This preview has intentionally blurred sections. Sign up to view the full version.
View Full 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 closedloop pole on each of the branches of the root locus is in the lefthalf plane, so the closedloop system is stable. Since two of the branches are also in the righthalf plane, the closedloop poles on those branches will be unstable for certain values of K. Since closedloop poles move from openloop poles to openloop zeros or to zeros located at ∞ , those parts of the branches that are in the righthalf plane correspond to larger values of K. Therefore, for this system, the closedloop system is stable for small K > and unstable for large K > , and there is one value of K that places two of the closedloop poles on the jω axis. (b) K < : One branch of the root locus starts at the openloop pole located at s = 0 , and it moves along the positive real axis toward in f nity. Therefore, this closedloop pole is in the righthalf plane for all K < , and the closedloop 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 closedloop system is stable for small K > and unstable for large K > , and there is one value of K that places two of the closedloop 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.
 Spring '08
 Cook,G

Click to edit the document details