针对分数阶系统的特殊情况设计非超调分数阶PI控制器。

IF 6.5
Mohammad Tabatabaei
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引用次数: 0

摘要

在各种应用中,获得非超调阶跃响应是至关重要的。另一方面,虽然文献中提出了各种方法来设计分数阶比例积分(FOPI)控制器,但它们都不能保证闭环系统的非超调单位阶跃响应(USR)。本文设计了一阶和二阶分数阶系统的非超调FOPI控制器。首先,选择FOPI控制器参数以实现闭环系统的单调幅频响应(MFR),从而实现非超调或最小超调USR。证明了当FOPI控制器的分数阶数与被控对象的最大阶数之和(对于分数阶数在1和0之间的一阶和二阶FOS)等于1时,可以得到单调的MFR。然后计算比例增益和积分器时间常数,以获得所需的相位裕度(PM)和环路增益交叉频率(GCF)。得到了PM的主要约束条件,并证明了闭环系统的稳定性。数值仿真结果表明,在存在扰动和模型参数不确定性的情况下,所提出的控制器是正确的。对比仿真证明了所设计的FOPI与文献中已经发表的工作相比的优越性。本文还验证了所提出的FOPI控制器对离子聚合物-金属复合驱动器的控制性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Designing non-overshooting fractional-order PI controllers for a particular case of fractional-order systems.

It is crucial to attain a non-overshooting step response in various applications. On the other hand, although various approaches have been presented to design fractional-order proportional-integral (FOPI) controllers in the literature, none of them can ensure a non-overshooting unit step response (USR) for the closed-loop system. This paper designs non-overshooting FOPI controllers for a fractional-order system (FOS) with one and two fractional orders. First, the FOPI controller parameters are chosen to achieve a monotonic magnitude-frequency response (MFR) for the closed-loop system, thereby achieving a non-overshooting or minimum overshoot USR. It is demonstrated that if the sum of the fractional order of the FOPI controller and the maximum order of the plant (for the FOS with one and two fractional orders, where the fractional orders are between one and zero) is equal to 1, a monotonic MFR can be attained. The proportional gain and the integrator time constant are then calculated to attain a desired phase margin (PM) and loop gain crossover frequency (GCF). The main constraints on PM are attained, and the stability of the closed-loop system is proved. Numerical simulations demonstrate the correctness of the presented controller in the presence of disturbance and uncertainty in model parameters. Comparative simulations demonstrate the superiority of the designed FOPI to an already published work in the literature. The performance of the proposed FOPI controller in controlling the ionic polymer-metal composite actuator is also demonstrated.

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