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Download Figure (1): Model of the speaker system.
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Contents Abstract: .................................................................................................................................................. 2 Objectives: .............................................................................................................................................. 2 Apparatus: ............................................................................................................................................... 2 Figure (1): Model of the speaker system. ............................................................................................... 2 Procedure:............................................................................................................................................... 3 Results: .................................................................................................................................................... 4 Discussion and Conclusions: ................................................................................................................... 5 Abstract: System identification methods maybe used to built mathematical models of dynamic systems based on observed and measured input and output data from the system. System identification is defined as: identification is the determination, on the bases of input and output of a system within a specified class of systems, to which the system is under test is equivalent. In this experiment the current was stable whilst changing the voltage to obtain and record the difference in position so it can be drawn with the variation of the frequency to obtain and discuss the resonance that occurs. Objectives: In this experiment the goal is to study the response of second order system and estimate its parameters. Also, learning how to perform reverse Engineering. Apparatus: The apparatus used in the experiment contain various parts. The main part was a speaker which starts at a position, and when an input is introduced the position of the speaker changes. The input of the speaker comes from oscilloscope and it’s varying from 2 to 70 Hz, then goes through an amplifier to control the current (which is constant in our case) of the system. A multi-meter is used to measure the output voltage (voltage of speaker). A sensor is used to detect the position displacement of the speaker and it’s connected to a computer to observe the output. Figure (1): Model of the speaker system. Procedure: - Select a reference value for the position of the speaker. Enter the desired value of frequency to the oscilloscope. Calibrate the amplifier to obtain the desired constant value of current Obtain the value of the output voltage. Obtain the value of the new position of the speaker Subtract the value of the new position from the reference value to change between them. Repeat for other frequencies. Then the variation of the magnitude with the frequency plot can be generated, in order to continue and find the Bode plot. Results: Figure(2): Variation of Magnitude with Frequency. Table (1) : Frequency Domain Results. Abs(log) Log(deltax/V) -10.8814 10.88136 -2.49877 2.498775 -1.58362 1.583625 -9.54243 9.542425 -16.902 16.90196 0 0 -13.9794 13.9794 -12.0412 12.0412 -15.563 15.56303 24.84615 24.84615 -26.0206 26.0206 -27.9588 27.9588 V 0.7 0.8 0.6 0.6 0.7 0.8 1 1 1.2 1.7 2 2.5 I 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 delta x 0.2 0.6 0.5 0.2 0.1 0 -0.2 -0.25 -0.2 29.7 -0.1 0.1 x 44.3 44.7 44.6 44.3 44.2 44.1 43.9 43.85 43.9 73.8 44 44.2 F 3 6 9 12 15 18 21 24 27 30 32 34 19.40074 26.0206 32.66937 32.86905 33.06425 33.25516 0 32.66937 0 30.103 10.74238 20.82785 16.25827 17.50123 16.25827 -19.4007 -26.0206 -32.6694 -32.8691 -33.0643 -33.2552 0 -32.6694 0 -30.103 -10.7424 -20.8279 -16.2583 -17.5012 -16.2583 2.8 4 4.3 4.4 4.5 4.6 4.7 4.3 4.4 3.2 3.1 2.2 1.3 1.5 1.3 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 -0.3 0.2 0.1 0.1 0.1 -0.1 0 -0.1 0 -0.1 -0.9 -0.2 -0.2 -0.2 -0.2 43.8 44.3 44.2 44.2 44.2 44 44.1 44 44.1 44 43.2 43.9 43.9 43.9 43.9 36 38 40 41 42 43 44 45 46 48 50 52 55 58 64 Discussion and Conclusions: From the obtained results the natural frequency has been obtained by changing the input over a wide range of frequencies. By changing the input the position of the speaker ( rubber material ) has been observed and recorded from the above table and it shows that the difference in the position was calculated and plotted with the frequency to obtain the natural frequency. Resonance which has been obtained from the graph and at that resonant frequency it has the ability to produce large amplitude oscillations this is because the system stores vibrational energy and when damping is small the resonant frequency is approximately equal to the natural frequency of the system.