< p J
4.6831 p J
4 4.6831 p
J Jp frfbĶěĶmgf shstlo jfrfrbĶgĶr.
NfrjbĶ Jp glělrblrh hàhm þrmljblol plrykgu Ws?4.446sm vl shstlo `hrhśh ehrho efsfofj kbofj
òzlrl shstlo àĶjĶśĶ C(z) fśfěĶgf àhzghrhbohśthr .
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^lrhblm jkmtrkb juteumf fht fśĶoĶ alsfpbfyfbĶo
6 4.8443 4.4843 4.8471 4.6rfg z i
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8/10/2019 Otomatik Kontrol - Sakarya Üniversitesi Finaller
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juteumf fht fśĶo glělrh (kbofsĶ `lrljlm) ehrehrhml lśht kbuśumgfm Jp glělrhmhm gkěru
alsfpbfmgĶěĶmĶ `þstlrhr.
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Efsfofj clvfeĶ vlrhblm HH. Glrlcl shstlo hàhm
f- trfmsnlr nkmjshykmumu eubumuz.
e- plrhykgumgf 64 fglt þrmlj fbfcfj
śljhbgl fyrĶj zfofm jutupbfrĶ eubumuz.
c- jrhtlrhml `þrl ylrblśol zfofmĶmĶ
eubumuz.
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þrmljblol plrykgu eubumofsĶ `lrljhr.
JfpfbĶ àlvrho þrmljblol plrykgu vlrhblm ehb`hblr jubbfmĶbfrfj fśfěĶgfjh `heh eubumur.
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Ktkofthj Jkmtrkb Nhmfb SĶmfvĶ 61/OfyĶs/5466
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o(t)h(t)
pfràf
frj\krt(t)
FjĶo jkmtrkbò sfyĶsfb hśbloch hbl yfpĶbfcfjtĶr.
f) Shstlol fht ghmfohj glmjbloblrh yfzĶmĶz. Jkmtrkb jurfbĶ TH kbofj òzlrl FyrĶj-zfofm Jkmtrkb
ebkj ghyf`rfoĶmĶ àhzhmhz.
e) Ehrho efsfofj `hrhś hàhm, 4.06<> vl %5 jrhtlrhml `þrl33.6*64
st sm kbofsĶ
hstlmoljtlghr. p h J vl J alsfpbfyĶmĶz, W?74us, B?6os, J?6. ( )
6 TH p h
z @ z J J
z
c) FyrĶj-zfofm TH jkmtrkbcòyò gkěrugfm prk`rfobfof yþmtloh hbl prk`rfobfyĶmĶz.
S-3
6 Ts
( 6)
J
s s
U(s) C(s)L(s)
ŝljhbgl vlrhblm shstlogl, f) Ehrho efsfofj clvfptfm yfrfrbfmfrfj J vl T yh alsfpbfyĶmĶz.
e) L(s) hnfglshmh lbgl lghmhz. Ehrho Ufopf `hrhś hàhm aĶz aftfsĶ 6 ssl kbofsĶ hàhm afm`h jftsfyĶ
fyfrbfmofbĶgĶr, glělrhmh alsfp lghmhz,(ghělr jftsfyĶ f) eubumfm glělrh kbfcfj).
S-7
5,7
4,<
sl
s
X(s)( ) ( )r t t
W?5 sm
t
r(t)
c) 4 J hàhm jfrfjtlrhsthj
glmjblo jþjblrhmhm glěhśhohmh
àhzhmhz. (h-Jkopbljs jutuptfm àĶjĶś
fàĶsĶ, hh-Ehrho gfhrlyh jlsol mkjtfsĶ, hhh-
Jkpof mkjtfsĶ)
g) ( )c z clvfeĶ jrhthj sþmòobò
kbfehbolsh hàhm ; J
ŝljhbgl ehr oltfb pfràf jfymfj
yfpĶbofjtfgĶr. FjĶo, àlvhrol krfmĶ
696 kbfm ehr fjĶo trfnksu hbl
þbàòboljtlghr. Frj `lrhbhohmhm fjĶof
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hv) sĶmĶr jfzfmà vl hofihmlr ljslmh jlsol mkjtfsĶ alsfeĶ: h) jfrfrbĶbĶj fmfbhzhmglm
Jfrfjtlrhsthj glmjblo9
5 5
5
N(s) s 5s Js 5Js 5J 4
N(s) s (J 6) 5s(6 J) 5J 4
5
6s
4
sJ 6 5J
5(6 J) 4
5J s
h) J+6=4 J=-6
hh)
5(6-J)=4 J26
hhh) 5J=4 J=4
4 J 6 Js?6 SĶmĶr Jfzfmà
** Hofihmlr ljslmh jlsol mkjtfsĶ9
5s s
56,5
(J 6)s 5J 4
5s 5 4 s i
lbgl lghbhr.
