OBJECTIVES: To produce Bode Diagram of unknown system with frequency response experiment To approximate transfer functio

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Objectives To Produce Bode Diagram Of Unknown System With Frequency Response Experiment To Approximate Transfer Functio 1 (122.34 KiB) Viewed 45 times

OBJECTIVES: To produce Bode Diagram of unknown system with frequency response experiment To approximate transfer function from Bode Diagram Frequency Response Experiment 1. Connect the output of signal generator to the input terminals of the black box Vin. Set the function generator to output a sine wave of magnitude 5V peak (10V peak-to-peak). Oscilloscope CH1 CH2 Black Box + Vin(s) G(s)=?? Vout(s) Black Box Function Generator Output (500) Vin Vout GND 2. Connect oscilloscope's probes to both the input Vin and output Vout of the black box. a. Set the frequency of the sinusoidal signal to 1Hz. b. Using the oscilloscope, measure the RMS voltage of Vin and Vout. Using the 'cursor' function of the oscilloscope to measure the time difference and hence the phase difference of the input and output. d. Repeat steps a, b and c for with different frequencies and complete the Table 1. You may record more data points. (sample data will be provided) c.

Vin Vout Gain Frequency (Hz) Lag time Period (Voltage) (Voltage) (seconds) (seconds) Gain (dB) Phase Difference (0) 1 10 100 500 750 1000 1500 2000 3000 5000 8000 10000 20000 30000 50000 100000 Table 1

3. From the sample data provided, calculate the gain and phase of the frequency response in dB and degrees plot the Bode diagram (gain and phase) of the black box. 4. From the Bode diagram and asymptotic approximation, estimate Transfer Function the black box. Vout(s) of Vin(s) 5. From Transfer Function in (4), plot the theoretical Bode diagram (gain and phase). Hint: You may use MATLAB Control Toolbox functions (tf and bode) to assist you. 6. Compare theoretical (5) and experimental Bode diagram (3) and comment on the difference, if any.

Deliverables (10%) A complete lab report with the following format: • Introduction • Main contents (Procedures on how the gain and phase response are obtained, tables, graphs, answer all questions) Conclusion .

w (rad/s) Vin (V) Vout (V) Freq (Hz) 1 10 100 500 750 1000 1500 2000 3000 5000 8000 10000 20000 30000 50000 100000 6.283185 1.44 62.83185 1.36 628.3185 1.36 3141.593 1.36 4712.389 1.36 6238.185 1.36 9424.778 1.40 12566.37 1.48 18849.56 1.44 31415.93 1.32 50265.48 1.36 62831.85 1.48 125663.7 1.44 188495.6 | 1.32 314159.3 1.36 628318.5 1.44 0.96 0.88 0.88 0.88 0.88 0.88 0.84 0.80 0.68 0.52 0.40 0.32 0.16 0.12 0.08 0 Gain, k Gain Lagtime Period (s) Phase (dB) (s) Diff (°) 0.666667 -3.521830 1 0 0.647059 -3.781120 0.1 0 0.647059 -3.78112 0.000082 0.01 2.952 0.647059 -3.78112 0.000043 0.002 7.74 0.647059 -3.78112 0.000044 0.00133333 11.88 0.647059 -3.78112 0.000040 0.001 14.4 0.600000 -4.43697 0.000040 0.00066667 21.6 0.540541 -5.34343 0.000040 0.0005 28.8 0.472222 -6.51707 0.000030 0.00033333 32.4 0.393939 -8.09141 0.000030 0.0002 54 0.294118-10.6296 0.0000212 0.000125 61.056 0.216216-13.3022 0.0000176 0.0001 63.36 0.111111 -19.0849 0.0000094 0.00005 67.68 0.090909 -20.8279 0.0000065 0.000033 70.2 0.058824 -24.6090 0.0000040 0.00002 0 0.0000212 0.00001 76.32 72 -DO