• Nuclear Engineering and Technology
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• v.21 no.2
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• pp.99-110
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• 1989

The optimal control of xenon concentration in a nuclear reactor is posed as a linear quadratic regulator problem with state feedback control. Since it is not possible to measure the state variables such as xenon and iodine concentrations directly, implementation of the optimal state feedback control law requires estimation of the unmeasurable state variables. The estimation method used is based on the Luenberger observer. The set of the reactor kinetics equations is a stiff system. This singularly perturbed system arises from the interaction of slow dynamic modes (iodine and xenon concentrations) and fast dynamic modes (neutron flux, fuel and coolant temperatures). The singular perturbation technique is used to overcome this stiffness problem. The observer-based controller of the original system is effected by separate design of the observer and controller of the reduced subsystem and the fast subsystem. In particular, since in the reactor kinetics control problem analyzed in the study the fast mode dies out quickly, we need only design the observer for the reduced slow subsystem. The results of the test problems demonstrated that the state feedback control of the xenon oscillation can be accomplished efficiently and without sacrificing accuracy by using the observer combined with the singular perturbation method.

• Kyungpook Mathematical Journal
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• v.60 no.3
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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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.4
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• pp.916-923
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• 1998

In this paper, an infinite determinant method is presenstd for stability analysis of parametrically excited systems. Unstable regions of the combination parametric resonance as well as principal resonance can be identified with the method. A numerical problem of relatively large amplitude of excitation is solved, and the results of the presented method are compared to those of the multiple scales perturbation method. It is found that the presented method obtains more accurate transition curves which divide stable and unstables in the parameter plane than those of the multiple scales perturbation method.

• Journal of Ship and Ocean Technology
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• v.12 no.2
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• pp.1-15
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• 2008

The main idea of this paper introduce stochastic structural parameters and random dynamic excitation directly into the dynamic functional variational formulations, and developed the nonlinear dynamic analysis of a stochastic variational principle and the corresponding stochastic finite element method via the weighted residual method and the small parameter perturbation technique. An interpolation method was adopted, which is based on representing the random field in terms of an interpolation rule involving a set of deterministic shape functions. Direct integration Wilson-${\theta}$ Method was adopted to solve finite element equations. Numerical examples are compared with Monte-Carlo simulation method to show that the approaches proposed herein are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.

• The Journal of the Acoustical Society of Korea
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• v.31 no.1
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• pp.11-18
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• 2012

In this paper, the occurrence of a stopband phenomenon when an acoustic wave propagates through periodically corrugated ducts is discussed using theoretical and BEM analyses. A 2-D duct with sinusoidally corrugated upper and lower walls is considered. When the magnitude of the sinusoidal corrugation is sufficiently small compared to the duct's height, the wave equation is solved with the multiple scaling perturbation method. Then stopbands for Bragg and non-Bragg resonances are computed from the condition where frequency becomes a complex number. A 2-D BEM analysis is performed to compute insertion loss of the duct, and stopbands are confirmed as predicted by analytical analysis.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.942-947
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• 2001

This paper provides a stability analysis of the transverse vibration of a spinning disk under the torque fluctuation from a permanent magnetic motor. An analytical model has been formulated for a flexible annular disk with its spinning velocity varying harmonically with the same frequency as the cogging torque. A perturbation method based on multiple time scales is applied to perform the stability analysis. Based on expressions for the amplitude and frequency of the parametric excitation, stability boundaries are determined in terms of a nominal spindle velocity, the least common multiple of poles and slots, the magnitude of torque fluctuation and the modal characteristics of. the disk. The stability diagrams predicted by perturbation have been verified numerically using the Floquet theory, which is in good agreement. In conclusion, the fluctuation in spinning velocity is found to affect the stability of the transverse vibration of a rotating disks. The results of this work can be applied to high precision spindle systems such as computer storage systems.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.8
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• pp.1833-1841
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• 1997

Rectangular dielectric waveguides, the most fundamental and indispensible elements in integrated optics, have been investigated by many researchers with various approaching methods including from the relatively approximate techniques to the numerical method. In this paper, the optimum equivalent waveguide model is adopted which is determined by a perturbation feedback process for analyzing the propagation constant by means of computer simulation, we have ascertained that the propagation constant from perturbation feedback method gives the best approximate value because it coincide with more exact value than obtained by other approximating methods. The technique also provides analytical expression for the modal field profile that should be useful in the design of various integrated optical devices.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.4
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• pp.764-774
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• 2002

Dynamic behaviors are analyzed for an automatic ball balancer (ABB) with triple races, which is a device to reduce the unbalanced mass of optical disk drives (ODD) such as CD-ROM or DVD drives. The nonlinear equations of motion are derived by using Lagrange's equations with the polar coordinate system. It is shown that the polar coordinate system provides the complete stability analysis while the rectangular coordinate system used in other previous studies has limitations on the stability analysis. For the stability analysis, the equilibrium positions and the linearized perturbation equations are obtained by the perturbation method. Based on the linearized equations, the stability of the system is analyzed around the equilibrium positions; furthermore, to confirm the stability, the time responses for the nonlinear equations of motion are computed by using a time integration method and experimental analyses are performed. Theoretical and experimental results show a superiority of the ABB with triple races.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.46 no.11
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• pp.902-910
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• 2018

This paper deals with spacecraft intercept problem on non-coplanar elliptical obit considering J2 perturbation. This disturbance addressed in this work is a major factor changing the trajectory of a spacecraft orbiting the Earth. To resolve this issue, a real-time intercept method is proposed. This method is based on the optimization problem which consist of the equation of motion considering spherical earth and impulse, and the optimal solution numerically obtained is set as the direction of the thrust of the interceptor. The position error is resolved by iteratively solving the optimization problem and modifying the direction of thrust of interceptor. The proposed method in this paper is verified by using various numerical examples.

• Nuclear Engineering and Technology
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• v.54 no.6
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• pp.2048-2054
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• 2022

The coolant temperature feedback coefficient is an important parameter of reactor core power control system. To study the coolant temperature feedback coefficient influence on the core power control system of small PWR, the core power control system is built with the nonlinear model and fuzzy control theory. Then, the uncertainty quantification method of reactor core parameters is established based on the Latin hypercube sampling method and the Bootstrap method. Finally, under the conditions of reactivity step perturbation and coolant inlet temperature step perturbation, uncertainty analysis for two cases is carried out. The result shows that with fuzzy controller and fuzzy PID controller, the uncertainty of the coolant temperature feedback coefficient affects the core power control system, and the maximum uncertainties of core relative power, coolant temperature deviation, fuel temperature deviation and total reactivity are acceptable.