What
you should know for this experiment
Read
Chapter 8 of your textbook for Frequency Response Analysis information.
Frequency
response can be presented in two forms:
 Graphically:
There are two methods; the Polar plot and Bode plot. The Bode plot is
the most used method.
o Polar
Plot: Gain vs phase with frequency as a parameter
o Bode
Plot: Usually plotted on semi log paper. One graph is plotted for gain
vs frequency, the other is plotted for phase vs frequency.
 Theoretically:
The frequency response can be found from the transfer function:
Gain
=  G(jw)

phase = the angle of G(jw)
Example
Suppose
that we want to find the frequency response of a system whose transfer
function is given by:
First
of all we rearrange the equation (i.e. the transfer function). This
becomes:
From
there we can write the numerator and denominator as follows:
a =
[0 2 5 ] and b = [4 3 2 ]
Now
by using the Matlab command bode(a,b) we’ll get the phase and gain:
When
plotting the frequency response from experimental results remember
that it must be plotted on semilog axes. If you are unaware how to do
this type "help semilogx" into the MATLAB command window for
instructions.
Given a sine wave input u(t)=2sin(2t) to the transfer transfer function in the
example above. Determine the output y(t) in steady state using the bode
plot above.
Draw bode plot for the
motor speed model that you found in experiment 2 without using the output
filter. It
will be needed for comparison of your results of this experiment.
Given two sine waves as shown in the figure below, where output is green and
input is blue. Determine the gain in dB as a ratio of peak to peak output over
peak to peak input. Determine the phase shift.
Note: If you have
difficulty to measure the phase difference simulate sin(t) and sin(t+f) using
different f and study the difference between the two waves in order to
figure out the relation between the wave forms and their phase difference.
You can also read Procedures of Experiment 3 for more information on how to
determine the phase shift.
