Nonlinear Identification with Constraints in Frequency Domain of Electric Direct Drive with Multi-Resonant Mechanical Part

Knowledge of a direct-drive model with a complex mechanical part is important in the synthesis of control algorithms and in the predictive maintenance of digital twins. The identification of two-mass drive systems with one low mechanical resonance frequency is often described in the literature. This...

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Autor principal:	Dominik Łuczak
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	nonlinear optimization with constraints complex mechatronic systems electric drive mechanical resonance multi-mass system identification Technology T
Acceso en línea:	https://doaj.org/article/ae32d0757db448ba8f3471c8cc1135f9
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spelling	oai:doaj.org-article:ae32d0757db448ba8f3471c8cc1135f92021-11-11T15:57:42ZNonlinear Identification with Constraints in Frequency Domain of Electric Direct Drive with Multi-Resonant Mechanical Part10.3390/en142171901996-1073https://doaj.org/article/ae32d0757db448ba8f3471c8cc1135f92021-11-01T00:00:00Zhttps://www.mdpi.com/1996-1073/14/21/7190https://doaj.org/toc/1996-1073Knowledge of a direct-drive model with a complex mechanical part is important in the synthesis of control algorithms and in the predictive maintenance of digital twins. The identification of two-mass drive systems with one low mechanical resonance frequency is often described in the literature. This paper presents an identification workflow of a multi-resonant mechanical part in direct drive with up to three high-frequency mechanical resonances. In many methods, the identification of a discrete time (DT) model is applied, and its results are transformed into a continuous-time (CT) representation. The transformation from a DT model to a CT model has limitations due to nonlinear mapping of discrete to continuous frequencies. This problem may be overcome by identification of CT models in the frequency domain. This requires usage of a discrete Fourier transform to obtain frequency response data as complex numbers. The main work presented in this paper is the appropriate fitting of a CT model of a direct-drive mechanical part to complex number datasets. Fitting to frequency response data is problematic due to the attraction of unexcited high frequency ranges, which lead to wrong identification results of multi-mass (high order) drive systems. Firstly, a CT fitting problem is a nonlinear optimization problem, and, secondly, complex numbers may be presented in several representations, which leads to changes in the formulation of the optimization problem. In this paper, several complex number representations are discussed, and their influence on the optimization process by simulation evaluation is presented. One of the best representations is then evaluated using a laboratory setup of direct drive with unknown parameters of three high mechanical resonance frequencies. The mechanical part of the examined direct drive is described by three mechanical resonances and antiresonances, which are characteristic of a four-mass drive system. The main finding is the addition of frequency boundaries in the identification procedure, which are the same as those in the frequency range of the excitation signal. Neither a linear least-square algorithm nor a nonlinear least-square algorithm is suitable for this approach. The usage of nonlinear least-square algorithm with constraints as a fitting algorithm allows one to solve the issue of modeling multi-mass direct-drive systems in the frequency domain. The second finding of this paper is a comparison of different cost functions evaluated to choose the best complex number representation for the identification of multi-mass direct-drive systems.Dominik ŁuczakMDPI AGarticlenonlinear optimization with constraintscomplex mechatronic systemselectric drivemechanical resonancemulti-mass systemidentificationTechnologyTENEnergies, Vol 14, Iss 7190, p 7190 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	nonlinear optimization with constraints complex mechatronic systems electric drive mechanical resonance multi-mass system identification Technology T
spellingShingle	nonlinear optimization with constraints complex mechatronic systems electric drive mechanical resonance multi-mass system identification Technology T Dominik Łuczak Nonlinear Identification with Constraints in Frequency Domain of Electric Direct Drive with Multi-Resonant Mechanical Part
description	Knowledge of a direct-drive model with a complex mechanical part is important in the synthesis of control algorithms and in the predictive maintenance of digital twins. The identification of two-mass drive systems with one low mechanical resonance frequency is often described in the literature. This paper presents an identification workflow of a multi-resonant mechanical part in direct drive with up to three high-frequency mechanical resonances. In many methods, the identification of a discrete time (DT) model is applied, and its results are transformed into a continuous-time (CT) representation. The transformation from a DT model to a CT model has limitations due to nonlinear mapping of discrete to continuous frequencies. This problem may be overcome by identification of CT models in the frequency domain. This requires usage of a discrete Fourier transform to obtain frequency response data as complex numbers. The main work presented in this paper is the appropriate fitting of a CT model of a direct-drive mechanical part to complex number datasets. Fitting to frequency response data is problematic due to the attraction of unexcited high frequency ranges, which lead to wrong identification results of multi-mass (high order) drive systems. Firstly, a CT fitting problem is a nonlinear optimization problem, and, secondly, complex numbers may be presented in several representations, which leads to changes in the formulation of the optimization problem. In this paper, several complex number representations are discussed, and their influence on the optimization process by simulation evaluation is presented. One of the best representations is then evaluated using a laboratory setup of direct drive with unknown parameters of three high mechanical resonance frequencies. The mechanical part of the examined direct drive is described by three mechanical resonances and antiresonances, which are characteristic of a four-mass drive system. The main finding is the addition of frequency boundaries in the identification procedure, which are the same as those in the frequency range of the excitation signal. Neither a linear least-square algorithm nor a nonlinear least-square algorithm is suitable for this approach. The usage of nonlinear least-square algorithm with constraints as a fitting algorithm allows one to solve the issue of modeling multi-mass direct-drive systems in the frequency domain. The second finding of this paper is a comparison of different cost functions evaluated to choose the best complex number representation for the identification of multi-mass direct-drive systems.
format	article
author	Dominik Łuczak
author_facet	Dominik Łuczak
author_sort	Dominik Łuczak
title	Nonlinear Identification with Constraints in Frequency Domain of Electric Direct Drive with Multi-Resonant Mechanical Part
title_short	Nonlinear Identification with Constraints in Frequency Domain of Electric Direct Drive with Multi-Resonant Mechanical Part
title_full	Nonlinear Identification with Constraints in Frequency Domain of Electric Direct Drive with Multi-Resonant Mechanical Part
title_fullStr	Nonlinear Identification with Constraints in Frequency Domain of Electric Direct Drive with Multi-Resonant Mechanical Part
title_full_unstemmed	Nonlinear Identification with Constraints in Frequency Domain of Electric Direct Drive with Multi-Resonant Mechanical Part
title_sort	nonlinear identification with constraints in frequency domain of electric direct drive with multi-resonant mechanical part
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/ae32d0757db448ba8f3471c8cc1135f9
work_keys_str_mv	AT dominikłuczak nonlinearidentificationwithconstraintsinfrequencydomainofelectricdirectdrivewithmultiresonantmechanicalpart
_version_	1718432433998659584

Nonlinear Identification with Constraints in Frequency Domain of Electric Direct Drive with Multi-Resonant Mechanical Part

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