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Parameter estimation of the fractional-order Hammerstein–Wiener model using simplified refined instrumental variable fractional-order continuous time
Allafi, Walid Zajic, Ivan Uddin, Kotub Burnham, Keith J.
Allafi, Walid
Zajic, Ivan
Uddin, Kotub
Burnham, Keith J.
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2017-07-05
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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.
Citation
Allafi, W., Zajic, I., Uddin, K., Burnham, KJ. (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) pp. 2591-2598 doi: 10.1049/iet-cta.2017.0284
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en
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© 2017 The Authors. Published by IET. This is an open access article available under a Creative Commons licence.
The published version can be accessed at the following link on the publisher’s website: https://doi.org/10.1049/iet-cta.2017.0284
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1751-8644