ЦСАУ

						151
5.3
i	EW(i – 1)(T)
1	E(0)
2	– 1/2 G(0) B E(0)
3	(HB) 1 H	ABG(0)B				BG(0)[A BG(0)] B		E(0)
				6		3

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 .

,

,

:

	DT (T) – GWT (T) T (T) = 0			[ 1]:
		D(T) – (T) GW (T) = 0.	(5.36)	[ 2]:

, (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)
:
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) :

		Y (z)		b z m b z m 1		... b	z
	W (z)			0	1	m		(6.5)
		R(z)		a0 z n a1z n 1 ... an z

-

:

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 :

d

p

(

k

)

d

p

n 1

i

p

d

d

p

i

j

i 0

j

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) , ,

, -

.

6.1.2

-

(6.3) ,

-

. , , -

,

.

:

z	1	w	.		(6.8)
1		w
(6.8) :
w		z 1		.	(6.9)
		z 1

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		j	sin T	j tg	T	.	(6.10)
	cos T j sin T 1			1 cos T
					2

,

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

,

:

	b z m b z m 1		... b		Q(z)
W (z)	0	1	m			,	(6.13)
	a0 z n a1z n 1 ... an				D(z)

156

(6.13) -

, , :

D(z)			Ts	a		(eTs )n a (eTs )n 1	... a	n	0	(6.14)
		z e			0	1

. -

(6.14) ( -

eTs),

s / 2.

D(z) :
D(z) = a0 (z – z1) (z – z2) … (z – zn)
:
z = e j ,	(6.15)
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

)

			e j – zi
					zi
	e j
			R

)

6.1

158

, -

, D(ej ),

W(ej ),

-

, =

, 2n , n –

.

,

, , -

.

4.2. ,

, .

K

s(s 1)

.

:

(z)		W (z)	,
1		W (z)

	K
W (z) Z		.
s(s 1)

z- , ,

z- :

K

K

K

Kz

Kz

Kz (1 e T )

W (z) Z

Z

.

z 1

z e T

(z 1) (z e T )

s(s 1)

s

s 1

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

,

, -

,
.						D(z) 8z (z 1)(z 0,2) .
	=10.
:
z	1	j	–1	–j
D(z)	8	–0,8+j6,8	–5,6	–0,8–j6,8

160

, -

.

6.1.4

( 6.2).

	r(kT)			y(kT)
			W(z)

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