stability10 - Stability QUESTION 10 Create the Routh table...

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Stability Q UESTION 10 Create the Routh table and determine how many poles of the following closed–loop transfer function are in the left s–plane, in the right s–plane, and on the imaginary axis: ( 29 6 5 4 2 6 6 6 T s s s s s s - = + - + + - . By inspection, what can be said about the stability of this closed–loop system? Explain. Numerically determine the location of the closed–loop poles. The closed–loop characteristic polynomial is 6 5 4 3 2 6 0 6 s s s s s s + - + + + - . Since the signs of the coefficients are not the same, there is at least one unstable pole. Therefore, the closed–loop system is unstable. The Routh table is 6 5 4 3 2 1 0 1 6 1 6 1 0 1 0 6 0 6 0 0 24 00 0 0 0 6 0 0 144 0 0 0 6 0 0 0 s s s s s s s ε + - - - + + + + - - - - - - - - + - - - + - - - . Since there is a zero in the first column of the s 2 row, it must be replaced by an arbitrarily small number denoted by ε . When the Routh table is complete, sign changes will be determined as ε goes to zero and is positive and as ε goes to zero and is negative. Since there is a row of zeros in
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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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stability10 - Stability QUESTION 10 Create the Routh table...

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