PID control algorithm based on multistrategy enhanced dung beetle optimizer and back propagation neural network for DC motor control

Traditional Proportional-Integral-Derivative (PID) control systems often encounter challenges related to nonlinearity and time-variability. Original dung beetle optimizer (DBO) offers fast convergence and strong local exploitation capabilities. However, they are limited by poor exploration capabilities, imbalance between exploration and exploitation phases, and insufficient precision in global search. This paper proposes a novel adaptive PID control algorithm based on enhanced dung beetle optimizer (EDBO) and back propagation neural network (BPNN). Firstly, the diversity of exploration is increased by incorporating a merit-oriented mechanism into the rolling behavior. Then, a sine learning factor is introduced to balance the global exploration and local exploitation capabilities. Additionally, a dynamic spiral search strategy and adaptive \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t$$\end{document}-distribution disturbance are presented to enhance search precision and global search capability. The BPNN is employed to fine-tune both PID and network parameters, leveraging its powerful generalization and learning ability to model nonlinear system dynamics. In the simplified motor experiments, the proposed controller achieved the lowest overshoot (0.5%) and the shortest response time (0.012 s), with a settling time of 0.02 s and a steady-state error of just 0.0010. In another set of experiments, the proposed controller recorded an overshoot and response time of 0.7% and 0.0010 s, across five DC motor tests. These results demonstrate the proposed adaptive PID control algorithm has superior performance in optimizing control system parameters, as well as improving system robustness and stability.