Root Locus Breakaway Calculator
Bracketed real root-locus stationary gain for independently chosen pole/zero-free real branch, positive gain checked; not all complex breakaway roots or automatic branch membership. Caller independently establishes units, regime, calibration and applicability; this does not establish design-code compliance, authenticity, operational safety, treatment efficacy or a validated forecast.
Description
A real root-locus stationary point satisfies a logarithmic gain-derivative condition.
A real root-locus stationary point satisfies a logarithmic gain-derivative condition.1
Finding a bracketed stationary point does not independently establish the applicable root-locus branch. Use this tool to calculate root Locus Breakaway from the supplied measurements and assumptions.
When to use Root Locus Breakaway Calculator
Use this tool to calculate root Locus Breakaway from the supplied measurements and assumptions. Establish the SI units or caller unit basis, load signs, measurement interval, model conditions and independently chosen coefficients or references.
How to use Root Locus Breakaway Calculator and understand its results
- Establish the SI units or caller unit basis, load signs, measurement interval, model conditions and independently chosen coefficients or references.
- Enter realOpenLoopPoles, realOpenLoopZeros, callerStationaryBracketLower, callerStationaryBracketUpper, using the field meanings and rules below, then run the tool.
- Read stationaryPoint, gain. Interpret the fields using their units, signs and evidence conventions below.
- If input validation fails, correct the reported field and run again. Before applying the result, check reference scope, model assumptions and any missing evidence or placeholder values.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| realOpenLoopPoles | Real open loop poles | list of number | Required |
| realOpenLoopZeros | Real open loop zeros | list of number | Required |
| callerStationaryBracketLower | Caller stationary bracket lower | number | Required |
| callerStationaryBracketUpper | Caller stationary bracket upper | number | Required |
Enter 1–32 finite real poles, zero to 32 real zeros and an ordered finite bracket containing none of them, including its endpoints. Residual Σ1/(s−pole)−Σ1/(s−zero) must change sign or be zero at exactly one endpoint. Use up to 100 bisection steps, then compute −Π(s−pole)/Π(s−zero) and require nonnegative gain. Nonisolated or unsuitable brackets fail; no complex-root search or real-branch validity test is supplied.
stationaryResidual(s)=Σ1/(s−pole)−Σ1/(s−zero)=0; gain=−Π(s−pole)/Π(s−zero) Use the exact units, boundary rules, ordering and missing-evidence conventions above.
| Output field | Meaning | Value type |
|---|---|---|
| stationaryPoint | Stationary Point; follow the units, sign, ordering and evidence convention stated above | number |
| gain | Gain; follow the units, sign, ordering and evidence convention stated above | number |
{
"input": {
"realOpenLoopPoles": [
0,
-2
],
"realOpenLoopZeros": [],
"callerStationaryBracketLower": -1.5,
"callerStationaryBracketUpper": -0.5
},
"output": {
"stationaryPoint": -1,
"gain": 1
}
}Limitations and assumptions
Finding a bracketed stationary point does not independently establish the applicable root-locus branch. Interpretation depends on the units, sampling scope and exact model described above.
All listed fields require explicit values. Unexpected fields, incorrect types, nonfinite numbers and sparse evidence arrays fail validation; the specific bounds and alignment requirements are stated above. Extremely large inputs or outputs can also be rejected. An input error is distinct from a successful result reporting false, no matches or missing evidence.
Alternative or Complementary methods
Use Nyquist Stability Calculator for this related task: A Nyquist polygon's winding about minus one connects contour geometry with a declared open-loop pole count.
Use Robot Jacobian Determinant Calculator when its separate inputs and assumptions fit the question: A planar two-link Jacobian determinant reflects local geometric sensitivity.
References
-
Root Locus Breakaway Calculator — tool.io
Similar or alternative tools
- Nyquist Stability Calculator
A Nyquist polygon's winding about minus one connects contour geometry with a declared open-loop pole count.
- Robot Jacobian Determinant Calculator
A planar two-link Jacobian determinant reflects local geometric sensitivity.