Model Predictive Control (MPC) - Advanced Constrained Optimization Strategy

Model Predictive Control (MPC) represents an advanced control methodology that employs mathematical models to forecast system behavior and compute optimal control actions for achieving target performance metrics. This approach proves particularly valuable for constrained systems, enabling real-time optimization while maintaining constraint satisfaction through predictive horizon management.

Implementation typically involves constructing a state-space or transfer function model in control software like MATLAB, where the MPC controller object can be configured using functions such as `mpc()` with specified prediction and control horizons. The algorithm solves a quadratic programming problem at each sampling interval to minimize a cost function J = Σ[(y-y_ref)²Q + u²R] while adhering to input/output constraints.

MPC finds extensive industrial applications across chemical processing (e.g., reactor temperature control), aerospace (flight path optimization), automotive (adaptive cruise control), and robotics (trajectory planning). Its efficacy has been demonstrated in managing complex multivariate systems including chemical reaction dynamics, aircraft maneuver stabilization, and autonomous vehicle path tracking.

The core MPC workflow comprises: 1) Developing a discrete-time system model (typically linearized for computational efficiency) 2) Predicting system states over a predefined horizon using model propagation 3) Solving constrained optimization to determine control sequence 4) Implementing the first control action while recomputing predictions at subsequent time steps. This receding horizon implementation ensures continuous adaptation through methods like Kalman filtering for state estimation.

Compared to conventional PID controllers, MPC offers distinct advantages including explicit constraint handling (through inequality constraints in optimization), inherent multivariable coordination, and capability to manage nonlinear systems via linear parameter-varying approaches. Computational requirements remain a consideration, with implementation often requiring real-time optimization solvers (e.g., active-set or interior-point methods) and accurate system identification for model development.