Transcript . Kazanç marjı, faz marjı, Bode diyagramı 6 ) s

6. Kazanç marjı, faz marjı, Bode diyagramı
R(s) 

G (s ) 
K
1
s(s 2  30s  200)
G (s )
C(s)
61
KG(s)
H(s ) 
1  KG(s)
KG(i)  KG(i) ei( )
M  20 log KG(i) (dB)
M  20 log(K )  20 log G(i)
k=1000;ng=1;dg=[1,30,200,0];sys1=tf(k*ng,dg);bode(sys1)
62
KG  düzlemi
Im
s  i
M(dB)
log 
0
1
GM
Re
a
M
 1
G M  20 log 
a
Nyquist diyagramı
GM : 6 dB
PM(deg)


PM : 65o
100
[gm,pm,w2,w1]=margin(sys1)

0
 180
log 
M
Bode diyagramı
K c  6000
G M  7 dB
( 7 / 20 )
 2.24
K=2000: gm=3, pm=32.61, w2=14.14 rad/s, w1=7.49 rad/s 10
Kc
6000
20 logK c 20 log K  20 log(3)  G M  9.54 dB
3
K
 2678.6
K
2.24
K=2678.6: gm=2.24, pm=23.52o, w2=14.14 rad/s, w1=9.05 rad/s
63
9.05 rad/s (1.44 Hz) te 65-23.52=41.48o faz ekle
Faz ekle (phase-lead) devresi
   z  p
s  düzlemi

1

T
2
m

1
aT2
1  aTs
1  Ts
a1
sin  m 
a1
i
o
1

aT
V1


R1

C
R2


V2

a
φM=41.48 : a=4.92
a1
G c (s ) 
ωM=9.05: T=0.0498
R1  R 2
R2
R1
 3.92
R2
aT  R 1C
R 1C  0.245
64
a1
Faz azalt (phase-lag) devresi
V1



G c (s ) 

R1
R2 V
2
C
a
R2
R1  R 2
1 (1  aTs)
a (1  Ts)
aT  R 2C

Faz ekle-azalt (phase lead-lag) devresi
Faz ekle devresi: PM artar, sönüm artar, aşma azalır, ess değişmez
Faz azalt devresi: PM azalır, sönüm azalır, ess (1/a) kadar azalır
M(i)
Mp
Mo
0.707Mo
0-ωb : Band genişliği (BW)
65
20 * log10(0.707)  3 dB
1
ess 
1  Mo
p
b

n  1
  0.05
a2
a1
a4
  0.3
  0.7
  0.05
a1
a
G (s ) 
sa
  0.3
a4
a2
g(t )  ae  at
Köşe frekansı=a (rad/s)
  0.7
n2
G (s )  2
s  2ns  n2
g(t )  Ae  t cos( t   )

 1 Rezonans
n