• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국내학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.482-485
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• 1993

This paper deals with structured singular value and mixed sensitivity problem for robust performance. We derive the sufficient condition that mixed sensitivity problem satisfies structured singular value in robust performance problem. And we show the bound of perturbation between structured singular value and norm of mixed sensitivity functions.

• 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.

• 대한전자공학회논문지
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• 제24권1호
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• pp.20-27
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• 1987

The hierarchical approach method is proposed to sperate each different time scale sub-systems from linear time invariant multi-parameter singular perturbation systems. By means of this proposal, the original multi-parameter singular perturbation systems is completely separated into independent subsystems with each different time scale. It is also investigated that the controllability of the system is invariant. And this paper applies singular perturbation methods to the minimum control effort problem for linear time invariant systems with constrained controls. Also near-optimum control theory, which is based on dividing the total time interval with the time scales respectively, is proposed. As a result, the time scale separation method is show to be particularly useful in a near optimum design which can be otained through a decentralized control structure.

• Nuclear Engineering and Technology
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• 제21권2호
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• pp.99-110
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• 1989

원자로 지논 농도의 최적 제어는 Linear Quadratic Regulator Problem이다. 지논 농도와 아이오다인 농도는 측정할 수 없기 때문에 최적 제어를 수행하기 위해서는 측정할 수 없는 상태 변수를 예측하는 것이 필요하다. 본 연구에서 사용된 예측방법은 Luenberger Observer를 기초로 했다. 원자로 상태 방정식은 빠른 상태 방정식(중성자 속, 핵연료 및 냉각재 온도)과 느린 상태 방정식(아이오다인, 지논)의 상호작용에 의해 Stiffness 문제가 발생되는데 이러한 시스템을 "Singularly Perturbed System"이라 한다. Stiffness문제를 해결하기 위해서 원 시스템을 느린 시스템과 빠른 시스템의 두 개의 모드로 나누는 Singular Perturbation Method를 사용한다. 예측기Observer를 이용한 원 시스템의 제어기는 느린 시스템과 빠른 시스템에 대한 분리된 예측기와 제어기의 설계에 의해 결정되어진다. 특히 원자로 상태 방정식에서는 빠른 모드는 빨리 사라지게 되므로 단지 느린 시스템에 대해서만 예측기를 설계하면 된다. 컴퓨터시뮬레이션을 통한 시험 결과는 원자로의 지논 진동은 Singular Perturbation Method와 예측기를 이용해서 거의 정확하게 효과적으로 짧은 시간내에 제어할 수 있음을 알았다.수 있음을 알았다.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.141-152
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• 2007

In this paper a numerical method is presented to solve singularly perturbed two points boundary value problems for second order ordinary differential equations consisting a discontinuous source term. First, in this method, an asymptotic expansion approximation of the solution of the boundary value problem is constructed using the basic ideas of a well known perturbation method WKB. Then some initial value problems and terminal value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial value problems are happened to be singularly perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples provided to illustrate the method.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.937-948
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• 2011

The method of Asymptotic Inner Boundary Condition for Singularly Perturbed Two-Point Boundary value Problems is presented. By using a terminal point, the original second order problem is divided in to two problems namely inner region and outer region problems. The original problem is replaced by an asymptotically equivalent first order problem and using the stretching transformation, the asymptotic inner condition in implicit form at the terminal point is determined from the reduced equation of the original second order problem. The modified inner region problem, using the transformation with implicit boundary conditions is solved and produces a condition for the outer region problem. We used Chawla's fourth order method to solve both the inner and outer region problems. The proposed method is iterative on the terminal point. Some numerical examples are solved to demonstrate the applicability of the method.

• 전기학회논문지
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• 제65권9호
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• pp.1524-1530
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• 2016

This paper deals with a robust $H_{\infty}$ sampled-data controller design problem for nonlinear systems in Takagi-Sugeno fuzzy form with singular perturbation. The employed controller takes a state-feedback form. The design condition is represented in terms of linear matrix inequalities. A numerical examples is included to show the effectiveness of the theoretical development.

• 대한전기학회논문지:시스템및제어부문D
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• 제54권6호
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• pp.359-365
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• 2005

This paper presents an reduced-order near-optimal controller for the congestion control of Available Bit Rate (ABR) service in Asynchronous Transfer Mode (ATM) networks. We introduce the model, of a class of ABR traffic, that can be controlled using a Explicit Rate feedback for congestion control in ATM networks. Since there are great computational complexities in the class of optimal control problem for the ABR model, the near-optimal controller via reduced-order technique is applied to this model. It is implemented by the help of weakly coupling and singular perturbation theory, and we use bilinear transformation because of its computational convenience. Since the bilinear transformation can convert discrete Riccati equation into continuous Riccati equation, the design problems of optimal congestion control can be reduced. Using weakly coupling and singular perturbation theory, the computation time of Riccati equations can be saved, moreover the real-time congestion control for ATM networks can be possible.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1279-1292
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• 2009

In this paper, a numerical method that uses standard finite difference scheme defined on Shishkin mesh for a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with a discontinuous source term is presented. An error estimate is derived to show that the method is uniformly convergent with respect to the singular perturbation parameter. Numerical results are presented to illustrate the theoretical results.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권4호
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• pp.281-292
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• 2009

The solution of the interface problem or Poisson problem with concave corner has singular perturbation at the interface corners or singular corners. The decoupled dual singular function method (DDSFM) which exploits the singular representations of the solutions was suggested in [3, 9] and estimated optimal accuracy in [10]. The convergence rates consist with theoretical results even for the problems with very strong singularity, with the efficiency depending on parameters used in the methods. Furthermore the errors in $L^2$ and $L^\infty$-spaces display some oscillation, in the cases with meshsize not small enough. In this paper, we present an answer to remove the oscillation via numerical experiments. We observe the effects of parameters in DDSFM, and show the consisting efficiency of the method over the strong singularity.