一种新的基于模型的分数阶微分器及其在分数阶PID控制器中的应用

Xing Wei, Dayan Liu, D. Boutat
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引用次数: 4

摘要

本文的目的是设计一个基于零初始条件的整数阶线性系统的分数阶微分器,该系统使用被非零均值噪声破坏的输出观测值来估计输出的分数阶导数。首先,利用适当的调制函数,精确地得到了连续无噪声情况下输出分数阶导数的积分代数公式;不同于分数阶导数定义中的反常积分,所得到的公式是由反常积分给出的。然后,在调制函数中加入一个附加条件来处理非零均值噪声。在构造了所需的调制函数后,提出了一种离散噪声情况下的数字分数阶微分器,并进行了误差分析。最后,将所提出的分数阶微分器应用于整阶线性系统的分数阶PID控制器设计。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A new model-based fractional order differentiator with application to fractional order PID controllers
This paper aims at designing a fractional order differentiator based on a integer order linear system with zero initial conditions, where the fractional derivatives of the output are estimated using the output observation corrupted by a non zero-mean noise. Firstly, an integral algebraic formula for the fractional derivatives of the output is exactly obtained in continuous noise free case, using an appropriated modulating function. Unlike the improper integrals in the definitions of the fractional derivatives, the obtained formula is given by a proper integral. Then, an additional condition is added to the used modulating function in order to deal with the non zero-mean noise. After constructing the needed modulating function, a digital fractional order differentiator is proposed in discrete noisy case with some error analysis. Finally, the proposed fractional order differentiator is applied to design a fractional order PID controller for an integer order linear system.
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