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Parameter estimation of the fractional-order Hammerstein–Wiener model using simplified refined instrumental variable fractional-order continuous time
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Allafi, Walid, Zajic , Ivan , Uddin , Kotub and Burnham , Keith J. (2017) Parameter estimation of the fractional-order Hammerstein–Wiener model using simplified refined instrumental variable fractional-order continuous time. IET Control Theory & Applications, 11 (15). 2591 -2598. doi:10.1049/iet-cta.2017.0284 ISSN 1751-8644.
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Official URL: http://doi.org/10.1049/iet-cta.2017.0284
Abstract
This study proposes a direct parameter estimation approach from observed input–output data of a stochastic single-input–single-output fractional-order continuous-time Hammerstein–Wiener model by extending a well known iterative simplified refined instrumental variable method. The method is an extension of the simplified refined instrumental variable method developed for the linear fractional-order continuous-time system, denoted. The advantage of this novel extension, compared with published methods, is that the static output non-linearity of the Wiener model part does not need to be invertible. The input and output static non-linear functions are represented by a sum of the known basis functions. The proposed approach estimates the parameters of the linear fractional-order continuous-time subsystem and the input and output static non-linear functions from the sampled input–output data by considering the system to be a multi-input–single-output linear fractional-order continuous-time model. These extra inputs represent the basis functions of the static input and output non-linearity, where the output basis functions are simulated according to the previous estimates of the fractional-order linear subsystem and the static input non-linear function at every iteration. It is also possible to estimate the classical integer-order model counterparts as a special case. Subsequently, the proposed extension to the simplified refined instrumental variable method is considered in the classical integer-order continuous-time Hammerstein–Wiener case. In this paper, a Monte Carlo simulation analysis is applied for demonstrating the performance of the proposed approach to estimate the parameters of a fractional-order Hammerstein–Wiener output model.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Engineering > WMG (Formerly the Warwick Manufacturing Group) | ||||||||
Library of Congress Subject Headings (LCSH): | Mathematical models -- Industrial applications | ||||||||
Journal or Publication Title: | IET Control Theory & Applications | ||||||||
Publisher: | The Institution of Engineering and Technology | ||||||||
ISSN: | 1751-8644 | ||||||||
Official Date: | 13 October 2017 | ||||||||
Dates: |
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Volume: | 11 | ||||||||
Number: | 15 | ||||||||
Page Range: | 2591 -2598 | ||||||||
DOI: | 10.1049/iet-cta.2017.0284 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 23 August 2017 | ||||||||
Date of first compliant Open Access: | 23 August 2017 | ||||||||
Funder: | Engineering and Physical Sciences Research Council | ||||||||
Grant number: | EP/M507143/1 and EP/N001745/1 | ||||||||
Open Access Version: |
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