hwsln-421-s06-09

hwsln-421-s06-09 - ECE 421, Spring 2006 Solutions to HW...

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Unformatted text preview: ECE 421, Spring 2006 Solutions to HW Assignment #9 Problem #B-7-9 G p ( s ) = 5 s (0 . 5 s + 1) = 10 s ( s + 2) (1) The phase shift of G p ( s 1 ) is − 210 ◦ = +150 ◦ , so the compensator’s phase shift at s 1 must be 6 G c ( s 1 ) = 30 ◦ . Since this angle is positive, a lead compensator is needed, as indicated in the problem statement. The pole/zero placement procedure presented in the text will be used, which yields the following calculation. The speci f ed point for the dominant closed-loop pole is s 1 = − 2 + j 2 √ 3 = − 2 + j 3 . 4641 . 6 ( s 1 ) = tan − 1 μ 3 . 4641 − − 2 − ¶ = 120 ◦ (2) 6 ( s 1 − z c ) = 120 + 30 2 = 75 ◦ , 6 ( s 1 − p c ) = 120 − 30 2 = 45 ◦ d zc = Im ( s 1 ) tan ( 6 ( s 1 − z c )) = 0 . 9282 , d pc = Im ( s 1 ) tan ( 6 ( s 1 − p c )) = 3 . 4641 The compensator zero is placed at s = − 2 . 9282 , and the compensator pole is placed at s = − 5 . 4641 . The compensator gain is computed so that the series combination of the plant and lead compensator satis...
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This note was uploaded on 10/25/2010 for the course ECE 421 taught by Professor Cook,g during the Spring '08 term at George Mason.

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hwsln-421-s06-09 - ECE 421, Spring 2006 Solutions to HW...

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