Lect11 - Root Locus - 3/8/2010 Lecture Note 11 :...

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3/8/2010 1 Lecture Note 11 : Introduction to Root Locus AE353, Spring 2010 Prof. Soon Jo Chung (sjchung@illinois.edu) Location of Poles and Zeros 2 |1 dn n jj    
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3/8/2010 2 Root Locus The graph of all possible roots of the characteristic equation. Legend X : poles o: zeros 1 1.5 Fig.5.2 Root locus of 1/s(s+1) 1( ) ( ) ( ) 0 DsGsHs  () ) 1 0 bs KL s K as as :[0, ] K -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -1.5 -1 -0.5 0 0.5 Imaginary Axis
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3/8/2010 3 Root Locus vs. any parameter change You can plot the effect of any parameter change on the pole locations. Fig.5.3 Root locus of 1/s(s+c) nary Axis 0 0.5 1 1.5 1( ) 0 Gs  1 10 () ss c  2 sc s  s c as Real A x is Imagin -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -1.5 -1 -0.5 2 1 s :[0, ] c Plot the poles as Key Definitions The root locus is the set of values of s for which 1+KL(s)=0 is satisfied as the real parameter K varies from 0 to +inf Typically from 0 to +inf. Typically, 1+KL(s)=0 is the characteristic equation of system, and in this case the roots on the locus are the
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This note was uploaded on 04/12/2010 for the course AE 353 taught by Professor Voulgaris,p during the Spring '08 term at University of Illinois, Urbana Champaign.

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Lect11 - Root Locus - 3/8/2010 Lecture Note 11 :...

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