Fixed pole based modeling and simulation schemes for fractional order systems

Yiheng Wei; Jiachang Wang; Tianyu Liu; Yong Wang

doi:10.1016/j.isatra.2018.10.001

Fixed pole based modeling and simulation schemes for fractional order systems

ISA Trans. 2019 Jan:84:43-54. doi: 10.1016/j.isatra.2018.10.001. Epub 2018 Oct 15.

Authors

Yiheng Wei¹, Jiachang Wang¹, Tianyu Liu¹, Yong Wang²

Affiliations

¹ Department of Automation, University of Science and Technology of China, Hefei, 230026, China.
² Department of Automation, University of Science and Technology of China, Hefei, 230026, China. Electronic address: yongwang@ustc.edu.cn.

PMID: 30348436
DOI: 10.1016/j.isatra.2018.10.001

Abstract

This paper mainly investigates the numerical implementation issue of fractional order systems. First, a pattern of fixed pole schemes are developed to approximate fractional integrator/differentiator, whose common is that the poles keep constant for different α. Then, two solutions are proposed to improve the approximation performance around α=0. Afterwards, the simulation schemes are introduced for two kinds of fractional order systems. In those schemes, the configuration problem of nonzero initial value is considered. Finally, a fair and solid comparison to the classical approximation methods is presented, demonstrating the effectiveness and efficiency of the elaborated algorithms.

Keywords: Block diagram scheme; Fixed pole approximation; Fractional order systems; Nonzero initial value.