Predictive Control

In industrial control, predictive control serves as a methodology particularly suited for complex industrial systems featuring significant lag components and integral elements. Generalized Predictive Control (GPC) stands as a widely adopted predictive control approach, fundamentally operating by utilizing the system's current and historical states to forecast its future behavior, subsequently deriving control actions based on these predictions. GPC demonstrates remarkable flexibility, enabling adaptation to diverse control systems while delivering robust control performance. Notably when addressing complex systems, GPC assists engineers in achieving deeper system comprehension and enhanced control capabilities, thereby improving overall system performance and stability.

From an implementation perspective, GPC typically involves solving a quadratic optimization problem at each sampling instant to determine optimal control moves. Key algorithmic components include: 1) A CARIMA (Controlled Auto-Regressive Integrated Moving Average) model for system representation, 2) A cost function minimizing weighted errors between predicted outputs and reference trajectories over a prediction horizon, 3) Recursive algorithms like Diophantine equations for step-response coefficient calculation. The controller can be implemented using MATLAB's Model Predictive Control Toolbox or through custom code solving quadratic programming problems with constraints.