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stability12

# stability12 - Stability QUESTION 12 For the system shown in...

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Stability Q UESTION 12 For the system shown in Figure 12 with ( 29 1 4 3 2 507 3 10 30 169 G s s s s s = + + + + and ( 29 2 1 G s s = , create the Routh table and determine how many closed–loop poles are in the left s–plane, in the right s–plane, and on the imaginary axis. Without the use of the Routh table, what can be said about the stability of this closed–loop system? Explain. Numerically determine the location of the closed–loop poles. G 1 (s) + - G 2 (s) R(s) E(s) Y(s) Figure 12 The closed–loop transfer function is ( 29 ( 29 ( 29 ( 29 1 5 4 3 2 1 2 507 1 3 10 30 169 507 G s s T s G s G s s s s s s = = + + + + + + . The closed–loop characteristic polynomial is 5 4 3 2 3 10 30 169 507 s s s s s + + + + + . Since the signs of the coefficients are the same and there are no missing powers of s, the poles may all be in the left s–plane. Therefore, the closed–loop system may be stable.

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stability12 - Stability QUESTION 12 For the system shown in...

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