IntermediateTopic 52 of 101Signals, Control & Comms
Root locus
Plot of closed-loop pole paths as gain varies.
In depth
Root locus plots closed-loop pole locations as a gain K varies from 0 to ∞, following rules (branches start at open-loop poles and end at zeros, asymptotes, breakaway points, imaginary-axis crossing). Used to choose gain and compensators to meet damping and speed.
Key points
- Angle and magnitude conditions
- Adding poles pushes locus right
- Adding zeros pulls locus left
ExampleIncreasing gain in a three-pole system eventually moves poles into the right half-plane.
What is Root locus?
Plot of closed-loop pole paths as gain varies.
Why is it important to understand root locus?
The root locus shows how closed-loop poles move as gain changes, which makes the effect of gain on stability and speed visible.
What is a root locus?
A plot of the closed-loop pole locations as the loop gain varies from zero to infinity.
What does a pole moving to the right half-plane mean?
The closed-loop system becomes unstable at that gain, so the locus shows the maximum stable gain.
How is Root locus used in practice?
Typical applications include choosing a gain for a loop that gives a damping ratio of 0.5, seeing where poles go unstable as gain increases and designing a lead compensator to move poles into a better region.
What should I learn before Root locus?
Study "Stability and Routh-Hurwitz" first (topic 51 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
What are the key points of Root locus?
Angle and magnitude conditions. Adding poles pushes locus right. Adding zeros pulls locus left.
Can you give an example of Root locus?
Increasing gain in a three-pole system eventually moves poles into the right half-plane.
What comes after Root locus?
The next topic is "Frequency response methods", which builds directly on this one.
How difficult is Root locus?
It is classed as Intermediate in Signals, Control & Comms (topic 52 of 101). It is an intermediate topic. Work through the beginner topics in Signals, Control & Comms first.