Bode_HW_Sol - 1 a 1 By checking the final slop 40 db/dec we...

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1.) a.) 1. By checking the final slop (– 40 db/dec), we know the difference of orders (Denominator – Numerator) is 2. Besides, no rising for phase plot but all the way through to – 180 ° , therefore, we conclude “no zeros” and with damping ratio less than 0.707 (due to the peak on the magnitude plot). 2. The Transfer Function should have the form as: + + 1 2 2 2 2 n n n S S K ω ζ . 3. Substitute i S = into T.F., we have our F.R.F. 4. From 90 ° crossing, we know 3 n (rad/sec). 5. For n << , ) ( 4 ) 3 log( 20 ) log( 20 2 db K FRF . 7 . 5 K 6. For n = , ) 2 log( 20 4 ) 2 log( 20 ) 3 log( 20 ) log( 20 2 ξ K FRF 19 . 0 ), ( 5 . 4 db
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7. Therefore, our T.F. is approximately: 9 14 . 1 7 . 5 2 + + S S [Note: The Bode plot above is actually generated by 9 5 . . 2
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Bode_HW_Sol - 1 a 1 By checking the final slop 40 db/dec we...

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