stability15

stability15 - 29 29 3 2 1 2 1 s s K s K The Routh table is...

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Stability Q UESTION 15 For the system shown in Figure 15 with ( 29 1 1 K G s s = + and ( 29 2 2 2 1 s G 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 15 The closed–loop transfer function is ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 1 3 2 1 2 1 1 1 2 1 K 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 ( 29 3 2 1 2 1 s s K s K + + + + + . The Routh table is 3 2 1 1 1 1 2 1 2 1 s K s K s K s K + +-+ . From the s 1 column, K < 0 and from the s column, K > –0.5. Therefore, the closed–loop system will be stable for –0.5 < K < 0....
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