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AE 383 System Dynamics
HW#3
Due: Dec. 27, 2005
1.
Using Routh’s stability test, examine the stability of the systems whose characteristic
equations are given below.
a.
7
6
5
4
3
2
2.3
4
5.6
7
11
18
12.3
s
s
s
s
s
s
s
+
+
+
+
+
+
+
b.
5
4
3
2
1
2
20
32
164
200
400
s
s
s
s
s
s
+
+
+
+
+
+
c.
8
7
6
5
4
3
2
3
48
21
35
19
4
14
56
s
s
s
s
s
s
s
s
+
+
+
+
+
+
+
+
2.
Following feedback control system is given.
Using Routh’s stability test, find the range
of values on K for the system to be stable.
3.
Approximately plot the unit step response of the following system whose characteristic
equation roots are at:
1
8
j
− ±
.
4.
The following 2
nd
order system is given:
2
100
( )
20
100
G s
s
s
ζ
=
+
+
.
Using Simulink
obtain the response of this system to step input for various values of the damping ratio,
(
0.1,
0.3,
0.7,
1.,
1.5)
ζ
=
.
Comment on your results. (Hint:
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- Spring '11
- Melin
- Characteristic polynomial, 10 seconds, 8 J, Routh’s stability
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