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