Consistent approximation of fractional order operators Article Swipe

MAKE IMPACT

Yiheng Wei , YangQuan Chen , Yingdong Wei , Xuefeng Zhang · YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2101.11163

Fractional order controllers become increasingly popular due to their versatility and superiority in various performance. However, the bottleneck in deploying these tools in practice is related to their analog or numerical implementation. Numerical approximations are usually employed in which the approximation of fractional differintegrator is the foundation. Generally, the following three identical equations always hold, i.e., $\frac{1}{s^α}\frac{1}{s^{1-α}} = \frac{1}{s}$, $s^α\frac{1}{s^α} = 1$ and $s^αs^{1-α} = s$. However, for the approximate models of fractional differintegrator $s^α$, $α\in(-1,0)\cup(0,1)$, there usually exist some conflicts on the mentioned equations, which might enlarge the approximation error or even cause fallacies in multiple orders occasion. To overcome the conflicts, this brief develops a piecewise approximate model and provides two procedures for designing the model parameters. The comparison with several existing methods shows that the proposed methods do not only satisfy the equalities but also achieve high approximation accuracy. From this, it is believed that this work can serve for simulation and realization of fractional order controllers more friendly.

Type

preprint

Language

en

Landing Page

http://arxiv.org/abs/2101.11163

PDF

https://arxiv.org/pdf/2101.11163

OA Status

green

Cited By

1

References

30

Related Works

10

OpenAlex ID

https://openalex.org/W3125390404

Raw OpenAlex JSON

OpenAlex ID

https://openalex.org/W3125390404

Canonical identifier for this work in OpenAlex

DOI

https://doi.org/10.48550/arxiv.2101.11163

Digital Object Identifier

Title

Consistent approximation of fractional order operators

Work title

Type

preprint

OpenAlex work type

Language

en

Primary language

Publication year

2021

Year of publication

Publication date

2021-01-27

Full publication date if available

Authors

Yiheng Wei, YangQuan Chen, Yingdong Wei, Xuefeng Zhang

List of authors in order

Landing page

https://arxiv.org/abs/2101.11163

Publisher landing page

PDF URL

https://arxiv.org/pdf/2101.11163

Direct link to full text PDF

Open access

Yes

Whether a free full text is available

OA status

green

Open access status per OpenAlex

OA URL

https://arxiv.org/pdf/2101.11163

Direct OA link when available

Concepts

Bottleneck, Alpha (finance), Realization (probability), Order (exchange), Fractional calculus, Mathematics, Piecewise, Approximation error, Applied mathematics, Orders of approximation, Computer science, Mathematical analysis, Statistics, Embedded system, Finance, Economics, Construct validity, Psychometrics

Top concepts (fields/topics) attached by OpenAlex

Cited by

1

Total citation count in OpenAlex

Citations by year (recent)

2023: 1

Per-year citation counts (last 5 years)

References (count)

30

Number of works referenced by this work

Related works (count)

10

Other works algorithmically related by OpenAlex

Full payload