1 ME 360: FUNDAMENTALS OF SIGNAL PROCESSING, INSTRUMENTATION AND CONTROL Experiment No. 5 System Identification with Frequency Response Techniques using the Dynamic Signal Analyzer 1. CREDITS Originated: N. R. Miller, February 1989 Last Updated: D. Block, August 2007 2. OBJECTIVES (a) Manually vary the frequency input to obtain the gain and phase-shift (Bode) plots of a motor-generator system. (b) Become familiar with the functionality and operation of a dynamic signal analyzer. (c) Use a dynamic signal analyzer to obtain the gain and phase-shift (Bode) plots of a motor-generator system. (d) Use a dynamic signal analyzer to obtain the gain and phase-shift (Bode) plots of a beam-mass system. 3. KEY CONCEPTS (a) A Bode plot of a system can be found by varying the frequency of a sine wave input to the system and measuring the gain and phase-shift between this input and the system output signal. (b) A dynamic signal analyzer is a dedicated instrument that determines the frequency spectrum of an arbitrary waveform using Fast Fourier Transform (FFT) techniques. (c) A dynamic signal analyzer can also determine the gain and phase shift (Bode) plots for a basic input-output system using either a sinusoidal input (sine-sweep method) or a noise input. 4. SYNOPSIS OF PROCEDURE (a) A Bode plot for a motor-generator system is manually found by applying different frequency sine waves to the system and measuring the gain and phase-shift of the output. (b) Bode plots for a motor-generator system are obtained with the dynamic signal analyzer using both the sine-swept and white-noise methods. The steady-state gain and time constant of the system are determined from the plots. (c) Bode plots for a beam-mass system are obtained with the dynamic signal analyzer using the sine-swept method. The resonant frequency is compared with the theoretical value calculated from beam and mass parameters. This part of the procedure is carried out as a demonstration by the Laboratory Assistant for the group as a whole. 5. PROCEDURE 5.1 Manual Sine Sweep Identification. To get a good understanding of what the DSA is capable of automating for you, you will first manually generate a Bode plot of the frequency response of the motor-generator system. This is done by applying a number of different frequency sine waves to the system and measuring the gain and phase shift change between the system’s input and output on the oscilloscope. Wire the System (a) Connect the function generator’s output to the amplifier input on the patch panel. (b) Connect the amplifier’s output to the motor’s plus, minus and ground jacks. (b) Connect oscilloscope Channel 1 to the amplifier input. (c) Connect oscilloscope Channel 2 to the motor’s tachometer output. (d) Connect the push button (Amp Inhibit button) to the amplifier.2 Program Function Generator (e) Program the function generator to produce a 0.2 Hz sine wave with an amplitude of 2 Vp-p and 4-V DC offset. Start Oscilloscope (c) Press "Run" on the oscilloscope. Then start the motor by depressing the amplifier push button. Observe the input and output waveforms on the oscilloscope. Make sure you see only two or three periods of the input and output on the oscilloscope so you can accurately measure the gain and phase-shift. Determine Frequencies for Constructing Bode Plots (d) Slowly sweep the frequency between 0.2 and 10 Hz using the dial on the function generator. Notice how the gain and phase shift change with frequency. Choose eight frequencies in this range at which quantitative determinations of the gain and phase shift will be made. Enter these frequencies on the Data Sheet. (e) Set the function generator to the first test frequency. Determine Gain G(f) and Phase Shift (f) at Each Test Frequency Using Oscilloscope Cursors (f) Turn the oscilloscope cursors on and select Channel 2 for the cursor source. Use the cursors to measure Vp-p,out, the peak-to-peak voltage of the generator output. Record this value on the Data Sheet. Compute the gain at this frequency from G(f) = Vpp,outputVpp,input where Vp-p,input = 2 V Record G(f) on the Data Sheet. (g) Measure the time delay delay of the generator output voltage with respect to the motor input voltage using the time cursors. Record the time delay on the Data Sheet. Compute the phase shift at this frequency from (f) = -360°  f delay . Record (f) on the Data Sheet. Construct Bode Plots Based on Results of Sinusoidal Inputs (h) Use the commands below to plot the bode plots. The values of the K and , determined from a graphical analysis of the Bode plots as described in the Appendix should be entered on the Data Sheet as Kmansweep, mansweep,-3dB, and mansweep, . MATLAB Command Action Clear clear all variables fs = [ x.x x.x x.x x.x x.x x.x x.x x.x ] enter the test frequencies into an array Gs = [ x.xx x.xx x.xx x.xx ... x.xx ] enter gains into an array phis = [ xx.x xx.x xx.x xx.x ... xx.x ] enter phase shifts into an array Gdbs = 20 * log10(Gs) convert gains to decibels [dB] semilogx (fs, Gdbs) plot gain in dB vs. frequency in Hz with frequency on a log scale xlabel ('f [Hz]') label x axis ylabel ('G [dB]') label y axis; print out gain plot semilogx (fs, phis) plot phase shift in degrees [°] vs. frequency in Hz with frequency on a log scale xlabel ('f [Hz]') label x axis ylabel ('phi [deg]') label y axis; print out phase-shift plot3 5.2 Frequency Response of Motor-generator System In this part of the experiment, we perform a frequency analysis of the motor-generator system using both a sinusoidal and a white-noise input. The frequency response captured by the signal analyzer will be used to determine the steady-state gain K and the time constant . The analyzer serves as the source of both the sinusoidal and white-noise inputs to the motor-generator. The output connector for the source is located on the rear of the analyzer. Because this is your first experience with the signal analyzer, detailed programming instructions are given for this instrument. Here, we use the following conventions for specifying keystrokes. (a) Bold text is used to denote hard keys. To aid in locating the proper key, the control section (system, marker, display, or measurement) and the letter at the lower right-hand corner of the key (if one exists) is given in