Purpose

This paper aims to design a modified fractional order proportional integral derivative (PID) (FO[PI]^λD^µ) controller based on the principle of fractional calculus and investigate its performance for a class of a second-order plant model under different operating conditions. The effectiveness of the proposed controller is compared with the classical controllers.

Design/methodology/approach

The fractional factor related to the integral term of the standard FO[PI]^λD^µ controller is applied as a common fractional factor term for the proportional plus integral coefficients in the proposed controller structure. The controller design is developed using the regular closed-loop system design specifications such as gain crossover frequency, phase margin, robustness to gain change and two more specifications, namely, noise reduction and disturbance elimination functions.

Findings

The study results of the designed controller using matrix laboratory software are analyzed and compared with an integer order PID and a classical FOPI^λD^µ controller, the proposed FO[PI]^λD^µ controller exhibit a high degree of performance in terms of settling time, fast response and no overshoot.

Originality/value

This paper proposes a methodology for the FO[PI]^λD^µ controller design for a second-order plant model using the closed-loop system design specifications. The effectiveness of the proposed control scheme is demonstrated under different operating conditions such as external load disturbances and input parameter change.

中文翻译：

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一类二阶系统的增强型分数阶PID控制器设计

目的

本文旨在基于分数阶微积分原理设计一种改进的分数阶比例积分微分 (PID) (FO[PI] ^λ D ^µ ) 控制器，并研究其在不同工况下对一类二阶被控对象模型的性能。 . 所提出的控制器的有效性与经典控制器进行了比较。

设计/方法/方法

与标准 FO[PI] ^λ D ^µ控制器的积分项相关的分数因子被用作所提出的控制器结构中比例加积分系数的公共分数因子项。控制器设计是使用常规闭环系统设计规范开发的，例如增益交叉频率、相位裕度、增益变化鲁棒性以及另外两个规范，即降噪和干扰消除功能。

发现

对使用矩阵实验室软件设计的控制器的研究结果进行了分析，并与整数阶 PID 和经典 FOPI ^λ D ^µ控制器进行了比较，所提出的 FO[PI] ^λ D ^µ控制器在稳定时间方面表现出高度的性能，快速响应，无超调。

原创性/价值

本文提出了一种使用闭环系统设计规范的二阶设备模型的 FO[PI] ^λ D ^µ控制器设计方法。在不同的操作条件下，如外部负载扰动和输入参数变化，证明了所提出的控制方案的有效性。