31_Exercise_14-3

31_Exercise_14-3 - Chap 14 = Frequency Response Analysis of...

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Unformatted text preview: Chap 14 = Frequency Response Analysis of Process Dynamics CHE 361 SEMD3 = “EXERCISE” 14.3 pg. 268. (In-class) A data acquisition system for environmental monitoring is used to record the temperature of an airstream as measured by a thermocouple. It shows an essentially sinusoidal variation after about 15s. The maximum recorded temperature is 127 oF, and the minimum is 119 oF at 1.8 cycles per min. It is estimated that the thermocouple has a time constant of 4.5 s. Estimate the actual maximum and minimum air temperatures. (Assume the calibration of the thermocouple was correct, thus the gain = 1.0 .) DIY = Do It Yourself Practice = Use complex numbers and the short-cut method to determine the AR and phase angle in degrees at a frequency of 3.00 rad/min for a first-order with time delay process where the gain is 20.0 oF/mA, the time constant is 4.00 minutes and the time delay is 0.50 minutes. Check your answer (to 3 significant figures) using freqg.p. Make up your own G(s) and repeat. Answers : AR = 1.66 oF/mA, PA = -171. degrees at a frequency of ω = 3 rad/min. >> freqg |----------------------------------------------------| | MATLAB Program "freqg" Winter 2012 version | | 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 = [20] Enter denominator coefficient vector: [10, 1] Denominator Vector = [4,1] Enter time delay: 0.2 Time Delay = 0.5 Enter minimum frequency, rad/time (0.01) = 3.0 Enter maximum frequency, rad/time (10) = 3.0 Enter number of frequencies to use (100) = 2 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) : |----------------------------------------------------------| | Data has been saved in a file named freqg.dat |----------------------------------------------------------| >> type freqg.dat 3.0000000e+000 -1.6412693e+000 -2.5466778e-001 3.0000000e+000 -1.6412693e+000 -2.5466778e-001 >> 1.6609096e+000 -1.7118003e+002 1.6609096e+000 -1.7118003e+002 ...
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