Week 07
Root Locus
I follow the saved course materials and calculations from modeling through stability, root locus, and frequency response.
What I connect in this unit
A root locus traces closed-loop poles from open-loop poles toward zeros or infinity as loop gain changes. Branch count, asymptotes, and breakaway points establish the geometry; the angle condition selects the valid path before gain is chosen.
Concept map
- Branches and asymptotes
- Breakaway points
- Angle condition
- Gain selection
Technical anchor
From 1+KG(s)H(s)=0, only points satisfying angle G(s)H(s)=(2q+1)180° lie on the locus. Real-axis breakaway candidates follow from dK/ds=0 applied to K(s)=-1/[G(s)H(s)].
How I review it
Overlay the desired damping-ratio line and natural-frequency circle on the s-plane, compute gain from the magnitude condition at their intersection, and inspect every remaining pole.
Connection to the full course
Unit 7 of 12. Unit numbers organize the concepts found in the materials and do not reproduce an attendance schedule.