Writing Model Predictive Control S-Functions

Model Predictive Control (MPC) is an advanced control strategy widely applied in industrial process control. Its core principle involves calculating optimal control inputs by optimizing system behavior over a future time horizon. Generalized Predictive Control (GPC), as a variant of MPC, is particularly suitable for handling systems with time delays and uncertainties.

In MATLAB, S-functions (System-functions) serve as powerful tools for creating custom blocks in Simulink. Implementing GPC through S-functions enables simulation and control of complex systems. Key implementation aspects include:

System Modeling: The S-function must incorporate discrete state-space models or transfer functions of the controlled plant, forming the foundation for predictions. This typically involves defining system matrices (A, B, C, D) or polynomial coefficients in the S-function's initialization routine. Optimization Objective: The cost function—usually comprising weighted sums of output tracking errors and control inputs—must be minimized within the S-function. Implementation requires formulating quadratic programming problems using MATLAB's quadprog function or custom optimization algorithms. Real-time Prediction: At each control interval, the S-function calculates multi-step output predictions and solves for optimal control sequences. This involves implementing prediction equations using system matrices and handling constraints through algorithm iterations. Receding Horizon: Only the first value of the control sequence is applied, with re-optimization occurring at each subsequent time step for closed-loop control. The S-function's output method must manage this rolling horizon implementation while maintaining state persistence.

GPC implementation via S-functions allows flexible adjustment of prediction and control horizons to adapt to systems with different dynamic characteristics. This approach proves particularly valuable in industrial automation for handling multivariate, nonlinear, or constrained control problems through customizable code structures.