ЦСАУ

131

, -

.

, -

		. , -
	(s )2 2

T = k (k = 0, 1, 2, …), z-

:

z 1e T sin T

Z

0.

2

2

1 2z

1

T

cos T z

2

e

2 T

(s )

e

, ( 0)

. -

, (i T) = (j T) i = 0, 1, 2, … N – 1 , -

4.3 4.8, -

.

-

-, , , – j

T k ,

k = 0, 1, 2, … .

4.10.

:

y(k 2) 2 y(k 1) y(k) r(k 1) r(k) .

,

.

:

x(k 1) Ax(k) Br(k), y(k) Cx(k),

	0	1	0
A		,	B , C 1 1 .
1		2	1

Q, -, 2 ( Q ) -

132

4.3

:

0	1
Q B AB	.
1	2

,

L:

L CT	1	1
	AT CT	.
	1	1

, .

, , 4.8, .

:

T CAB CB 1 1 .

, 1, , ,

.

, , -

, :

	0		1	1
	A		, B		, C 1 0 .
	1		2	1
-
, ,
Q B	1	1		– -
	AB
;	1		1
L CT	AT CT	1	0	– ;
		0	1
T CAB CB 1			1 – .

-

,

W (z)	Y (z)		z 1		z 1		1
							z 1
	R(z)		z 2 2z 1 (z 1)2

,

4.16 .

133

5

,

, ,

. -

3 4.

. -

, .

-

-

.

-

.

. -

,

-

-

, . -

-

.

-

-

:

- ; - ;

- z- ;

- .

5.1

, -

134

.

, -

,

.

,

.

5.1. ,

5.1.

r(t)					k				y(t)
			1		s

5.1

,

W(s) 1 e sT , s

( 5.2, ), -

( 5.2, ).

.

, 5.2, , -

, s- :

E(s) = R(s) – Y(s),

Y (s) W	(s)			k	E * (s)	(1 e Ts )k	E * (s).
0		1		s		s(s 1)

, -

( 5.3). 5.3 -

:

W	* (s)		(1 e Ts )k *		.
1			s(s 1)

135

r(t)

e(t)

e*(t)

y(t)

k

W0(s)

1 s

					)
r(t)	e(t)							y(t)
					k
			1		s

W0(s) y*

)

5.2

R*(s) E*(s) W1*(s) Y*(s)

– W1*(s)

5.3

,

z:

	(1 e Ts )k
	Z
			s(s 1)				k(1 e T )
Y (z)						, R(z)		R(z). (5.1)
							z e T k(1 e T )
1 Z		(1 e Ts )k
		s(s 1)

136

R(z), -

: r(t) = V t.

(5.1) :

Y (z)	V k z T (1 e T )	(5.2)
	[z e T k(1 e T )](z 1)2 .

, -

5.2, , -

:

			k
	Z R(s)								V k z[T (z e T ) (z 1)(e T 1)]
Y (z)			1 s							.	(5.3)
					k				[z e T k(1 e T )](z 1)2
	1 Z W0	(s)
			1		s

(5.2) (5.3) ,

, , , -

, -

.

-

,

-

.

5.2

-

, , -

. , -

-

.

, -

. s –1

. -

,

s –1 -

-

.

137

,

, : -

, -

s –1

.

, , -

, .

5.2.1

, , -

, ,

, ,

( )

( -

).

s –1.

5.4, ( ) 5.4, (

).

x1(t)

x2(t)

W0(s)

s –1

)

x1(t)

x2(t)

W0(s)

s –1

)

5.4

138

5.4, ,

:

X 2

(z)

1

1

T

(1

z

) Z

.

(5.4)

X1 (z)

z 1

s2

(5.4) -

:

x2[(k + 1)T] = x2(kT) + T x1(kT).

-5.4, :

X	2	(z)	z (1 z 1 ) Z1	1				Tz		.	(5.5)
X1 (z)								z
				s2					1

,

z.

(5.5) :

x2[(k + 1)T] = x2(kT) + T x1[(k + 1)T].

5.2. 5.1.

r(t)		K		y(t)
		1 s

, -

-

.

-

.

r(t)	1	s–1		K	y(t)

–1–K

139

–1									T
s										.
									z 1
r(t)	1				T		K	y(t)
				z 1
R(z)			–1–K					Y(z)

, -

:

Y (z)

T

K

TK

W (z)

z 1

.

R(z)

1

T

(1 K )

z 1 T TK

z 1

, , -

, z- :

Y (z) W (z) R(z)		TK		z		TKz	.
	z 1
		T TK z 1 z 2 (T TK 2)z (1 T TK )

5.2.2

,

,

.

-

( ). -

5.5.

	x1(t)					x2(t)
					s –1

5.5

-

(2.44) :

140

eTs e Ts 2

W1 (s) Ts2 ,

-

5.5

:

X 2 (z)

z z 1

2

1

T

z 1

Z

.

(5.6)

X1 (z)

T

s3

2 z 1

-

,

.

-

, , , -

.

-

( -

). -

– z .

5.3 z-

(t) :

	F (s) (t)e st dt,			(5.7)
	0		c j
		1
	(t)		F (s)est ds.	(5.8)
		2 j
			c j

(5.8)

:

		1	c j s / 2	1	c j s / 2	1	c j
	(t)		F (s)est ds		F (s)est ds		F (s)est ds. (5.9)
		2 j		2 j		2 j
			c j		c j s / 2		c j s / 2

(

s ), -