A novel approach of fractional-order time delay system modeling based on Haar wavelet
Abstract
In this paper, fractional-order time delay system modeling is presented using Haar wavelet operational matrix of integration. Therefore, it does not require any prior knowledge of transfer function structure or partial information about fractional differentiation order. It allows the estimation of the implicit time delay parameter together with other model parameters by utilizing new delay operational matrix of Haar wavelet based on Riemann-Liouville definition. The proposed technique reduces the complexity of identification by converting the complex fractional calculus equations into simple algebra. The efficacy of the approach is verified on various integer and non-integer (fractional) order systems in simulation. For realistic condition, proposed method is verified in the presence of noise in simulation and also demonstrated on the real-time process control temperature system.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The Haar wavelet delay matrix was derived in [35] using the generalized delay matrix.
“The Haar wavelet delay matrix was derived in [35] using the generalized delay matrix.”
From Application of Fractional Calculus for Parameter Estimation of Nonlinear Wiener Systems With Time Delay (2024) · cites this paper as [35]
Cited by
Sorted by citations
Kothari, K. (2024) · IEEE Access · doi:10.1109/access.2024.3367441 · Cited by 10 · see citing works
“In the presented work, the fractional calculus and HWOM-based method [35] developed for the linear system is integrated and further expanded for the modeling of the Wiener-type nonlinear system.”
BackgroundMethodInfluentialSelf-citation
- Authors
- Kothari, K., Mehta, U., & Vanualailai, J.
- Affiliations
- University of the South Pacific (FJ)
- Corresponding author
- Kothari, Kajal
- Venue
- ISA Transactions
- Publisher
- Elsevier BV
- Published
- 2018-09
- Volume
- 80
- Pages
- 371-380
- ISSN
- 0019-0578 (ISSN-L)
- OpenAlex
- W2884819607
- Cited by
- 52
- References
- 0
- Citations by year
- 2026: 2 · 2025: 6 · 2024: 6 · 2023: 11 · 2022: 6 · 2021: 6 · 2020: 8 · 2019: 6 · 2018: 1
- FWCI
- 3.13
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- ISA Transactions (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Advanced Control Systems Design
- Physical Sciences › Engineering › Control and Systems Engineering › Control Systems and Identification
- Physical Sciences › Mathematics › Modeling and Simulation › Fractional Differential Equations Solutions
- Keywords
- fractional-order systems, time-delay systems, Haar wavelet, operational matrix of integration, Riemann-Liouville fractional derivative, system identification, time delay estimation, fractional calculus, temperature control
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
