Inverse eigenvalue problems in vibration absorption: Passive modification and active control
TL;DR: In this paper, the state of the art of the mathematical theory of vibration absorption is presented and illustrated for the benefit of the reader with numerous simple examples, including structural modification by passive elements and active control.
About: This article is published in Mechanical Systems and Signal Processing.The article was published on 2006-01-01. It has received 125 citations till now. The article focuses on the topics: Noise, vibration, and harshness & Harshness.
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TL;DR: The review clearly demonstrates that the TMDs have a potential for improving the wind and seismic behaviors of prototype civil structures and shows that the MTMDs and d-MTMDs are relatively more effective and robust, as reported.
263 citations
Cites methods from "Inverse eigenvalue problems in vibr..."
...A review of the inverse methods used for passive modification nd control can be found in Mottershead and Ram (2006) where ome useful direct formulae for updating the measured response ith unit-rank modifications were presented....
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TL;DR: In this paper, the pole/zero assignment problem is addressed using a method based on measured receptances, which is well known in passive structural modification, has not been used before in active vibration control, and is demonstrated that all the poles may be assigned actively by the equivalent of a rank-1 modification to the dynamic stiffness matrix of the system.
Abstract: The pole/zero assignment problem is addressed using a method based on measured receptances. The approach, which is well known in passive structural modification, has not been used before in active vibration control. A number of significant advantages are claimed over the conventional state-space approach that uses the mass, damping, and stiffness matrices formed, for example, by finite elements. In fact, because the method is based solely upon measured vibration data, there is no need to evaluate or to know the M, C, and K matrices. It is demonstrated that all the poles may be assigned actively by the equivalent of a rank-1 modification to the dynamic stiffness matrix of the system. The assignment of zeros has a special significance in vibration suppression, because the vibration response at coordinatep vanishes completely when sinusoidal excitation is applied at coordinate q at the frequency of a zero of receptance H nn . A pole ofH pq may be eliminated by assigning a zero at the same frequency.
138 citations
Cites background from "Inverse eigenvalue problems in vibr..."
...Introduction T HE problem of eigenvalue assignment has received considerable attention from the active-control and vibrations communities over several decades [1]....
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TL;DR: In this paper, an output feedback approach is described that makes use of measured receptances, there being no requirement at all for the M, C, K matrices usually obtained by finite elements.
80 citations
Cites background from "Inverse eigenvalue problems in vibr..."
...Mottershead and Ram [13] reviewed the field of inverse eigenvalue problems for vibration absorption by structural modification and active control....
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...An alternative approach that uses the measured receptances directly and makes no assumption about damping was proposed by Ram and Mottershead [26]....
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TL;DR: In this paper, the authors address the problem of suppressing vibrations by active control using vibration measurements, in the form of receptances, typically available from a modal test, for both single-input and multiple-input-multiple-output vibration control of practical engineering structures.
72 citations
TL;DR: In this article, the theory and practical application of the receptance method for vibration suppression in structures by multi-input partial pole placement is described, in particular there is no need to know or evaluate the structural matrices M, C, K and in practical experimentation the measurement of "receptance" may be generalised so that explicit modelling of actuator dynamics becomes unnecessary.
66 citations
Cites background from "Inverse eigenvalue problems in vibr..."
...Introduction The problem of pole placement has received considerable attention from the active-control and vibrations communities over several decades [1]....
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References
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TL;DR: Numerical methods are described for determining robust, or well-conditioned, solutions to the problem of pole assignment by state feedback such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized.
Abstract: Numerical methods are described for determining robust, or well-conditioned, solutions to the problem of pole assignment by state feedback. The solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized. It is shown that for these solutions, upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized. A measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed-loop poles, and hence the suitability of the given poles for assignment.
1,035 citations
TL;DR: In this paper, it was shown that controllability of an open-loop system is equivalent to the possibility of assigning an arbitrary set of poles to the transfer matrix of the closed loop system, formed by means of suitable linear feedback of the state.
Abstract: It is shown that controllability of an open-loop system is equivalent to the possibility of assigning an arbitrary set of poles to the transfer matrix of the closed-loop system, formed by means of suitable linear feedback of the state. As an application of this result, it is shown that an open-loop system can be stabilized by linear feedback if and only if the unstable modes of its system matrix are controllable. A dual of this criterion is shown to be equivalent to the existence of an observer of Luenberger's type for asymptotic state identification.
853 citations