4.
II-
.
II- :
W(s) = K/[(T1s + 1)(T2s + 1)]
K ; T1 T2 , , .. . (T1 > 0 T2 > 0).
.
II- :
(T1T2)d2(t)/dt2 + (T1 + T2)d(t)/dt + (t) = K(t)
.
II- I- , .. () , . II- .
.
II- :
h(t) = L-1[W(s)1(t)] = L-1[K/[s(T1s + 1)(T2s + 1)]] =
= K[1 (T1/(T1 T2))e-t/T1 (T2/(T2 T1))e-t/T2]
, T1 = T2 = T :
h(t) = L-1[W(s)1(t)] = L-1[K/[s(Ts + 1)2]] =
= K[1 e-t/T (t/T)e-t/T]
. 4.1. - .
II- . , . : h = K.
T ( ) II- 3 5 .
T ≈ (3 ÷ 5)T2
.
II- :
w(t) = L-1[W(s)] = L-1[K/ [(T1s + 1)(T2s + 1)]] =
= K[(1/(T1 T2))e-t/T1 + (1/(T2 T1))e-t/T2]
, T1 = T2 = T :
w(t) = L-1[W(s)] = L-1[K/ (T1s + 1)2] =
= (Kt/T2)e-t/T
II- : 1) t = T , T1 = T2 = T; 2) t = T ( ) , T1 ≠ T2.
T :
. 4.2. - .
.
(, , ) II- .
: , T1 > T2. I- w1 = 1/T1 w2 = 1/T2, : , .
|
|
: w << w1; . : L(w) = 20lgK. .
: w >>w2; . L(w) = 20lgK 20lgT1w 20lgT2w. -40/.
: w1 > w > w2. , .. L(w) = 20lgK 20lgT1w. -20/.
. 4.3. , , , II- .
.
:
W(s) = K/[T2s2 + 2Tξs + 1]
K ; T , , .. . (T > 0); ξ () , (0 < ξ < 1).
ξ 1 - .
.
:
T2d2(t)/dt2 + 2T ξd(t)/dt + (t) = K(t)