How do I install the Root Locus Design skill?

Run npx skillmds@latest add ashfordeou/root-locus-design in your terminal (requires Node.js), paste this page's agent-chat prompt into Claude, Cursor, or any MCP-connected agent, or download the SKILL.md file and copy it into your agent's skills directory.

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Is Root Locus Design free to use?

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Who published Root Locus Design?

ashfordeOU (@ashfordeou) published this skill. Their other Agent Skills are listed on their SkillMD profile.

Root Locus Design by ashfordeou — Agent Skill

Name: Root Locus Design
Author: ashfordeOU

Root Locus Design

Use when you must design a feedback loop with the classical root locus method: compute the closed loop pole locations as the forward-path gain K varies, find the gain that places the dominant poles at a target damping ratio zeta, and judge closed loop stability from the characteristic equation 1 + K*G(s) = 0. Applies to the canonical type-1 plant G(s) = 1/(s(s + a)) used in flight control analysis. Produces the pole pair, the gain for the requested zeta, and the stability verdict that feeds control law iteration. Trigger: root locus, closed loop poles, damping ratio, gain selection, characteristic equation, pole locations, zeta, stability.

ashfordeOU 5f6ea77 3 files · 11.2 KB Updated Sep 17, 2026

File contents

Root Locus Design (gnc-autonomy/control/root-locus-design)

Use when the task is classical root locus design for a feedback loop: tracing closed-loop pole trajectories against forward-path gain, picking the gain for a target damping ratio, and judging closed-loop stability from the characteristic equation.

Domain quick reference

For the canonical type-1 plant G(s) = 1/(s(s + a)) the closed loop is 1 + KG(s) = 0, which reduces to s^2 + as + K = 0.
The closed-loop poles are the roots of that quadratic; their motion in the complex plane as K grows is the root locus.
Underdamped poles sit at -a/2 +/- jwd with wd = sqrt(K - a^2/4) and damping ratio zeta = a/(2sqrt(K)).
The gain for a target damping ratio is K = a^2/(4*zeta^2).
All poles with negative real part give a stable closed loop; a pole on the imaginary axis is marginal, not stable.
Units: a in rad/s (open-loop pole location), K dimensionless, zeta dimensionless, poles as (re, im) pairs in rad/s.

Workflow

Write the plant as G(s) = 1/(s(s + a)) with the open-loop pole location a in rad/s.
Pick a forward-path gain K and locate the closed-loop poles with closed_loop_poles(a, K).
Read the damping ratio of the resulting poles with damping_ratio(a, K).
Choose the gain for the target damping with gain_for_damping(a, zeta).
Confirm stability of the chosen loop with stability_verdict(a, K); iterate on K until the verdict is stable and the damping target is met.

Pitfalls

Reading the damping ratio from the gain formula when the loop is overdamped (K < a^2/4); the ratio is reported as 1 by convention.
Calling a pole on the imaginary axis (K = 0, pole at the origin) stable; marginal cases are not asymptotically stable.
Mixing units: a is in rad/s and K is dimensionless, so wd and the pole coordinates stay in rad/s throughout.
Forgetting to validate that a > 0 and K >= 0 before computing.

Behavior contract (gate 3)

The pole, gain, damping, and stability logic is exercised by the gate 3 contract test: scripts/test_root_locus_logic.py against scripts/root_locus_logic.py (stdlib unittest, offline). Run: python3 scripts/test_root_locus_logic.py

Compliance

ARP4754A is proprietary (SAE); name + paraphrase only per standards-map.yaml (ARP4754B supersedes; this skill keys to A, the certification-baseline revision).
compliance: STANDARDS-REF, gated: false.

---name: root-locus-designdescription: Use when you must design a feedback loop with the classical root locus method: compute the closed loop pole locations as the forward-path gain K varies, find the gain that places the dominant poles at a target damping ratio zeta, and judge closed loop stability from the characteristic equation 1 + K*G(s) = 0. Applies to the canonical type-1 plant G(s) = 1/(s(s + a)) used in flight control analysis. Produces the pole pair, the gain for the requested zeta, and the stability verdict that feeds control law iteration. Trigger: root locus, closed loop poles, damping ratio, gain selection, characteristic equation, pole locations, zeta, stability.license: Apache-2.0---# Root Locus Design (gnc-autonomy/control/root-locus-design)Use when the task is classical root locus design for a feedbackloop: tracing closed-loop pole trajectories against forward-pathgain, picking the gain for a target damping ratio, and judgingclosed-loop stability from the characteristic equation.## Domain quick reference- For the canonical type-1 plant G(s) = 1/(s(s + a)) the closed loop is 1 + K*G(s) = 0, which reduces to s^2 + a*s + K = 0.- The closed-loop poles are the roots of that quadratic; their motion in the complex plane as K grows is the root locus.- Underdamped poles sit at -a/2 +/- j*wd with wd = sqrt(K - a^2/4) and damping ratio zeta = a/(2*sqrt(K)).- The gain for a target damping ratio is K = a^2/(4*zeta^2).- All poles with negative real part give a stable closed loop; a pole on the imaginary axis is marginal, not stable.- Units: a in rad/s (open-loop pole location), K dimensionless, zeta dimensionless, poles as (re, im) pairs in rad/s.## Workflow1. Write the plant as G(s) = 1/(s(s + a)) with the open-loop pole location a in rad/s.2. Pick a forward-path gain K and locate the closed-loop poles with closed_loop_poles(a, K).3. Read the damping ratio of the resulting poles with damping_ratio(a, K).4. Choose the gain for the target damping with gain_for_damping(a, zeta).5. Confirm stability of the chosen loop with stability_verdict(a, K); iterate on K until the verdict is stable and the damping target is met.## Pitfalls- Reading the damping ratio from the gain formula when the loop is overdamped (K < a^2/4); the ratio is reported as 1 by convention.- Calling a pole on the imaginary axis (K = 0, pole at the origin) stable; marginal cases are not asymptotically stable.- Mixing units: a is in rad/s and K is dimensionless, so wd and the pole coordinates stay in rad/s throughout.- Forgetting to validate that a > 0 and K >= 0 before computing.## Behavior contract (gate 3)The pole, gain, damping, and stability logic is exercised by thegate 3 contract test: scripts/test_root_locus_logic.py againstscripts/root_locus_logic.py (stdlib unittest, offline). Run:python3 scripts/test_root_locus_logic.py## Compliance- ARP4754A is proprietary (SAE); name + paraphrase only per standards-map.yaml (ARP4754B supersedes; this skill keys to A, the certification-baseline revision).- compliance: STANDARDS-REF, gated: false.

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