Download - ASL - Luciano Bittencourt
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1j
j
1jT+1
jT+ 1
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(s)
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G(j) = 5
G(j) = 1/j
G(j) =j
G(j) = 1jT+1
G(j) =j T+ 1
G(j) = 1[1+2(j/n)+(j/n)2]
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k
k
k
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vo(t) vi(t)
vo = R2
R1 + R2vi,
vo= 20
10 + 2012
vo = 8 V
vo(t) vi
vo(t)
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u(t) 1/sr(t) 1/s2
(t)
u(t) K r(t)
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R
RC 1/sCL sL
Vo(s) =
1/sC
1/sC+ R
V i
s
Vo(s) = 1/sC
(RCs + 1)/sC
V i
s
Vo(s) =
1
RCs + 1
V i
s
Vo(s) =
1/RC
s+ 1/RC
V i
s
Vo(s) = V i/RC
(s + 1/RC)s
Vo(s) =Vi
s Vi
s + 1/RC
vo(t) =vi viet/RC
vo(t) =vi(1 et/RC)
vi
vo(t) = 12(1 e100t) V
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vo(t)
vo(t) vi
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vo(t) vi= 5V
I(s)
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I(s) =
5/s
10 + 2 + 8/s
= 5/s
12 + 8/s
= 5/s
(12s + 8)/s
I(s) = 5
12s + 8
Vo(s) 2
Vo(s) = 2I(s)
= 2 5
12s + 8
= 10
12s + 8=
0, 83
s + 2/3
vo(t) = 0, 83e2t/3 V
vo(t)
i1(t) i2(t)
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50s
+ 120I1+ 80I1 80I2= 0
I1(200) + I2(80) =50s
I1(80) + I2
92 +2000
s
= 0
I1 I2
A=
200 8080 92 + 200/s
.
I1
I2
=
50/s
0
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= Det(A)= 18400 + 4.105/s 6400
= 12000s + 4.105
s
1
A1 = 50/s 80
0 92 + 200/s
1 = Det(A1)
= 4600s + 105
s2
A2 =
200 50/s
80 0
1 = Det(A2)
= 4000
s
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I1 =
1
= 4600s + 105
s(12000s + 4.105)
= 0, 38s + 8, 33
s(s + 33, 3)
I1 = 0, 25s
+ 0, 13s + 33, 3
I1
i1(t) = 0, 25 + 0, 13e33,3t A
I2
I2 = 2
=4000s
12000s+4.105
s
= 0, 33
s + 33, 3
i2(t) = 0, 33e33,3t A
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80
Ix Ix =I1 I2
Ix = 0, 25 + 0, 13e33,3t 0, 33e33,3t
= 0, 25 0, 2e33,3t
vo(t)
vo(t)
vo(t)
io(t) is(t) = 2A.
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B(s)
E(s)
F T M A=B(s)
E(s)=G(s)H(s)
C(s)
E(s)
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FTRD=C(s)
E(s)=G(s)
C(s)
R(s)
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C(s) = G(s)E(s)E(s) = R(s) B(s)B(s) = C(s)H(s)
E(s) = R(s) C(s)H(s)C(s) = G(s)[R(s) C(s)H(s)]C(s) = G(s)R(s) G(s)C(s)H(s)
C(s) + G(s)C(s)H(s) = G(s)R(s)
C(s)[1 + G(s)H(s)] = G(s)R(s)
C(s)
R(s)=
G(s)
1 + G(s)H(s)
G(s) = 1/s
H(s) = 0, 5
F T M A= B(s)E(s)
=1s
0, 5 =0, 5s
FTRD=C(s)
E(s)=
1
s
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F T M F =
C(s)
R(s)
= G(s)
1 + G(s)H(s)
=1s
1 + 1s
0, 5
= 1
s + 0, 5
T(s) = C(s)/R(s)
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t
c(t)
c(t) =ctr(t) + css(t),
s
s
C(s) = s + 2
s(s + 5)
s =2
C(s) = 0
2
s = 0 s =5
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RC
C(s)
R(s)=
1
T s + 1
1/s
R(s) = 1/s
C(s) = 1
T s + 1.1
s,
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C(s) =1s
+ TT s + 1
=1s 1
s + (1/T).
