• Journal of applied mathematics & informatics
• /
• 제26권5_6호
• /
• pp.1057-1069
• /
• 2008

We consider singularly perturbed Boundary Value Problems (BVPs) for third and fourth order Ordinary Differential Equations(ODEs) of convection-diffusion type with discontinuous source term and a small positive parameter multiplying the highest derivative. Because of the type of Boundary Conditions(BCs) imposed on these equations these problems can be transformed into weakly coupled systems. In this system, the first equation does not have the small parameter but the second contains it. In this paper a computational method named as 'An asymptotic finite element method' for solving these systems is presented. In this method we first find an zero order asymptotic approximation to the solution and then the system is decoupled by replacing the first component of the solution by this approximation in the second equation. Then the second equation is independently solved by a fitted mesh Finite Element Method (FEM). Numerical experiments support our theoritical results.

• Nuclear Engineering and Technology
• /
• 제37권2호
• /
• pp.139-150
• /
• 2005

A robust control design procedure for a nuclear reactor has been developed and experimentally validated on the Penn State TRIGA research reactor. The utilization of the robust controller as a component of an autonomous control system is also demonstrated. Two methods of specifying a low order (fourth-order) nominal-plant model for a robust control design were evaluated: 1) by approximation based on the 'physics' of the process and 2) by an optimal Hankel approximation of a higher order plant model. The uncertainty between the nominal plant models and the higher order plant model is supplied as a specification to the ,u-synthesis robust control design procedure. Two methods of quantifying uncertainty were evaluated: 1) a combination of additive and multiplicative uncertainty and 2) multiplicative uncertainty alone. The conclusions are that the optimal Hankel approximation and a combination of additive and multiplicative uncertainty are the best approach to design robust control for this application. The results from nonlinear simulation testing and the physical experiments are consistent and thus help to confirm the correctness of the robust control design procedures and conclusions.

• Applied Chemistry for Engineering
• /
• 제10권1호
• /
• pp.166-172
• /
• 1999

Fixed-bed adsorption of metal ions on chitosan bead was studied to remove heavy metal ions in waste water. Chitin was extracted from carb shell and chitosan was prepared by deacetylation of the chitin. The chitosan in bead was used as an adsorbent for heavy metal ions. Freundlich and Langmuir isotherm was determined from the experimental results of equilibrium adsorption for individual metal ion ($Cu^{2+}$, $Co^{2+}$, $Ni^{2+}$) on chitosan bead. Adsorption strength of metal ions decreased in the order of $Cu^{2+}$>$Co^{2+}$>$Ni^{2+}$ ion. Breakthrough curves of single and multicomponent adsorption for metal ions were obtained from the experimental results of fixed-bed adsorption. The breakthrough curves were analyzed by simulation with fixed-bed adsorption equation based on LDFA (linear driving force approximation) adopted LAS (ideal adsorbed solution) theory which can predict multi-component adsorption isotherm from individual adsorption isotherm. The behavior of fixed bed adsorption for single and multi-component system could be nicely simulated by the equation.

• Journal of the Society of Naval Architects of Korea
• /
• 제31권2호
• /
• pp.91-98
• /
• 1994

An efficient optimization procedure combining the frequency approximation technique and the component-mode synthesis method is proposed for the structural dynamic optimization of the large structures subject to prescribed natural frequency constraints. Frequency constraints are approximated by using the first-order sensitivities with respect to both design parameters and their reciprocals. The component-mode synthesis method proposed by the authors in Ref.[8] is used for the repetitive detail finite-element analysis and sensitivity analysis. The validity of the proposed optimization procedure is confirmed through the numerical implementation of some examples. The presented approximation technique requires much smaller number of repetitive analysis than that using the sensitivities with respect to design parameters only, and further improvement in the numerical efficiency is achieved by the adoption of the introduced component-mode synthesis.

