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 zeros: -9 The asymptotes have angles + 90 and meet the real axis at 5 . 2 = a . The complex branches cross the imaginary axis at 45 . 4 j . 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 + + K s K s s 9 ) 11 ( 4 2 3 + + + + |_ 2 2 n n s s + + s s s n n 2 2 3 + + ) 4 ( n s + _____________________________________ K s K s n n 9 ) 11 ( ) 4 ( 2 2 + + + 2 2 ) 4 ( ) 4 ( ) 4 ( n n n n n s s + + _____________________________________________________ 2 ) 4 ( 9 ) 4 11 ( n n n K s K + + remainder K s K...
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solution_hw_7 - MAE 4310 SOLUTIONS TO HW # 7 B-6-9) The...

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