week7 Solution0.pdf - University of Wollongong MECH321...

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1 n n R ( s ) Response ( d B ) University of Wollongong MECH321 Autumn 2016 - Tutorial 7 Solution 1. Calculate the DC gains (in dB) of the three systems described by the following transfer functions (2 Marks), 6 ω 2 G 1 ( s ) = , G 2 ( s ) = s 2 + 2 ζ ω n s + w 2 s 2 + 7 s + 22 ( s + 3)( s 2 + 2 s + 3) , G 3 ( s ) = s ( s + 1) ( s 2 + 9)( s 2 + 2 s + 4) Answer: G 1 ( s 0) = 6 15 . 56 dB , G 2 ( s 0) = 2 . 44 7 . 76 dB , G 3 ( s 0) = 0 −∞ 2. For a suspected second order dynamic system the transfer function cannot b e determined mathematically. Instead the magnitude plot of the transfer function G ( s ) = C ( s ) is experimentally measured and is given below, M ag n it ud e plo t of t h e second o r d e r s y s t e m 10 5 0 5 10 15 20 25 30 35 40 45 50 55 60 10 1 10 0 10 1 10 2 F r e q u e n c y (r a d / s ) An A4 copy of this graph and an expanded graph showing the peak detail are available on e-Learning if needed. (a) Determine the damping ratio ζ , the natural frequency ω n and th e bandwidth ω b of the system. (1 Mark)
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