Time-delayed systems frequently appear, especially in sectors such as fluid flow processes, chemical procedures, and the food industry. This paper addresses the optimization of parameters for a fractional order PID (FOPID) controller, which is used to control a time-delayed system, using five distinct algorithms inspired by nature. These algorithms are NewBAT, Cuckoo search (CS), Firefly (FF), Gray Wolf Optimizer (GWO), and Whale optimization algorithm (WOA). The FOPID controller parameters, namely K_P, K_I, K_D, λ and μ, have been optimized using these algorithms. During the optimization process, the integral of the time absolute error (ITAE) was considered as the primary measurement criterion. In addition to this value, the maximum overshoot, settling time, time to reach the maximum value, and error values were examined. Simulations conducted with the obtained parameters tested the system's resilience to disturbances introduced at the output, and the controller responses were also evaluated during these tests. The reactions of the determined parameters to different reference inputs were analyzed, and the results are presented in graphs and tables. The efficiency and reliability of the optimization algorithms were substantiated by comprehensive statistical analyses. These analyses play a critical role in algorithm selection and objective evaluation of the results. Simulation studies were conducted in the Matlab and Simulink environments. The FOMCON Toolbox was used for fractional-order processes.

中文翻译：

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用于优化时滞系统中分数阶 PID 控制器的受自然启发的算法

时滞系统经常出现，特别是在流体流动过程、化学过程和食品工业等领域。本文讨论了分数阶 PID (FOPID) 控制器的参数优化，该控制器用于控制时滞系统，使用五种受大自然启发的不同算法。这些算法是NewBAT、布谷鸟搜索(CS)、萤火虫(FF)、灰狼优化器(GWO)和鲸鱼优化算法(WOA)。FOPID 控制器参数，即K _P、K _I、K _D、λ和μ，已使用这些算法进行了优化。在优化过程中，时间绝对误差积分（ITAE）被视为主要测量标准。除了该值之外，还检查了最大超调、稳定时间、达到最大值的时间以及误差值。使用获得的参数进行的仿真测试了系统对输出端引入的干扰的恢复能力，并且在这些测试期间还评估了控制器响应。分析了确定的参数对不同参考输入的反应，结果以图表形式呈现。通过全面的统计分析证实了优化算法的效率和可靠性。这些分析在算法选择和结果的客观评估中发挥着关键作用。仿真研究是在 Matlab 和 Simulink 环境中进行的。FOMCON 工具箱用于分数阶过程。