• Title/Summary/Keyword: Matrix geometric method

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Study on an optimum solution for discrete optimal $H_{\infty}$-control problem (이산 최적 $H_{\infty}$-제어 문제의 최적해를 구하는 방법에 대한 연구)

  • 하철근
    • 제어로봇시스템학회:학술대회논문집
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    • 1996.10b
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    • pp.565-568
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    • 1996
  • In this paper, a solution method is proposed to calculate the optimum solution to discrete optimal H$_{.inf}$ control problem for feedback of linear time-invariant system states and disturbance variable. From the results of this study, condition of existence and uniqueness of its solution is that transfer matrix of controlled variable to input variable is left invertible and has no invariant zeros on the unit circle of the z-domain as well as extra geometric conditions given in this paper. Through a numerical example, the noniterative solution method proposed in this paper is illustrated.

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Geometric nonlinear analysis of steel structures with external pretension using the multi-noded cable element (다절점 케이블요소를 이용한 외부 긴장된 강구조 시스템의 기하학적 비선형해석)

  • Lee, Jun Seok;Kim, Moon Young;Han, Man Yop;Kim, Sung Bo;Kim, Nak Kyung
    • Journal of Korean Society of Steel Construction
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    • v.18 no.6
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    • pp.727-735
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    • 2006
  • In this paper, a geometric nonlinear analysis procedure of the beam-column element including multi-noded cable element in extension of companion paper (Kim et al., 2005) is presented. First, a stiffness matrix was derived about the beam-column element that considers the second effect of the initial force supposing the curved shape at each time-step, with Hermitian polynomials as the shape function. Second, the multi-noded cable element was also subjected to the tangent stiffness matrix. To verify the geometric nonlinearity of this newly developed multi-noded cable-truss element, the Innovative Prestressed Support (IPS) system using this theory was analysed by geometric nonlinear method and the results were compared with those produced by linear analysis.

Mutual Detectability and System Enlargement of Detection Filters: An Invariant Zero Approach

  • Kim, Yong-Min;Park, Jae-Hong
    • International Journal of Control, Automation, and Systems
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    • v.4 no.6
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    • pp.769-774
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    • 2006
  • In this paper, we discuss the problem of non-mutual detectability using the invariant zero. We propose a representation method for excess spaces by linear equation based on the Rosenbrock system matrix. As an alternative to the system enlargement method proposed by White[1], we propose an appropriate form of an enlarged system to make a set of faults mutually detectable by assigning sufficient geometric multiplicity of invariant zeros. We show the equivalence between the two methods and a necessary condition for the system enlargement in terms of the geometric and algebraic multiplicities of invariant zeros.

A Study on the Elastic-Plastic Contact Problem for Large Deformation (대변형 탄소성 접촉문제에 관한 연구)

  • 전병희
    • Proceedings of the Korean Society for Technology of Plasticity Conference
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    • 1992.03a
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    • pp.11-26
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    • 1992
  • In this research, a numerical algorithm has been developed, which can be applied to the large deformation and large displacement contact problems between angle change have been proposed considering the change in geometric shape and rate of contact force. A set of linear simultaneous equations is constructed by adding the geometric shape change and contact conditions to the original stiffness matrix. A new method to determine time increment has been proposed based on Euler method, in which the condition to prevent the contact bodies from penetrating and overrunning each other has been taken into consideration. Practical application to contact problem is extrusion in which bodies are sliding along the contact boundary.

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Dynamic Simulation of Underwater Vehicle-Manipulator Systems Using Principle of Dynamical Balance (동적 발란스의 원리를 이용한 수중 잠수정-매니퓰레이터 시스템의 동역학 시뮬레이션)

  • Han, Jong-Hui;Chung, Wan-Kyun
    • The Journal of Korea Robotics Society
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    • v.2 no.2
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    • pp.152-160
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    • 2007
  • In this paper, two schemes are introduced for dynamic simulation of underwater robotic systems. One is principle of dynamical balance, which is an easy and powerful tool for formulating dynamic equations of composite systems such as underwater vehicle-manipulator system. In the dynamic modeling, this principle gives us the closed-form of dynamic equations on matrix Lie group. The other is geometric integration algorithm, called 4-th order explicit Munthe-Kaas method. By this method, the derived differential equations can be integrated preserving geometric structure. Adopting these two schemes, dynamic simulation of underwater vehicle- manipulator system can be conducted more easily and more reliably.

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Ground Plane Detection Using Homography Matrix (호모그래피행렬을 이용한 노면검출)

  • Lee, Ki-Yong;Lee, Joon-Woong
    • Journal of Institute of Control, Robotics and Systems
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    • v.17 no.10
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    • pp.983-988
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    • 2011
  • This paper presents a robust method for ground plane detection in vision-based applications based on a monocular sequence of images with a non-stationary camera. The proposed method, which is based on the reliable estimation of the homography between two frames taken from the sequence, aims at designing a practical system to detect road surface from traffic scenes. The homography is computed using a feature matching approach, which often gives rise to inaccurate matches or undesirable matches from out of the ground plane. Hence, the proposed homography estimation minimizes the effects from erroneous feature matching by the evaluation of the difference between the predicted and the observed matrices. The method is successfully demonstrated for the detection of road surface performed on experiments to fill an information void area taken place from geometric transformation applied to captured images by an in-vehicle camera system.

