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mpc-horizon-tuning skill

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This skill helps you tune MPC horizons and cost matrices for tension control, balancing tracking performance and actuator effort.

npx playbooks add skill benchflow-ai/skillsbench --skill mpc-horizon-tuning

Review the files below or copy the command above to add this skill to your agents.

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SKILL.md

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---
name: mpc-horizon-tuning
description: Selecting MPC prediction horizon and cost matrices for web handling.
---

# MPC Tuning for Tension Control

## Prediction Horizon Selection

**Horizon N** affects performance and computation:
- Too short (N < 5): Poor disturbance rejection
- Too long (N > 20): Excessive computation
- Rule of thumb: N ≈ 2-3× settling time / dt

For R2R systems with dt=0.01s: **N = 5-15** typical

## Cost Matrix Design

**State cost Q**: Emphasize tension tracking
```python
Q_tension = 100 / T_ref²  # High weight on tensions
Q_velocity = 0.1 / v_ref²  # Lower weight on velocities
Q = diag([Q_tension × 6, Q_velocity × 6])
```

**Control cost R**: Penalize actuator effort
```python
R = 0.01-0.1 × eye(n_u)  # Smaller = more aggressive
```

## Trade-offs

| Higher Q | Effect |
|----------|--------|
| Faster tracking | More control effort |
| Lower steady-state error | More aggressive transients |

| Higher R | Effect |
|----------|--------|
| Smoother control | Slower response |
| Less actuator wear | Higher tracking error |

## Terminal Cost

Use LQR solution for terminal cost to guarantee stability:
```python
P = solve_continuous_are(A, B, Q, R)
```

Overview

This skill helps select an MPC prediction horizon and design state/control cost matrices specifically for web-handling tension control. It provides practical rules of thumb for horizon sizing, concrete Q/R scaling suggestions, and guidance on terminal cost selection to ensure stability. The guidance is tuned for roll-to-roll (R2R) systems and fast sampling rates.

How this skill works

The skill evaluates system sampling time and typical settling behavior to recommend a prediction horizon that balances disturbance rejection and computation. It prescribes how to scale state cost Q to prioritize tension tracking and how to choose control cost R to trade off aggression versus actuator wear. It also recommends computing an LQR terminal cost (P) to guarantee stability at the horizon.

When to use it

Tuning MPC for web tension control on roll-to-roll lines or drying ovens.
Balancing controller performance vs available computation for fast‑sampled systems (e.g., dt ≈ 0.01 s).
When disturbance rejection (tension spikes) is critical and needs explicit weighting.
Designing controllers where actuator effort or wear must be limited.
Before deploying to hardware—use these rules for simulation-first validation.

Best practices

Select N roughly 2–3 times the system settling time divided by dt; for R2R with dt=0.01 s, start with N = 5–15.
Scale Q to emphasize tension tracking: use a high weight on tension terms (e.g., Q_tension = 100 / T_ref^2) and lower weights on velocities.
Choose R in the 0.01–0.1 range per actuator (smaller values drive more aggressive control; larger values smooth commands and reduce wear).
Compute the terminal cost P by solving the continuous-time algebraic Riccati equation (CARE) for A, B, Q, R to improve closed-loop stability.
Validate settings in simulation across disturbance profiles and then iterate: increase N if rejection is poor, raise R if actuators saturate.

Example use cases

Tuning an MPC for a roll-to-roll coating line to reduce tension excursions during splicing events.
Designing an MPC for web transport where sampling is fast and computational budget is limited.
Adjusting trade-offs between tracking and actuator life on a high-speed printing press.
Rapidly choosing initial Q and R values for offline simulation before hardware-in-the-loop testing.
Applying terminal LQR cost to guarantee stability when using a finite horizon controller.

FAQ

How do I choose the initial prediction horizon N?

Start with N ≈ 2–3 × (settling time / dt). For typical R2R with dt=0.01 s use N = 5–15 and increase if disturbance rejection is insufficient.

What if actuators saturate with my chosen Q?

Increase R to penalize actuator effort more, or reduce Q on less critical states; also test slower horizon growth or add actuator constraints and re‑tune.