stability10

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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online