How are Roots Found in a Root Locus?

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SUMMARY

The discussion centers on the identification of roots in a root locus plot, specifically focusing on closed loop poles derived from the characteristic equation. User Splint emphasizes the necessity of analyzing the closed loop transfer function G(s) to accurately determine these roots. This method is crucial for understanding system stability and response in control theory.

PREREQUISITES
  • Understanding of control theory concepts
  • Familiarity with root locus plots
  • Knowledge of closed loop transfer functions
  • Basic skills in analyzing characteristic equations
NEXT STEPS
  • Study the derivation of closed loop transfer functions in control systems
  • Learn how to construct and interpret root locus plots
  • Explore the implications of pole placement on system stability
  • Investigate software tools for simulating root locus analysis
USEFUL FOR

Control engineers, students of control systems, and anyone involved in system stability analysis will benefit from this discussion.

Splint
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Hi,

In the attached image the roots are shown for the characteristic equation. I don't know how the roots were found. Anyone able to help?

Thanks
Splint

Root locus.jpg
 
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When drawing the root locus you need the closed loop poles. So I'd suggest looking at the closed loop G(s).
 

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