Elio Saade
Note

Root Locus Centroid

Topics: Feedback Control Systems

The centroid of a root locus, aka center of gravity, is a single point on the real axis which acts as the center from which all straight-line asymptotes originate at symmetric angles.

σ=∑(Real part of open-loop poles)−∑(Real part of open-loop zeros)P−Z\sigma = \frac{\sum (\text{Real part of open-loop poles}) - \sum(\text{Real part of open-loop zeros})}{P-Z}

where

  • PP is the number of open-loop poles
  • ZZ is the number of open-loop zeros

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