This work presents the design and validation of an Adaptive Fuzzy PID (PIDFA) controller for real-time stabilization of nonlinear and underactuated systems, using the inverted pendulum as a benchmark. Conventional PID controllers, while widely used, lack robustness in dynamic environments due to their fixed parameters and reliance on precise models. The proposed PIDFA architecture embeds a fuzzy inference mechanism that continuously adjusts the PID gains based on an instantaneous system error and its derivative, eliminating the need for offline tuning and improving performance under uncertainty.

The control design integrates fuzzification, rule-based gain scheduling, and defuzzification. Separate fuzzy systems regulate the proportional, integral, and derivative components, enabling real-time gain adaptation. A set of 49 linguistic rules per gain ensures interpretable and efficient control logic. Simulations conducted in MATLAB/Simulink evaluate the controller under three scenarios: stabilization from initial deviation, step disturbance rejection, and structural parameter variation.

Results confirm that the PIDFA achieves fast stabilization (settling time <1.2 s), low overshoot (<5%), and robust performance without saturation or chattering. The controller adapts to parameter shifts and external disturbances without manual reconfiguration, demonstrating strong real-time applicability. This study supports the use of fuzzy adaptive controllers in managing uncertain and nonlinear systems and outlines a methodology transferable to broader domains such as robotics and power systems.