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Research Papers

Orthogonal Eigenstructure Control for Vibration Suppression

[+] Author and Article Information
Mohammad Rastgaar, Steve Southward

Department of Mechanical Engineering, Center for Vehicle Systems and Safety (CVeSS), Virginia Tech, Blacksburg, VA 24061

Mehdi Ahmadian1

Department of Mechanical Engineering, Center for Vehicle Systems and Safety (CVeSS), Virginia Tech, Blacksburg, VA 24061ahmadian@vt.edu

1

Corresponding author.

J. Vib. Acoust 132(1), 011001 (Jan 08, 2010) (10 pages) doi:10.1115/1.4000598 History: Received March 06, 2007; Revised September 12, 2008; Published January 08, 2010

Orthogonal eigenstructure control is a novel active control method for vibration suppression in multi-input multi-output linear systems. This method is based on finding an output feedback control gain matrix in such a way that the closed-loop eigenvectors are almost orthogonal to the open-loop ones. Singular value decomposition is used to find the matrix, which spans the null space of the closed-loop eigenvectors. This matrix has a unique property that has been used in this new method. This unique property, which has been proved here, can be used to regenerate the open-loop system by finding a coefficient vector, which leads to a zero gain matrix. Also several vectors, which are orthogonal to the open-loop eigenvectors, can be found simultaneously. The proposed method does not need any trial and error procedure and eliminates not only the need to specify any location or area for the closed-loop eigenvalues but also the requirements of defining the desired eigenvectors. This method determines a set of limited number of closed-loop systems. Also, the elimination of the extra constraints on the locations of the closed-loop poles prevents the excessive force in actuators.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

The difference between achievable and desirable eigenvectors

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Figure 2

Open-loop eigenvectors are the intersections of the open-loop and achievable eigenvectors sets

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Figure 3

The system of ten masses with interconnecting springs and dampers

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Figure 4

Displacement of m1 with operating eigenvalues ( λ1, λ3, and λ5) due to an impulse input on m10; Case 1: r1=U¯31, r2=U¯32, and r3=U¯33; Case 2: r1=U¯21, r2=U¯12, and r3=U¯13

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Figure 5

Phase plane for the closed-loop systems with orthogonal eigenvectors to the open-loop eigenvector

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Figure 6

Eigenvalues of the open-loop system (case 1) and closed-loop system (case 2)

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Figure 7

Displacements of the masses due to a chirp input

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Figure 8

Actuation forces for the system under a chirp input disturbance

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