solution_hw_7

# solution_hw_7 - MAE 4310 SOLUTIONS TO HW 7 B-6-9 The...

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Unformatted text preview: MAE 4310 SOLUTIONS TO HW # 7 B-6-9) The open-loop transfer function is ) 11 4 ( ) 9 ( ) ( 2 + + + = s s s s K s G poles: 0, j 7 2 µ − zeros: -9 The asymptotes have angles ° + 90 and meet the real axis at 5 . 2 = a σ . The complex branches cross the imaginary axis at 45 . 4 j µ . The angle of departure from the complex pole in the upper half s plane is ° − 5 . 16 To locate the closed-loop poles on the root loci such that the dominant closed-loop poles have a damping ratio equal to 0.5 we use “long division ” method. Characteristic equation of the system K s K s s 9 ) 11 ( 4 2 3 + + + + must be divisible by 2 2 n n s s ω ω + + K s K s s 9 ) 11 ( 4 2 3 + + + + |_ 2 2 n n s s ω ω + + s s s n n 2 2 3 ω ω + + ) 4 ( n s ω − + _____________________________________ K s K s n n 9 ) 11 ( ) 4 ( 2 2 + − + + − ω ω 2 2 ) 4 ( ) 4 ( ) 4 ( n n n n n s s ω ω ω ω ω − + − + − _____________________________________________________ 2 ) 4 ( 9 ) 4 11 ( n n n K s K ω ω ω − − + − + remainder ⇒ K s K...
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## This note was uploaded on 06/15/2009 for the course MAE 4310 taught by Professor Staff during the Fall '08 term at UT Arlington.

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solution_hw_7 - MAE 4310 SOLUTIONS TO HW 7 B-6-9 The...

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