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

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

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:

P = solve_continuous_are(A, B, Q, R)