Solutions_hw7 - Homework 7 ECE147A November 24, 2009 The...

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Unformatted text preview: Homework 7 ECE147A November 24, 2009 The Solutions from the Solution Manual follow at the end, first points and some remarks. Problem 1 For full points, you need to explain in a few words why your sketch looks the way it looks, e.g. The magnitude starts at 0dB while the phase is 0 , so the Nyquist Plot starts at (1 , j ). 3 points for each Nyquist Plot, 2 each for the statement whether we have a stable system for the K you picked in your sketch or not. Problem 2 Do not be confused by the last figure where it seems like you could move the point- 1 K out of the contour you cannot, because the semi-circle has infinite radius, which is just a little hard to draw. 15, if you explained what you are drawing why. Problem 3 2 points for the Phase Margin, 5 points for finding all Gain Margins. 4 points for describing what happens for small and large gains and in between - stability changes 3 times! The sketch of the Bode Plot is a little unsatisfactory, heres what I would suggest: The phase starts at -90 . 1 point The phase is -180 at , L and H . Furthermore, < L < H . 2 points Between and L and after H , the phase is below -180 , between L and H it is above. 3 points 1 the phase approaches -270 for . 2 points The magnitude at * is 0dB, at L it is dB = 20log( ) and at H it is dB . 2 points The phase at * is - 180 . 2 points An example Bode Plot is shown in Figure 1. The system I used is H ( s ) = 2000 s 2 + 6000 s + 4500 s 5 + 40 . 2 s 4 + 408 s 3 + 80 . 4 s 2 + 4 s . Dont worry how I found that, it took me a while. The relevant part of the root locus is shown in Figure 2. The Nyquist Plot also resembles the one shown in the book somewhat, however, you need to zoom a lot to see that, so I did not include it here. 4 points for a root locus that has the porperty that the closed loop is stable, then unstable, then stable and finally unstable again for increasing k . Bode Diagram Frequency (rad/sec) 10-2 10-1 10 10 1 10 2 10 3-270-225-180-135-90 Phase (deg)-150-100-50 50 100 150 Magnitude (dB) H * L -180 dB dB Figure 1: Problem 3: An example Bode Plot Problem 4 For each of the ranges 3 points, for the number of unstable poles 2 points and 3 points for the sketch of the root locus....
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This note was uploaded on 08/03/2010 for the course ECE PROF. VOLK taught by Professor Volkanrodoplu during the Spring '10 term at UCSB.

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Solutions_hw7 - Homework 7 ECE147A November 24, 2009 The...

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