MATLAB Code Implementation for Multivariable Generalized Predictive Control Algorithm

This article explores the MATLAB code implementation for controlling multivariable generalized predictive systems. The algorithm demonstrates significant utility across various domains including economics, engineering, and scientific research. We will examine key implementation aspects such as the Diophantine equation solution for predictor derivation, recursive parameter estimation methods, and the optimization approach for control signal computation using quadratic cost functions. The implementation typically involves MATLAB's System Identification Toolbox for model parameter estimation and Control System Toolbox for validation. We will introduce fundamental concepts including CARIMA (Controlled Auto-Regressive Integrated Moving-Average) model formulation, receding horizon optimization principles, and feedback correction mechanisms. The article provides practical MATLAB code examples showcasing functions like mpc for controller object creation, predict for output forecasting, and nlmpc for nonlinear implementations. These examples will help readers understand algorithm implementation strategies and their application to real-world problems involving multi-input multi-output (MIMO) systems with constraints handling capabilities.