• Title/Summary/Keyword: Singular System

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Design of Approximate Feedback Controller for Two-Time-Scale Aircraft Dynamics (양시등급 항공기 동력학의 근사 궤환 제어기 설계)

  • Shim, Kyu-Hong;Sawan, M.E.;Hong, Sung-Kyung
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.32 no.5
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    • pp.58-64
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    • 2004
  • A new method to obtain approximate solutions by placing the only poles of the slow subsystem for the two-time-scale aircraft dynamic systems. The two kinds of approximate solutions are obtained by a matrix block diagonalization. One is called the uncorrected solution, and the other is called the corrected solution. The former has an error of $O({\varepsilon})$, and the latter has an error of $O({\varepsilon}^2)$. Of course, both solutions are robust enough even though they are reduced solutions. The excellence of the proposed method is illustrated by an numerical example of an aircraft longitudinal dynamics.

ALGEBRAIC METHOD FOR COMPUTATION OF EIGENPAIR SENSITIVITIES OF DAMPED SYSTEMS WITH REPEATED EIGENVALUES (중복근을 갖는 감쇠 시스템의 고유진동수와 모드의 고차 민감도 해석)

  • Choi, Kang-Min;Ji, Han-Rok;Yoon, Woo-Hyun;Lee, In-Won
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2004.11a
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    • pp.721-726
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    • 2004
  • A simplified method for the computation of first second and higher order derivatives of eigenvalues and eigenvectors derivatives associated with repeated eigenvalues is presented. Adjacent eigenvectors and orthonormal conditions are used to compose an algebraic equation whose order is (n+m)x(n+m), where n is the number of coordinates and m is the number of multiplicity of the repeated eigenvalues. The algebraic equation developed can be used to compute derivatives of both eigenvalues and eigenvectors simultaneously. Since the coefficient matrix in the proposed algebraic equation is non-singular, symmetric and based on N-space it is numerically stable and very efficient compared to previous methods. This method can be consistently applied to structural systems with structural design parameters and mechanical systems with lumped design parameters. To verify the effectiveness of the proposed method, the finite element model of the cantilever beam is considered.

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Application of Optimal Control Techniques to SWATH Motion Control (반잠수 쌍동선의 최적 운동제어기 설계)

  • Chan-Wook Park;Bo-Hyeon Heo;Chun-Tae Song
    • Journal of the Society of Naval Architects of Korea
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    • v.31 no.2
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    • pp.65-77
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    • 1994
  • This paper presents a derailed application procedure of the linear quadratic(LQ) theory for a SWATH heave and pitch control. A time domain model of coupled, linear time-invariant second order differential equations is derived from the frequency response model with the frequency dependent added mass and damping approximated as constant values at the heave natural frequency. Wave exciting forces are modeled as a sum of sinusoids. A systematic selection procedure of state and control weighting matrices is presented to obtain good transient behavior and acceptable fin movement. The validity of this controller design process is throughly investigated by simulations both in time domain and frequency domain and singular value plots of transfer function matrices. The finally designed control system shows good overall performances revealing that the applicability of the present study is proved successful.

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Experimental validation of the seismic analysis methodology for free-standing spent fuel racks

  • Merino, Alberto Gonzalez;Pena, Luis Costas de la;Gonzalez, Arturo
    • Nuclear Engineering and Technology
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    • v.51 no.3
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    • pp.884-893
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    • 2019
  • Spent fuel racks are steel structures used in the storage of the spent fuel removed from the nuclear power reactor. Rack units are submerged in the depths of the spent fuel pool to keep the fuel cool. Their free-standing design isolates their bases from the pool floor reducing structural stresses in case of seismic event. However, these singular features complicate their seismic analysis which involves a transient dynamic response with geometrical nonlinearities and fluid-structure interactions. An accurate estimation of the response is essential to achieve a safe pool layout and a reliable structural design. An analysis methodology based on the hydrodynamic mass concept and implicit integration algorithms was developed ad-hoc, but some dispersion of results still remains. In order to validate the analysis methodology, vibration tests are carried out on a reduced scale mock-up of a 2-rack system. The two rack mockups are submerged in free-standing conditions inside a rigid pool tank loaded with fake fuel assemblies and subjected to accelerations on a unidirectional shaking table. This article compares the experimental data with the numerical outputs of a finite element model built in ANSYS Mechanical. The in-phase motion of both units is highlighted and the water coupling effect is detailed. Results show a good agreement validating the methodology.

