An optimization approach for minimum norm and robust partial quadratic eigenvalue assignment problems for vibrating structures

Brahma, Sanjoy Kumar; Datta, Biswa Nath

doi:10.1016/j.jsv.2009.02.020

Cited by 70 publications

(47 citation statements)

References 19 publications

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“…DefineM;K by (8) and (9), where E is given by Eq. (11). Then the pencilQ ðkÞ ¼ kM ÀK has the following properties:…”

Section: The Solution Of Problem Speapmentioning

confidence: 99%

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Symmetry preserving partial eigenvalue assignment for undamped structural systems

Liu

2014

Applied Mathematical Modelling

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a b s t r a c tIn this paper, the partial eigenvalue assignment problem for undamped structural systems by output feedback control where the output matrix is also a designing parameter is considered. We propose a method to solve this problem in which the unwanted eigenvalues are move to desired values and all other eigenpairs remain unchanged. In addition, our method can preserve symmetry of the systems. Numerical example shows that the proposed method is effective.

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“…DefineM;K by (8) and (9), where E is given by Eq. (11). Then the pencilQ ðkÞ ¼ kM ÀK has the following properties:…”

Section: The Solution Of Problem Speapmentioning

confidence: 99%

“…Carvalho [3] propose a symmetry preserving eigenvalue embedding method in finite element model updating. Recently, the related articles are given by [4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Symmetry preserving partial eigenvalue assignment for undamped structural systems

Liu

2014

Applied Mathematical Modelling

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“…Only two papers that deals with the robustness of the PQEVAP have been published so far. They are: the paper by Qian and Xu [33] and the recent papers by Brahama and Datta [3,4]. The method proposed by Qian and Xu is not an optimization-based and has limitations.…”

Section: Q2mentioning

confidence: 99%

“…Compare the proposed algorithm with Brahma-Datta's algorithm [4] and also with both the single and multi-input versions of Ram-Elhay's algorithm [34].…”

Section: Q2mentioning

confidence: 99%

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Minimum norm partial quadratic eigenvalue assignment with time delay in vibrating structures using the receptance and the system matrices

Bai

Chen

Datta

2013

Journal of Sound and Vibration

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a b s t r a c tThe partial quadratic eigenvalue assignment problem (PQEVAP) concerns reassigning a few undesired eigenvalues of a quadratic matrix pencil to suitably chosen locations and keeping the other large number of eigenvalues and eigenvectors unchanged (no spillover). The problem naturally arises in controlling dangerous vibrations in structures by means of active feedback control design. For practical viability, the design must be robust, which requires that the norms of the feedback matrices and the condition number of the closed-loop eigenvectors are as small as possible. The problem of computing feedback matrices that satisfy the above two practical requirements is known as the Robust Partial Quadratic Eigenvalue Assignment Problem (RPQEVAP). In this paper, we formulate the RPQEVAP as an unconstrained minimization problem with the cost function involving the condition number of the closed-loop eigenvector matrix and two feedback norms. Since only a small number of eigenvalues of the open-loop quadratic pencil are computable using the state-of-the-art matrix computational techniques and/or measurable in a vibration laboratory, it is imperative that the problem is solved using these small number of eigenvalues and the corresponding eigenvectors. To this end, a class of the feedback matrices are obtained in parametric form, parameterized by a single parametric matrix, and the cost function and the required gradient formulas for the optimization problem are developed in terms of the small number of eigenvalues that are reassigned and their corresponding eigenvectors. The problem is solved directly in quadratic setting without transforming it to a standard first-order control problem and most importantly, the significant ''no spill-over property'' of the closed-loop eigenvalues and eigenvectors is established by means of a mathematical result. These features make the proposed method practically applicable even for very large structures. Results on numerical experiments show that the proposed method considerably reduces both feedback norms and the sensitivity of the closed-loop eigenvalues. A study on robustness of the system responses of the method under small perturbations show that the responses of the perturbed closed-loop system are compatible with perturbations.& 2009 Published by Elsevier Ltd.

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Design Scheme II of FTZNN

2022

Zeroing Neural Networks

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An optimization approach for minimum norm and robust partial quadratic eigenvalue assignment problems for vibrating structures

Cited by 70 publications

References 19 publications

Symmetry preserving partial eigenvalue assignment for undamped structural systems

Symmetry preserving partial eigenvalue assignment for undamped structural systems

Minimum norm partial quadratic eigenvalue assignment with time delay in vibrating structures using the receptance and the system matrices

Design Scheme II of FTZNN

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