Oustaloup分抗电路的运算特征与逼近性能分析

Operational characteristic and approximation performance analysis of Oustaloup fractance circuits

摘要:

从全新的分数微积分运算角度考察Oustaloup分抗有理逼近的运算特征与逼近性能. 以阶频特征函数与相频特征函数为理论分析基础，从零极对子系统的运算特征入手，通过子系统的零极点分布情形，探究Oustaloup分抗有理逼近的运算特征，使用相对误差函数，逼近带宽， 指标，复杂度与逼近效益等指标对其运算性能与逼近效果进行分析. 本文理论分析结果表明，阶频特征可以简洁、准确的分析Oustaloup分抗有理逼近，该分抗有理逼近速度较快、复杂度较低. 为Oustaloup分抗电路的应用提供了坚实的基础，为分数阶控制器设计提供了一定的理论依据.

Abstract:

In this paper, we investigated operational characteristics and approximation performance of Oustaloup fractance rational approximation from a new perspective of fractional calculus operation. Based on order-frequency characteristic and phase-frequency characteristic theoretical analysis, we start from the operational characteristics of pole-zero sub-systems, by the pole-zero recursive distribution of which, we study operational characteristics of Oustaloup fractance, and in order to analyze its operational characteristics and approximation results, relative error function，approximation bandwidth, K-index, complexity and approximation effect were used. Theoretical results showed that fractional order-frequency characteristics can analyse Oustaloup fractance rational approximation simply and exactly, the fractance rational approximation has faster approximation speed and lower complexity. Providing a solid foundation for the application of Oustaloup fractance circuit, to provide a theoretical basis for the design of fractional controller.