The use of grey wolf and red fox optimization algorithms in determining the parameters of the pid controller for a DC-DC boost converter

In this study, a PID-based control system was designed to maintain the output voltage of a DC-DC boost converter at a fixed reference value, and the PID gain parameters were optimized using the Grey Wolf Optimization (GWO), Red Fox Optimization (RFO), and Artificial Bee Colony (ABC) algorithms. The system performance was evaluated in terms of transient response behavior, overshoot, settling time, and error criteria such as ISE, IAE, and ITAE. Additionally, the adaptive control capabilities of the algorithms were tested under variations in load resistance (R) and input voltage (Vin). According to the analysis results, the GWO algorithm stood out under both steady and load-varying conditions by achieving the lowest error criteria. In these scenarios, it outperformed the other algorithms in terms of IAE, ISE, and ITAE values and enabled the system to quickly reach the reference value. Under input voltage variations, all three algorithms—GWO, RFO, and ABC—produced similar error levels. Although the GWO algorithm exhibited slightly higher overshoot compared to the others, this overshoot was rapidly damped, and the system quickly settled to a stable state. Furthermore, a Friedman test was applied to statistically compare the algorithms based on the error criteria (IAE, ISE, ITAE). The results of this multi-comparison analysis showed that GWO statistically achieved the best overall performance. GWO had the lowest average ranks for all three error criteria, statistically confirming its more consistent and successful performance under both steady and variable conditions. In conclusion, all three algorithms produced effective results in PID optimization. However, GWO emerged as the most suitable method due to its superior error performance, fast transient response, and statistical advantages. While the ABC algorithm provided a smoother yet slower control response, the RFO algorithm offered low overshoot but fell behind in some error metrics. Based on these findings, optimization algorithms like GWO—with strong global search capabilities and rapid convergence—are recommended for improving the performance of control systems in similar applications.