HOMEWORK 1. EE 5329 - University of Texas at Arlington Sol.pdf · HOMEWORK 1. EE 5329 Kristian...
Transcript of HOMEWORK 1. EE 5329 - University of Texas at Arlington Sol.pdf · HOMEWORK 1. EE 5329 Kristian...
HOMEWORK 1. EE 5329
Kristian Hengster Movric, 1000676470
-6 -4 -2 0 2 4 6-5
-4
-3
-2
-1
0
1
2
3
4
5a=0.05
Figure 1. Phase portrait of Van der Pol oscillator, a=0.05
-5 -4 -3 -2 -1 0 1 2 3 4 5-6
-4
-2
0
2
4
6a=0.9
Figure 2. Phase portrait of Van der Pol oscillator, a=0.9
0 5 10 15 20 25 30 35 40-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5a=0.05,y(0)=0.2,y'(0)=0
Figure 3. Time response of Van der Pol oscillator a=0.05, y(0)=0.2, y’(0)=0
0 5 10 15 20 25 30 35 40-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5a=0.9,y(0)=0.2,y'(0)=0
Figure 4. Time response of Van der Pol oscillator a=0.9, y(0)=0.2, y’(0)=0
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6a=0.05,y(0)=0.2,y'(0)=0
Figure 5. Phase portrait of Van der Pol oscillator a=0.05, y(0)=0.2, y’(0)=0
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5-3
-2
-1
0
1
2
3Phase portrait a=0.9,y(0)=0'.2,y'(0)=0
Figure 6. Phase portrait of Van der Pol oscillator a=0.9, y(0)=0.2, y’(0)=0
0 50 100 1500
50
100x3
0 50 100 150-20
0
20x1
0 50 100 150-50
0
50x2
Figure 7. Time response of the Lorentz system for x1(0)=x2(0)=x3(0)=0.3
-20-10
010
20
-40
-20
0
20
400
10
20
30
40
50
The Strange Attractor
Figure 8. The strange (chaotic) attractot of the Lorentz system
-5
0
5
-5
0
5
0
2
4
6
8
s
Magnitude of H(s)
w
abs(
H(s
))
Figure 9. Magnitude 3D plot of the given transfer function
-5
0
5
-5
0
5
-2
-1
0
1
2
s
Phase of H(s)
w
arg(
H(s
))
Figure 10. Phase 3D plot of the given transfer function
-40
-30
-20
-10
0Bode diagram of H(s)
Mag
nitu
de (
dB)
10-1
100
101
102
-90
-45
0
Pha
se (
deg)
Bode Diagram
Frequency (rad/sec)
Figure 11. Bode amplitude and phase frequency characteristics