Linear Control Systems Engineering
线性控制系统工程
Module 7 Higher-Order Systems
(高阶系统)
Module 7 Higher-order Systems
Module 7 Higher-order Systems
◆
◆
Reduction to Lower Order Systems
Reduction to Lower Order Systems
Example:
Example:
A Higher-order System
A Higher-order System
There are two forms:
There are two forms:
Evans form
Evans form
➡
➡
Bode form
Bode form
➡
➡
-2
-10
)10)(2(
100
)(
ss
s
R
C
)10)(2(
100
)(
ss
s
R
C
)10/1)(2/1(
5
)(
ss
s
R
C
1. For the Evans form, if
1. For the Evans form, if
2. For the bode form, if
2. For the bode form, if
then
then
then
then
Conclusion: the Bode form must be
used in order to correctly obtain the
transfer function of the reduced-order
system.
2
100
sR
C
50
2
100
lim
0
s
C
s
ss
2/1
5
)(
s
s
R
C
5
)2/1(
5
lim
0
s
C
s
ss
◆
◆
Third Order System
Third Order System
•
The advantage of reducing higher order system to
second order system: the time-domain response
may be estimated quickly from Fig 4.16 , 4,17.
=1.2
=0.2
=0.4
=0.6
=2
=0.8
=4
=1.0
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
1 2 4 5 6 7 8 9 103
Time (s)
Fig.4.16 Second-order step response
A
m
p
l
i
t
u
d
e