On numerically reliable frequency-domain system identification: new connections and a comparison of methods

Voorhoeve, RJ Robbert; Oomen, Tae Tom; Herpen, Rma Robbert van; Steinbuch, M Maarten

doi:10.3182/20140824-6-za-1003.02264

Cited by 5 publications

(3 citation statements)

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“…A 16 th order successful industrial case study is presented in [22]. Furthermore, an experimental example and comparison with pre-existing approaches is presented in [39]. Finally, recent experiments [40] have shown good results on a 100 th order model.…”

Section: Discussionmentioning

confidence: 99%

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Bi-Orthonormal Polynomial Basis Function Framework With Applications in System Identification

Herpen

Bosgra

Oomen

2016

IEEE Trans. Automat. Contr.

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Abstract-Numerical aspects are of central importance in identification and control. Many computations in these fields involve approximations using polynomial or rational functions that are obtained using orthogonal or oblique projections. The aim of this paper is to develop a new and general theoretical framework to solve a large class of relevant problems. The proposed method is built on the introduction of bi-orthonormal polynomials with respect to a data-dependent bi-linear form. This bi-linear form generalises the conventional inner product and allows for asymmetric and indefinite problems. The proposed approach is shown to lead to optimal numerical conditioning (κ = 1) in a recent frequency-domain instrumental variable system identification algorithm. In comparison, it is shown that these recent algorithms exhibit extremely poor numerical properties when solved using traditional approaches. I. INTRODUCTIONApplications of system identification and control often involve numerical computations. The accuracy of these computations determines the quality of the resulting model or controller. This has led to considerable research to develop numerically reliable algorithms, see, e.g., [38] and [8], [4] for a general overview. Many computations involve weighted least-squares type problems for systems that are parametrized in terms of (vector) polynomials or rational forms, where orthogonal or oblique projections play a central role.In the field of system identification, weighted nonlinear least-squares criteria are particularly common, see [29]. Established identification algorithms include [26], the SK-iteration [34], and the Gauss-Newton iteration [1], which (iteratively) compute the least-squares solution to a linear systems of equations, for polynomial models or rational parametrizations. Although conceptually straightforward, the associated numerical conditioning is often extremely poor, as is evidenced by the developments in [1 , a fundamentally different solution strategy is pursued. The strategy is based upon the construction of orthogonal polynomials with respect to a data-dependent inner product, which directly provides the solution to the approximation problem in terms of polynomials. Essentially, this yields optimal conditioning of the associated linear system of equations, i.e., κ = 1.Besides developments in view of reliable algorithms that involve least-squares type solutions, recently, more general

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Section: Discussionmentioning

confidence: 99%

“…Let X and W 1 , W 2 be defined in (38)- (39). Let K,L denote bi-orthonormal vector-bases for K, L in (34)- (35), respectively, withk 1 ,l 1 defined in (42)- (43).…”

Section: Bi-orthonormal Vector-bases For Krylov Subspacesmentioning

confidence: 99%

Bi-Orthonormal Polynomial Basis Function Framework With Applications in System Identification

Herpen

Bosgra

Oomen

2016

IEEE Trans. Automat. Contr.

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“…Second, the identification of accurate models of complex high-tech systems is numerically challenging. To enable the accurate and fast identification of nominal models, new approaches that enable a numerically reliable implementation are being developed, see, e.g., [27], [24], see also [68] for a recent benchmark comparison.…”

Section: Model-based Control For High-tech Mechatronic Systemsmentioning

confidence: 99%

Model-Based Control for High-Tech Mechatronic Systems

Oomen¹,

Steinbuch²

2020

Mechatronics and Robotics

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DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

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Identification of System Dynamics with Time Delay: a Two-Stage Frequency Domain Approach

Beauduin

Fujimoto

2017

IFAC-PapersOnLine

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On numerically reliable frequency-domain system identification: new connections and a comparison of methods

Cited by 5 publications

References 20 publications

Bi-Orthonormal Polynomial Basis Function Framework With Applications in System Identification

Bi-Orthonormal Polynomial Basis Function Framework With Applications in System Identification

Model-Based Control for High-Tech Mechatronic Systems

Identification of System Dynamics with Time Delay: a Two-Stage Frequency Domain Approach

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