Large-scaled truss topology optimization with filter and iterative parameter control algorithm of Tikhonov regularization

  • Nguyen, Vi T.;Lee, Dongkyu
    • Steel and Composite Structures
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    • v.39 no.5
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    • pp.511-528
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    • 2021
  • There are recently some advances in solving numerically topology optimization problems for large-scaled trusses based on ground structure approach. A disadvantage of this approach is that the final design usually includes many bars, which is difficult to be produced in practice. One of efficient tools is a so-called filter scheme for the ground structure to reduce this difficulty and determine several distinct bars. In detail, this technique is valuable for practical uses because unnecessary bars are filtered out from the ground structure to obtain a well-defined structure during the topology optimization process, while it still guarantees the global equilibrium condition. This process, however, leads to a singular system of equilibrium equations. In this case, the minimization of least squares with Tikhonov regularization is adopted. In this paper, a proposed algorithm in controlling optimal Tikhonov parameter is considered in combination with the filter scheme due to its crucial role in obtaining solution to remove numerical singularity and saving computational time by using sparse matrix, which means that the discrete optimal topology solutions depend on choosing the Tikhonov parameter efficiently. Several numerical examples are investigated to demonstrate the efficiency of the filter parameter control algorithm in terms of the large-scaled optimal topology designs.

Multiple unequal cracks between an FGM orthotropic layer and an orthotropic substrate under mixed mode concentrated loads

  • M. Hassani;M.M. Monfared;A. Salarvand
    • Structural Engineering and Mechanics
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    • v.86 no.4
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    • pp.535-546
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    • 2023
  • In the present paper, multiple interface cracks between a functionally graded orthotropic coating and an orthotropic half-plane substrate under concentrated loading are considered by means of the distribution dislocation technique (DDT). With the use of integration of Fourier transform the problem is reduced to a system of Cauchy-type singular integral equations which are solved numerically to compute the dislocation density on the surfaces of the cracks. The distribution dislocation is a powerful method to calculate accurate solutions to plane crack problems, especially this method is very good to find SIFs for multiple unequal cracks located at the interface. Hence this technique allows considering any number of interface cracks. The primary objective of this paper is to investigate the effects of the interaction of multiple interface cracks, load location, material orthotropy, nonhomogeneity parameters and geometry parameters on the modes I and II SIFs. Numerical results show that modes I/II SIFs decrease with increasing the nonhomogeneity parameter and the highest magnitude of SIF occurs where distances between the load location and crack tips are minimal.

Multi-wavelength view of SPT-CL J2106-5844: A massive galaxy cluster merger at z~1.13

  • Kim, HyeongHan;Di Mascolo, Luca;Mroczkowski, Tony;Perrott, Yvette;Rudnick, Lawrence;Jee, M. James;Churazov, Eugene;Collier, Jordan D.;Diego, Jose M.;Hopkins, Andrew M.;Kim, Jinhyub;Koribalski, Barbel S.;Marvil, Joshua D.;van der Burg, Remco;West, Jennifer L.
    • The Bulletin of The Korean Astronomical Society
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    • v.46 no.1
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    • pp.34.2-34.2
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    • 2021
  • SPT-CL J2106-5844 is the most massive galaxy cluster at z>1 discovered to date. It has been known to be an isolated system with a singular, well-defined halo. However, recent studies provide lines of evidence for its merging state. We strengthen the case with the multi-wavelength observations from ALMA, ACA, ASKAP, ATCA, and Chandra. With the sensitive, high resolution ALMA+ACA observations, we reconstruct the ICM pressure map from the thermal SZ effect. It reveals two main gas components that are associated with the mass clumps inferred from the weak-lensing analysis. Furthermore, the X-ray hardness map supports the bimodal gas distribution. With these multi-wavelength data, we probe the merger phase in SPT-CL J2106-5844.

