. y(t), .
³, , x(t). , , .
h(t). , , l(t) . .
w(t). ϳ , , - . w(t) .
,
x(t) y(t) ; ai, bj ;
n .
, (3.1) y(t) - y (t),
, y(t), , (3.1), '. y (t), , , .
y(t)
p .
ϳ (3.3) (3.1) , :
. , (3.3) , p (3.4). n , n
yi (t). , , n yi (t) ,
Ci .
³, (3.5) , pi . - pj r, (3.5) r (3.3)
y(t) , , x(t).
. 3.1. -
|
|
|
h(t) w(t). . h(t). :
p = -1T.
h(t) h(t) = C2. ϳ , C2 = k. h(0) = 0. :
1 = -k
:
. 3.1
.3.1 h(t)
w(t)
, x(t) = 1(t).
:
w(t) = h(t)
. 3.2.
. 3.2 w(t)
. 3.3, 3.1 x(t) = 2t, . 3.3, -
. 3.3
.
ճ :
1. (3.1) :
2. (3.7) Y(s) X (s):
3. y(t).
y(t) (L-1 - ),
г-:
a=Re s >c0 - >c0.
,
F (s) y(t).
,
F (s) y(t).
, - , l<r, ci, d j - , :
sj - D(s) = 0; N - ;
kj - j - .
s j kj =1. (3.10)
:
(3.11)
D(s) q1 q2 , (3.11)
,
| a ×1(t) | s | |
| -- | d(t) | |
| . |
3.2. h(t) w(t) 3.1 . .
h(t). , x(t) =1(t):
- ,
. :
г D(s) = Ts2 + s = 0 : s1 = 0 s2 = -1T. (3.11), :
w(t) , x(t) =d(t). :
|
|
|
(3.11), :
3.3. г
h(t) T = 0,3 ; x= 0,5; k =10. .
:
. : C(s) =10
г
: s1=0
(3.11), :
: 10 = Asinj0; 5,774 = Acosj0.
, :
h(t) . 3.4
. 3.4 h(t)
- , . ֳ , . :
(3.13) :
(3.1), (3.14). y(t).
, y(t)
| 1(t) |
y1(t) :
:
W(jw) . (3.18) W(s),
, W(jw) W(s) s = jw.
,
: , ' .
W(jw), - , .
:
P(w) Q(w) - .
:
- , 
-
ϳ (3.20) (3.17), :
(3.21)
2(t)
(3.21) (3.22)
, (yc(t) = 0) , . ,
W(jw). , 0 ¥,
- ().
, , :
()
A(w) = W(jw);
() j(w) = Arg W(jw);
P(w) = Re W(jw);
Q(w) = Im W(jw).
(3.23) (3.13) - '.
3.4. 3.3.
.
:
s = jw,:
W(jw):
³ . 3.5.
. 3.5