HH. jfrfjtlrhsthj glmjblogl s?iw
5N(iw) (iw) (J 6) 5(iw)(6 J) 5J 4 hsl,
5w (J 6) 5 iw(6 J) 5J 4 kbofsĶ hàhm rllb vl hofihmlr jĶsĶobfr fyrĶ fyrĶ sĶnĶrf lśht kbofbĶgĶr.
s
5 5 5
5w(6 J) 4 6 J 4 hsl J J 6
w (J 6) 5J 4 w (6 6) 5*6 4 hsl w 6 w i Kbfrfj lbgl lghbhr.
e) J?4.1 hàhm aĶz aftfsĶ lss?;
4bho .
v s
j s
5( 5 5) J s s
s
( 5)
6 6 66, 5<
4,1
v
v
j J s
lssj J
S-59
6U(s)
s J
s 65 sl
C(s)
W?6
+
-
śljhbgl vlrhblm shstlo hàhm:
f) 6U(s)s
hàhm C(z)?;
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e) C(j)‘yĶ lbgl lghmhz.
c) Shstlohm jfrfrbĶbĶj fmfbhzhmh Iury tlsth yfrgĶoĶ hbl yfpĶmĶz.
C-59
f)
Wg?jW5
5
6
6( ) ( 6)
6 ( 6)
s
sW
s
l z @ z Y z s
s s z l
5( ) , ( )( 4,3>08) 6W
z J z @ z z U z
z z z z l
( )( ) ( )
6 ( )
@ z C z U z
@ z
5
( 4,3>08)( )
6 ( 4,3>08 )( 6)6
( 4,3>08)
J z Jz z z
C z J z z z J z
z z
e) f) śĶjjĶmĶ yfpfmf e) śĶjjĶmgf tfo pufm vlrhblcljthr.
5 ( )( )( 6)( 4,3>08 )( 6)
Jz Jz
z f z e z z z J z
6( ) ( ) ( 6)c jW Y C z z
( )( ) ( 6)
Jz
z f z e z
6
6
( )j
z
z z f
( )
Jz
z f
6
( )( 6)
( )
j
z f
z
z e z
z e
( ) ( )
Jz
z f z e
6
( 6)
j
z e
z z
c) JfrfbĶbĶj fmfbhzh9
5
( ) 6 ( ) 4
6 4 4,3>08 4( 4,3>08)
N z @ z
J z z J
z z
6) @lrlj jkśubbfr:
5
(6) 6 4,3>08 4 4
6 ( 6) 6 4,3>08 4 4
N J J
N J J
5) Xltlr jkśub:
4
6 6
mf f
J J
kbofbĶgĶr.
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S-39
( ) B
t
t
6
C(t)
6.47
4.81
6.45
ts?7 sm
lss?4
C-39
%5 jrhtlrhml `þrl ylrblśol zfofmĶ, 7 7 s
m
t
w 6
mw
5 56 67%
644f śĶo l l
5 5bm(4.47) bm( ) 3.5611
6 6l
55 5 5 5 5
5(3.5611) 64.3> 64.3>
6
5
5 5
64.3> 64.3>
64.3> 64.3>
6 66.3803
4.06<>m mw w
rfg/sm gkěfb fàĶsfb nrljfms lbgl lghbhr.
5 5
5 5 5 5
6.3803( )
5 5*4.06<>*6.3803 6.3803m
m m
wW s
s w s w s s
5
6.8<5>( )
5 6.8<5>W s
s s
lbgl lghbhr.
4.06<> lbgl lghbhr.
Þrmljblol zfofmĶ W?4.>73 sm kbofj òzlrl HH.
Glrlclglm fyrĶj -zfofm trfmsnlr nkmjshykmu:
5
fzW(z)
z ez c
hnfglshmgl f,e,c jftsfyĶbfrĶmĶ
ehrho efsfofj `hrhś clvfeĶ yujfrĶgf vlrhbghěh `heh
kbfcfj śljhbgl alsfpbfyĶmĶz.
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5
6,5 6m m
s w iw hnfglsh hbl jþjblr alsfp lghbhr.
5
6,5 4.06<>*6.3803 6.3803 6 4.06<> s i vlm
w pfrfoltrl glělrblrh ylrblrhml yfzĶbĶr.
6,5 6 4.80> s i sòrljbh- zfofm jfrfjtlrhsthj glmjblo jþjblrh.
6,5 6 4.80> s i vl 4.>730>W sm jubbfmĶbfrfj
6,5 s jfrśĶbĶj `lblm fyrĶj -zfofm jþjblr
6,5 z
alsfpbfmfcfjtĶr.
6 ( 6 4.80>)*4.>731 4.>731
6 (cks(4.>513) shm(4.>513)) 4.<33<(4.1484+ i4.<101) s W i z l l l i
6z ?4.736>+i 4.363> H. fyrĶj -zfofm jkopbljs jþj.
5 ( 6 4.80>)*4.>731 4.>731
5 (cks(4.>513) shm(4.>513)) 4.<33<(4.1484- i4.<101) s W i z l l l i
5z ?4.736>-i 4.363> HH. fyrĶj - zfofm jkopbljs lśblmhj jþj.
