• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1035-1054
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• 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.

• 한국정보통신학회논문지
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• 제4권5호
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• pp.1111-1116
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• 2000

혼합 $H_2/ H_\infty$ 제어 방법은 $H_2성능과 H_\infty$ -강건성을 결합한 제어기 설계를 위한 적극적인 접근법의 하나이다. 이 논문에서는, 먼저 설계하고자 하는 제어시스템의 추종특성을, 불확실성이 포함된 제어대상에 대하여, $H_2$노름으로 표현하고, 다음으로 $H_\infty$노름으로 제어 시스템의 강건 안정성을 얻도록 하였다. 혼합 $H_2/ H_\infty$ 디지털 제어기는 도립진자 시스템을 제어대상으로 하여 설계하였다. 도립진자 시스템에 대하여 설계한 혼합$H_2/ H_\infty$디지털 제어기는, 불안정 시스템을 안정화하면서 동시에 추종 성능을 향상시키고자 하였다.

• Journal of Advanced Marine Engineering and Technology
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• 제24권3호
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• pp.88-98
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• 2000

In this paper, a robust controller using $H_{\infty}$ control theory has been designed for the load frequency control of interconnected 2-area power system. The main advantage of the proposed $H_{\infty}$ controller is that uncertainties of power system can be included at the stage of controller design. Representation of uncertainties is modeled by multiplicative uncertainly. In the mixed sensitivity problems, disturbance attenuation and uncertainty of the system is treated simultaneously. The robust stability and the performance of model uncertainties are represented by frequency weighted transfer function. The design of load frequency controller for each area was based on state-space approach. The comparative computer simulation results for the proposed controller and the conventional techniques such as the optimal control and the PID one were analyzed at the additions of various disturbances. Their deviation magnitude of frequency and tie line power flow at each area were mainly evaluated. Also the testing results of robustness for the cases that the perturbations of the all parameters of power system were amounted to about 20% were introduced. It was approved that the resultant performances of the proposed $H_{\infty}$ controller with mixed sensitivity were more robust and stable than the one of conventional controllers.

• 대한수학회지
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• 제53권3호
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• pp.597-621
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• 2016

We present regularity conditions for suitable weak solutions of the Navier-Stokes equations with slip boundary data near the curved boundary. To be more precise, we prove that suitable weak solutions become regular in a neighborhood boundary points, provided the scaled mixed norm $L^{p,q}_{x,t}$ with 3/p + 2/q = 2, $1{\leq}q$ < ${\infty}$ is sufficiently small in the neighborhood.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 22-24 Oct. 1991
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• pp.248-251
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• 1991

A robust monitor AGC(Automatic Gauge Control) system for a hot strip mill plant of POSCO Is designed by minimizing the H.inf. norm of a so called mixed sensitivity function. In order to solve the mininizatlon problem, a polynomial approach proposed by Kwakernaak[5] is used. The controller performance is tested by a computer simulation under various circumstances.

• Journal of information and communication convergence engineering
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• 제2권3호
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• pp.193-197
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• 2004

In this paper, a combination problem of controllers which are the same type of $H_{\infty}$ controllers designed with different weighting functions. This approach can remove the difficulty in the selection of the weighting functions. As a sub-controller, the Youla type of $H_{\infty}$ controller is used. In the $H_{\infty}$ controller, Youla parameterization is used to minimize $H_{\infty}$ norm of mixed sensitivity function by using polynomial approach. Computer simulation results show the robustness improvement and the performance improvement.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.47.6-47
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• 2001

In this paper a new indirect robust self-tuning regulator is proposed including an inverse system of a plant and a robust compensator such that it achieves the desired frequency shape specified by solving the mixed H$\infty$ sensitivity problem within a prescribed tolerance in the H$\infty$ norm. Consequently, in the proposed self-tuning regulator, robust stability is guaranteed in spite of the identification error.

• 전자공학회논문지B
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• 제33B권6호
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• pp.12-22
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• 1996

A numerous designs of PI controllers have been suggested to solve out trade-off between tracing and regulating problems. We constructed the PI controller system with two-degree-of-freedom that is more analytic and a better approach to a practical one. In the conventional H$_{2}$ design of optimal PI controllers, the cost function includes only the plant output terms due to the divergent problems. Since the platn input temr is not considered in PI controller design, occasionally, the plant input thends to be either very large or saturated. To solve the prior mentioned problems, we employed a mixed $H_2/H_{\infty}$ method that combines the H$_{2}$ design method to decide optimal parameters of PI controller and the $H_2/H_{\infty}$ design method to minimize the maximum amplitude of plant input. The calculation time of the H$_{infty}$ norm was considerably reduced by the simple scalar function obtained by the wiener-hopf factorization of non-scalar functions.

• Journal of applied mathematics & informatics
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• 제33권5_6호
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• pp.485-502
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• 2015

A computational method for solving singularly perturbed boundary value problem of differential equation with shift arguments of mixed type is presented. When shift arguments are sufficiently small (o(ε)), most of the existing method in the literature used Taylor's expansion to approximate the shift term. This procedure may lead to a bad approximation when the delay argument is of O(ε). The main idea for this work is to deal with constant shift arguments, which are independent of ε. In the present method, we construct the formally asymptotic solution of the problem using the method of composite expansion. The reduced problem is solved numerically by using operator compact implicit method, and the second problem is solved analytically. Error estimate is derived by using the maximum norm. Numerical examples are provided to support the theoretical results and to show the efficiency of the proposed method.

• 한국해양공학회지
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• 제10권3호
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• pp.153-161
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• 1996

This paper presents a design method of dynamic positioning control system for floating platform with rotatable and retractable thruster using $H_{\infty}$ control technique. The norm band of uncertainty is captured by multiplicative perturbation between nominal model and reduced order model. A controller robust to the uncertainty is designed applying $H_{\infty}$ synthesis. The control law satisfying robust stabillity and nominal performance condition is determined through the mixed sensitivity approach. The evaluation for the resultant controller obtained by $H_{\infty}$ synthesis is done through simulations of the closed loop system. The results of $H_{\infty}$ synthesis are compared to those of the traditional LQ synthesis method.