• 한국항공우주학회지
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• 제32권7호
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• pp.76-82
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• 2004

본 논문에서는 델타연산자를 이용한 통합시스템에서 사전에 민감도가 낮게 설정된 폐루프 궤적을 성취해주는 상태 궤환 제어기의 설계기법이 제안되었다. 양시등급 시스템에서는 빠른 모드를 무시함으로써 수행되는 특이섭동기법에 의해서 그 차수가 감소된다. 제안된 기법은 특이성동상수의 범위에서 실제 궤적의 변화를 다룬다. 물론 최적화를 위한 필요조건들도 유도된다. 이전의 연구는 연속시스템에서 이루어졌으나 본 논문에서는 이산 시스템 및 델타통합시스템으로 확장하였다. 제안된 기법의 우수성은 수치예제를 통하여 확인되었다.

• 조명전기설비학회논문지
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• 제13권1호
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• pp.119-127
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• 1999

본 논문에서는 비모형화특성과 유계인 외란을 고려한 선형 시불변 연속시간 계통에 대해 수정된 제어칙과 시그마수정법의 단점을 보완한 적응칙을 이용하여 강인한 직접적응제어기를 제시하고자 한다. 비모형화특성이 특이섭동(singular perturbation)형태로 존재할 때 적용 가능한 알고리즘으로서 기존의 제어칙을 변형하였을 뿐만 아니라 제어기 파라미터를 추정하기 위한 기존의 적응칙인 o-수정법을 보완하여 재구성된다. 재구성된 적응제어칙을 이용하므로써 전체 적응제어 계통의 성능이 기존의 적응제어 알고리즘을 이용했을 때보다 강인하고 시스템의 성능이 향상됨을 보인다. 제시된 알고리즘의 타당성을 보이기 위하여 n차 플랜트에 대한 폐루프내의 모든 신호들이 유계가 됨을 입증하고, 컴퓨터 모의실험 결과는 1차 플랜트에 한해 그 효용성을 보인다.

• 제어로봇시스템학회논문지
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• 제22권9호
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• pp.679-685
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• 2016

This paper addresses an observer-based output-feedback sampled-data controller design problem for nonlinear systems in Takagi-Sugeno (T-S) form including singular perturbations. The design condition is represented in terms of linear matrix inequalities. The separation principle is also investigated.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1273-1287
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• 2008

In this paper, the numerical integration method for general singularly perturbed two point boundary value problems with mixed boundary conditions of both left and right end boundary layer is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.49-65
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• 2006

A robust numerical method for a singularly perturbed second-order ordinary differential equation having two parameters with a discontinuous source term is presented in this article. Theoretical bounds are derived for the derivatives of the solution and its smooth and singular components. An appropriate piecewise uniform mesh is constructed, and classical upwind finite difference schemes are used on this mesh to obtain the discrete system of equations. Parameter-uniform error bounds for the numerical approximations are established. Numerical results are provided to illustrate the convergence of the numerical approximations.

• 대한수학회지
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• 제51권4호
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• pp.679-702
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• 2014

Investigation of the numerical solution of singularly perturbed turning point problems dates back to late 1970s. However, due to the presence of layers, not many high order schemes could be developed to solve such problems. On the other hand, one could think of applying the convergence acceleration technique to improve the performance of existing numerical methods. However, that itself posed some challenges. To this end, we design and analyze a novel fitted operator finite difference method (FOFDM) to solve this type of problems. Then we develop a fitted mesh finite difference method (FMFDM). Our detailed convergence analysis shows that this FMFDM is robust with respect to the singular perturbation parameter. Then we investigate the effect of Richardson extrapolation on both of these methods. We observe that, the accuracy is improved in both cases whereas the rate of convergence depends on the particular scheme being used.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1996년도 추계학술대회 논문집
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• pp.301-305
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• 1996

$\mu$ theory can handle the parametric uncertainty and produces more non-conservative controller than H$_{\infty}$ control theory. However an existing solution of the theory, D-K iteration, creates a controller of huge order and cannot handle the real or mixed real-complex perturbation sets. In this paper, we use genetic algorithms to solve these problems of the D-K iteration method. The Youla parameterization is used to obtain all stabilizing controllers and the genetic algorithms determines the values of the state feedback gain, the observer gain, and Q parameter to minimize $\mu$, the structured singular value, of given system. From an example, we show that this method produces lower order controller which controls a real parameter-perturbed plant than D-K iteration method.

• Journal of Power Electronics
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• 제13권5호
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• pp.814-828
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• 2013

The LCL resonant inductive power transfer (IPT) system is increasingly used because of its harmonic filtering capabilities, high efficiency at light load, and unity power factor feature. However, the modeling and controller design of this system become extremely difficult because of parameter uncertainty, high-order property, and switching nonlinear property. This paper proposes a frequency and load uncertainty modeling method for the LCL resonant IPT system. By using the linear fractional transformation method, we detach the uncertain part from the system model. A robust control structure with weighting functions is introduced, and a control method using structured singular values is used to enhance the system performance of perturbation rejection and reference tracking. Analysis of the controller performance is provided. The simulation and experimental results verify the robust control method and analysis results. The control method not only guarantees system stability but also improves performance under perturbation.

• Kyungpook Mathematical Journal
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• 제60권3호
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• pp.629-645
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• 2020

A uniformly convergent numerical method is developed for solving singularly perturbed 1-D parabolic convection-diffusion problems. The developed method applies a non-standard finite difference method for the spatial derivative discretization and uses the implicit Runge-Kutta method for the semi-discrete scheme. The convergence of the method is analyzed, and it is shown to be first order convergent. To validate the applicability of the proposed method two model examples are considered and solved for different perturbation parameters and mesh sizes. The numerical and experimental results agree well with the theoretical findings.

• 대한수학회논문집
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• 제39권1호
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• pp.149-160
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• 2024

In this paper, we give sufficient conditions for the generalized Ornstein-Uhlenbeck operators perturbed by regular potentials and inverse square potentials A_Φ,G,V,c=∆-∇Φ·∇+G·∇-V+c|x|^-2 with a suitable domain generates a quasi-contractive, positive and analytic C₀-semigroup in L^p(ℝ^N , e^-Φ(x)dx), 1 < p < ∞. The proofs are based on an L^p-weighted Hardy inequality and perturbation techniques. The results extend and improve the generation theorems established by Metoui [7] and Metoui-Mourou [8].