A Review on Eigenstructure Assignment Methods and Orthogonal Eigenstructure Control of Structural Vibrations

Abstract

Abstract. This paper provides a state-of-the-art review of eigenstructure assignment methods for vibration cancellation. Eigenstructure assignment techniques have been widely used during the past three decades for vibration suppression in structures, especially in large space structures. These methods work similar to mode localization in which global vibrations are managed such that they remain localized within the structure. Such localization would help reducing vibrations more effectively than other methods of vibration cancellation, by virtue of confining the vibrations close to the source of disturbance. The common objective of different methods of eigenstructure assignment is to provide controller design freedom beyond pole placement, and define appropriate shapes for the eigenvectors of the systems. These methods; however, offer a large and complex design space of options that can often overwhelm the control designer. Recent developments in orthogonal eigenstructure control offers a significant simplification of the design task while allowing some experience-based design freedom. The majority of the papers from the past three decades in structural vibration cancellation using eigenstructure assignment methods are reviewed, along with recent studies that introduce new developments in eigenstructure assignment techniques.

The Adjugate Method: Reassignment with System Classification

“…We, therefore, resort to the joint solution of ( 12) and (13). It is the intersection of the two solutions given by ( 12) and (13).…”

“…We, therefore, resort to the joint solution of ( 12) and (13). It is the intersection of the two solutions given by ( 12) and (13). It is systematically obtained via the null space solution of the following augmented matrix [18] (p. 8), [19] (p. 328)…”

“…The viability of eigenstructure assignment methods is eminent regarding vibration cancellation and suppression. Large space structures have been reviewed in [13], where some experience-based designs proven effective.…”

Structural Modifications for Torsional Vibration Control of Shafting Systems Based on Torsional Receptances

“…Dynamic performance of structures plays an important role in engineering; however, there are always some circumstances in which structural dynamic performance does not meet the design requirements or actual situations in practice. Therefore, it is common that some existing structures need to be modified in order to acquire desired dynamic performance [1]. Many researchers have put forward many methods for the eigenstructure assignment problems [2][3][4][5].…”

A New Approach for Symmetry Preserving Partial Eigenstructure Assignment of Undamped Vibrating Systems

“…The extensive research results can be found in review articles [1,2] and references therein. As the dynamics of a structural system is naturally described by a set of second-order differential equations and control theory and estimation techniques are established for first-order realization of the systems, the majority of previous researches are made via transferring second-order equations to firstorder configuration (see, e.g., [3]). In the past ten years, in order not to increase the dimension of the equations and to preserve the symmetry and sparsity of the structural matrices, many authors proposed their works based directly on the second-order equation models [4][5][6][7][8][9][10][11][12].…”