Abstract This article presents a novel fractional order proportional–integral–derivative (FOPID) controller with fractional filter for an automatic voltage regulator (AVR) system. The proposed controller has seven independent parameters to be set. These parameters are optimally tuned by using sine–cosine algorithm (SCA) capable of balancing exploration and exploitation phases to find the optimal solution. The optimally tuned controller named as SCA-FOPIDFF is employed to enhance the performance of the AVR system. In order to show the effectiveness of the proposed controller, a FOPID controller with integer filter called as SCA-FOPIDF, a traditional FOPID controller without filter called as SCA-FOPID, a PID controller with fractional filter called as SCA-PIDFF, and a PID controller with integer filter called as SCA-PIDF are also designed for the AVR system using the SCA with the same objective function. In addition, the superiority of the proposed controller is also validated by the comparison with published studies proposing optimally tuned PID and FOPID controllers for the AVR system. Frequency response characteristics of the proposed controller obtained from bode analysis are presented. Finally, the robustness of the designed controllers are examined separately against both parameter uncertainties in the AVR system and external disturbances injected into the AVR system. Considering the overall results presented, it is clear that the fractional filter in the proposed SCA-FOPIDFF controller has significantly improve the AVR system performance and that the proposed controller can be successfully applied to the AVR system.

中文翻译：

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用于自动电压调节器的带分数滤波器的 FOPID 控制器

摘要 本文提出了一种用于自动电压调节器 (AVR) 系统的带有分数滤波器的新型分数阶比例积分微分 (FOPID) 控制器。建议的控制器有七个要设置的独立参数。这些参数通过使用能够平衡探索和开发阶段以找到最佳解决方案的正弦-余弦算法 (SCA) 进行优化调整。名为 SCA-FOPIDFF 的优化调谐控制器用于提高 AVR 系统的性能。为了显示所提出的控制器的有效性，带有整数滤波器的 FOPID 控制器称为 SCA-FOPIDF，不带滤波器的传统 FOPID 控制器称为 SCA-FOPID，带有分数滤波器的 PID 控制器称为 SCA-PIDFF，还为使用具有相同目标函数的 SCA 的 AVR 系统设计了一个称为 SCA-PIDF 的带有整数滤波器的 PID 控制器。此外，所提出的控制器的优越性也通过与已发表的研究进行比较来验证，这些研究提出了 AVR 系统的最佳调谐 PID 和 FOPID 控制器。提出了从波特分析中获得的所提出控制器的频率响应特性。最后，针对 AVR 系统中的参数不确定性和注入 AVR 系统的外部干扰，分别检查设计控制器的鲁棒性。考虑到所呈现的总体结果，