Phase Margin From Damping⚠ unverified
Physics / Controls · Approximate the phase margin from the damping ratio
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| zeta | ζ | — | 1.0 | Damping ratio (dimensionless) |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | PM | — | Phase margin, in degrees |
The science & history
Understanding the Parameters
-
$\zeta$ — larger damping → larger phase margin in this correlation (e.g. $\zeta \approx 0.5$ ~ 50 deg class margins in textbook charts when expressed in degrees).
-
PM — design bridge: choose $\zeta$ for overshoot, infer required PM, or vice versa.
Derivation (Approaching a Proof)
For the standard second-order open-loop / closed-loop relations used in many textbooks, the phase at gain crossover can be written in terms of $\zeta$ alone; rearranging yields an $\arctan$ expression equivalent to the registry formula. It is model-specific, not universal for arbitrary $G(s)$.
History
$\zeta$–PM correlations appear throughout classical design (e.g. $\mathrm{PM}\approx 100\zeta$ rough rule in degrees for a range of $\zeta$).
Related Concepts: Phase Margin, Peak Overshoot, Damping Ratio From Overshoot, Gain Crossover Frequency
Notes: Registry calculator phase-margin-from-damping (unverified). Confirm radian vs degree
output on the live calculator.