Performance Evaluation of a Two-Product CONWIP System with Poisson Demand Processes (Poisson 수요과정을 갖는 두 품목 콘윕시스템의 성능평가)

  • Park, Chan-Woo;Kim, Su-Min;Bang, Woo-Hyung;Lee, Hyo-Seong
    • Journal of Korean Institute of Industrial Engineers
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    • v.39 no.3
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    • pp.172-182
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    • 2013
  • In this study we consider a flow line CONWIP system in which two types of product are produced. The processing times of each product type at each station follow an independent exponential distribution and the demands for the finished products of each type arrive according to a Poisson process. The demands that are not satisfied instantaneously are either backordered or lost according to the number of unsatisfied demands that exist at their arrival instants. For this system we develop an approximation method to obtain the performance measures such as steady state probabilities of the number of parts of each product type at each station, mean waiting times of backordered demands and the proportion of backordered demands. For the analysis of the proposed CONWIP system, we model the CONWIP system as a two class closed queueing network with a synchronization station and analyze the closed queueing network using a product-form approximation method for multiple classes developed by Baynat and Dallery. In the approximation method, each subsystem is analyzed using a matrix geometric method. Comparisons with simulation show that the approximation method provides fairly good results for all performance measures.

An Anthropometric Product Design Approach Using Design Structure Matrix (DSM): Application to Computer Workstation Design (Design Structure Matrix를 활용한 인체측정학적 제품설계 방법: 컴퓨터 워크스테이션 설계 적용)

  • Jung, Ki-Hyo;Kwon, O-Chae;You, Hee-Cheon
    • Journal of the Ergonomics Society of Korea
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    • v.26 no.3
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    • pp.111-115
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    • 2007
  • Design equations for anthropometric product design are developed by considering the geometrical relationships of design dimensions and anthropometric dimensions. The present study applied the design structure matrix (DSM) method to the development of design equations for a computer workstation, and compared design values from the design equations with corresponding design values of ergonomic recommendations and existing products. The relationships between design dimensions (e.g., legroom and worktable) were analyzed by a DSM, and then the application order of design equations (e.g., seatpan, backrest, armrest, legroom, and worktable in descending order) was determined. Next, design equations were developed by analyzing the geometric relationships between computer workstation design dimensions and anthropometric dimensions. Finally, design values for a computer workstation were determined by considering a standard posture defined and representative human models (5th, 50th, 95th %ile). The design values calculated using the design equations were similar with those of ergonomic recommendations found in literature and two commercial products measured in the study; however, some design values (e.g., seatpan height) were different due to discrepancy in standard posture. The DSM method would be utilized to systematically analyze the relationships between design dimensions for anthropometric product design.

Geometric Non-linear Analysis of the Plane Frame Structures including Shear Deformation Effect (전단변형(剪斷變形)을 고려(考慮)한 평면(平面)뼈대 구조물(構造物)의 기하적(幾何的)인 비선형(非線形) 해석(解析))

  • Kim, Moon Young;Chang, Sung Pil
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.10 no.1
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    • pp.27-36
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    • 1990
  • Two beam/column elements in order to analyze the geometric nonlinear plane framed structures including the effects of transverse shear deformation and bending stretching coupling are developed. In the case of the first element (finite segment method), tangent stiffness matrix are derived by directly integrating the equilibrium equations whereas in the case of the second element (finite element method) elastic and geometric stiffness matrices are calculated by using the hermitian polynomials including shear deformation effect as the shape function. Both elements possess the usual six degree of freedoms. Numerical results are presented for the selected test problems which demonstrate that both elements represent reliable and highly accurate tools.

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The Optimization Method of Symmetrical Building Plan Using Point Group Theory (포인트그룹 이론을 이용한 대칭적 건물 평면형태의 최적대안 결정방안)

  • 진경일
    • Korean Institute of Interior Design Journal
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    • no.38
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    • pp.75-82
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    • 2003
  • The symmetry is general geometric design principal in contemporary architecture shape. But, Symmetry sometimes easily causes unreasonable design. In some reason, two of symmetric units in the apartment, one side of unit have very reasonable plan and arrangement but opposite side unit nay not. For example, if the kitchen on right unit had right-handed arrangement, the symmetrical other would have left-handed kitchen arrangement. In addition to this, if each house unit has the same plan but different direction, each unit has different usage or affects the residents' life pattern. Nevertheless, Architects use only one unit plan to design public housing development by using symmetric operator (mirror, proper rotation, inversion center) at their option. This study suggests that using group theory and mathematical matrix rather than designer's discretion can solve this symmetry problem clearly. And, this study analysis the merits and demerits between each symmetrical pair of unit plan shapes by using mathematical point group theory and matrix.