Implementing GPC Algorithm for Predictive Control Using MATLAB

Generalized Predictive Control (GPC) is a model-based predictive control strategy widely applied in industrial process control. Implementing the GPC algorithm in MATLAB typically involves the following key steps: System Modeling and Identification: The core of GPC lies in establishing a predictive model of the controlled object. The CARIMA (Controlled Auto-Regressive Integrated Moving Average) model is commonly used to describe system dynamics, with parameters obtained through Recursive Least Squares (RLS) or other identification methods. In MATLAB, system identification can be implemented using functions like `arx()` or `pem()` from the System Identification Toolbox. Prediction Equation Construction: Based on the identified model, derive the predictive output expression of the system. Through Diophantine equation decomposition, future outputs are divided into free response (unaffected by future control actions) and forced response (influenced by future control inputs). MATLAB implementation requires matrix operations to solve Diophantine equations recursively. Optimization Objective Function Design: GPC's optimization objective typically minimizes the error between future outputs and reference trajectories while incorporating constraints on control increments. MATLAB's optimization tools such as `quadprog()` for quadratic programming or `fmincon()` for constrained nonlinear optimization can solve this quadratic optimization problem. The cost function formulation involves weighting matrices for output errors and control efforts. Receding Horizon Strategy Implementation: At each control interval, GPC solves the optimization problem and implements only the first control action, then updates the system state and repeats the prediction and optimization process. This requires implementing a real-time loop structure with proper initialization and state updates. When implementing in MATLAB, the Control System Toolbox can be used for model simulation, combined with custom scripts for optimization logic. Key considerations include appropriate selection of prediction and control horizons, and ensuring numerical stability through techniques like regularization or constraint handling. Critical implementation aspects involve efficient matrix computations for prediction equations and proper handling of constraints using MATLAB's optimization solvers.