Predictive Control MATLAB Program: Dynamic Matrix Prediction Method Implementation

In control theory, predictive control represents a widely-used methodology that employs prediction models to forecast future system states. The dynamic matrix prediction method serves as a fundamental predictive control approach that formulates prediction models in matrix format for future state projections. This technique leverages historical system states and control inputs to predict future states and control actions. The implementation typically involves constructing a dynamic matrix from step response coefficients, where each column represents the system's response to a unit step input at different time intervals.

Key implementation aspects include: - Building the dynamic matrix A using system identification data - Formulating the prediction equation: Y = A*ΔU + Y0 - Solving the quadratic programming problem for optimal control increments - Implementing receding horizon control with constraints handling The core MATLAB functions would involve: 1. dmpc() - Main function for dynamic matrix predictive control 2. buildDynamicMatrix() - Constructs the prediction matrix from step response data 3. optimizeControl() - Solves the optimization problem using quadprog() 4. applyConstraints() - Handles input and output constraints This method enables more accurate future state predictions, facilitating appropriate control actions for enhanced system performance. The dynamic matrix prediction approach therefore holds significant promise for practical control applications, particularly in process industries where system dynamics can be adequately captured through step response models.