Fractional Fuzzy Inference System (FFIS) Design and Implementation for Temperature Control

Precise temperature regulation is essential in various industrial applications, particularly in environments requiring high accuracy and stability, such as egg incubation. Conventional control strategies, including Proportional-Integral-Derivative (PID) controllers and Fuzzy Inference Systems (FIS), often exhibit limitations in handling nonlinearities, disturbances, and uncertainties. To address these challenges, this research proposes a Fractional Fuzzy Inference System-based PID (FFIS-PID) controller, which enhances the adaptability and robustness of temperature control mechanisms. Unlike traditional fuzzy systems that rely solely on membership degrees, FFIS introduces fractional membership functions and fractional indices, enabling a more flexible and dynamic interpretation of fuzzy rules. The key innovation lies in the fractional compositional rule of inference, which allows the system to intelligently balance the influence of rules by adjusting their impact based on both the truth degree and the information volume. This enhances the adaptability of the control strategy without altering the fundamental rule base structure. The study involves designing fractional membership functions, selecting optimal fractional indices, and evaluating their effects on system behavior. A comparative analysis between FIS-PID and FFIS-PID controllers is conducted through simulations and experimental validation on an incubator system. The results confirm that the FFIS-PID controller provides superior temperature regulation by enabling real-time adaptability to changing conditions. This work contributes to the field of intelligent control by providing a novel approach to fuzzy inference enhancement through fractional compositional rule of inference mechanism. Future research could extend this methodology to other nonlinear control applications, further leveraging fractional indices for improved decision-making and stability.