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Velocity and Acceleration of Root-Locus Points
  • Masoud Alghoniemy
Masoud Alghoniemy

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We show that the roots of the characteristic equation of a closed-loop feedback system can be interpreted as moving roots, on the root-locus, with specific velocity and acceleration as the loop gain increases from zero to infinity. In particular, we show that each root on the root-locus travels with a non-trivial velocity and acceleration which depend on the open-loop pole-zero locations as well as the rate of change of the gain with time. Moreover, the phase of the root velocity provides information about the traveling directions of each root on the root-locus. The relation between root sensitivity and root velocity is also explained. The concept of root velocity and acceleration helps us to better understand the behavior of the roots on the root-locus as the gain increases. Simulation provides visual interpretations for the derived results.
31 May 2024Submitted to TechRxiv
07 Jun 2024Published in TechRxiv