MATLAB Code Implementation of Generalized Predictive Control (GPC)

Generalized Predictive Control (GPC) is an advanced control strategy widely used in industrial applications, particularly suitable for systems with time-varying or nonlinear characteristics. This control method is based on the CARIMA (Controlled Auto-Regressive Integrated Moving Average) model, which effectively handles system dynamics variations and external disturbances. Implementing Generalized Predictive Control in MATLAB requires establishing a CARIMA model to describe the dynamic characteristics of the controlled object. The CARIMA model structure effectively represents system integration effects and random disturbances, making it well-suited for predictive control frameworks. The implementation steps primarily include: Model Parameter Identification: The initial step involves identifying CARIMA model parameters, typically accomplished using least squares methods or other system identification techniques. In MATLAB, this can be implemented using functions like `arx` or `pem` from the System Identification Toolbox. These identified parameters are essential for subsequent prediction and control calculations. Prediction Equation Construction: Based on the CARIMA model, future output prediction equations are derived. The core of predictive control lies in utilizing historical data and current inputs to calculate output values for multiple future time steps. MATLAB's matrix operations capabilities make this computation efficient through appropriate vectorization techniques. Optimization Objective Function: GPC determines control inputs by optimizing an objective function that typically includes tracking errors of future outputs and penalty terms for control inputs. This ensures system stability and robustness. MATLAB's Optimization Toolbox provides functions like `fmincon` or `quadprog` for solving this optimization problem efficiently. Receding Horizon Implementation: At each sampling period, GPC recalculates optimal control inputs based on the latest measurement data and applies them to the controlled object, achieving closed-loop control. This involves implementing a real-time optimization loop that continuously updates control actions. In MATLAB, the powerful matrix computation capabilities and Optimization Toolbox enable efficient implementation of the Generalized Predictive Control algorithm. By adjusting parameters such as prediction horizon and control horizon, engineers can balance system response speed and stability to meet different control requirements. The implementation typically involves creating custom functions for prediction matrix generation and quadratic programming solutions. The advantages of Generalized Predictive Control include its adaptability to complex systems and excellent disturbance rejection capabilities, making it widely applicable in industrial process control sectors such as chemical processing and power systems.