ЦСАУ

161

z- . -

-

W(z) z

( . . 6.3, ).

											1
									2			s
			s
		j
		2
		s
		j
	2
									)				z
													R

2

)

6.3

( . 6.2) :

(z)		W (z)	.
1		W (z)

:

162
1 W (z) 1	Q(z)		D(z) Q(z)	,	(6.17)
	D(z)		D(z)

D(z) = a0 z n + a1 z n – 1 + … + a n, Q(z) = b0 z m + b1 z m – 1 + … + b m.

(6.17) – -

, – .

z z = 1 D(z),

, 2 (n – r), r – -

, (

),

(6.17) (

)	2 n. ,
(6.17) :
	2 n – 2 (n – r) = 2 r.	(6.18)
z	z =

:						a0 b0
									const, m n,
							a0
1 W (z)
		z
						a0		1,	m n,
					a0

(6.17) .

(6.17)

W(z) ,

2 r W(z) (W*(s))

(– 1, j 0) z(s) 2.

, -

.

( r = 0), -

W(z) ( W*(s))

(– 1, j 0), z -

( -

s j	s	j	s	).
2		2

163

W(z) W*(s)).

.

1.z-

z e j T W(z) – s / 2

+ s / 2.

4.3. , 4.2.

( =0,57 )

W (z)

K 0,8z

.

(z

1)(z 0,8)

W(e

j T

)

0,8 e j T

0,8(cos T j sin T)

.

(e j T 1)(e j T

(cos T j sin T 1)(cos T j sin T 0,2)

0,2)

-

n

s

n

s

, n=1,2,..,

2

2

W (e j T ) .

, -

.

jIm

-1

Re

0

K=1 W (e j T ) -

–0,33; (–1, j0)

164

, , -

.

,

, -

. , K>3.

2. (3.9):

		1
	W * (s)		W (s jn s ).	(6.19)
	T n

s = j , (– s / 2 s / 2).

W(s+jn s) n ,

W*(s) (6.19)

.

3.

w (6.8):

z1 w .

1w

-

z w w = jw, w

, (6.10), :

w tg T . (6.20) 2

, W(z) -

:

z	1		j w	(6.21)
		1	j w

w – + ( 0 -

),

.

-

,

,

165

.

, , ,

( ) .

6.2

, R*(s)

Y*(s) :

Y*(s) = W*(s) R*(s),

W*(s) – .

Y*(s) ,

y(nT). y(t) -

y(nT) , –

.* -

y(nT) -

, .

-

, : -

, , ,

, . ,

,

, -

, .

, , , -

-

. ,

-

. -

, si – , zi = esiT . -

, (6.3) : a0 z n = 0, 1 = 2 = … = n = 0.

*

.

166

-, :

	b z m b z m 1		... b		1	(b z m n b z m n 1		... b z n ). (6.22)
W (z)	0	1	m
		a0 z n			a0	0	1	m

W(z) z-

( ) :

W (z) w(kT )z k .	(6.23)

k 0

(6.22) (6.23) ,

, n

, . , -

, nT.

, -

. , , -

(

-). -

.

-

, , -

.

6.3

, -

, .

.

, ,

. . 6.4).

e(t) -

: e(t) = r(t) – z(t).

z- -

:

e * lim e * (t) lim e(kT ) lim(1 z 1 )E(z).			(6.24)
t	k	z 1

167

r(t)		e(t) e*(t)									y(t)
									G(s)

z(t)	H(s)

6.4

. 6.4, z E(z)

:

E(z)	R(z)	,	(6.25)
	1 GH (z)

R(z) = Z{r(t)},

:

			1	G(s) H (s)
	GH (z) Z{W0 (s) G(s) H (s)} (1 z			)Z			. (6.26)
						s
	(6.25) (6.24), -
	:	R(z)
	e * lim(1 z 1 )					,	(6.27)
		1 GH (z)
	z 1

,

, .

, -

( -

):

) Kp -

r(t) = R 1(t);

) KV -

,

r(t) = V t 1(t);

168

) Ka

, -

r(t) At 2 1(t) ; 2

) .

, , . 6.4, -

, , -

:

K p

lim G(s) H (s),

(6.28)

s 0

KV

lim s G(s) H (s) ,

(6.29)

s 0

Ka

lim s2 G(s) H (s) ,

(6.30)

s 0

– :

) e

R

,

(6.31)

1 K p

) e

V

,

(6.32)

KV

) e

A

.

(6.33)

Ka

.

r(t)

= R 1(t) z-

:

Rz

R(z)

.

(6.34)

z 1

(6.34) (6.27), :

e *

lim(1 z 1 )

Rz

R

.

(z 1)(1

z 1

GH (z)) 1 lim GH (z)

z 1

(6.31), :

K p limGH (z).

(6.35)

:

z 1

R

e *

.

(6.36)

K p

1

169

r(t) = V t 1(t) z-

:

	R(z)	VTz	.	(6.37)
		(z 1)2

(6.37) (6.27) :

e * lim(1 z 1 )				VTz			V		.
	(z 1)2			(1 GH (z))			z 1
z 1						lim		GH (z)
:						z 1 T
KV		1	lim(z 1)GH (z),						(6.38)
	T z 1

, (6.32):

e *		V	.					(6.39)
		KV						2
						r(t)	At		1(t) z-
							2
:
	AT 2 z(z 1)
R(z)					.			(6.40)
	2(z 1)			3

(6.40) (6.27), -

:

e * lim(1 z 1 )	AT	2 z(z 1)				A			.
	2(z 1)	3 (1	GH (z))			(z 1)	2
					lim			GH (z)
						T 2
					z 1

-

	Ka	1	lim(z 1)2 GH (z)			(6.41)
	T 2		z 1
	(6.33):			A
	e *				.	(6.42)
				Ka

, -

?

, ,

170

( ., , (6.38)(6.41)) . , .

-

:

	K (1 d 1s)(1 d 1s) ... (1 d 1s)
G(s) H (s)	1	2	m	,	(6.43)
	sr (1 c 1s)(1 c 1s) ... (1 c 1s)
	1	2	n

r – , di cj –

(

, ).

(6.28)–(6.30) (6.43) , :

)

r = 0 ( )

Kp = K;

) -

r = 1

KV = K.

) -

r = 2

K = K.

-

.

(6.43) (6.26)

(r = 0), :

GH (z) (1 z 1 )Z	K (1		d 1s)(1		d 1s) ... (1		d	1s)
			1		2			m	.
		s(1	c 1s)(1	c 1s) ... (1
						c 1s)
			1		2		n

z- -

, :

	1	K
GH (z) (1 z		)Z
		s

(1 z	1			Kz
		)				.
		z 1
-
:								Kz
			K p		lim GH (z) lim(1 z 1 )				K.
						z 1	z 1	z 1