integral-action-design

integral-action-design is a skill for Claude Code, Codex from benchflow-ai/benchflow. It costs 16 tokens per session (323 once invoked), scanned A, a copy of integral-action-design, Apache-2.0.

A guide to adding integral action to model predictive control for roll-to-roll web systems, where material moves through machines under controlled tension. Integral action accumulates tracking error to correct steady-state offset.

In plain words
What is it for?
Use it to add a leaky integral term, tune its gain and decay, apply anti-windup limits, and control tension separately in multiple sections.
Why use it?
It helps remove persistent tension errors caused by differences between the control model and the real system, while limiting oscillation and integral windup.

Skill for Claude CodeCodex

Install

Getting it into your agent

One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.

agentmods
npx agentmods add skills/benchflow-ai/benchflow/integral-action-design
Any agent
npx skills add benchflow-ai/benchflow --skill integral-action-design
Clone the repo
git clone --depth 1 https://github.com/benchflow-ai/benchflow

Made for: Claude Code, Codex.

Wrote this? Show the measurements

A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.

agentmods badge for integral-action-design

README.md
[![agentmods](https://agentmods.dev/badge/skills/benchflow-ai/benchflow/integral-action-design.svg)](https://agentmods.dev/skills/benchflow-ai/benchflow/integral-action-design)
Your own site
<a href="https://agentmods.dev/skills/benchflow-ai/benchflow/integral-action-design"><img src="https://agentmods.dev/badge/skills/benchflow-ai/benchflow/integral-action-design.svg" alt="Measured on agentmods" height="20"></a>
Per session 16 Skills are progressive disclosure: only the name and description are preloaded; the body loads when the skill is used.
When invoked 323 The whole file, excluding the scripts and references it only reads on demand.
Security scan A 0 findings. Scan, not verified.
Origin 100% copy Near-identical to another mod in the catalogue.
Token cost

What it costs to keep this loaded

Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.

ModelPer sessionOnce invoked
Fable 5 $0.00016 $0.00323
Opus 5 $0.00008 $0.00161
Sonnet 5 $0.00003 $0.00065
Haiku 4.5 $0.00002 $0.00032

Measured 5d ago against content hash e3368f03c7c5, method: parsed. Prices are Anthropic first-party input rates as of 2026-08-30, from the pricing page.

Security

Grade A, and why

integral-action-design scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 5d ago.

A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.

Nothing flagged

None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.

Origin

This is a copy

100% identical to integral-action-design — 0 lines differ, which has more behind it and is treated as the original. This page carries a canonical link to it rather than competing with it.

tests/fixtures/skillsbench_slice/r2r-mpc-control/environment/skills/integral-action-design/SKILL.md · 51 lines

What it actually says

Integral Action for Offset-Free Control

Why Integral Action?

MPC with model mismatch may have steady-state error. Integral action eliminates offset by accumulating error over time.

Implementation

u_I = gamma * u_I - c_I * dt * (T - T_ref)
u_total = u_mpc + u_I

Where:

  • u_I: Integral control term
  • gamma: Decay factor (0.9-0.99)
  • c_I: Integral gain (0.1-0.5 for web systems)
  • dt: Timestep

Tuning Guidelines

Integral gain c_I:

  • Too low: Slow offset correction
  • Too high: Oscillations, instability
  • Start with 0.1-0.3

Decay factor gamma:

  • gamma = 1.0: Pure integral (may wind up)
  • gamma < 1.0: Leaky integrator (safer)
  • Typical: 0.9-0.99

Anti-Windup

Limit integral term to prevent windup during saturation:

u_I = np.clip(u_I, -max_integral, max_integral)

For R2R Systems

Apply integral action per tension section:

for i in range(num_sections):
    u_I[i] = gamma * u_I[i] - c_I * dt * (T[i] - T_ref[i])
Changes

What this file has done since we first saw it

Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.

  1. 5d ago First seen · 51 lines · 16 tokens per session scan A e3368f03c7c5

Subscribe to this mod's changes

integral-action-design is a skill published in the GitHub repository benchflow-ai/benchflow (340 stars, last pushed today), licensed Apache-2.0. It adds 16 tokens to every session and 323 once invoked, about $0.0001 per session on Opus 5. A static security scan graded it A with 0 findings. It is 100% identical to integral-action-design, differing in 0 lines, and is treated as a copy.

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