d2 y dy +5 = 10x(t) 2 dt dt
x(t) =
Ky(t) + r(t)
R(s) Y (s) R(s)
=
K s2 +5s+10K
Y (s) R(s)
=
10 s2 +5s+10+K
Y (s) R(s)
=
10 s2 +5s+10K
Y (s) R(s)
=
10K s2 +5s+10K
Y (s) R(s)
=
K s2 +(5+K)s+10K
2
d2 u(t) du(t) + 14 + 20u(t) dt2 dt
=
d2 y(t) dy(t) +4 + 3y(t) 2 dt dt
u(t)
Y( s)(s2 +5s) = 10X(s) X(s) =
KY (s) + R(s) 20s2 +14s+2 s2 +4s+3 s2 +4s+3 s2 +14s+20 2
Y (s)(s + 5s) = 10( KY (s) + R( s))
2s2 +14s+20 s2 +4s+3 3s2 +4s+1 2s2 +14s+20
Y (s)(s2 + 5s + 10K) = 10R(s)
Y (s) 10 = 2 R(s) s + 5s + 10K
20s2 +14s+2 3s2 +4s+1
y(t)
2s2 U + 14sU + 20U = s2 Y + 4sY + 3Y
P (s) R
Y
(2s2 + 14s + 20)U = (s2 + 4s + 3)Y Y 2s2 + 14s + 20 = U s2 + 4s + 3
P (s) =
G(s) 1 + G(s)
G(s) = f racKs(s + 10)
P (s) =
(1
K s(s+10) K + s(s+10) )
P (s) =
s2
=
K s(s + 10) + K
K Y (s) = + 10s + K R(s)
y1 = lim sY (s) s
0
R(s) = 1/s
Y (s) = P (s)R(s) =
(s2
K 1 . + 10s + K) s
y(t) 1 K 1/K 10 1/10
y1 = lim s
y1 =
0
(s2
sK 1 . + 10s + K) s
K K = =1 (0 + 10.0 + K) K