Data-driven brain emotional learning-based intelligent controller-PID control of MIMO systems based on a modified safe experimentation dynamics algorithm

Abstract

The increasing complexity of modern plant systems and the limitations of precise mathematical modeling have led to a shift towards data-driven control methods. These methods present an effective alternative that treats plants as black-box systems without requiring explicit models. The safe experimentation dynamics algorithm (SEDA) is one such method that optimizes controller parameters using data-driven techniques. Nonetheless, control performance can be limited by the fixed probability coefficient used in the original SEDA to disrupt design parameters, especially when balancing exploration and exploitation phases. This study proposes an enhanced version of the SEDA: the modified SEDA (MSEDA), to address this issue. The MSEDA introduces a dynamic probability coefficient that decreases with each iteration. The adjustment improves the balance between exploration and exploitation phases, which enhances control accuracy. The MSEDA was used to tune the brain emotional learning-based intelligent controller (BELBIC) together with a proportional-integral-derivative (PID) controller. The result was the BELBIC-PID controller inspired by the limbic system of the human brain, which has high precision. The effectiveness of the proposed MSEDA-BELBIC-PID was validated using simulations on multi-input multi-output (MIMO) systems, with a focus on tracking performance and computational efficiency. The statistical analysis of 30 independent trials demonstrated that the proposed MSEDA-BELBIC-PID was significantly improved over the original SEDA-BELBIC-PID. Wilcoxon's rank test yielded a fitness function p-value < 0.05, which confirmed the robustness and effect of the proposed enhancement. The comparative results demonstrated that the MSEDA-BELBIC-PID consistently performed better than the original approach and had improved fitness function values, reduced total integral square error, and lower total integral square input. These findings underscored the MSEDA suitability as a data-driven tool for controller design parameter optimization. Furthermore, the low computational burden of MSEDA rendered it a strong alternative to heuristic multi-agent algorithms, which frequently encounter high computational costs with large controller design parameters.