Frequency-band complex noninteger differentiator: Characterization and synthesis
Frequency-band complex noninteger differentiator: Characterization and synthesis
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DOI：
10.1109/81.817385
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发表时间：
2000-01-01
期刊：
影响因子：
--
通讯作者：
Nanot, FM
中科院分区：
文献类型：
--
作者：
Oustaloup, A;Levron, F;Nanot, FM
概述了物理和工程科学中关于广义(或任意阶)导数的最新进展，以证明非整数微分的重要性。然后阐述了在实时运算中使用它所带来的问题，以便激发通过递归的零极点分布来综合它的想法。为了支持这一想法，还提出了对现有工作的分析。对作用于任意给定频带的整数阶、非整数阶、实数阶或复数阶微分器的综合问题进行了全面的研究。首先，在四维Banach代数的数学空间中，给出了频带复数非整数阶微分器在运算域和频域的定义。然后，给出了用复递归因子的复零点和复极点的递归分布来确定其综合形式，并将复数非整数微分阶表示为这些递归因子的函数。零点和极点的个数被计算到尽可能少，同时仍然确保合成微分器的稳定性，并提供与要综合的初始微分器适当的近似值。给出了时间验证。最后，对综合微分器的概念提出了指导思想。
The state-of-the-art on generalized (or any order) derivatives in physics and engineering sciences, is outlined for justifying the interest of the noninteger differentiation. The problems subsequent to its use in real-time operations are then set out so as to motivate the idea of synthesizing it by a recursive distribution of zeros and poles. An analysis of the existing work is also proposed to support this idea. A comprehensive study is given of the synthesis of differentiators with integer, noninteger, real or complex orders, and whose action is limited to any given frequency bandwidth. First, a definition, in the operational and frequency domains, of a frequency-band complex noninteger order differentiator, is given in a mathematical space with four dimensions which is a Banach algebra. Then, the determination of its synthesized form, by a recursive distribution of complex zeros and poles characterized by complex recursive factors, is presented, The complex noninteger differentiation order is expressed as a function of these recursive factors. The number of zeros and poles is calculated to he as low as possible while still ensuring the stability of the synthesized differentiator and providing a suitable approximation to the initial differentiator to be synthesized. A time validation is presented. Finally, guidelines are proposed for the conception of the synthesized differentiator.