hwsln-421-s06-07

# hwsln-421-s06-07 - ECE 421 Spring 2006 Solutions to HW...

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

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.

Unformatted text preview: ECE 421, Spring 2006 Solutions to HW Assignment #7 1. Zero located at s = − 8 G 1 ( s ) H 1 ( s ) = K ( s + 8) s ( s + 1) ( s + 2) ( s + 3) (1) (a) K > : For small values of K, the closed-loop pole on each of the branches of the root locus is in the left-half plane, so the closed-loop system is stable. Since two of the branches are also in the right-half plane, the closed-loop poles on those branches will be unstable for certain values of K. Since closed-loop poles move from open-loop poles to open-loop zeros or to zeros located at ∞ , those parts of the branches that are in the right-half plane correspond to larger values of K. Therefore, for this system, the closed-loop system is stable for small K > and unstable for large K > , and there is one value of K that places two of the closed-loop poles on the jω axis. (b) K < : One branch of the root locus starts at the open-loop pole located at s = 0 , and it moves along the positive real axis toward in f nity. Therefore, this closed-loop pole is in the right-half plane for all K < , and the closed-loop system is unstable for all K < . 2. Zero located at s = − 4 G 2 ( s ) H 2 ( s ) = K ( s + 4) s ( s + 1) ( s + 2) ( s + 3) (2) (a) K > : Similar to the f rst system. The closed-loop system is stable for small K > and unstable for large K > , and there is one value of K that places two of the closed-loop poles on the...
View Full Document

## This note was uploaded on 10/25/2010 for the course ECE 421 taught by Professor Cook,g during the Spring '08 term at George Mason.

### Page1 / 3

hwsln-421-s06-07 - ECE 421 Spring 2006 Solutions to HW...

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

View Full Document
Ask a homework question - tutors are online