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# HW3Sol - MANE4050 Modeling and Control Homework...

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1 MANE4050 – Modeling and Control Homework Assignment #3 1. Given a transfer function ) 9 9 . 0 )( 4 ( 5 . 22 ) ( 2 + + + = s s s s G a. Show the Bode or normalized form of the transfer function. b. Sketch on the attached log paper on page #3 the magnitude and phase asymptotes for each term and the composite asymptotes for the transfer function as well. Clearly label each slope and corner frequency. c. Determine the magnitude corner correction for the quadratic term. Solution: a. The Bode form of the transfer function G ( j ! ) = 22.5 4( j ! 4 + 1) " 9( # ! 2 9 + 0.1 j ! + 1) = 0.625 ( j ! 4 + 1)( # ! 2 9 + 0.1 j ! + 1) b. See attached sheet for the magnitude and phase asymptotes. c. From the quadratic term, we get the natural frequency 3 9 = = n ! rad/second and 15 . 0 3 2 9 . 0 2 9 . 0 9 . 0 2 = ! = = " = n n # \$ \$# So, the magnitude corner correction for the quadratic term is ) 15 . 0 2 log( 20 ) 2 log( 20 ! " = ! " # =10.4576

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2 2. Evaluate gain margin and phase margin from the Bode plots shown below. Solution: Gain margin = 26.8 dB Phase margin = 70.8 degree 3. Given the unit feedback system shown below.
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HW3Sol - MANE4050 Modeling and Control Homework...

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