Бутковский А.Г. Методы управления системами с распределенными параметрами

159

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. [

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.

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,

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1

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t.

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ero

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v·

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6

(x-x.)

i =

I,

2,

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1 cx,jr(xj)

I'

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160

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p(X,.)

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.

I=J

I0

T.

e.

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r

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T)],

r.n.e

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o

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n,

no

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1

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i=

I,

2,

. (65)

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1'.

e.

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p~

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..

r

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no

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j

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1

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0

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n

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o

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o

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2

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l

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a) eCJIIi

F (t) = °rrOqTli

BClO,ny

Ha

MHO)KeCTBe

B

1

~

t <2n '

II

T E[Bf' 2n],

TO

u

(t)~

F

(t);

(19)

6)

npH

T < B

1

<!>YHKUIIH

u

(t),

HBJIHlOlUaHCH

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He

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<l>yHl<UIIII u (t), HBJIHlOlUYlOqI

perneHlleM

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(11)-(13),

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(T)

~

1.

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B

CHJIe

npll

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aJ

, T. e.

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vrai

max

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~

1.

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y,noBJIeTBOpHeT

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paBeHcTB (11), (12). 003TOMY

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~

u (t)

<p

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(t)

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o

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t,

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t E

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~

vrai

max

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rrpH t E [0, 2n]"'K.,

{

°

f.

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=

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n

u

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t~

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,-.J

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170

METO,l{ MOMEHT.oB B

rEOPHC~;PABJIEHIHI

I .

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u

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I

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/.

o

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(COcToSlHHe

paBHoBecHSI)

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T)

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0

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t) =

k~

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k

cos

kt

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k

sin

kt

+

In

]

+

n~

SS u (s,

-r)

sin

k

(t--r)

sin

ks

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(24)

.

00

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n n

a

k

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1{Hq,q,epeHUHpy51

Q(x,

t)

B q,opMyJIe (24)

no 't.

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k

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~

.

In

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~

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51BHbUl

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(24) H (26)

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U (x,

t)

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n]:

t

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kT

+

k=l

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]

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ks

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kx=O,

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Tn

]

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n]

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TO

paBeHcTBa

(27) H (28)

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kx

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g'5

U(x, t)

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k

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_

t)sin:kxdxdt

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n:

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k

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(29)

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Tn

.

55

U(x, t) cos k

(T

- t)

sin

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dt

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~

(ka

k

sin

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k

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(30)

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,

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(29)

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i H

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ero C

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(30),

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•

(33)

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.

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113 (37)

1I

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I

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(45)

11

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000

k=

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o

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t)

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o

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,

..

113 COOTHorneHHH (46), (47)

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Бутковский А.Г. Методы управления системами с распределенными параметрами

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