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A Study on the concept of 'Open space' in Coop Himmelblau's (Coop Himmelblau의 ‘열린 공간’ 개념에 관한 연구)

  • 윤재은;이규홍
    • Korean Institute of Interior Design Journal
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    • no.40
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    • pp.34-41
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    • 2003
  • A purpose of this study is to comprehend a concept of 'Open Space', realization of a deconstruction, presented in his works, based on a deconstruction and surrealism Coop Himmelblau's philosophical contemplation and to look into how this concept is interpreted in spaces. A concept of 'Open Space' is functioned as not a singular meaning but a multiple meaning accompanied with other formative ingredient and contemplation, scientific paradigm and a realation with a surroundings. The concept of 'Open Space' in their architentural space is applied. First, the space openness that represents to the extreme a concept 'Open Space', as a 3D designing ways that demolishes a structure and outgrows an ex siting thinking pattern, represents multiple grade spaces and an anti-gravity space. In a material, using glass and iron provides a spacial transparency and through this, visibly liberal sense that an interior and exterior is felt as an unification. Second, an non-expressive box pattern repulses to a spatial rank nature, outgrowing an uniform geometrical system, through demolishing a geometrical system, an edge and fold pattern. This is, as an anti-gravity, dynamic a typical structure, outgrowing an orthogonal system, interpreted as a composite meaning without division in spatial area. Third, the collage is used to represent a complexity and pluralism in representing 'Open space'. The collage that forms a image through combining a fragmentary elements into being a space change, composite constitution and spatial amusement. Thus, It is worthwhile to study how the collage that forms a diverse shape will be developed making what impact as an age and surroundings changed. As we contemplate in former part, Coop Himmelblou has deployed 'deconstruction beyond deconstruction' realm as just their midterm concept in their works like the words 'The architecture must climb', the deconstructive architect. A studying for their works reflecting the 'Open Space' concept based on deconstruction must be lasted and this enables us to comprehend space concept containing an architecture and interior design.

Power and Offset Allocation for Spatial-Multiplexing MIMO System with Rate Adaptation for Optical Wireless Channels (다중 입출력 무선 광채널에서의 공간 다중화 기법의 적응적 전송을 위한 광출력과 오프셋 할당 기법)

  • Park, Ki-Hong;Ko, Young-Chai
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.36 no.1A
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    • pp.8-18
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    • 2011
  • Visible light communication (VLC) using optical sources which can be simultaneously utilized for illumination and communication is currently an attractive option for wireless personal area network. Improving the data rate in optical wireless communication system is challenging due to the limited bandwidth of the optical sources. In this paper, we design the singular value decomposition (SVD)-based multiplexing multi-input multi-output (MIMO) system to support two data streams in optical wireless channels. In order to improve the spectral efficiency, the rate adaptation using multi-level pulse amplitude modulation (PAM) is applied according to the channel condition and we propose the method to allocate the optical power, the offset and the size of modulation scheme theoretically under the constraints of the nonnegativity of the modulated signals, the aggregate optical power and the bit error rate (BER) requirement. The simulation results show that the proposed allocation method gives the better performance than the method to allocate the optical power equally for each data stream.

Reduction Method based on Sub-domain Structure using Reduced Pseudo Inverse Method (축소 의사역행렬과 영역분할 기반 축소모델 구축 기법 연구)

  • Kim, Hyun-Gi;Cho, Meang-Hyo
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2009.04a
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    • pp.139-145
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    • 2009
  • Reduction scheme is remarkably useful in the case requiring the repeated calculation procedure. Recently, the efficiency of the reduction scheme has been improved by combining scheme of sub-domain method. But, when the global domain is partitioned into a few sub-domains, sub-domains without constraints can be produced. it is needed to extract the ritz vector from each sub-domain to construct the reduced system of each sub-domain. it is easy to extract the ritz vector from sub-domain with constraint. on the other hand, pseudo inverse method should be employed to extract the ritz vector from sub-domain without constraint. generally, the pseudo inverse takes a large number of computing time to obtain a reduced system of a sub-domain without boundary condition. This trouble can be overcome by the reduced pseudo inverse scheme which proposed in this study. This scheme is based on the static condensation that is not related with selection of the primary degrees of freedom. Numerical examples demonstrate that present method saves computational cost effectively and predicts the accurate eigenvalues.

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