Meta-heuristic algorithms (MHAs) have gained popularity in recent years due to their successful results in solving a wide variety of scientific problems. They offer ease of use, fast implementation, and effective convergence toward the optimal solution. Although MHAs have been extensively tested in solving well-known mathematical benchmark problems with one or more dimensions as well as civil and mechanical engineering problems in their initial demonstrations, controller design problems are not typically considered. Furthermore, the literature lacks a standardized optimization process for controller design problems using MHAs. Due to variations in iteration numbers, population sizes, number of trials, objective functions, and insufficient analysis presented in research papers, it becomes challenging to compare and evaluate the controller design performance of MHAs in a successful and fair manner. This work aims to establish a standardized approach for evaluating the performance of MHAs in controller design by proposing a consistent function evaluation metric. To achieve this goal, we present the most comprehensive and comparative study of MHAs’ performance in controller design conducted to date. In this paper, we utilize two commonly used objective functions in controller design: Zwe Lee Gaing and Integral Time Absolute Error. Additionally, we employ a total of twenty algorithms, consisting of ten classical algorithms and ten recently popular algorithms. We evaluate the performance of these algorithms on the “automatic voltage regulation” electric power system problem, which serves as a widely used benchmark for meta-heuristically optimized controllers. We consider three different controllers with three (PID), five (FOPID), and seven (FOPIDD) parameters. The performance results of the selected algorithms are thoroughly discussed, considering various analysis techniques such as box plot analysis, convergence curves, and transient response performances, as well as statistical tests like Wilcoxon and Friedman tests. As a result, symbiotic organisms search, teaching–learning based optimization, chaos game optimization, supply–demand based optimization, and jellyfish search algorithms generally emerge as the best-performing algorithms across all optimization processes for the three types of controllers. Researchers interested in conducting further analysis and comparing the improved algorithms can access all the models,parameters, and codes used in this study from the provided link (https://www.mathworks.com/matlabcentral/fileexchange/161336-fractional-order-controller-optimization-for-avr).

近年来，元启发式算法（MHA）因其在解决各种科学问题方面的成功成果而受到欢迎。它们易于使用、快速实施并能有效收敛到最佳解决方案。尽管在最初的演示中，MHA 在解决著名的一维或多维数学基准问题以及土木和机械工程问题方面已经进行了广泛的测试，但通常不考虑控制器设计问题。此外，文献缺乏使用 MHA 来解决控制器设计问题的标准化优化过程。由于迭代次数、总体规模、试验次数、目标函数的变化以及研究论文中提出的分析不充分，以成功且公平的方式比较和评估 MHA 的控制器设计性能变得具有挑战性。这项工作旨在通过提出一致的功能评估指标来建立评估控制器设计中 MHA 性能的标准化方法。为了实现这一目标，我们提出了迄今为止对 MHA 在控制器设计中的性能进行的最全面和比较的研究。在本文中，我们在控制器设计中利用了两个常用的目标函数：Zwe Lee Gaing 和积分时间绝对误差。此外，我们总共采用了二十种算法，其中包括十种经典算法和十种最近流行的算法。我们评估这些算法在“自动电压调节”电力系统问题上的性能，该问题是元启发式优化控制器广泛使用的基准。我们考虑三种不同的控制器，具有三个 (PID)、五个 (FOPID) 和七个 (FOPIDD) 参数。充分讨论了所选算法的性能结果，考虑了箱线图分析、收敛曲线和瞬态响应性能等各种分析技术，以及 Wilcoxon 和 Friedman 测试等统计测试。因此，共生生物搜索、基于教学的优化、混沌博弈优化、基于供需的优化和水母搜索算法通常成为这三种类型控制器的所有优化过程中表现最好的算法。有兴趣进行进一步分析和比较改进算法的研究人员可以从提供的链接访问本研究中使用的所有模型、参数和代码 (https://www.mathworks.com/matlabcentral/fileexchange/161336-fractional-order- avr 的控制器优化）。