stability9 - to obtain 6 s , place this coefficient in the...

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

View Full Document Right Arrow Icon
Stability Q UESTION 9 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 2 4 3 2 4 3 4 8 20 15 s s T 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 4 3 2 4 8 20 15 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. The Routh table is 4 3 2 1 0 1 8 15 4 20 0 3 15 0 06 0 0 15 0 0 s s s s s . Since there is a row of zeros in the s 1 row, the characteristic equation contains a 2 nd order even polynomial. The even polynomial is in the s 2 row and is 3 s 2 +15 = 0. Differentiate this polynomial
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: to obtain 6 s , place this coefficient in the s 1 row, and continue. Investigate sign changes from the s 1 row to the s row to determine the stability of the 2 nd order even polynomial. Since there are no sign changes and the roots of an even polynomial are symmetric about the origin, both poles are on the imaginary axis. To determine the location of the other poles, investigate sign changes from the s 2 row to the s 4 row. Since there are no sign changes, the remaining poles are in the left s–plane. Therefore, there are two poles on the imaginary axis and two poles in the left s–plane. Stability The Matlab code for computing the closed–loop pole locations is roots([1 4 8 20 15]) The closed–loop poles are located at –3, –1, and ± 2.236 j . 2...
View Full 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

stability9 - to obtain 6 s , place this coefficient in the...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online