model predictive control

Model Predictive Control (MPC) is an advanced control strategy that uses a mathematical model of the system to predict future behavior — and solves an optimization problem at each time step to determine the optimal control inputs over a finite prediction horizon, subject to constraints.

What Is MPC?

- Principle: At each time step:
1. Predict system behavior over a horizon of N steps using the model.
2. Solve an optimization problem to minimize a cost function (tracking error + control effort).
3. Apply only the first control input.
4. Repeat at the next time step (receding horizon).
- Constraints: Naturally handles input/output constraints (actuator limits, safety bounds).

Why It Matters

• Semiconductor Manufacturing: MPC is used for run-to-run (R2R) process control in etch, CMP, and CVD.
• Optimal: Finds the best control action considering future consequences, not just current error.
• Constraint Handling: The only mainstream control method that explicitly handles constraints in the optimization.

MPC is the chess-playing controller — looking several moves ahead and choosing the optimal action at each step while respecting the rules of the game.