C(s)
c(t) = 1 et/T, para t 0
c(t)
c(t)
t= T
c(t)
0, 632
c(t)
63, 2%
t = T
c(t)
c(T) = 1 e1 = 0, 63
T
t= 0
1/T
dc
dt
t=0
= 1
Tet/T
t=0
= 1
T
c(t)
t= 5T
99, 3%
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n
C(s)
R(s)=
2ns2 + 2ns + 2n
,
n
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n
G(s) = 36
s2 + 4, 2s + 36
2n = 36
n= 6 2n= 4, 2 = 0, 35
n
s1,2= n n
2 1
= 0
0 < < 1
= 1
> 1
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n
n
n
Tr
Tp
%SP
Ts
2%
Tp
Tp =
n
1 2
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%SP
%SP =e(/12) 100
Ts
Ts= 4
n
G(s) = 100s2 = 15s + 100
Tp %SP Ts
n
Tp = 0, 475s %SP = 2, 84
Ts= 0, 533s
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j
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j
s
s0
s
s
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s0
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KG(s)H(s) = K(s + 2)
s(s + 4)(s + 3)
sp1 sz1
sp2 sz2 sp3 sz3
= 3 1 = 2,
=r.180
,
r= +1, 1, +2, 2, +3, 3, +4, 4...
1 =1.180
2 = 90,
2 =1.180
2 = 90,
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a = polos
zeros
a=(0 3 4) (2)
2 =
7 + 22
= 2, 5
dG(s)H(s)
ds = 0
dds
(s + 2)
s(s + 4)(s + 3)
= 0
s= 3, 45
1 + KG(s)H(s) = 0
1 + K(s+ 2)
s(s + 4)(s + 3)= 0
s(s + 4)(s + 3) + K(s + 2) = 0
s3 + 7s2 + (12 + K)s + 2K= 0
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s3 1 12 + K
s2 7 2K
s1 (84 + 3K)/7s0 2K
K
s1
(84 + 3K)/7>0
K >28 K= 28
90 2, 5
3, 45
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t
e1() = 0 e2() = 0
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H(s)
1
E(s)
R(s)
C(s)
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E(s) =R(s) C(s)
C(s) =E(s)G(s)
E(s) = R(s)
1 + G(s)
e() = lims0
sE(s)
e() = lims0
s R(s)
1 + G(s)
R(s) G(s)
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R(s) = 1/s
e() = lims0
s 1/s
1 + G(s)
e() = lims0
1
1 + G(s)
e() = 11 + lims0 G(s)
lims0
G(s)
Kp
e() = 11 + Kp
Kp G(s)
lims0
G(s) =
G(s)
G(s)
R(s) = 1/s2
e() = lims0
s 1/s2
1 + G(s)
e() = lims0
1
s+ sG(s)
e() = 1lims0 sG(s)
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lims0
sG(s)
Kv
e() = 1Kv
lims0
sG(s) =
G(s)
R(s) = 1/s3
e() = lims0
s 1/s3
1 + G(s)
e(
) = lim
s0
1
s2
+ s2
G(s)e() = 1
lims0 s2G(s)
lims0
s2G(s)
Ka
e() = 1Ka
lims0
s2G(s) =
G(s)
Kp Kv Ka
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Kp
Kp = lims0
G(s)
Kp = 120(0 + 2)
(0 + 3)(0 + 4)
Kp = 20
e() = 11 + 20
= 1
21
Kv
e() = 1lims0 sG(s)
=10
=
e() = 1lims20 sG(s)
=1
0=
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Ge(s) =
G(s)
1 + G(s)H(s) G(s)
Ge(s) =
100s(s+10)
1 + 100s(s+10)
100s+5
100s(s+10)
Ge(s) = 100(s + 5)
s3 + 15s2 50s 400
e()
e() = lims0
sGe(s)
e() = 11 + lims0 s
100(s+5)s3+15s250s400
e() = 11 + 5
4
e() = 4
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G(s)
G(s) = Y(s)X(s)
X(s)
Y(s)
(s)
