HW3_Sol - ENGR4050 Modeling and Control Spring 2004...

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1 ENGR4050 – Modeling and Control Spring 2004 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:
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This note was uploaded on 04/11/2010 for the course MANE 4050 taught by Professor Li during the Fall '08 term at Rensselaer Polytechnic Institute.

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HW3_Sol - ENGR4050 Modeling and Control Spring 2004...

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