apostila controle aeronautica
DESCRIPTION
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d2y
dt2+ 5
dy
dt= 10x(t)
x(t) = �Ky(t) + r(t)
R(s)
Y (s)R(s) =
K
s
2+5s+10K
Y (s)R(s) =
10s
2+5s+10+K
Y (s)R(s) =
10s
2+5s+10K
Y (s)R(s) =
10Ks
2+5s+10K
Y (s)R(s) =
K
s
2+(5+K)s+10K
Y(s)(s2+5s) = 10X(s)
X(s) = �KY (s) +R(s)
Y (s)(s2 + 5s) = 10(�KY (s) +R(s))
Y (s)(s2 + 5s+ 10K) = 10R(s)
Y (s)
R(s)=
10
s2 + 5s+ 10K
2
d2u(t)
dt2+ 14
du(t)
dt+ 20u(t)
=
d2y(t)
dt2+ 4
dy(t)
dt+ 3y(t)
u(t) y(t)
20s2+14s+2s
2+4s+3
s
2+4s+3s
2+14s+20
2s2+14s+20s
2+4s+3
3s2+4s+12s2+14s+20
20s2+14s+23s2+4s+1
2s2U + 14sU + 20U = s2Y + 4sY + 3Y
(2s2 + 14s+ 20)U = (s2 + 4s+ 3)Y
Y
U=
2s2 + 14s+ 20
s2 + 4s+ 3
y(t)
1
K
1/K
10
1/10
P (s)
R Y
P (s) =G(s)
1 +G(s)
G(s) = fracKs(s+ 10)
P (s) =
K
s(s+10)
(1 +
K
s(s+10))=
K
s(s+ 10) +K
P (s) =K
s2 + 10s+K=
Y (s)
R(s)
y1 = lim
s 0sY (s)
R(s) = 1/s
Y (s) = P (s)R(s) =K
(s2 + 10s+K)
.1
s
y1 = lim
s 0
sK
(s2 + 10s+K)
.1
s
y1 =
K
(0 + 10.0 +K)
=
K
K= 1