Centroid of a root locus

  • Thread starter magnifik
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  • #1
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i just want to make sure i'm doing this correctly as there is some discrepancy in my textbook. i know the centroid is equal to (Ʃpoles - Ʃzeros) / (# of poles - # of zeros)

the equation i have is s2 + 2s + 8 / s(s2 + 2s + 10)

so the zeros are -1 + i√7 and -1 - i√7
and the poles are 0, -1 + 3i, -1 - 3i

and the centroid = (0 - 1 - 1) - (-1 -1) / (3-2) = 0

in my textbook they say that the answer is -2.. am i missing something?
my textbook has been wrong before........
 

Answers and Replies

  • #2
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(0-2)/1= -2 The 2nd order pole is complex. The sum of the roots are 0. The zeros should be (-4,2) {not -1-1 as shown} or -4+2=-2. Your denominator calculation is correct that 3poles -2zeros is 1. The correct answer should be -2
 

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