A novel combination of fuzzy PID and deep neural controller in feedback-error-learning framework

This paper proposes a novel hybrid control strategy that integrates fuzzy logic, deep neural networks (DNNs), and classical proportional-integral-derivative (PID) control within the feedback-error-learning (FEL) framework. The proposed method dynamically adapts PID parameters using a fuzzy inference system (FIS) while employing a DNN to learn the system's inverse dynamics, thereby enhancing adaptability and robustness. Notable features include offline pre-training of the DNN using data from PID and FIS-tuned PID controllers, a novel single-sample normalization layer for DNN input preprocessing, and the seamless integration of FIS-adapted PID gains within the FEL framework. Extensive simulations demonstrate significant average improvements over other control methods. Specifically, the proposed method achieves average reductions of 53 % in steady-state error (SSE), 21 % in rise time, 41 % in mean absolute error (MAE), and 21 % lowering of control effort, indicating enhanced disturbance rejection and efficient control effort under uncertainties. These results validate the proposed hybrid framework as a versatile and efficient solution for diverse industrial and engineering applications.