Fractional observer to estimate periodical forces

In the present work we propose a fractional state observer with constant gain to estimate the periodical force exerted on a mechanical system by measuring only its displacement. The state observer is designed from both the Fourier series that approximates the periodical force and the equations of th...

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Bibliographic Details
Published in:ISA transactions 2018-11, Vol.82, p.30-41
Main Authors: Coronel-Escamilla, A., Gómez-Aguilar, J.F., Torres, L., Escobar-Jimnez, R.F., Olivares-Peregrino, V.H.
Format: Article
Language:English
Subjects:
Fourier coefficients
Fractional calculus
Mechanical systems
Parameter identification
Periodical signals
State observers
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Summary:In the present work we propose a fractional state observer with constant gain to estimate the periodical force exerted on a mechanical system by measuring only its displacement. The state observer is designed from both the Fourier series that approximates the periodical force and the equations of the damped harmonic oscillator that represents the behavior of the system. Specifically, the reconstruction of the force is carried out from the estimates of the series coefficients, which in fact are part of the dynamical system that composes the observer. Adams-Bashforth-Moulton method is used to compute the fractional derivatives of the observer in the Liouville-Caputo sense. Experiments based on real data are presented to show the advantages of using a fractional observer in the reconstruction of forces. •Design of a fractional state observer with constant gain to estimate the periodical force exerted on a mechanical system.•Fourier series approximates the periodical force and the equations of the damped harmonic oscillator that represents the behavior of the system.•Numerical evaluation of the fractional state observer, using experimental data.
ISSN:0019-0578
1879-2022
DOI:10.1016/j.isatra.2017.11.003