Download Figure (1): Model of the speaker system.

Contents
Abstract: .................................................................................................................................................. 2
Objectives: .............................................................................................................................................. 2
Apparatus: ............................................................................................................................................... 2
Figure (1): Model of the speaker system. ............................................................................................... 2
Procedure:............................................................................................................................................... 3
Results: .................................................................................................................................................... 4
Discussion and Conclusions: ................................................................................................................... 5
Abstract:
System identification methods maybe used to built mathematical models of dynamic systems based
on observed and measured input and output data from the system. System identification is defined
as: identification is the determination, on the bases of input and output of a system within a
specified class of systems, to which the system is under test is equivalent.
In this experiment the current was stable whilst changing the voltage to obtain and record the
difference in position so it can be drawn with the variation of the frequency to obtain and discuss
the resonance that occurs.
Objectives:
In this experiment the goal is to study the response of second order system and estimate its
parameters. Also, learning how to perform reverse Engineering.
Apparatus:
The apparatus used in the experiment contain various parts. The main part was a speaker
which starts at a position, and when an input is introduced the position of the speaker
changes. The input of the speaker comes from oscilloscope and it’s varying from 2 to 70 Hz,
then goes through an amplifier to control the current (which is constant in our case) of the
system. A multi-meter is used to measure the output voltage (voltage of speaker). A sensor is
used to detect the position displacement of the speaker and it’s connected to a computer to
observe the output.
Figure (1): Model of the speaker system.
Procedure:
-
Select a reference value for the position of the speaker.
Enter the desired value of frequency to the oscilloscope.
Calibrate the amplifier to obtain the desired constant value of current
Obtain the value of the output voltage.
Obtain the value of the new position of the speaker
Subtract the value of the new position from the reference value to change between
them.
Repeat for other frequencies.
Then the variation of the magnitude with the frequency plot can be generated, in order to
continue and find the Bode plot.
Results:
Figure(2): Variation of Magnitude with Frequency.
Table (1) : Frequency Domain Results.
Abs(log) Log(deltax/V)
-10.8814
10.88136
-2.49877
2.498775
-1.58362
1.583625
-9.54243
9.542425
-16.902
16.90196
0
0
-13.9794
13.9794
-12.0412
12.0412
-15.563
15.56303
24.84615
24.84615
-26.0206
26.0206
-27.9588
27.9588
V
0.7
0.8
0.6
0.6
0.7
0.8
1
1
1.2
1.7
2
2.5
I
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
delta x
0.2
0.6
0.5
0.2
0.1
0
-0.2
-0.25
-0.2
29.7
-0.1
0.1
x
44.3
44.7
44.6
44.3
44.2
44.1
43.9
43.85
43.9
73.8
44
44.2
F
3
6
9
12
15
18
21
24
27
30
32
34
19.40074
26.0206
32.66937
32.86905
33.06425
33.25516
0
32.66937
0
30.103
10.74238
20.82785
16.25827
17.50123
16.25827
-19.4007
-26.0206
-32.6694
-32.8691
-33.0643
-33.2552
0
-32.6694
0
-30.103
-10.7424
-20.8279
-16.2583
-17.5012
-16.2583
2.8
4
4.3
4.4
4.5
4.6
4.7
4.3
4.4
3.2
3.1
2.2
1.3
1.5
1.3
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
-0.3
0.2
0.1
0.1
0.1
-0.1
0
-0.1
0
-0.1
-0.9
-0.2
-0.2
-0.2
-0.2
43.8
44.3
44.2
44.2
44.2
44
44.1
44
44.1
44
43.2
43.9
43.9
43.9
43.9
36
38
40
41
42
43
44
45
46
48
50
52
55
58
64
Discussion and Conclusions:
From the obtained results the natural frequency has been obtained by changing the input over a
wide range of frequencies. By changing the input the position of the speaker ( rubber material ) has
been observed and recorded from the above table and it shows that the difference in the position
was calculated and plotted with the frequency to obtain the natural frequency. Resonance which
has been obtained from the graph and at that resonant frequency it has the ability to produce large
amplitude oscillations this is because the system stores vibrational energy and when damping is
small the resonant frequency is approximately equal to the natural frequency of the system.