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.
