ЦСАУ
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5.3 |
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EW(i – 1)(T) |
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1 |
E(0) |
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2 |
– 1/2 G(0) B E(0) |
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3 |
(HB) 1 H |
ABG(0)B |
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BG(0)[A BG(0)] B |
E(0) |
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5.3 ,
E(T) .
,
, , -
. , -
(5.28), G(T) GW (T). :
H D (T) = H (T) GW (T).
:
DT (T ) HT GWT (T ) T (T ) H(T )
:
DT (T ) GWT (T ) T (T ) HT .
n
n .
,
,
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DT (T) – GWT (T) T (T) = 0 |
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[ 1]: |
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D(T) – (T) GW (T) = 0. |
(5.36) |
[ 2]: |
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, (5.36) -
, (5.29).
152
6
, , -
,
.
6.1
6.1.1
, -
,
.
, , ,
:
a0 y(k + n) + a1 y(k + n – 1) + … + an y(k) = b0 r(k + m) +
+b1 r(k + m – 1) + … + bm r(k). (6.1)
(6.1) , [1],
y (k) -
(6.1) y (k):
y(k) = y (k) + y (k).
y (k) ,
y (k) – ( ) .
:
y (k) = c1 z1 k + c2 z2 k + … + c n z nk, |
(6.2) |
ci – , ( ) -
, zi –
a0 z n + a1 z n – 1 + … + a n z = 0. |
(6.3) |
( , z1) |
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y (k) = c1 z1 k + c2 k z1 k + c3 k2 z1 k + … + c r k r – 1 z 1 k, |
(6.4) |
r – z1.
(6.2), (6.4) ,
( ),
zi . -
,
153
, (6.1), -
:
zi 1, i = 1, … n,
zi – (6.3).
, z- . -
(6.1) :
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Y (z) |
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b z m b z m 1 |
... b |
z |
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W (z) |
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1 |
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(6.5) |
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R(z) |
a0 z n a1z n 1 ... an z |
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-
:
z = e Ts. (6.6)
s – -
, (6.6) -
, , ,
(6.5)
.
: x (k + 1) = A x (k) + B r (k),
(k) = Ak
k , -
.
,
, k (k) -
. -
-, , k -
(k) . , -
Ak :
n 1
Ak i Ai ,
i0
n – , i
:
n 1
kj i ij i 0
154
j :
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j.
k ( j)k.
k , j 1, ,
j = 1, , j 1.
-
k k j k – 1. ,
k , j 1,
, j 1.
, -
, :
– = 0 |
(6.7) |
.
-
(6.3) (6.7) , ,
, -
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6.1.2
-
(6.3) ,
-
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,
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z |
1 |
w |
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(6.8) |
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(6.8) : |
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w |
z 1 |
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(6.9) |
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z 1 |
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155
z -
:
z = e j T = cos T + j sin T, n s (n + 1) s, n = 0, 1, 2, …
(6.9) :
w |
cos T j sin T 1 |
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j |
sin T |
j tg |
T |
. |
(6.10) |
cos T j sin T 1 |
1 cos T |
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2 |
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z w, -
( )
.
6.1. -
:
a0 z + a1 = 0. |
(6.11) |
(6.11) (6.8), : |
1 w
a0 1 w a1 0
a0 (1 + w) + a1 (1 – w) = (a0 + a1) w + (a0 – a1) = 0. (6.12)
( )
,
a0 a1 0, a0 a1 0.
., -
-
–
, (6.11) -
.
6.3.1
,
:
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b z m b z m 1 |
... b |
Q(z) |
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W (z) |
0 |
1 |
m |
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(6.13) |
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a0 z n a1z n 1 ... an |
D(z) |
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156
(6.13) -
, , :
D(z) |
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Ts |
a |
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(eTs )n a (eTs )n 1 |
... a |
n |
0 |
(6.14) |
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z e |
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1 |
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. -
(6.14) ( -
eTs),
s / 2.
D(z) : |
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D(z) = a0 (z – z1) (z – z2) … (z – zn) |
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z = e j , |
(6.15) |
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D(e j ) = a0 (e j – z1) (e j – z2) … (e j – zn). |
(6.16) |
(6.16) – + -
D(e j ). D(e j )
, -
(6.16).
:
) R zi -
( . . 6.1, ), -
;
) R zi -
( . . 6.1, ).
e j – zi,
6.1, , 2 , -
(6.16) 2 n.
e j – zi
, ,
D(z) zi 1,
(6.16)
D(ej ) , 2 n.
s z z = e Ts,
, (6.15), :
157
s j , T
– s j s j s , 2 2
z z = 1.
D(e Ts) 2 n, -
, ,
2 n, .
0 ,
0 s j s ,
2
.
.
e j – zi
e j
R zi
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e j – zi |
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e j |
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R |
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)
6.1
158
, -
, D(ej ),
W(ej ),
-
, =
, 2n , n –
.
,
, , -
.
4.2. ,
, .
K
s(s 1)
.
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(z) |
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W (z) |
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1 |
W (z) |
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K |
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W (z) Z |
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s(s 1) |
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z- , ,
z- :
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K |
K |
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K |
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Kz |
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Kz |
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Kz (1 e T ) |
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W (z) Z |
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Z |
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z 1 |
z e T |
(z 1) (z e T ) |
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s(s 1) |
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s 1 |
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Kz (1 e T )
(z) (z 1) (z e T ) Kz (1 e T ) .
159
–
:
D(z) (z 1) (z e T ) Kz (1 e T ) .
T=1,57 , e–T 0,2
D(z) 0,8z (z 1) (z 0,2) .
=1, D(z) 0,8z (z 1)(z 0,2) . -
z -
, .
z.
z |
1 |
j |
–1 |
–j |
D(z) |
0,8 |
–0,8–j0,4 |
1,6 |
–0,8+j0,4 |
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, -
, |
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D(z) 8z (z 1)(z 0,2) . |
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=10. |
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z |
1 |
j |
–1 |
–j |
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D(z) |
8 |
–0,8+j6,8 |
–5,6 |
–0,8–j6,8 |
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160
, -
.
6.1.4
( 6.2).
r(kT) |
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y(kT) |
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W(z) |
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6.2
,
W(z).
s -
1 ( . . 6.3, ), -
( )
(– 1, j 0) -
.
s -
W*(s) -
, -
W*(s). -
-
, , s 2 -
W*(s),
.
2 z-
6.3, . s
-
z, s