• Title/Summary/Keyword: Iteration Method

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Analysis of a Nonlinear Integrated-Mirror Etalon by the Characteristic Matrix Method (특성행렬을 이용한 비선형 집적거울 Etalon의 해석)

  • 김덕봉
    • Korean Journal of Optics and Photonics
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    • v.4 no.3
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    • pp.317-322
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    • 1993
  • In this paper we propose a method to analyze the nonlinear behavior of an integrated-mirror etalon by the characteristic matrix method. If the dependence of the refractive index and the absorption coefficient upon the light intensity are known, we can couple this with an equation by which we can evaluate the light intensity distribution inside an etalon for the given values of the refractive index and the absorption coefficient. By solving these coupled equations by the iteration method, we evaluate the transmission characteristics of a nonlinear integrated-mirror etalon. By the characteristic matrix method, we have demonstrated the static and dynamic bistable behavior of a nonlinear integrated-mirror etalon.

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Design of Robust $H_\infty$ Control for Interconnected Systems: A Homotopy Method

  • Chen Ning;Ikeda Masao;Gui Weihua
    • International Journal of Control, Automation, and Systems
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    • v.3 no.2
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    • pp.143-151
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    • 2005
  • This paper considers a robust decentralized $H_\infty$ control problem for uncertain large-scale interconnected systems. The uncertainties are assumed to be time-invariant, norm-bounded, and exist in subsystems. A design method based on the bounded real lemma is developed for a dynamic output feedback controller, which is reduced to a feasibility problem for a nonlinear matrix inequality (NMI). It is proposed to solve the NMI iteratively by the idea of homotopy, where some of the variables are fixed alternately on each iteration to reduce the NMI to a linear matrix inequality (LMI). A decentralized controller for the nominal system is computed first by imposing structural constraints on the coefficient matrices gradually. Then, the decentralized controller is modified again gradually to cope with the uncertainties. A given example shows the efficiency of this method.

Free vibration analysis of stiffened laminated plates using layered finite element method

  • Guo, Meiwen;Harik, Issam E.;Ren, Wei-Xin
    • Structural Engineering and Mechanics
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    • v.14 no.3
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    • pp.245-262
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    • 2002
  • The free vibration analysis of stiffened laminated composite plates has been performed using the layered (zigzag) finite element method based on the first order shear deformation theory. The layers of the laminated plate is modeled using nine-node isoparametric degenerated flat shell element. The stiffeners are modeled as three-node isoparametric beam elements based on Timoshenko beam theory. Bilinear in-plane displacement constraints are used to maintain the inter-layer continuity. A special lumping technique is used in deriving the lumped mass matrices. The natural frequencies are extracted using the subspace iteration method. Numerical results are presented for unstiffened laminated plates, stiffened isotropic plates, stiffened symmetric angle-ply laminates, stiffened skew-symmetric angle-ply laminates and stiffened skew-symmetric cross-ply laminates. The effects of fiber orientations (ply angles), number of layers, stiffener depths and degrees of orthotropy are examined.

Finite Element Analysis of Electromagnetic Systems Considering Hysteresis Characteristics (히스테리시스 특성을 고려한 전자계의 유한 요소 해석)

  • Kim, Hong-Gyu;Hong, Seon-Gi;Jeong, Hyeon-Gyo
    • The Transactions of the Korean Institute of Electrical Engineers B
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    • v.48 no.3
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    • pp.118-123
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    • 1999
  • This paper describes the finite element procedure including the magnetic hysteresis phenomena. The magnetization-dependent Preisach model is employed to simulate the magnetic hysteresis and applied to each elements. Magnetization is calculated by the Fibonacci search method for the applied field in the implementation of the magnetization-dependent model. This can calculate the magnetization very accurately with small iteration numbers. The magnetic field intensity and the magnetization corresponding to the magnetic flux density obtained by the finite element analysis(FEA) are computed at the same time under the condition that these balues must satisfy the constitutive equation. In order to reduce the total calculation cost, pseudo-permeability is used for the input for the FEA. It is found that the presented method is very useful in combining the hysteresis model with the finite element method.

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Topology Design of a Structure with a Specified Eigenfrequency (주어진 고유주파수를 갖는 구조물의 위상최적설계)

  • Lee, Jong-Hwan;Min, Seung-Jae
    • Proceedings of the KSME Conference
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    • 2001.06c
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    • pp.392-397
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    • 2001
  • Topology optimization is applied to determine the layout of a structure whose eigenfrequency coincides with a specified frequency. The topology optimization problem is formulated to minimize the difference between the structural frequency and a given frequency using the homogenization method and the modified optimality criteria method. It turns out that the value of a weighting factor in the updating scheme plays an important role to achieve both a suitable speed and a stable convergence of an algorithm. Unlike a constant weighting factor in previous works, it is suggested that a weight factor is varied during the iteration to control the amount of the frequency change. To substantiate the proposed approach two-dimensional structural design problems are presented and the resulted topology layouts for the specified eigenfrequency are compared to layouts for maximizing the corresponding eigenfrequency.

