Predictive Functional Control (PFC) Algorithm Based on Finite Impulse Response (FIR) Model

In this paper, we present a Predictive Functional Control (PFC) algorithm utilizing a Finite Impulse Response (FIR) model framework. The control law derivation includes analytical solutions for single-basis (step function) and dual-basis (step and ramp functions) configurations, where basis functions define the structure of future control sequences. Code implementation typically involves FIR coefficient identification through system impulse response data and predictive horizon optimization using quadratic programming. Steady-state analysis of the closed-loop system confirms zero steady-state error for both reference tracking and disturbance rejection, achieved through implicit integral action in the prediction structure. Furthermore, we propose a Fuzzy Adaptive PFC (FAPFC) strategy that synergizes T-S fuzzy modeling for nonlinear system approximation with recursive parameter adaptation mechanisms. This hybrid approach employs fuzzy rules to weight local FIR models and incorporates real-time adaptation loops for robust performance under dynamic uncertainties. The proposed methodology advances PFC techniques by introducing computational frameworks for complex systems, providing significant implications for industrial applications requiring high-precision control under varying operating conditions.