<![CDATA[This paper presents a novel direct control strategy using a polynomial fuzzy neural network-based adaptive fractional order proportional integral derivative (PFNN-AFOPID) controller for nonlinear and time-varying systems. The proposed approach integrates the enhanced flexibility of fractional order calculus PID with the superior nonlinear approximation capabilities of polynomial fuzzy models, enabling dynamic adjustment of all control parameters without requiring precise mathematical modeling of system dynamics. By extending traditional PID control with fractional-order operations, the controller achieves improved frequency response and robustness against disturbances. Experimental validation on a DC motor position control system demonstrates significant performance improvements. Compared to traditional PID, the proposed PFNN-AFOPID achieved a performance improvement of 53.69% in RMSE, 78.56% in ISE, 69.92% in IAE, and 83.98% in ITAE. When compared to the existing fuzzy neural network-based adaptive PID (FNN-APID), our approach delivered improvements of 21.06% in RMSE, 28.79% in ISE, 5.69% in IAE, and 32.86% in ITAE. These results confirm the superior capability of the proposed approach in handling system nonlinearities while maintaining precise control under varying operational conditions, without requiring prior system dynamics knowledge or extensive offline training.]]>
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