Glossary · Control theory and process control
Root locus
Also known as: Root locus plot, Root locus method
German: Wurzelortskurve
In control engineering, the root locus is a graphical method that shows how the poles of a closed control loop move in the complex plane as one parameter, usually the controller gain, varies from zero to infinity.
- Control theory
In one sentence
The root locus shows how the closed-loop poles move as controller gain changes, revealing where a loop becomes oscillatory or unstable.
Example
The root locus of a position loop shows that the poles cross into the right half-plane above a gain of 12, which sets the upper limit for tuning.
How it applies
- Engineering: The root locus connects tuning directly to damping and stability: poles closer to the imaginary axis mean slower decay, poles in the right half-plane mean instability. It requires a model of the loop, so it is a design tool rather than a commissioning tool.
- Training: Root locus diagrams are standard in control engineering education and appear in design reports.
- Documentation: When design reports include root locus diagrams, state the model, the varied parameter and the chosen operating point. Reviewers and later maintainers need this context to reuse the analysis.
Root locus vs. frequency response methods
The root locus works with pole positions in the complex plane; Bode plot and Nyquist plot work with the frequency response and can use measured data. Frequency response methods handle dead time more easily.