Abstract In this study, an improved version of artificial electric field (AEF) algorithm, named as opposition-based AEF (ObAEF), has been proposed for the first time ever to tune a fractional order PID (FOPID) controller used in a magnetic ball suspension system. The basic AEF algorithm is a novel physics-inspired, population-based meta-heuristic optimization method that mathematically mimics Coulomb’s electrostatic force between charged particles. The proposed ObAEF algorithm is the improved version of the AEF which utilizes the opposition-based learning strategy to enhance the AEF algorithm’s exploration capability. To validate the performance, the novel ObAEF algorithm was applied to 6 well-known benchmark optimization problems of Sphere, Rosenbrock, Schwefel, Ackley, Egg Crate and Easom. The results were also compared with other algorithms such as basic AEF, atom search optimization (ASO) and artificial bee colony (ABC). It was also used to tune FOPID controller (ObAEF-FOPID) to improve the transient response of a magnetic levitation (maglev) system by minimizing a new objective function having a simple structure. The latter was proposed to minimize the maximum overshoot, settling and rise times along with steady state error of magnetically suspended ball’s position. The convergence profile and statistical analyzes were conducted to illustrate the success of the proposed algorithm. The effectiveness and superiority of the ObAEF-FOPID controller was further investigated through frequency response analysis and again compared with AEF, ABC and ASO based FOPID controllers as in statistical success, convergence profile and transient analyses. The results showed that the proposed ObAEF-FOPID has better control performance than those tuned by AEF, ASO and ABC algorithms.

中文翻译：

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基于对抗的人工电场算法及其在不稳定磁球悬浮系统FOPID控制器设计中的应用

摘要 在这项研究中，首次提出了人工电场 (AEF) 算法的改进版本，称为基于对立的 AEF (ObAEF)，用于调整磁球中使用的分数阶 PID (FOPID) 控制器。悬挂系统。基本的 AEF 算法是一种新颖的受物理学启发、基于群体的元启发式优化方法，它在数学上模拟了带电粒子之间的库仑静电力。所提出的ObAEF算法是AEF的改进版本，它利用基于对立的学习策略来增强AEF算法的探索能力。为了验证性能，将新颖的 ObAEF 算法应用于 Sphere、Rosenbrock、Schwefel、Ackley、Egg Crate 和 Easom 的 6 个著名的基准优化问题。结果还与其他算法进行了比较，例如基本 AEF、原子搜索优化 (ASO) 和人工蜂群 (ABC)。它还用于调整 FOPID 控制器 (ObAEF-FOPID)，通过最小化具有简单结构的新目标函数来改善磁悬浮 (maglev) 系统的瞬态响应。后者被提议最小化最大过冲、稳定和上升时间以及磁悬浮球位置的稳态误差。进行了收敛曲线和统计分析以说明所提出算法的成功。通过频率响应分析进一步研究了 ObAEF-FOPID 控制器的有效性和优越性，并再次与基于 AEF、ABC 和 ASO 的 FOPID 控制器进行比较，在统计上取得成功，收敛剖面和瞬态分析。结果表明，所提出的 ObAEF-FOPID 比通过 AEF、ASO 和 ABC 算法调整的那些具有更好的控制性能。