Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 1 Frequency response:
31
03.05.200 4 Bode plots 1 Introduction to Feedback Systems / Önder YÜKSEL ) s ( Q ) s ( P K ) s ( T ) p s ( ) p s )( p s ( ) z s ( ) z s )( z s ( K n m 2 1 2 1 ) s ( T ) s ( T ) s ( T 3 2 1 Frequency response: ) j ( T ) j ( T ) j ( T ) j ( T 3 2 1
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Transcript of Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 1 Frequency response:
03.05.2004 Bode plots 1
Introduction to Feedback Systems / Önder YÜKSEL
)s(Q
)s(PK)s(T
)ps()ps)(ps(
)zs()zs)(zs(K
n
m
21
21
)s(T)s(T)s(T 321
Frequency response:
)j(T)j(T)j(T)j(T 321
03.05.2004 Bode plots 2
Introduction to Feedback Systems / Önder YÜKSEL
Let
)j(jii
ie)j(T)j(T
Then
)j(T)j(T i
and
)j()j( i
03.05.2004 Bode plots 3
Introduction to Feedback Systems / Önder YÜKSEL
)j(Glogˆ)j(G db 20
Therefore;
)j(Tlogˆ)j(T db 20
)j(Tlogˆ i 20
)j(Tlogˆ i 20
dbi )j(T
03.05.2004 Bode plots 4
Introduction to Feedback Systems / Önder YÜKSEL
)j(T)j(T i
Overall db gain=sum of individual db gains
+dbT1 + dbT2 = dbT
03.05.2004 Bode plots 5
Introduction to Feedback Systems / Önder YÜKSEL
)j(T)j(T i
Overall phase=sum of individual phases
+1 + 2 =
03.05.2004 Bode plots 6
Introduction to Feedback Systems / Önder YÜKSEL
Bode plot
Plot of db magnitude vs. Log frequency
Plot of phase vs. Log frequency
log
log
)j(T
)j(T
03.05.2004 Bode plots 7
Introduction to Feedback Systems / Önder YÜKSEL
Semi-log paper
Bode Diagram
Frequency (rad/sec)
Ph
ase
(d
eg
)M
ag
nitu
de
(d
B)
10-1
100
101
102
1 decade
1 1 octaveoctave
03.05.2004 Bode plots 8
Introduction to Feedback Systems / Önder YÜKSEL
Procedure
• Factorize the transfer function in to “simple” factors
• Obtain magnitude(db) versus frequency and phase versus frequency characteristics for each
• Obtain overall magnitude(db) versus frequency characteristics by adding those of factors
• Obtain overall phase versus frequency characteristics by adding those of factors
03.05.2004 Bode plots 9
Introduction to Feedback Systems / Önder YÜKSEL
“simple” factors
Origin zero s
Constant multiplier K
Origin pole s1
Finite real zero zs1 Finite real pole
ps11
Conjugate zero pair
221
nn
ss
Conjugate pole pair
221
1
nn
ss
03.05.2004 Bode plots 10
Introduction to Feedback Systems / Önder YÜKSEL
Constant multiplier K
K)j(T
Klog)j(T db 20
0
00
K
KK)j(T
log
)j(T
log
)j(T
2020loglogKK
03.05.2004 Bode plots 11
Introduction to Feedback Systems / Önder YÜKSEL
j)j(T
)j(T
2 )j(T
log)j(T db 20
log
)j(T
2
=1
Slope =20 db/decade
)j(T
logdb0
Origin zero: s
03.05.2004 Bode plots 12
Introduction to Feedback Systems / Önder YÜKSEL
s1
j)j(T 1
1)j(T
2 )j(T
log)j(T db 20
log
)j(T
2
=1)j(T
logdb0
Slope =-20 db/decade
Origin pole:
03.05.2004 Bode plots 13
