Parameter Identification of Fractional Order Systems Using a Hybrid of Bernoulli Polynomials and Block Pulse Functions Through Two-Stage Algorithm

This paper deals with fractional order system identification using a hybrid function identification method through a two-stage algorithm. The proposed method adopts the fractional integral operational matrix of hybrid Bernoulli polynomials and block pulse functions to transform the fractional order system into a linear parameter regression equation. Then, a two-stage algorithm is developed to simultaneously identify the coefficients and fractional differentiation orders. First, with the orders fixed, the coefficients are identified using the instrumental variable based recursive least square algorithm to overcome the influence of noise. Then, with the identified coefficients fixed, the orders are estimated using the Gauss-Newton iterative algorithm. The above process iterates until the stop criterion is met. Two identification examples are given to verify the effectiveness of the proposed method. Supplementary Material File (zww_zb_tang.pdf) - Download - 586.60 KB Information & Authors Information Version history Copyright This work is licensed under a Non Exclusive No Reuse License.

Authors Metrics & Citations Metrics Article Usage 203views 81downloads Citations Download citation Weiwei Zhang, Bo Zhang, Yinggan Tang. Parameter Identification of Fractional Order Systems Using a Hybrid of Bernoulli Polynomials and Block Pulse Functions Through Two-Stage Algorithm. Authorea. 11 November 2025. DOI: https://doi.org/10.22541/au.176283728.83290872/v1 DOI: https://doi.org/10.22541/au.176283728.83290872/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu.