• 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.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2005년도 춘계학술대회 논문집
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• pp.1120-1124
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• 2005

We reviewed controllers with a time delay estimation in this paper. Time delay control (TDC) and sliding mode control (SMC) are well known robust control schemes. Basically, the TDC has a main characteristic called a time delay estimation from which we can estimate the total uncertainty of a system. . The TDC causes the stick-slip in the case of systems with a friction. The so-called TDCSA which are short for TDC with switching action was developed to reduce the stick-slip. The TDC has the additional switching action term in the TDC structure. In the other hand, the SMC dose not have a time delay estimation but instead it can estimate the system uncertainty through the switching action. The SMC has a difficulty to estimate the total uncertainty of a system because it does not have a time delay estimation. In order to solve the difficulty, some control schemes were developed. Among them, we need to focus our attention on two control schemes: SMCPE and SMCTE, which are short for sliding mode control with a perturbation estimation and sliding mode control with a time delay estimation, respectively. In this paper, we analyzed and compared the characteristic of above three controllers. Even though the motives for the development of three control schemes are different, three control schemes have much in common in terms of their controller structures.

• Journal of applied mathematics & informatics
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• 제39권3_4호
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• pp.419-435
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• 2021

This paper deals with numerical treatment of singularly perturbed differential equations involving small delays. The highest order derivative in the equation is multiplied by a perturbation parameter 𝜀 taking arbitrary values in the interval (0, 1]. For small 𝜀, the problem involves a boundary layer of width O(𝜀), where the solution changes by a finite value, while its derivative grows unboundedly as 𝜀 tends to zero. The considered problem contains delay on the convection and reaction terms. The terms with the delays are approximated using Taylor series approximations resulting to asymptotically equivalent singularly perturbed BVPs. Inducing exponential fitting factor for the term containing the singular perturbation parameter and using central finite difference for the derivative terms, numerical scheme is developed. The stability and uniform convergence of difference schemes are studied. Using a priori estimates we show the convergence of the scheme in maximum norm. The scheme converges with second order of convergence for the case 𝜀 = O(N^-1) and for the case 𝜀 ≪ N^-1, the scheme converge uniformly with first order of convergence, where N is number of mesh intervals in the domain discretization. We compare the accuracy of the developed scheme with the results in the literature. It is found that the proposed scheme gives accurate result than the one in the literatures.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.675-694
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• 2022

In this article, we investigate the solution of the inverse problem for one dimensional heat equation with Neumann and Robin boundary conditions, that is, we determine the temperature and source term with given initial and boundary conditions. Three radial basis functions(RBFs) have been used for numerical solution, and Homotopy perturbation method for analytic solution. Numerical solutions which are obtained by considering each of the three RBFs are compared to the exact solution. For appropriate value of shape parameter c, numerical solutions best approximates exact solutions. Furthermore, we have shown the impact of noisy data on the numerical solution of u and f.

• 한국조명전기설비학회:학술대회논문집
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• 한국조명전기설비학회 2004년도 춘계학술대회 논문집
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• pp.347-352
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• 2004

The author present a modified multi-loop algorithm including feedforward for controlling a 55kW step down chopper in the power supply of Maglev. The control law for the duty cycle consists of three terms. The first is the feedforward term which compensates for variations in the input voltage. The second term consists of the difference between the slowly moving inductor current and output current. The third term consists of proportional and integral terms involving the perturbation in the output voltage. This perturvation is derived by subtracting the desired output voltage from the actual output voltage. The proportional and integral action stabilizes the system and minimizes output voltage error. In order to verify the validity of the proposed multi-loop controller, simulation study was tried using Matlab simulink.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2003년도 하계학술대회 논문집 B
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• pp.1262-1264
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• 2003

The author Present a modified multiloop algorithm including feedforward for controlling a 45kW step down chopper in the power supply of Maglev. The control law for the duty cycle consists of three terms. The first is the feedforward term which compensates for variations in the input voltage. The second term consists of the difference between the slowly moving inductor current and output current. The third term consists of proportional and integral terms involving the perturbation in the output voltage. This perturvation is derived by subtracting the desired output voltage from the actual output voltage. The proportional and integral action stabilizes the system and minimizes output voltage error. To verify the validity of the proposed multiloop controller, simulation study was tried using Matlab/sirnulink.

• 조명전기설비학회논문지
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• 제18권6호
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• pp.128-135
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• 2004

본 논문은 자기부상열차용 전원의 문제점을 개선시키기 위해서 다중루프 제어기를 제시하였다. 제시된 제어기는 3개의 부분으로 구성되어 있다. 첫 번째는 입력전압의 변동에 대하여 보상할 수 있는 Feed Forward제어기이며 두 번째는 리액터 전류와 출력 전류의 차를 보상하며, 세 번째는 비례적분제어기를 사용하여 출력전압에 포함된 리플을 감소시키므로써, 안정화된 시스템을 구현하였다. 이 시스템의 특성을 확인하기 위해서 Matlab Simulink와 고성능 DSP소자인 TMS320F240을 이용하여 비교 분석하였다.

• 대한토목학회논문집
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• 제14권6호
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• pp.1445-1451
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• 1994

해안구조물에 작용하는 설계파압(設計波壓)을 수치적으로 계산하기 위해서는 먼저 쇄파한계(碎波限界)에 가까운 큰 중복파랑을 수치적으로 재현할 필요가 있다. 이를 위해서는 지배방정식(支配方程式)과 비선형항(非線形項)을 포함하는 경계조건을 효과적으로 반영해야 하며 특히, 자유표면(自由表面) 경계조건(境界條件)에서의 속도의 제곱항의 처리가 중요하다. 본 연구에서는 Newton 방법을 이용하여 제곱항을 충실히 반영하므로써 일반적인 셜계파 성향에 거의 상응하는 중복파랑을 재현하였으며 기존의 섭동법(攝動法) 또는 Fourier 전개 기법 및 수리실험 결과와 비교하여 그 정확도를 검토하였다.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.39-53
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• 2014

In this paper, a non-asymptotic method is presented for solving singularly perturbed delay differential equations whose solution exhibits a boundary layer behavior. The second order singularly perturbed delay differential equation is replaced by an asymptotically equivalent first order neutral type delay differential equation. Then, Simpson's integration formula and linear interpolation are employed to get three term recurrence relation which is solved easily by Discrete Invariant Imbedding Algorithm. Some numerical examples are given to validate the computational efficiency of the proposed numerical scheme for various values of the delay and perturbation parameters.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.441-452
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• 2009

In this paper, a fifth order numerical method is presented for solving singularly perturbed differential-difference equations with negative shift. In recent papers the term negative shift has been using for delay. Similar boundary value problems are associated with expected first exit time problem of the membrane, potential in models for neuron and in variational problems in control theory. In the numerical treatment for such type of boundary value problems, first we use Taylor approximation to tackle terms containing small shifts which converts it to a boundary value problem for singularly perturbed differential equation. 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 and is solved using the boundary conditions. Several numerical examples are solved and compared with exact solution. It is observed that present method approximates the exact solution very well.