ABSTRACT In this paper, a simple method is proposed to tune the parameters of Fractional Integral-Fractional Derivative (FIFE) Iλ Dμ controllers based on the Bode diagram. The proposed technique provides a practical approach for tuning FIFE controllers to compensate stable plants. Using the small gain theorem and based on the sensitivity functions analysis, it is proved that by applying the designed FIFE controller the robustness of the compensated system in the presence of plant uncertainties is improved in comparison to the PI controller in a similar structure. Moreover, the closed-loop phase margin and gain crossover frequency are adjustable by tuning the free controller parameters. Simulation results are presented to demonstrate the simplicity of application and effectiveness of the tuned controller.

中文翻译：

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使用小增益定理的分数阶 $I^{\lambda}D^{\mu}$ 控制器的鲁棒性分析和设计

摘要 在本文中，提出了一种简单的方法来调整分数阶积分-分数阶微分 (FIFE) Iλ Dμ 控制器的参数，该方法基于波特图。所提出的技术提供了一种用于调整 FIFE 控制器以补偿稳定设备的实用方法。使用小增益定理并基于灵敏度函数分析，证明了通过应用设计的 FIFE 控制器，与类似结构的 PI 控制器相比，在存在工厂不确定性的情况下，补偿系统的鲁棒性得到了提高。此外，可以通过调整自由控制器参数来调整闭环相位裕度和增益交叉频率。仿真结果展示了应用的简单性和调谐控制器的有效性。