Design and Implementation of a SNA-PID controller based on RFNNI applied for the Ball and Beam System

Abstract

This paper proposes an adaptive control approach for the ball and beam system using a Single Neuron Adaptive PID (SNA-PID) controller integrated with a Recurrent Fuzzy Neural Network Identifier (RFNNI). The main contribution of this study is the development of an online identification and parameter adaptation scheme, in which the RFNNI is employed to identify the nonlinear system dynamics and provide real-time Jacobian estimation, while the SNA-PID controller updates its parameters online to improve tracking accuracy and robustness against uncertainties. The combination of the single-neuron adaptive structure and the recurrent fuzzy neural network enables effective compensation for nonlinearities and dynamic variations of the system. The proposed control framework is first validated through MATLAB/Simulink simulations and subsequently implemented in real-time experiments with online parameter updating. The experimental setup is based on a DSP control platform and utilizes an infrared (IR) sensor for real-time measurement of ball position. Comparative simulation and experimental results demonstrate that the proposed SNA-PID-RFNNI scheme significantly outperforms the conventional PID controller, achieving a reduction in overshoot from 44.26% to 6.28% and a decrease in settling time from 23 s to 17 s. These results confirm the effectiveness and practical applicability of the proposed adaptive control strategy.