• Journal of the Korean Institute of Intelligent Systems
• /
• v.19 no.6
• /
• pp.840-847
• /
• 2009

This paper deals with an $H_{\infty}$ output feedback controller design for uncertain singularly perturbed T-S fuzzy systems. Integral quadratic constraints are used to describe various kinds of uncertainties of the plant. It is shown that the $H_{\infty}$ norm of the uncertain singularly perturbed fuzzy system is less than $\gamma$ for a sufficiently small $\varepsilon$ > 0 if the $H_{\infty}$ norms of both the slow and fast subsystem are less than $\gamma$. Using this fact, we develop a linear matrix inequality based design method which is independent of the singular perturbation parameter $\varepsilon$. A numerical example is provided to demonstrate the efficacy of the proposed design method.

• Proceedings of the KIEE Conference
• /
• 2007.10a
• /
• pp.51-52
• /
• 2007

이 논문에서는 다중입출력 선형 시스템에 대한 외란 관측기설계 방법을 제안하고자 한다. 제안된 방법을 특이 섭동(Singular Perturbation) 이론을 사용하여 해석하며, 그 결과 Q 필터의 상수가 매우 작다면 외란 제거와 시스템 불확실성에 대한 보상을 통하여 실제 시스템을 공칭 시스템으로 근사화 시켜주는 것을 볼 수 있다.

• 전기의세계
• /
• v.29 no.10
• /
• pp.667-677
• /
• 1980

A new approach for optimal decentralized load-frequency control in a multi-area interconnected power system is presented, which includes the optimal determination of decentralized load-frequency controller, observer for unmeasurable local states and load disturbances, quadratic estimator for tie-line power flow information transmitted at intervals. The optimal design of the decentralized controller is based on a modified application of the singular perturbation theory, and the decentralized Luenberger obeserver uses techniques of state augmentation for exponential disturbance functions and the representation of tie-line power flow states as non-directly-controlled inputs. The approach presented herein is numerically tested through Elgerd's two-area load-frequency system model, and the results demonstrate remarkable advantages over the conventional ones.

• Proceedings of the KIEE Conference
• /
• 1998.11b
• /
• pp.438-441
• /
• 1998

In this paper, we proposes an adaptive flux observer to estimate initial values of rotor fluxes and unknown rotor resistance. The error system between the model of induction motor and a proposed observer is devided as a fast subsystem and a slow one by a singular perturbation system. The fast subsystem is exponentially convergent on a boundary-layer. And the overall error system is reduced to a quasi-steady-state system. The adaptive law for an unknown rotor resistance is designed to stabilize the approximate error system. As computer simulation results show, the proposed adaptive flux observer estimates fast initial values of rotor fluxes and unknown rotor resistance.

• Journal of applied mathematics & informatics
• /
• v.28 no.5_6
• /
• pp.1035-1054
• /
• 2010

We consider a mixed type singularly perturbed one dimensional elliptic problem with discontinuous source term. The domain under consideration is partitioned into two subdomains. A convection-diffusion and a reaction-diffusion type equations are posed on the first and second subdomains respectively. Two hybrid difference schemes on Shishkin mesh are constructed and we prove that the schemes are almost second order convergence in the maximum norm independent of the diffusion parameter. Error bounds for the numerical solution and its numerical derivative are established. Numerical results are presented which support the theoretical results.

• Journal of the Korean Institute of Telematics and Electronics S
• /
• v.34S no.3
• /
• pp.24-32
• /
• 1997

This paper is on a discrete controller order reduction with the closed-loop stability and performance guaranteed. to achieve this, after finding the solutionsof two lyapunov inequalities and balancing the full order controller system, we find the reudced order controlers using the balanced truncation (BT) and the balanced singular perturbation approximation (BSPA). When the solutions of the two lyapunov inequalities exist, it is shown that the resulting controllers guarantee the closed-loop stability, and .inf.-norm error bounds are derived for the closed-loop performance region for the BT and in low frequency region for the BSPA. Finally, a numerical example is given to illustrate the validity of the proposed method.

• Proceedings of the KIEE Conference
• /
• 1994.11a
• /
• pp.6-8
• /
• 1994

In this paper an attempt is made to understand the voltage stability when the power system networks are represented by the differential-algebraic equations (DAEs) form. The problem is analyzed by interpreting the shape of constraint manifold, based on the singular perturbation model. The global picture or constraint manifold is given to show how the local shape or constraint manifold can be used to guess for the system behavior. The gradient analysis is used systematically to obtain a local shape or the constraint manifold.

• Kyungpook Mathematical Journal
• /
• v.61 no.3
• /
• pp.591-612
• /
• 2021

In this paper, a uniformly convergent numerical scheme is designed for solving singularly perturbed reaction-diffusion problems. The problem is converted to an equivalent weak form and then a Galerkin finite element method is used on a piecewise uniform Shishkin mesh with linear basis functions. The convergence of the developed scheme is proved and it is shown to be almost fourth order uniformly convergent in the maximum norm. To exhibit the applicability of the scheme, model examples are considered and solved for different values of a singular perturbation parameter ε and mesh elements. The proposed scheme approximates the exact solution very well.

• Journal of applied mathematics & informatics
• /
• v.39 no.5_6
• /
• pp.655-676
• /
• 2021

A parameter uniform numerical scheme is proposed for solving singularly perturbed parabolic partial differential-difference convection-diffusion equations with a small delay and advance parameters in reaction terms and spatial variable. Taylor's series expansion is applied to approximate problems with the delay and advance terms. The resulting singularly perturbed parabolic convection-diffusion equation is solved by utilizing the implicit Euler method for the temporal discretization and finite difference method for the spatial discretization on a uniform mesh. The proposed numerical scheme is shown to be an ε-uniformly convergent accurate of the first order in time and second-order in space directions. The efficiency of the scheme is proved by some numerical experiments and by comparing the results with other results. It has been found that the proposed numerical scheme gives a more accurate approximate solution than some available numerical methods in the literature.

• Journal of the Korean Society of Industry Convergence
• /
• v.24 no.4_1
• /
• pp.397-409
• /
• 2021

This study proposes a new approach to implimentation of robust control and torque control response analysis based on monitoring simulator for smart factory. According to the physical properties of a flexible manipulator, a two time-scale approach, namely, singular perturbation ap proach, is further utilized for thorough analysis and general controller design. It is shown that asymptotic motional tracking can be effectively achieved, whereas the force regulation errors can be made arbitrarily small. For demonstration of the proposed technology performance, experiments of a eight joint flexible manipulator are performed for the proposed control method, and the reliability of proposed control results are illustrated based on monitoring simulator.