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EXPLICIT BOUNDS FOR THE TWO-LEVEL PRECONDITIONER OF THE P1 DISCONTINUOUS GALERKIN METHOD ON RECTANGULAR MESHES

  • Kim, Kwang-Yeon
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.13 no.4
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    • pp.267-280
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    • 2009
  • In this paper we investigate a simple two-level additive Schwarz preconditioner for the P1 symmetric interior penalty Galerkin method of the Poisson equation on rectangular meshes. The construction is based on the decomposition of the global space of piecewise linear polynomials into the sum of local subspaces, each of which corresponds to an element of the underlying mesh, and the global coarse subspace consisting of piecewise constants. This preconditioner is a direct combination of the block Jacobi iteration and the cell-centered finite difference method, and thus very easy to implement. Explicit upper and lower bounds for the maximum and minimum eigenvalues of the preconditioned matrix system are derived and confirmed by some numerical experiments.

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Development of Vision System Model for Manipulator's Assemble task (매니퓰레이터의 조립작업을 위한 비젼시스템 모델 개발)

  • 장완식
    • Journal of the Korean Society of Manufacturing Technology Engineers
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    • v.6 no.2
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    • pp.10-18
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    • 1997
  • This paper presents the development of real-time estimation and control details for a computer vision-based robot control method. This is accomplished using a sequential estimation scheme that permits placement of these points in each of the two-dimensional image planes of monitoring cameras. Estimation model is developed based on a model that generalizes know 4-axis Scorbot manipulator kinematics to accommodate unknown relative camera position and orientation, etc. This model uses six uncertainty-of-view parameters estimated by the iteration method. The method is tested experimentally in two ways : First the validity of estimation model is tested by using the self-built test model. Second, the practicality of the presented control method is verified in performing 4-axis manipulator's assembly task. These results show that control scheme used is precise and robust. This feature can open the door to a range of application of multi-axis robot such as deburring and welding.

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Numerical Solutions of Compressible Navier-Stokes Equations on Hybrid Meshes Using Newton-GMRES Method (Newton-GMRES 법을 사용한 혼합격자에서의 압축성 Navier-Stoke 방정식 수치 해석)

  • Choi Hwan-Seok
    • 한국전산유체공학회:학술대회논문집
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    • 2000.05a
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    • pp.178-183
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    • 2000
  • An efficient Newton-GMRES algorithm is presented for computing two-dimensional steady compressible viscous flows on unstructured hybrid meshes. The scheme is designed on cell-centered finite volume method which accepts general polygonal meshes. Steady-state solution is obtained with pseudo-transient continuation strategy. The preconditioned, restarted general minimum residual(GMRES) method is employed in matrix-free form to solve the linear system arising at each Newton iteration. The incomplete LU fartorization is employed for the preconditioning of linear system. The Spalart-Allmars one equation turbulence model is fully coupled with the flow equations to simulate turbulence effect. The accuracy, efficiency and robustness of the presently developed method are demonstrated on various test problems including laminar and turbulent flows over flat plate and airfoils.

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Application of the Implicit Restarted Arnoldi Method to the Small-Signal Stability of Power Systems

  • Kim, Dong-Joon;Moon, Young-Hwan
    • Journal of Electrical Engineering and Technology
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    • v.2 no.4
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    • pp.428-433
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    • 2007
  • This paper describes the new eigenvalue algorithm exploiting the Implicit Restarted Arnoldi Method (IRAM) and its application to power systems. IRAM is a technique for combining the implicitly shifted mechanism with a k-step Arnoldi factorization to obtain a truncated form of the implicitly shifted QR iteration. The numerical difficulties and storage problems normally associated with the Arnoldi process are avoided. Two power systems, one of which has 36 state variables and the other 150 state variables, have been tested using the ARPACK program, which uses IRAM, and the eigenvalue results are compared with the results obtained from the conventional QR method.

A study on the rigid bOdy placement task of robot system based on the computer vision system (컴퓨터 비젼시스템을 이용한 로봇시스템의 강체 배치 실험에 대한 연구)

  • 장완식;유창규;신광수;김호윤
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 1995.10a
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    • pp.1114-1119
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    • 1995
  • This paper presents the development of estimation model and control method based on the new computer vision. This proposed control method is accomplished using a sequential estimation scheme that permits placement of the rigid body in each of the two-dimensional image planes of monitoring cameras. Estimation model with six parameters is developed based on a model that generalizes known 4-axis scara robot kinematics to accommodate unknown relative camera position and orientation, etc. Based on the estimated parameters,depending on each camers the joint angle of robot is estimated by the iteration method. The method is tested experimentally in two ways, the estimation model test and a three-dimensional rigid body placement task. Three results show that control scheme used is precise and robust. This feature can open the door to a range of application of multi-axis robot such as assembly and welding.

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