ASL - Luciano Bittencourt

7/24/2019 ASL - Luciano Bittencourt

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1j

j

1jT+1

jT+ 1


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7/90

(s)


8/90

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


18/90

vo(t) vi(t)

vo = R2

R1 + R2vi,

vo= 20

10 + 2012

vo = 8 V

vo(t) vi

vo(t)


19/90

u(t) 1/sr(t) 1/s2

(t)

u(t) K r(t)


20/90

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


21/90

vo(t)

vo(t) vi


22/90

vo(t) vi= 5V

I(s)


23/90

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)


24/90


25/90

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


26/90

= 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


27/90

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


28/90

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.


29/90


30/90

B(s)

E(s)

F T M A=B(s)

E(s)=G(s)H(s)

C(s)

E(s)


31/90

FTRD=C(s)

E(s)=G(s)

C(s)

R(s)


32/90

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


33/90

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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36/90

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


37/90

RC

C(s)

R(s)=

1

T s + 1

1/s

R(s) = 1/s

C(s) = 1

T s + 1.1

s,


38/90

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%


39/90

n

C(s)

R(s)=

2ns2 + 2ns + 2n

,

n


40/90

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


41/90

n

n

n

Tr

Tp

%SP

Ts

2%

Tp

Tp =

n

1 2


42/90

%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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45/90

j


46/90

j

s

s0

s

s


47/90

s0


48/90

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,


49/90

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


50/90

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


51/90


52/90


53/90

t

e1() = 0 e2() = 0


54/90

H(s)

1

E(s)

R(s)

C(s)


55/90

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)


56/90

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)


57/90

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


58/90

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=


59/90


60/90

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


61/90


62/90


63/90


64/90

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)


65/90

|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


66/90

90


67/90

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


68/90

C= 1FR= 1k 280 Hz

K

(j)1

(jT+ 1)1

[1 + 2(j/n) + (j/n)2]1

G(j)

K


69/90

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


70/90

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()


71/90

|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


72/90

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


73/90

G(j) =j

|G(j)|dB = 20.log

1

|G(j)|dB = 0

= 1/T


74/90

|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


75/90

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


76/90

G(j) =j T+ 1

0<


77/90

G(j) = 1[1+2(j/n)+(j/n)2]


78/90


79/90


80/90


81/90


82/90

u(t)

e(t)

u(t)

u(t) = U1, para e(t)> 0

= U2, para e(t)< 0

U1 U2 U2 U1

u(t)


83/90


84/90

h(t)

t

u(t)

e(t)

u(t) =Kpe(t)

s

U(s) =KpE(s)

U(s)

E(s)=Kp

Kp


85/90

u(t)

e(t)

du(t)

dt =Kie(t)

u(t) =Ki

t0

e(t)dt

Ki


86/90

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


87/90

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)


88/90

u(t)

u(t) =Kpe(t) +Kp

Ti

t0

e(t)dt + KpTdde(t)

dt


89/90

U(s)

E(s)=K p1 +

1

Tis+ Tds

Kp Td Ti

e(t)

u(t)


90/90

Documents

ASL - Luciano Bittencourt