An improved brain emotional learning-based intelligent controller-PID control with adaptive learning rates for MIMO systems

• The improved SbLR-BELBIC-PID controller addresses restricted emotional learning as a key limitation of the standard BELBIC-PID. • The proposed sigmoid-based adaptive learning rates dynamically adjust in response to variations in the tracking error signals. • The SbLR-BELBIC-PID controller is validated on the twin rotor MIMO system and gantry crane system and outperforms the BELBIC-PID, NEPID, and PID controllers. • Superior robustness against measurement noise disturbances is achieved compared with the standard BELBIC-PID. Advanced multi-input multi-output (MIMO) systems pose significant challenges for trajectory tracking and control energy minimization due to inherent nonlinearities and dynamic coupling. While PID controllers remain widely used, their limited adaptability restricts performance in such environments. Bio-inspired approaches, particularly the brain emotional learning-based intelligent controller (BELBIC), offer improved adaptability; however, the fixed learning rate in standard BELBIC limits responsiveness under varying error signal conditions. This study proposes a BELBIC-PID control scheme with a sigmoid-based adaptive learning rate (SbLR-BELBIC-PID), where the learning rates of the BELBIC components are continuously adjusted, with the PID formulation providing sensory input and reward signals. This adaptive mechanism intensifies or attenuates emotional responses according to deviations from the reference signal, enabling faster convergence and improved control accuracy. Controller parameters are optimized using a modified safe experimentation dynamics algorithm (MSEDA) within a data-driven control framework. The proposed method is validated on the twin-rotor MIMO system and the gantry crane system. Results indicate reductions of 5.24% and 7.82% in the fitness function relative to the standard BELBIC-PID. Moreover, the proposed controller achieves lower integral square error, reduced control effort, and enhanced transient response, consistently outperforming conventional PID, NEPID, and standard BELBIC-PID controllers. Robustness evaluations under measurement noise further confirm that SbLR-BELBIC-PID attains lower trajectory-tracking error indices, including IAE, ISE, ITAE, and ITSE. These outcomes demonstrate the effectiveness of adaptive emotional learning for advanced nonlinear control applications.