Selected gain
—
K
Root Locus Designer — Stability Analyzer
Explore how closed-loop poles move as gain changes for a unity negative-feedback system. Visualize the locus, open-loop poles and zeros, asymptotes, damping targets, stability regions, Routh-Hurwitz results, breakaway candidates and selected-gain performance.
Unity negative feedback
Mobile & touch compatible
Runs locally in browser
Root locus in the s-plane
Root locus
×Open-loop pole
Open-loop zero
Selected closed-loop pole
Closed-loop stability
—
—
Dominant damping ratio
—
ζ estimate
Natural frequency
—
rad/s
Approx. overshoot
—
dominant-pole estimate
Approx. settling time
—
2% criterion
Open-loop poles
—
count
Open-loop zeros
—
count
Selected closed-loop poles
| Pole | σ | ωd | ζ | ωn |
|---|
Stability analysis
Analyze a system to calculate stability.
Root-locus geometry
Design-target interpretation
Open-loop singularities
Poles
Zeros
Root Locus Designer — Stability Analyzer
Design and analyze unity-feedback root loci with poles, zeros, stability ranges, damping metrics, gain selection and representative plant templates.
What this tool does
This control-systems calculator analyzes how nonnegative feedback gain moves the closed-loop roots of D(s) + K·N(s). It draws the root locus in the s-plane, evaluates selected gain performance and reports classical stability and transient estimates.
Who this is for
- Control and mechatronics engineers studying feedback gain selection
- Students learning root locus, poles, zeros and classical stability analysis
- Designers comparing representative servo, mechanical, thermal, fluid-level and unstable-plant examples
How to use this tool
- Load a representative template or enter numerator and denominator coefficients in descending powers of s
- Set the gain range and locus density, then analyze the system
- Move the gain slider or enter K to inspect closed-loop poles
- Review stability, Routh-Hurwitz right-half-plane pole count, damping, overshoot and settling estimates
- Set overshoot and settling targets, inspect the target region, and export the locus CSV or plot PNG
Inputs
Inputs are numerator and denominator coefficient arrays, maximum gain, locus sample density, selected gain K, overshoot and 2% settling-time targets, plus display toggles for damping grid, target region, asymptotes and real-axis locus.
Outputs
Outputs include the root locus, open-loop poles and zeros, selected closed-loop poles, stable gain intervals, Routh-Hurwitz counts, asymptote geometry, breakaway candidates, damping ratio, natural frequency, overshoot, settling-time estimates and CSV/PNG exports.
Limitations and responsible use
The calculator uses unity negative feedback with K ≥ 0 and numerical root solving. Overshoot and settling time are dominant-second-order estimates for higher-order systems, and the included plant templates are representative study models rather than certified designs.
Example use cases
- Load a representative template or enter numerator and denominator coefficients in descending powers of s
- Set overshoot and settling targets, inspect the target region, and export the locus CSV or plot PNG
Frequently asked questions
How is the locus calculated?
The page numerically solves D(s) + K·N(s) = 0 over many gain values, then combines those roots with analytical geometry such as asymptotes and real-axis candidates.
Are the transient metrics exact?
No. Overshoot and settling time are approximate dominant-pole estimates; additional poles and zeros can make the actual response differ materially.
Explore more SolvProb engineering tools
Need a custom engineering tool?
SolvProb builds browser-based engineering calculators, visualizers and workflow tools.
Request a custom tool