Root-Locus Centroid

Correct Answer

A — Zero

Concept and Reasoning

The poles are at 0 and −1±j, whose sum is −2, and the finite zero is at −2. With P−Z=2, the centroid is [Σpoles−Σzeros]/(P−Z)=0.

Calculation / Key Relation

σa=(Σp−Σz)/(P−Z)=[−2−(−2)]/2=0

Exam Takeaway

Use algebraic sums of pole and zero locations.

Common Mistake

Do not use magnitudes of complex poles when calculating the centroid.