This preview shows page 1. Sign up to view the full content.
Unformatted text preview: Page 1 of 3 Computer Shortcut: freqg.p CHE 361 Task: Use the MATLAB "program" file freqg.p to determine the frequency response of: G( s) = 2e −0.2 s
for the freqency range of ω from 0.01 to 10 rad/min
10s + 1 Then check the amplitude ratio and phase angle at 2 rad/min by "hand" using the shortcut method. To
"run" the program, simply type >>freqg at the prompt in the MATLAB Command Window. Here's
what you should see, with bold letters indicating what you enter:
>> freqg


MATLAB Program "freqg"

 Uses "shortcut" method to calculate frequency

 response of G(s) where G(s) has a polynomial

 numerator and denominator and a single time delay. 
 Saves results freq,RePart,ImPart,AR,Phase in deg

 in columns in a file specified by the user.


Example: 2s^2 + 0s + 1 = [2, 0, 1]


Dr. K.L. Levien Nov. 12, 2003


Revisions: 11/8/04, 2/20/08, 2/15/12

 Chemical Engineering, Oregon State University


Enter numerator coefficient vector: [2]
Numerator Vector = [2]
Enter denominator coefficient vector: [10, 1]
Denominator Vector = [10, 1] G ( s) = N ( s ) −θ s
e
D( s) Enter time delay: 0.2
Time Delay = 0.2
Enter minimum frequency, rad/time (0.01) = 0.01
Enter maximum frequency, rad/time (10)
= 10
Enter number of frequencies to use (100) = 100
Hit Enter to use default data file name 'freqg.dat'
or enter the desired name of the file.
Enter name of data file to save (freqg.dat) : freqg1.dat

 Data has been saved in a file named freqg1.dat

>> The main problem in applying the shortcut method using a computer is the need to keep track of the
phase angle properly as the frequency increases. This is difficult because trig functions are
periodic with a period of 2π radians. For example, the polar angle of a point in the G(jω) plane at
+1  1j could be at  45 deg or 45  360 =  405 deg. From a practical standpoint, if more frequencies
are used between the lower and upper limits, it is easier for the MATLAB command "unwrap" to be
able to draw a nice Bode plot. Page 2 of 3 Once you have created the freqg.dat, you can enter the following command in the Command
Window to draw the Bode plot for the data: >>chebode Amplitude Ratio 10
10
10 1 Bode Plot: made by chebode using freqg.dat 0 1 2 10 2
10 10 1 0 1 0 10
Frequency (rad/min) 10 1 0
Phase (deg) 45
90
135
180
225
270 2
10 Amplitude Ratio 10 10 10 1 10 10
Frequency (rad/min) 10 1 Amplitude Ratio Plot: made by chebode using freqg.dat 0 1 2 10 2
10 10 1 10
Frequency (rad/min) 0 10 1 Page 3 of 3 Phase Angle (degs) Plot: made by chebode using freqg.dat
0 45 Phase (deg) 90 135 180 225 270 2
10 10 1 10
Frequency (rad/min) 0 10 1 chebode.p = makes one curve on a Bode plot using data in the file freqg.dat in format with 5
columns: freq, RealG, ImgG, AR, phase angle in degrees = the "freqg.p" format.
chebodei.p = similar, but interactive to ask for name of file.
When you want to compare two Bode plots on the same set of axes, you can use the file
chebode2i.p, which reads two (2) data files with names entered by the user. The data in the first
data file is plotted using solid lines while the second data file is plotted with dashed lines. The same
3 plots are made, but each displays 2 curves.
When you use the “pulse experiment analysis button”, for example with the Bioreactor Project, a file
freqg.dat is created. Simply copy or rename that file for appropriate use with chebode2i.p. The
command "grid" can be entered in the MATLAB Command Window to turn OFF the grid lines for
easier comparisons of the curves. Each subplot needs to be clicked on to become the active region. Amplitude Ratio 10
10
10 1 Bode Plot: chebode2, solid=freqg1.dat, dash=freqg2.dat 0 1 2 10 2
10 10 1 0 1 0 10
Frequency (rad/min) 10 1 0 Phase (deg) 45
90
135
180
225
270 2
10 10 10
Frequency (rad/min) 10 1 ...
View Full
Document
 Winter '08
 Staff
 pH

Click to edit the document details