Бутковский А.Г. Методы управления системами с распределенными параметрами
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a:
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1';
_
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't'
q>
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2"
zsin
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f); (21),
OqeBHJl.HO,
~(Or
=~
(j)
;
tl;
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-_
,.()
'to
't
'
't
(
')
+'-
-t
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't' ( )
(22)
q>
z =
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ZSIn"2
z.......,
J
"2
SIn
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z
cos
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z-
J,
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-,
(
.)
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't
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't,.
't
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q>
J
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(20)
npHH.HMaeT
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o6pa30M, <popMyJla
. - -
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)
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.
't
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q02
e
.
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z-J
.
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z
z-1
2
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eme
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U
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np
H z =
ro
B
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ro.
B pe3YJlbTaTe
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.
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o
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.
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t
+q01-q02T
sign
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sign
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o
~
t
~
T,
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=
T.
§ 4. <l>HHHTHoe
ynpaBJleHHe
B
oOOolI.{eHHblX
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B
npeJ{bIJ{ylI.{HX
naparpaq,ax
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u
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T],
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2
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196
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=
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qa
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o.
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npe06pa30BaHHe
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YCJlOBHH (29),
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jroqd
ro
)-qol
=qa
(ro),
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(ro)-q02
=U
(ro).
(30)
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9TH
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OTHOCHTeJlbHO ql
(ro)
H
q2
(ro),
HaHJ{eM
q
-
(ro)
= u(ro)+i
ro
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1
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I
jz
IizE - A
1=
0
q-
(ro)
=
u(ro)+Q02
(31)
I
jro'
CHCTeMbI (28)
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BH,lt
1 I .
jz =
O.
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nOJlYllaeM
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KopeHb
Zl
= 0
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(22) § 2.
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q,yHKU.HH
ql
(ro)
H
q:
(ro)
B (31)
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KOMnJleKCHOro,nepeMeHHoro
z,
nOJlytIHM
(32)
2,
T.
e.
(Xl
= 2 B
BCIO nJlOCKOCTb
ql
(z)
=
U(Z)+~q::+qoa,
q2
(z)
U(Z)j;qoa. (33)
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HHTepnOJIHu.HoHHaH
np06JIeMa
J{JIH U(z),
KaK
BHJ{HO'
H3
(22) § 2,
HMeeT
BH,lt
U(0) =
-q02t
U'
(0) =
-jqol'
(34)
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COOTHOIlIeHHH (34)
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nOJIYllHTb
B J{aH-
H,OM
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He
npH6eraH
K
06lI.{eH
q,op-
MyJIe
(22) § 2.
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HHTepnOJIHu.HoHHOA
q,OPMYJlbI
JIarpaH1Ka
,ltJIH
CJlYlIaH
KpaTHblx
KopHeH
B
KalleCTBe
~
(z)
B03bMeM
~(z)=(1-e-iZ't)2.
(35)