Introduction to Feedback Systems / Önder YÜKSEL
zs)s(T 1
zj)j(T 1
21z
)j(T
As 1)j(T
As z)j(T
0
Finite real zero
03.05.2004 Bode plots 14
Introduction to Feedback Systems / Önder YÜKSEL
Asymptotes
1)j(T
db0
z)j(T
0
0db)j(T
zloglog)j(T db 2020
decade/db20z
03.05.2004 Bode plots 15
Introduction to Feedback Systems / Önder YÜKSEL
Deviations from actual
db0
decade/db20
z
3 db
1 octave
1 db
1 octave
1 db
03.05.2004 Bode plots 16
Introduction to Feedback Systems / Önder YÜKSEL
Finite real zero:Phase vs. Frequency
zj)j(T 1
00 )j(
ztan)j(T)j( 1
2)( j 0
2
4
=10z
=z/10
4)( zj
=z
1 decade1 decade
03.05.2004 Bode plots 17
Introduction to Feedback Systems / Önder YÜKSEL
1 decade1 decade
2
=z
0
0.1 rad0.1 rad
03.05.2004 Bode plots 18
Introduction to Feedback Systems / Önder YÜKSEL
ps)s(T
11
pj)j(T
11
211
p
)j(T
1)j(T
p)j(T
0
0db)j(T
ploglog)j(T db 2020
Finite real pole
03.05.2004 Bode plots 20
Introduction to Feedback Systems / Önder YÜKSEL
decadedb /20
db0
z
3 db
1 octave
1 db
1 octave
1 db
03.05.2004 Bode plots 21
Introduction to Feedback Systems / Önder YÜKSEL
Finite real pole:Phase vs. Frequency
pj)j(T
11
ptan)j(T)j( 1
1 decade1 decade
2
4
=z
0
0.1 rad0.1 rad
03.05.2004 Bode plots 22
Introduction to Feedback Systems / Önder YÜKSEL
221
nn
ssConjugate zero pair:
nn
j)j(T
21
2
22241
nn
)j(T
201
n
03.05.2004 Bode plots 23
Introduction to Feedback Systems / Önder YÜKSEL
01200 log)j(T db
db0
decade/db40z
ndb logloglog)j(Tn
404020
2
03.05.2004 Bode plots 24
Introduction to Feedback Systems / Önder YÜKSEL
1 octave1 octave1
10.
Magnitude vs. frequency
6 db1 db
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Introduction to Feedback Systems / Önder YÜKSEL
1
10.
00
Phase vs. frequency
03.05.2004 Bode plots 26
Introduction to Feedback Systems / Önder YÜKSEL
2211
ns
ns
Conjugate pole pair:
nn
j)j(T
21
12
1222
41
nn
)j(T
2
01
n
03.05.2004 Bode plots 27
Introduction to Feedback Systems / Önder YÜKSEL
01200 log)j(T db
db0
decade/db40
z
logloglog)j(T ndbn 4040202
03.05.2004 Bode plots 28
Introduction to Feedback Systems / Önder YÜKSEL
1 octave1 octave
1
10.
Magnitude vs. frequency
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Introduction to Feedback Systems / Önder YÜKSEL
110.
00
--
Phase vs. frequency
03.05.2004 Bode plots 30
Introduction to Feedback Systems / Önder YÜKSEL
T
4
T3
T
2
T
1
Example
)42(
18)(
2
sss
ssG
)21(
12 2
2221 sss
s
03.05.2004 Bode plots 31
Introduction to Feedback Systems / Önder YÜKSEL
Frequency (rad/sec)
Ph
ase
(d
eg
)M
ag
nitu
de
(d
B)
)21(
12)( 2
2221 sss
ssG
0.1 1 10 100
db62log20
0
-20
-40
-6090
0
-90
-180
03.05.2004 Bode plots 32
Introduction to Feedback Systems / Önder YÜKSEL
-60
-40
-20
0
20
Mag
nitu
de (
dB)
10-1
100
101
102
-180
-135
-90
-45
Pha
se (
deg)
Frequency (rad/sec)
