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.