stability16

# Stability16 - G s G s G s = = The closed–loop characteristic polynomial is 3 2 2 s s s K Stability The Routh table is 3 2 1 1 2 1 2 s s K s K s K

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Stability Q UESTION 16 For the system shown in Figure 16 with ( 29 2 1 G s s = , ( 29 2 2 K G s s = , ( 29 3 2 G s s = and ( 29 4 1 1 G s s = + , create the Routh table and determine for what range of K the closed–loop system is stable. Determine the frequency of oscillation at marginal stability. G 2 (s) + - G 3 (s) G 4 (s) G 1 (s) + + R(s) Y(s) Figure 16 Denote the output of the top summing junction by E ( s ). Write one equation for E ( s ) and one for Y ( s ): ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 4 3 E s G s R s G s Y s G s E s = - + and ( 29 ( 29 ( 29 2 Y s G s E s = . Combining equations and rearranging, the closed–loop transfer function is ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 1 2 3 2 2 3 4 1 2 1 G s G s Ks s T s s s s K

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Unformatted text preview: G s G s G s + = = + + + + + . The closed–loop characteristic polynomial is 3 2 2 s s s K + + + . Stability The Routh table is 3 2 1 1 2 1 2 s s K s K s K-. There is a sign change in the first column for K > 2 and K < 0; therefore, the closed–loop system is stable if 0 < K < 2. When K = 2, the s 1 row becomes a row of zeros. The even polynomial is in the s 2 row and is 2 2 s + = . Solving for s , the frequency of oscillation is 1.414 rad/s. 2...
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## This note was uploaded on 02/01/2012 for the course MECH ENG 279 taught by Professor Landers during the Spring '11 term at Missouri S&T.

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Stability16 - G s G s G s = = The closed–loop characteristic polynomial is 3 2 2 s s s K Stability The Routh table is 3 2 1 1 2 1 2 s s K s K s K

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