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)
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.