Optimal Brain Emotional Learning with PID Control for Flexible Joint Manipulators

This study introduces a data-driven Brain Emotional Learning-Based Intelligent Controller integrated with a Proportional-Integral-Derivative structure (BELBIC-PID) for a flexible joint manipulator (FJM) system. The controller is designed to enhance trajectory accuracy and dynamic performance in nonlinear plants where conventional PID controllers often exhibit shortcomings. To this end, the Modified Safe Experimentation Dynamics Algorithm (MSEDA) is employed to optimize the controller parameters, focusing on reducing tracking errors and minimizing input energy consumption. The nonlinear emotional learning process of the BELBIC further strengthens the controller’s capability to manage complex system dynamics. The proposed BELBIC-PID is evaluated through fitness function minimization, time-domain analysis, and standard trajectory tracking indices. Two control schemes are implemented: one dedicated to angular position regulation and the other to link deflection suppression. The trajectory tracking results reveal that the BELBIC-PID achieves reductions of up to 26.56% in the Integral of Time multiplied Squared Error (ITSE), 37.55% in the Integral of Time multiplied Absolute Error (ITAE), 20.79% in the Integral of Squared Error (ISE), and 25.11% in the Integral of Absolute Error (IAE) compared with the PID controller for both system outputs, while also outperforming the Fractional-Order Proportional-Integral-Derivative (FOPID) and the Real Proportional-Integral-Derivative with Second-Order Derivative (RPIDD2) controllers. Furthermore, robustness evaluations under external disturbance and measurement noise conditions confirm that the BELBIC-PID maintains stable tracking performance and superior resilience. Overall, simulation outcomes demonstrate that the BELBIC-PID provides enhanced control accuracy and robustness for nonlinear systems.