, z . x(t) (2.1) f(t)=0 zt,
.
z1, z2 ,
.
z1 = z2,
.
- z1,2 = aib
.
r z1, j .
, .
1. .
.
: z1 = 3, z2 = 2.
: .
2. .
.
: .
z1,2 = aib . 2.1.
. 2.1:
r = 2, . : .
, . , , 2 (0) =2; (1) =4. t=0 t=1:
.
. 2.1.
2 = 2, 1 = . , .
. , , .. f(t) (2.1):
f(t) , ;
f(t) , ;
f (t) =sin kt cos kt, c1sinkt+c2coskt.
1 2 , .
3.
.
.
=. , , =2.
.
1, 2 1=2+2, , .
1.2. z -
z - . , F(p) f(t). F(z) z f(t) ( , ) .
, 1/ , z z-1 . z-1 .
|
|
F(p) F(z). , F(p) = 1 - f(t) = d(t), F(z) = 1, . .
z - .22 (.1.2).
n -
(2.3)
.
z - :
z - (2.3), f(t) F(z), y(t) Y(z); y(t+ 1 ) z(Y(z)-y0) ..;
Y(z);
Y(z) ;
.1.2 (.22), z -.
.
4.
y0, y1 un = 1.
:
z -
;
Y(z) :
;
z :
,
Matlab [R,P,K]=residue(B,), z; residue Y(z) : [R,P,K]=residue([1],[1 -6 11 -6]), R , P , K ;
z - (.1.2, .22) iztrans SYMBOLIC Matlab : .
. (. .1.1).
: y0 = 0; y1 = 0.
: un = 1.
a b . 2.1.
2.1
a b
. un = 1, , z - y2, , y5 (. .1.2).
: y0 = 0; y1 = 0.
a b . 2.2.
2.2
a b
b | -1.3 | -0.7 | -0.2 | -2 | -1.6 | 1.6 | -1.6 | 1.9 | -2.8 | 2.5 |
a | 0.3 | -0.6 | -0.48 | 0.96 | 0.6 | 0.55 | 0.48 | 0.6 | 1.8 |
b | 0.5 | -0.72 | -1.28 | -2 | 2.88 | -0.5 | -0.72 | -1.28 | -2 | -2.88 |
a | -0.27 | -0.4 | -0.7 | -1.1 | 1.6 | -0.25 | -0.37 | -0.66 | -1.1 | 1.5 |
, , yn.
|
|
:
1) , | 2) , |
3) , | 4) , |
5) , | 6) , |
7) , | 8) , |
9) , | 10) |
11) , | 12) , |
13) | 14) |
:
) ;
) z -.
3