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HW solutions - MEEN 411 Solutions to Mid-term Exam 1 Solutions to Exam 1 1 Figure(a Figure(4 The phase of the system is asymptotic from 0 degrees

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Unformatted text preview: MEEN 411 Solutions to Mid-term Exam 1 Solutions to Exam 1 1) Figure (a) Figure (4) The phase of the system is asymptotic from 0 degrees to -90 degrees. The magnitude plot has a -20 dB roll-off. So it can be concluded that it is a first order system. Figure (b) Figure (1) In this case, the phase of the system is asymptotic from 0 degrees to -180 degrees. The magnitude plot has a -40 dB roll-off. This corresponds to a second order system. It can also be noted that, there is very high damping in the system, which is evident by the absence of the "hump" near the natural frequency. Figure (c) Figure (3) In this case, the phase of the system is asymptotic from 0 degrees to -180 degrees. The magnitude plot has a -40 dB roll-off. This corresponds to a second order system. It can also be noted that, there is very less damping in the system, which is evident by the presence of the "hump" near the natural frequency. Figure (d) Figure (2) Since the phase plot rolls off as frequency increases, this is a typical case of a system with a delay. MEEN 411 Solutions to Mid-term Exam 2 2a) Poles: 0, -2, (3 ± j √ 391)/2; system unstable – two RHP poles and one pole at the origin Zeros: 4, -1 ± j4 √ 3; system non-minimum phase – one zero on the RHP. The transfer function is converted to the following form by substituting ω j s = , ( ) ( ) ( ) ( ) . 1 100 3 10 1 2 ) ( 1 49 2 7 1 4 100 ) ( 3 ) ( 2 ) ( 98 49 ) ( 2 ) ( 4 100 ) ( 2 2 2 2 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = + − + + + − = ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω j j j j j j j j j j j j j j j G From the above transfer function; the corner frequencies can be obtained as...
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This note was uploaded on 09/20/2009 for the course MEEN 651 taught by Professor Staff during the Fall '08 term at Texas A&M.

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HW solutions - MEEN 411 Solutions to Mid-term Exam 1 Solutions to Exam 1 1 Figure(a Figure(4 The phase of the system is asymptotic from 0 degrees

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