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Skillsbench integral-action-design

Adding integral action to MPC for offset-free tension tracking.

install
source · Clone the upstream repo
git clone https://github.com/benchflow-ai/skillsbench
Claude Code · Install into ~/.claude/skills/
T=$(mktemp -d) && git clone --depth=1 https://github.com/benchflow-ai/skillsbench "$T" && mkdir -p ~/.claude/skills && cp -r "$T/tasks/r2r-mpc-control/environment/skills/integral-action-design" ~/.claude/skills/benchflow-ai-skillsbench-integral-action-design && rm -rf "$T"
manifest: tasks/r2r-mpc-control/environment/skills/integral-action-design/SKILL.md
source content

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])