In this article, the tuning rules of fractional order PID controller are derived using Indirect Design Approach‐1. In Indirect Design Approach‐1, the plant is shifted in the frequency domain using the shifting parameter ψ. The tuning rules of stochastically optimized fractional order PID controllers exist in literature for the fixed values of maximum sensitivity. Maximum Sensitivity or robustness of the process is application dependent. Due to complex fractional order mathematics, the design of fractional order PID controller is complex. Therefore, in this article, new optimal tuning rules for FOPID controller are proposed using the shifted version of the plant. The adjustable robustness is achieved by varying tuning variable ψ which has a linear relation with the Maximum Sensitivity, Gain margin and Phase Margin. The range of ψ within which it can be varied is also proposed for both stable and unstable processes. Simulation is carried out in the MALTAB environment for validating the proposed methodology. A stable and an unstable first order process with time delay is considered for simulation. For the practical viability and novelty, a real‐time experiment on the level control of Canonical Tank using the proposed methodology is shown.

中文翻译：

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分数阶比例积分微分控制器的间接最优调整规则

在本文中，分数阶PID控制器的调整规则是使用间接设计方法-1导出的。在间接设计方法-1中，使用偏移参数ψ在频域中偏移植物。对于最大灵敏度的固定值，文献中存在随机优化的分数阶PID控制器的调节规则。过程的最大灵敏度或鲁棒性取决于应用程序。由于分数阶数学复杂，分数阶PID控制器的设计非常复杂。因此，在本文中，使用工厂的转移版本提出了针对FOPID控制器的新的最佳调整规则。可调节的鲁棒性是通过改变调谐变量ψ实现的它与最大灵敏度，增益裕度和相位裕度呈线性关系。对于稳定过程和不稳定过程，都提出了ψ可以变化的范围。为了验证所提出的方法，在MALTAB环境中进行了仿真。考虑具有时滞的稳定和不稳定的一阶过程用于仿真。为了实现实用性和新颖性，显示了使用所提出的方法对Canonical Tank进行液位控制的实时实验。