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stability7

# stability7 - 29 3 2 2 1 s s K s K The Routh table is 3 2 1...

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Stability Q UESTION 7 For the system shown in Figure 7 with ( 29 1 K G s s = and ( 29 2 2 1 2 1 s G s s s - = + + , create the Routh table and determine for what range of K the closed–loop system is stable. G 1 (s) + - G 2 (s) R(s) E(s) Y(s) Figure 7 The closed–loop transfer function is ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 1 3 2 1 2 2 1 1 2 1 K s s G s T s G s G s s s K s K + + = = + + + + - . The closed–loop characteristic polynomial is
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Unformatted text preview: ( 29 3 2 2 1 s s K s K + + +-. The Routh table is 3 2 1 1 1 2 3 2 2 s K s K K s s K +-+-. There will only be a sign change in the first column if K < –2/3 or K > 0. Therefore, the closed– loop system will be stable for 2 3 K-< < ....
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