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
Unformatted text preview: + . The closedloop characteristic equation is ( K +1) s 2 + (33 K ) s + (2+2 K ) = 0. Substituting s = j ( 29 ( 29 ( 29 2 1 3 3 2 2 K K j K + ++ + = (1) Root Locus The real and imaginary parts, respectively, must be simultaneously zero ( 29 2 1 2 2 K K + + + = (2) ( 29 3 3 K= (3) One solution is K = 1 and = 2 ; therefore, for K = 1, root locus branches cross the imaginary axis at 2 . Another solution is K = 1 and = 0; however, this is not a valid solution since K should be positive. The Matlab code for producing the Root Locus Diagram is sys = zpk([1 2],[1 2],1); figure; rlocus(sys), title('G_C(s)G(s) = [(s1)(s2)]/[(s+1)(s+2)]'); The Root Locus Diagram is shown below.21 1 21.510.5 0.5 1 1.5 G C (s)G(s) = [(s1)(s2)]/[(s+1)(s+2)] Real Axis Imaginary Axis 2...
View
Full
Document
 Spring '11
 LANDERS

Click to edit the document details