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• 제52권5호
• /
• pp.263-270
• /
• 2003

In field applications, to represent the degree of voltage unbalance, the maximum voltage deviation from the average is preferred to the voltage unbalance factor based on symmetrical component analysis. This paper first clarifies the relationship between the voltage unbalance factor and the maximum deviation factor showing that the maximum deviation factor approximates the voltage unbalance factor under relatively low unbalanced conditions. Several alternative ways of approximation are introduced and examined by comparing with the conventional maximum deviation factor. It appears that these alternatives provide more accurate approximation to the voltage unbalance factor over wider range of voltage unbalance while maintaining simplicity in their formula.

• Applied Microscopy
• /
• 제33권3호
• /
• pp.169-178
• /
• 2003

In this review, theoretical approaches of imaging and diffraction in electron microscopy are introduced which allows the diffraction patterns and images to be treated with equal facility and emphasized the relationships between them. The coherent wave optics, incoherent wave imaging theory were introduced. The idea of Abbe theory was also introduced. Varoius phase contrast theories in small angle approximation were derived including the wave theory on Multi-component system.

• ETRI Journal
• /
• 제31권1호
• /
• pp.42-50
• /
• 2009

A new method for simulating voltage and current distributions in transmission lines is described. It gives the time domain solution of the terminal voltage and current as well as their line distributions. This is achieved by treating voltage and current distributions as distributed state variables (DSVs) and turning the transmission line equation into an ordinary differential equation. Thus the transmission line is treated like other lumped dynamic components, such as capacitors. Using backward differentiation formulae for time discretization, the DSV transmission line component is converted to a simple time domain companion model, from which its local truncation error can be derived. As the voltage and current distributions get more complicated with time, a new piecewise exponential with controllable accuracy is invented. A segmentation algorithm is also devised so that the line is dynamically bisected to guarantee that the total piecewise exponential error is a small fraction of the local truncation error. Using this approach, the user can see the line voltage and current at any point and time freely without explicitly segmenting the line before starting the simulation.

• International Journal of Control, Automation, and Systems
• /
• 제2권2호
• /
• pp.238-246
• /
• 2004

In displaying a virtual wall using a passive haptic device equipped with passive actuators such as electric brakes, unsmooth motion frequently occurs. This undesirable behavior is attributed to time delay due to slowness in the virtual environment update and force approximation due to the inability of a brake to generate torque in arbitrary directions. In this paper a new control scheme called direct control is proposed to achieve smooth display on the wall-following task with a passive haptic device. In direct control, brakes are controlled so that the normal component of a resultant force at the end-effector vanishes, based on the force analysis at the end-effector of the passive haptic device using the passive FME (Force Manipulability Ellipsoid). Various experiments have been conducted to verify the validity of the direct control scheme with a 2-link passive haptic system.

• Journal of applied mathematics & informatics
• /
• 제12권1_2호
• /
• pp.267-279
• /
• 2003

The present investigation deals with the application of Adomian's decomposition method to blood flow through a constricted artery in the presence of an external transverse magnetic field which is applied uniformly. The blood flowing through the tube is assumed to be Newtonian in character. The expressions for the two-term approximation to the solution of stream function, axial velocity component and wall shear stress are obtained in this analysis. The numerical solutions of the wall shear stress for different values of Reynold number and Hartmann number are shown graphically. The solution of this theoretical result for a particular Hart-mann number is compared with the integral method solution of Morgan and Young［17］.

• Proceedings of the KIPE Conference
• /
• 전력전자학회 2012년도 전력전자학술대회 논문집
• /
• pp.244-245
• /
• 2012

본 논문에서는 이산 웨이블릿 변환(DWT;discrete wavelet transform)의 다해상도 분석(MRA;multi-resolution analysis)을 통해 분해된 배터리의 저주파 전압 성분(approximation;$A_n$) 기반 SOC(State-of-charge) 추정방법을 소개한다. 급격한 전압 변화의 특성을 나타내는 고주파 전압 성분(detail;$D_n$)이 제거되고 저주파 전압 성분만이 SOC 추정을 위해 사용된다. 이 경우 기존 확장 칼만필터(EKF;extended Kalman filter)에서 SOC 추정에러를 개선하기 위해 사용되었던 노이즈 모델의 생략이 가능하여 알고리즘의 복잡성이 개선된다. 개선된 확장 칼만필터 기반 SOC 추정 결과를 통해 제안된 방법을 검증하였다.