O ’z b e k ist o n r e sp u b L ik a si o L iy va o ’r t a m a X su s t a ’lim V a z ir L ig I o ’zbek jsto n r e sp u b L ik a si

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Bog'liq
boshqarish tizimlarini kompyuterli
Elektr mash. fan.

A Y ( t ) = B V ( t ) bu y e rd a m a tritsa la r A = [Ah\ В = [в\„„

A v to m a t
boshqaruv
tiz im in i (A B T )
differensial
ten g la m a la r orq ali
ifo d a la sh
Q ulaylik nuqtai nazarid an t a ’sirlarni kirish y o 'li ta ’sirlarini yag o n a vektori
V
= f v ,.....
V',...,vt )
g a te g is h li deb h iso b lay m iz. C h iq ish y o 'li o 'z g a ru v c h ila rn in g
v e k to rin i
Y = (y,,...,yl,...,v ),
holat
o 'z g a ru v c h ila rin in g
v e k to rin i
X = (xl,...,xy,...,xn)
o rq a li b e lg ila y m iz .
«K irish y o 'li — chiqish y o 'li»
o 'z g aru v ch ilarig a nisbatan d iffe re n s ia l
te n g la m a la r n in g s ta n d a rt s h a k li q u y id a g ic h a :
Х
ў -
(2 .3 )
n=u
at
l=,
m~o
at
(2 .3 )n i d iffe re n s ia lla sh o p e ra to ri y o rd a m id a ifo d alay m iz:
ok(D )yk =YJbl(D)v,;
к = \,q
i=
I
bu y e rd a
at(D ) = Y jab,D": b,(D)
=
j^bimD"‘; к
=
\,q
n=l
m»l
Y u q o rid a g i ifo d a n i v e k to r - m a tr its a s h a k lid a y o z is h m u m k in :
A Y ( t ) = B V ( t )
bu y e rd a m a tritsa la r
A = [Ah\
В =
[в\„„

m o s h o ld a
(qxq), (qxs)
o 'lc h a m la r g a ega.
R eal A B T larn i
ifo d a la g a n d a o lin a d ig a n d iffe re n s ia l ten g lam alar chiziqli
b o 'lm a slig i m um kin. Bunday h o llard a ten g lam alar kichik chetlashishlar usuli yor-
15

dam ida ch iziq lash tirilad i. C h iz iq lim a slik te k is b o 'ls a , uni h is o b g a o lm asa ham
b o ‘la d i. O lin g a n d iffe re n s ia l te n g la m a n i
c h iz iq la s h tiris h m a q s a d id a , uni
T e y lo r q a to rig a y o y is h va c h e k siz k ic h ik c h iz iq li b o ‘lm a g a n h a d la rin i h iso b g a
o lm a s lik k e ra k .
C h iz iq la sh tirish tex n ik asin i k o 'rib chiqam iz.
B o g 'Ia n is h n in g o p erato r ten g lam asi
X ( t ) —F {X o;Ua;Zo}
ni um um iylikni
sa q la g a n h o ld a o 'z g a ru v c h ila r va u la rn in g h o s ila la ri b o ‘y ic h a
funksional
te n g la m a k o ‘rin ish id a yozam iz.

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