In this paper, Lagrangian-based method has been proposed for tuning the parameters of fractional order PIαDβ controller. In this method, the five parameters (Kp, Ki, Kd, α and β) of fractional order PIαDβ controller (FOPID) are suitably optimized, and successfully applied to a benchmark stable second-order feedback system. To prove the performance of the proposed method, several state-of-the-art approaches were compared. The computational complexity, robustness and stability analysis has been performed to investigate the performance of all these algorithms. Moreover, the precision and flexibility analysis among all these approaches has also been carried out in this paper. The closed loop response of the second-order bench mark stable plant in Simulink has also been depicted in this paper.

中文翻译：

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理想闭环系统基于拉格朗日的 FOPID 控制器设计

在本文中，提出了基于拉格朗日的方法来调整分数阶的参数磷一世αDβ控制器。在这个方法中，五个参数（ķp,ķ一世,ķd,α和β) 分数阶磷一世αDβ控制器（FOPID）进行了适当优化，并成功应用于基准稳定二阶反馈系统。为了证明所提出方法的性能，比较了几种最先进的方法。已经进行了计算复杂性、鲁棒性和稳定性分析，以研究所有这些算法的性能。此外，本文还对所有这些方法进行了精度和灵活性分析。本文还描述了 Simulink 中二阶基准稳定设备的闭环响应。