1. г :
k - ,
[k] = [y] / [x];
T - , .
2. :
4. :
:
. 3.6 .
. 3.12
, L(w), . L*(w), , .
() , T2w2 L(w) .
() ,
T2w2 >>1 .
,
:
w, ,
w = 1T
:
- L(w) = 20 lg k w;
- [w; 20lgk]
- 20 /.
w = w :
³, W = W
, , w , w > w - , .
4. - :
-
. 3.13.
. 3.13 : ) h(t); ) w(t)
1. г :
k , [k] = [y] / [x];
, .
:
2. :
3. :
:
. 3.14 L, φ (lg ɷ)
. 3.14
, L(w),
. -, , :
:
w = w 1 = 1 T
w = w :
³ , w = w:
|
|
, ,
w
, w > w - , .
j (¥) = p2.
4. :
-
-
1. г :
k - , [k] = [y] / [x];
T - , ; ξ - (), .
ξ.
0 < ξ < 1. ξ = 0 ,
ξ ³ 1 - .
, 0 < ξ < 1.
2. :
3. :
:
. 4.9
. 3.15
, L (w), ξ.
L(w) , w max = 1-2x2T, , L (w) = 20 lg k - 20 lg 2x 1- x 2. , ξ>V2/2~0,707 (wmax > 0), .
ξ ->0, wmax ~^1 T L(wmax)^.
, , .
, [w 1 = 1 T; L(w 1) = 20lg k ].
1 (2ξTw)2:
:
w, , L(w ) = L(w ),
w = 1 T.
:
- L(w) = 20 lg k w;
- [w; 20 lg k]
- 40 /.
:
, , w
, w > w - , .
4. .
.
, :
-.
p 1,2=-αj β hc(t):
hc(t) . :
h(t) - C1 C2,
, :
|
|
,
h (t) = 5. ϳ x(t) = 1(t), 5 = k. :
:
, ,
A j0:
:
. 3.16.
. 3.16 :
) h(t); ) w(t)
h(t) , :
T - ; n - ,
.
T.
:
x T.
x:
, ξ hm ( 1 - ξ 2 , ξ π).
.
, Y , , , Y , . , Y .
, , :
³ m = ba .
Y = 1-e-2pm.
, α,
(α = 0 = > = ba Y = 0), , b, (b = 0 = > m = 0 = > Y = 1).
' x
' m, Y x :
m | Y | x |
, m Y x.
, x = 0 .
b.
x ³ 1 .
' . ,
1. г :
t - , .
2. :
3. : :
. 3.17 .
. 3.17
, ,
, .
4. :
-
-
. 3.18.
. 3.18
, , , . , ' .
W(s) - :
- . ϳ , , - , .
|
|
ϳ 쳺 , . .
. 3.19
, (. 3.19). , " ", , . " ", , .
³ :
y(t) = y(t) + y(t).
y(t) - , :
aoy(n) + a1y(n-1) +... + a(n-1)y + a(n)y = 0.
Գ , , . . y(t) - , 쳺 . Գ , u(t). . .
, . 3.20, 3.21. ³ , , . , .
t = 0 , . ϳ , , , y = y(t ). P=Posin( t+ ), , , ,
y = ymaxsin( t + y).
. t . ³ n
pi D(p) = a0pn + a1pn-1 + a2pn-2 +... + an = 0. pi = ai, pi = ai j i. i , u, y t = 0 t .
y(t)i, - ,
y(t)i = const (.). i, - ,
- . 3.22.
y(t) = 0, y(t). :
, , , .
|
|
, -
. 3.33. : , , , . , . ( , an = 0), , . , .
, , . ( , ) ( ).
. :
1) a1 an;
2) , ;
3) n .
: , , , n .
ֳ .
:
1) n = 1 => : a0p + a1 = 0. :
= 1 = a1 > 0 a0 > 0, : a0 > 0, a1 > 0;
2) n = 2 => : a0p2 + a1p + a2 = 0. : 1 = a1 > 0, D2 = a1a2 - a0a3 = a1a2 > 0, a3 = 0, :
a0 > 0, a1 > 0, a2 > 0;
3) n = 3 => : a0p3 + a1p2 + a2p + a3 = 0. : 1 = a1 > 0, 2 = a1a2 - a0a3 > 0, 3 = a3 2 > 0, : a0 > 0, a1 > 0, a2 > 0, a3 > 0, a1a2 - a0a3 > 0;
n 2 .
n > 2 ' .
n 4.
. , .
- . - . .
n = an n-1 = 0 , . an = 0 - , n-1 = 0 - . , , - Ki n-1. , Ki n-1 , - .. , .
, . , , .
. () , . , , . , '.
, , , , ; , , , .
|
|
(. 3.34) t = 0 , , f . h(t) = y(t) = y(t) - y0 = -e(t) .. .
1. e = y0 - y = -h - . . 3.34 , , f ( ) , - .3.35.
. 3.34
2. t - , , |h(t)-h| . = 0.05h.
.3.35
2. s - , :
s = .
hmax1 - . , .. s . 0.1...0.3, 0.7.
. 3.36
4. = 2 /T, T - .
5. n t.
6. k, : .
, . , (. 3.37).
.3.37
.
, 0 + ' . .
, , , , , . 3.38. , .
, , :
Joo = .
Joo . , . Joo. A, Joo = f(A) . 3.38. , dJoo/d = 0, A.
. 3.38
:
(a0pn + a1pn-1 + a2pn-2 +... + an)y = (b0pm + b1pm-1 +... + bm)u.
³ :
(a0pn + a1pn-1 +... + an)y = 0,
:
y =
y =
Joo = (t)dt = .
t = 0 :
y(0) = y0, = y0,..., = y0(n-1).
y() = 0, () = 0,..., () = 0,
t . ϳ , :
Joo = (a0y0(n-1) + a1y0(n-1) +... + an-1y0)/(an.
, . , , :
J01 = (t) t dt; J0n = (t) tndt.
. 3.39
. 3.40
.3.41
˳ . , y(t) , Joo 䳺 (.). , ,
J20 = y2(t)dt.
y2(t) , (.).
J20 y(t) , (.). , , a0...an,b0...bm. , .
J20 , y(t) , , . , , , y(t).
J21 = 2(t) + t2 (y(t))2]dt,
- , y y. . , .
.3.42
, (.). , , , , .