• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.689-706
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• 2008

In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

• 한국광학회지
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• 제14권1호
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• pp.72-79
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• 2003

본 논문에서는 고차 편광모드분산(PMD: polarization-mode dispersion)을 효과적으로 보상하기 위한 방법으로, DOP (degree of polarization)를 1차 PMD 보상을 위한 피드백 신호와 고차 PMD 보상을 위한 feed forward 신호로 사용하는 알고리즘을 제안하였다. 1차 보상이 끝난 후의 DOP값이 남아있는 고차 PMD의 정도를 나타내는 척도로써 인식하여 고차 PMD를 보상하는 시스템이 되겠다. 이러한 시스템은 고차 보상기의 자유도를 1차 보상기의 자유도로 제한하기 때문에 안정적이고 비교적 간단하게 구성할 수 있다는 장점이 있다. 제안된 알고리즘의 성능을 분석하기 위하여 10Gbps NRZ시스템의 전송 모의 실험을 수행하였으며, 그 결과 시스템 다운 시간인 outage probability가 약 세 배 가량 감소되는 것을 확인하였다.

• 대한전기학회논문지:시스템및제어부문D
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• 제55권1호
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• pp.1-13
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• 2006

This paper presents the problems of designing low-order controller for a linear time-invariant(LTI) system in parameter space, wherein both transient response requirements and stability shall be considered in the same space. For a LTI system, we, (1) develop a method determining the existence of low-order stabilizers of the first-order and PID structures, (2) develop an algorithm of finding such a stabilizing region. (3) Both procedures are carried out by means of a parametric approach in the same frame work. This leads to easily obtain a subset of controller gains from the stabilizing set, that meet good time response requirements. It is illustrated by examples.

• 융복합기술연구소 논문집
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• 제5권2호
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• pp.37-42
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• 2015

This paper presents the effects of the computational time-varying delay on the stability of the haptic system that includes a virtual wall and a first-order-hold method. The model of a haptic system includes a haptic device model with a mass and a damper, a virtual wall model, a first-order-hold model and a computational time-varying delay model. In this paper, the maximum of the computational time-varying delay is assumed to be as much as the sampling time. Using the simulation, it is analyzed how the sample-hold methods and the computational time-varying delay affect the maximum available stiffness. As the maximum of computational time-varying delay increases, the maximal available stiffness of a virtual wall model is reduced.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권4호
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• pp.55-68
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• 2007

First-order least-squares method of a distributed optimal control problem for the incompressible Navier-Stokes equations is considered. An optimality system for the optimal solution are reformulated to the equivalent first-order system by introducing velocity-flux variables and then the least-squares functional corresponding to the system is defined in terms of the sum of the squared $L^2$ norm of the residual equations of the system. The optimal error estimates for least-squares finite element approximations are obtained.

• 한국산학기술학회논문지
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• 제18권1호
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• pp.572-578
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• 2017

사용자가 원격으로 가상환경에 접속하여 가상물체를 조작할 때 현실감을 증강시키기 위해서 햅틱 시스템이 사용된다. 그러나 원격 시스템 환경에는 통신시간지연이 발생하며, 발생된 통신시간지연은 햅틱 시스템을 불안정하게 만들 수 있다. 본 논문에서는 종래의 샘플-홀드 방식인 영차홀드 (ZOH; Zero-Order-Hold)가 아닌 일차홀드 (FOH; First-Order-Hold)를 포함하는 햅틱 시스템에서 시뮬레이션을 통해 통신시간지연과 햅틱 장치의 물성치 변화에 따른 가상 스프링상수의 안정성 영역을 분석하고 이를 통해 안정적인 햅틱 시스템을 구현하고자 한다. 통신시간지연이 없으면 일차홀드 (FOH) 방식이 영차홀드(ZOH) 방식보다 가상 스프링상수의 안정성 영역을 증가시킬 수 있었다. 그러나 통신시간지연이 증가하면, 샘플-홀드 방식보다 통신시간지연이 시스템 안정성에 더 큰 영향을 끼치므로, 샘플-홀드 방식에 따른 가상 스프링상수의 안정성 영역 크기에는 차이가 없어진다. 또한 통신시간지연과 일차홀드 방식이 포함되면 가상 스프링상수의 안정성 영역은 통신시간지연 크기에 반비례하고, 햅틱 장치의 댐핑상수 ($B_d$)에 정비례하여 증가하지만, 햅틱 장치의 질량 ($M_d$)에는 영향받지 않음을 알 수 있었다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국내학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.931-936
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• 1993

Optimal model following control scheme is to design the controller which makes the response of real system follow that of desirable model. This kind of design scheme is developed for first order system. We extends the scheme for second order system regarding the characteristics of mechanical second order system for vibration suppression of flexible structures. The model of mechanical second order system is obtained using suitable damping ratios and natural frequencies. Using this scheme, we can design the good controller which uses the characteristic of second order system. Numerical examples are presented which were used optimal model following control scheme.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.151.3-151
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• 2001

A design of PI controller to be used to control the first-order lag plus dead time process, such as a flow process, by the coefficient diagram method (CDM) is investigated. The factor of the dead time of process is first approximated to be the first-order by the Pade approximation. The response of the flow control system designed by CDM satisfy both transient and steady state specifications. However, the transient response generally still has long rise time. In order to improve the speed of the system response, a feedforward controller (FFC) is added into the PI control system. The structure of the FFC is a phase lead structure with two designed parameters and one derivative time obtained from the reaction curve of the flow process ...

• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.449-471
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• 2023

In this paper, we study a linear system of homogeneous commensurate /incommensurate fractional-order differential equations by developing a new semi-analytical scheme. In particular, by decoupling the system into two fractional-order differential equations, so that the first equation of order (δ + γ), while the second equation depends on the solution for the first equation, we have solved the under consideration system, where 0 < δ, γ ≤ 1. With the help of using the Adomian decomposition method (ADM), we obtain the general solution. The efficiency of this method is verified by solving several numerical examples.

• 대한수학회논문집
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• 제12권3호
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• pp.813-827
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• 1997

Multigrid methods for two first-order system least squares (FOSLS) using bilinear finite elements are developed for the pure traction problem of planar linear elasticity. They are two-stage algorithms that first solve for the gradients of displacement, then for the displacement itself. In this paper, concentration is given on solving for the gradients of displacement only. Numerical results show that the convergences are uniform even as the material becomes nearly incompressible. Computations for convergence rates are included.