Lbgl lghblm6,5
z jþjblrh, ( )W z gl ylrblrhml jkyubur hgl,
6 5
( )( )( ) ( 4.736>-i 4.363>)( 4.736>+i 4.363>)
fz fz W z
z z z z z z
5
( )( )
( ) 4.1>35 4.51<3
C z fz W z
U z z z
lbgl lghbhr.
( )( )
( )
C z W z
U z ‑hm jfzfmcĶmĶm Ehrho kbfehbolsh hàhm skm glělr tlkrlohmglm ehrho efsfofj `hrhś
hàhm ‒ f ‟ alsfpbfmofbĶgĶr. ( )6
z U z
z
kbofj òzlrl,
5( )
6 4.1>35 4.51<3
z fz C z
z z z
kbur. Skm glělr tlkrlohmglm,
FyrĶj -zfofm HH. glrlclglm trfmsnlr nkmjshykm,6 5
( ) ( )( )
fz
W z z z z z ghr.
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6( ) bho ( 6)
z
C z z
6
z
z 5
*66
4.1>35 4.51<3
f
z z
6 4.75566 4.1>35 4.51<3
f
f
vl trfmsnlr nkmjshykmumgf ylrhml jkyubur.
f? 4.7556, e?-4.1>3, c?4.51<3 lbgl lghbhr.
S-79
n U
n B( )
n l t
n h
f U
( )f
l t
fh set
I
E yW
, w
hf?sfeht
Io,E
o
o
Wyòj?4
C-79
t-gkolmhmgl ghmfohj glmjbloblr yfzĶbĶr .
6-)( )
( ) ( ) n
n n n n
gh t ^ t U h t B
gt
( ) ( ) n n t j h t
5-) ( ) ( ) ( ) ( ) ( ) ( )l f f n f f n h n W t t j h t j j h t h t J h t
3-)( )
( ) ( )o y
gw t W t I Ew t W
gt Wy?4
7-) ( ) ( )l oW t W t ( sòrljbh rlihogl)
<-) og
wgt
FyrĶj -zfofm HH. glrlclglm trfmsnlr nkmjshykm,
5
( ) 4.7556( )
( ) 4.1>35 4.51<3
C z z W z
U z z z
kbfrfj lbgl lghbhr.
Fbfm jkmtrkbbò GC ofjhml hbl pkzhsykm jkmtrkbò yfpĶbofjtfgĶr.
f) o (s) àĶjĶś vl n ^ (s) `hrhś kbofj òzlrl fbfm jkmtrkbbò GC ofjhmlyl fht
ghmfohj glmjblolblrhmh yfzĶmĶz vl jkmtrkb ebkj ghyf`rfoĶmĶ àhzhmhz. (Io9 ftfblt
okolmth, Eo9 vhsjkz sòrtòmolshghr.)
e) o (t) pkzhsykm jkmtrkbò hàhm:
h) sòrljbh zfofm
hh) fyrĶj zfofm sfyĶsfb
jfpfbĶ –àlvrho jkmtrkb ebkj ghyf`rfobfrĶmĶ fyrĶ fyrĶ àhzhmhz.
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s-gkolmhmgl ghmfohj glmjbloblrh yfzfbĶo.
6-)( )
( ) ( ) ( ) ( ) n
n n n n n n
n n
L s L s U H s sB H s H s
sB U
5-) ( ) ( )l h n W s J H s
3-)( )
( ) ( ) ( ) ( ) ( ) 4 ( ) oo y y
W sW s sI s E s W s W s s
sI E
7-) ( ) ( )l o
W s W s (sòrljbh rlihogl)
<-) 6
*o
s
6
n n sB U
6
sI E
( ) n ^ s ( )oW s
( )lW s
( ) s
Fbfm jkmtrkbbò GC ofjhmf jkmtrkb ebkj ghyf`rfoĶ
( ) n
H sh
J
( )X W s
Wy?4
6
s
o (s)
e)
h) Sòrljbh zfofm jfpfbĶ –àlvrho jkmtrkb ebkj ghyf`rfoĶ:
6
n n sB U
6
sI E
( ) n ^ s ( )oW s
( )lW s
( ) s( ) n H s
h J
( )X W s
Wy?4
6
s
o (s)
G(s)
þbàol
-
+Uln
Jkmtrkbþr
hh) FyrĶj -zfofm sfyĶsfb jfpfbĶ –àlvrho jkmtrkb ebkj ghyf`rfoĶ:
6
n n sB U6
sI E
( )oW s
( )lW s
( ) s( ) n H s
h J
( )X
W sWy?4
6
s
o (s)
G(z)
þbàol
-
+Uln
W W
Y.K.A
FGC GFC
SfyĶsfbĴśbloch
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Fbtlrmfthn ebkj ghyf`rfo9
6
n n sB U
6
sI E
( ) n
^ s( )
oW s
( )l
W s
( ) s( ) n
H s
h J
( )X
W sWy?4
6
s
o(s)
þbàol
-
+Uln
G(z)W
Y.K.A
W
FGC
GFCSfyĶsfbĴśbloch
@þrgòěòmòz aftfbfrĶ, ofhb ykbu hbl yfgf sþzbò kbfrfj hblthmhz…………….
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