• Journal of the Chungcheong Mathematical Society
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• v.36 no.2
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• pp.77-86
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• 2023

The purpose of this paper is to show that a certain finite dimensional representation of the rational Cherednik algebra of type A has a basis consisting of simultaneous eigenvectors for the actions of a certain family of commuting elements, which are introduced in the author's previous paper. To this end, we introduce a combinatorial object, which is called a restricted arrangement of colored beads, and consider an action of the affine symmetric group on the set of the arrangements.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.618-621
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• 1995

In this paper, in order to obtain a disturbance decouplable as well as effective and disturbance suppressible controller, a simultaneous assignment methodology of the left and right eigenstructure is proposed. The biorthogonality property between the left and right model matrices of a system as well as the relations between the achievable right model matrix and states selsction matrices are used to develop the methodology. the proposed concurrent eigenstructure assignment methodologh guarantees that the desired eigenvalues are achieved exactly and the desired left and right eigenvectors are assigned to the best possible(achievable) sets of eigenvectors in the least square sense, respectively.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.398-401
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• 2001

There are two methods to calculate design sensitivity such as direct differentiation method and adjoint method. A sort of direct differentiation method for design sensitivity analysis costs too much when number of design variables is much larger than the number of response functions whose design sensitivity analyses are required. Therefore, an adjoint method is suggested for the case that the dimension of design variables is lager than the number of response function. An adjoint method is required to compute adjoint variables from the simultaneous linear system equation, the so-called adjoint equation, requiring only the eigenvalue and its associated eigenvectors for mode being differentiated. This method has been extended to the repeated eigenvalue problem. In this paper, we propose an adjoint method for deign sensitivity analysis of damped vibratory systems with distinct eigenvalues.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.6
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• pp.176-182
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• 1999

In this paper, we consider a decoupling control and a servo control for the JINAMCHA of which the cart and the pointer is coupled very strongly. The right eigenstructure assignment(i.e. simultaneous assignment of eigenvalues and right eigenvectors) is used for decoupling the motions of the cart and the pointer. The CGT(Command Generator Tracker) is used for a servo control of the JINAMCHA. The performance of the proposed control scheme, that is the combination of the right eigenstructure assignment and the CGT, is evaluated by simulations. The results show that the proposed controller has better performance than the LQR with limiting properties and the conventional LQ servo.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.11 s.242
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• pp.1527-1533
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• 2005

Three methods for design sensitivity analysis such as finite difference method(FDM), direct differentiation method(DDM) and adjoint variable method(AVM) are well known. FDM and DDM for design sensitivity analysis cost too much when the number of design variables is too large. An AVM is required to compute adjoint variables from the simultaneous linear system equation, the so-called adjoint equation. Because the adjoint equation is independent of the number of design variables, an AVM is efficient for when number of design variables is too large. In this study, AVM has been extended to the eigenproblem of damped systems whose eigenvlaues and eigenvectors are complex numbers. Moreover, this method is implemented into a commercial finite element analysis program by means of the semi-analytical method to show applicability of the developed method into practical structural problems. The proposed_method is compared with FDM and verified its accuracy for analytical and practical cases.