Module 15 Bode Diagram
(3 hours)
Plot the Bode diagram of a complex system
Write the transfer function of system through
the Bode diagram
Bode diagram are the third method (root locus and Nyquist
Methods are the other two),used to design a stable closed-loop
system,Bode diagrams are similar to the Nyquist diagrams,in
the sense that we plot the phase and magnitude of the open-loop
TF,but this time against the frequency,
In comparison with the Nyquist diagrams,the Bode diagrams
contain additional information about the system in the frequency
data,Knowing the Bode diagram one can construct the
corresponding Nyquist diagram,but the reverse is not possible.
Consider the closed-loop system described below:
CR
G
H
15.1 The Definition of Bode Diagram
(Bode 图的定义 )
)(lg
)(lg20(?jGHM a g n itu d e
)(lg
)(?jGH?
d ecib eldb
)(lg20
lg20
jGH
MM db
dbM
)(dB
1.0 1 10 100
1.0 1 10 100
90
180
15.2 Bode Diagram of Simple system
)(lg
)(lg
dbM
)(dB
1.0 1 10 100
1.0 1 10 100
90
180
Klg20
KsGHC a s e?)(:3

0
lg20
KM db
)1()( Tss
KsGH
1)(lg20lg20lg20 2 TKM db
Ttg 190
Ex,1
)(lg
)(lg20?jGH
)(lg )(?jGH?
0
90
180
Klg20
1
lg20?
decdB /20?
T1
decdB /40?
decdB /20?
lg20lg20?K
Ex,2
)1()( 2 Tss
KsGH
1)(lg20lg40lg20 2 TKM db
Ttg 11 8 0
)(lg )(?jGH?
0
180
270
T1
)(lg
)(lg20?jGH
decdB /40?
decdB /60?
)()1( )1()( 21
2
2
1 TT
sTs
sTKsGH?
Ex,3
1)(lg20
lg40
1)(lg20
lg20
2
2
2
1


T
T
KM
db


180
180
2
1
1
1

Ttg
Ttg
)(lg )(?jGH?
0
180
90
1
1T
)(lg
)(lg20?jGH
decdB /20?
decdB /40?
2
1T
decdB /40?
)()1( )1()( 21
2
2
1 TT
sTs
sTKsGH?
Ex,4
1
1T )(lg
)(lg20?jGH
decdB /60?
decdB /40?
2
1T
)(lg )(?jGH?
270
180
decdB /40?
1)(lg20
lg40
1)(lg20
lg20
2
2
2
1


T
T
KM
db


180
180
2
1
1
1

Ttg
Ttg
Ex,5
15.3 The Steps of Plotting the Bode Diagram
( P307,Sample Problem 15.2 )
Preparation Step – Writing the open-loop frequency response in
Bode form firstly:
)1 0 04)(20(
)2(5 0 0)(
2

ssss
ssGH
)1
100
4
100
1
)(1
20
1
(
)1
2
1
(5.0
)(
2
ssss
s
sGH
Step 1– Calculate the break frequencies:
20;10;2 321
Step 2– Determine the frequency range to be plotted:
1 0 01.0 1
Step 3–Plot the straight line magnitude approximation (近似直线幅值）
Step 4– Graphically add all element magnitude.
Step 5– Plot Deviations (画出转折频率处的偏差）
Step 6– Complete the magnitude curve.
)3,1( 1 dbisd e r ia ti o nth eTw h e n
Step 7– Plot the phase-frequency curve.
)1
10
1
)(1
5
1
(
)2(
)(
3
2

sss
s
sGH
Ex,6
1)( Ts
KsGH
Ex,7 1)(lg20lg20 2TKM db
Ttg 1180
15.4 The correspondence relationships between the
Magnitude-frequency curve and the Phase-frequency
curve of a minimum phase system
)11)(11(
1 0 0)(
21

ss
sGH

Ex,8
)1
1
(
)1
1
(
)(
2
2
1
ss
sK
sGH
Ex,9
Ex,10
)11)(11(
)(
32

ss
KssGH

10
20lg20
K
dBK
101 21
Ex,11
ω1 ω2
)1
1 0 0
1
)(1
1
(
)1
1
(1 0 0
)(
1
2

ss
s
sGH
100
1000
1
2
21

Ex,12
)1
1
(
)1
1
(
)(
2
2
1
ss
sK
sGH
1 0 040lg20 KdBK?
16.310102140 10lg20lglg2010lg40 2
1
11
1
dBdB
316100 12
Instructional objectives:
At the end of this lecture students should
be able to
Plot the Bode Diagram of a complex system expressed
in TF,
Determine the phase-frequency curve according to the
magnitude-frequency curve for a minimum-phase
system.
Determine the Transfer Function of a minimum-phase
system according to the magnitude-frequency curve,