A comparison of control techniques for large flexible systems

Meirovitch, L.; Baruh, H.; Öz, H.

doi:10.2514/3.19833

Cited by 215 publications

(73 citation statements)

References 9 publications

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“…Адаптируя уравнения углового движения КА с КНЭК, полученные в работе [5], под сформулированную в пункте 1.1 задачу, получаем уравнения движения макета на столе Отправной точкой при разработке закона управления   t u в задачах гашения вибраций в нежестком элементе конструкции является построение линейно-квадратичного гауссового регулятора (LQG регулятора) (см. [6], [7]), которое происходит в два этапа: …”

Section: рис 1 схема расположения вентиляторовunclassified

Linear Quadratic Methods of Vibration Suppression in the Mock-Up Flexible Appendage

Shestopyorov

Tkachev

2017

KIAM Prepr.

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Section: рис 1 схема расположения вентиляторовunclassified

Linear Quadratic Methods of Vibration Suppression in the Mock-Up Flexible Appendage

Shestopyorov

Tkachev

2017

KIAM Prepr.

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“…It has been shown, however, that a small amount of damping greatly reduces the possibility of instability due to spillover. 22 The spillover problem will not be addressed in this paper. where the function GðQ, PÞ ¼ e ÀikR =4R is the free-space Green's function in which R ¼ Q À P , Q is any point on S, and P maybe outside, inside, or on S; k ¼ !=c is the wavenumber, where c is the speed of sound and n is the outward unit normal on S. The coefficient C(P) can be calculated by…”

Section: Conventional Feedback Control For Pole Assignmentmentioning

confidence: 99%

Simulation study of active control of vibro-acoustic response by sound pressure feedback using modal pole assignment strategy

2016

Journal of Low Frequency Noise, Vibration and Active Control

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The active control of vibro-acoustic response using sound pressure feedback is numerically studied. An output feedback approach based on sound pressure measurement for modal pole placement is proposed. The control performance is evaluated for the case of a baffled plate. The finite element method and the Rayleigh integral are used to model the structural vibration and sound radiation. Measures of observability of a mode in pressure outputs and the effect of time delay in the pressure feedback loop are discussed. Numerical results show that the chosen poles may be assigned to predetermined values by the active control with complex gains. It is also demonstrated that the pressure feedback control may make a very large reduction in acoustic radiation and structural vibration of the controlled modes in a wide frequency band when using constant gain at a lower frequency.

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“…Inspite of several attempts by numerical linear algebra researchers, effective numerical model reduction techniques that work exclusively in secondorder model are rare. Similarly, the state-of-the-art independent modal space control (IMSC) approach (see Inman [23]), Meirovitch et al [27,28], also is not practical for the large and sparse PQEVAP. For open-loop decoupling, the IMSC approach needs the knowledge of the complete spectrum and eigenvectors of PðlÞ, and for closed-loop decoupling, a stringent requirement of the number of sensors and actuators must be met [23,28].…”

Section: Q2mentioning

confidence: 99%

“…Similarly, the state-of-the-art independent modal space control (IMSC) approach (see Inman [23]), Meirovitch et al [27,28], also is not practical for the large and sparse PQEVAP. For open-loop decoupling, the IMSC approach needs the knowledge of the complete spectrum and eigenvectors of PðlÞ, and for closed-loop decoupling, a stringent requirement of the number of sensors and actuators must be met [23,28]. On the other hand, the state-of-the-art computational technique, the Jacobi-Davidson method (see Datta [10] and Tisseur and Meerbergen [38]) for the quadratic eigenproblem, is capable of computing only a few extremal eigenvalues and eigenvectors of a large quadratic pencil.…”

Section: Q2mentioning

confidence: 99%

Robust and minimum norm partial quadratic eigenvalue assignment in vibrating systems: A new optimization approach

Bai

Datta

Wang

2010

Mechanical Systems and Signal Processing

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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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A comparison of control techniques for large flexible systems

Cited by 215 publications

References 9 publications

Linear Quadratic Methods of Vibration Suppression in the Mock-Up Flexible Appendage

Linear Quadratic Methods of Vibration Suppression in the Mock-Up Flexible Appendage

Simulation study of active control of vibro-acoustic response by sound pressure feedback using modal pole assignment strategy

Robust and minimum norm partial quadratic eigenvalue assignment in vibrating systems: A new optimization approach

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