Y(s) = 1/sC
1/sC+ RX(s)
Y(s)
X(s)=
1
RCs + 1
G(s) = 1
RCs + 1
s
j
G(j) = 1
jRC+ 1
G(j)
G(j)
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|G(j)| =
12
(RC)
2
+ 1
2
G(j)
G(j) = 1
jRC+ 1
jRC+ 1jRC+ 1
G(j) = 1 jRC(RC)2 + 12
G(j) = 1
RC)2 + 1j RC
RC)2 + 1
G(j)
G(j) =tg1RC
RC)2+1
1RC)2+1
G(j) =tg1 RC
R= 1k C= 1F
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90
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log(P1.P2) =log(P1) + log(P2)
log(P1/P2) =log(P1) log(P2)
log(P)n =n.log(P)
log(1) = 0
G(j)
|G(j)|dB= 20.log(k)
k
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C= 1FR= 1k 280 Hz
K
(j)1
(jT+ 1)1
[1 + 2(j/n) + (j/n)2]1
G(j)
K
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G(j) =K
|G(j)|dB= 20.log(k)
G(j)
= tg1Im{G(j)}/Re{G(j)} = tg10/K
= 0
K = 5
1j
G(j) = 1
j
G(j) = j1
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G(j) = 5
|G(j |dB = 20.log
122
|G(j |dB = 20.log 1|G(j |dB = 20.log1|G(j |dB = 20.log()
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|G(j |dB = 20.log(10)|G(j |dB = 20
= 100
|G(j |dB =40
= 1000 |G(j |dB =60
20dB
G(j
= 90
j
G(j)
|G(j)|dB = 20.log()
= 90
1jT+1
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G(j) = 1/j
G(j) = 1
jT+ 1
jT+ 1
|G(j)|dB = 20.log
12
(wT)2 + 12
|G(j)|dB = 20.log
(wT)2 + 1
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G(j) =j
|G(j)|dB = 20.log
1
|G(j)|dB = 0
= 1/T
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|G(j)|dB = 20.log 1TT)2
+ 1
|G(j)|dB = 20.log
2
|G(j)|dB = 3dB
= 1/T
c
10/T
|G(j)|dB = 20.log
10
TT)
2+ 1
|G(j)|dB = 20.log
101
|G(j)|dB = 20dB
0 = 1/T >> T
= 0
45 90
jT+ 1
G(j) =jT+ 1
jT+ 1
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G(j) = 1jT+1
G(j) = [1 + 2(j/n) + (j/n)2]1
G(j) = 1
[1 + 2(j/n) + (j/n)2]
n
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G(j) =j T+ 1
0<
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G(j) = 1[1+2(j/n)+(j/n)2]
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u(t)
e(t)
u(t)
u(t) = U1, para e(t)> 0
= U2, para e(t)< 0
U1 U2 U2 U1
u(t)
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h(t)
t
u(t)
e(t)
u(t) =Kpe(t)
s
U(s) =KpE(s)
U(s)
E(s)=Kp
Kp
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u(t)
e(t)
du(t)
dt =Kie(t)
u(t) =Ki
t0
e(t)dt
Ki
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U(s)E(s)
= Kis
e(t) u(t)
u(t)
u(t) =Kpe(t) +Kp
Ti
t0
e(t)dt
U(s)
E(s)=Kp
1 +
1
Tis
Ki Ti Kp Ti
Kp
Ti
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e(t)
u(t)
u(t) =Kpe(t) + KpTdde(t)
dt
U(s)
E(s)=KP(1 + Tds)
Kp Td
Kp
Td
Td
e(t)
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u(t)
u(t) =Kpe(t) +Kp
Ti
t0
e(t)dt + KpTdde(t)
dt
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U(s)
E(s)=K p1 +
1
Tis+ Tds
Kp Td Ti
e(t)
u(t)
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