• Structural Engineering and Mechanics
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• 제16권3호
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• pp.327-340
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• 2003

Variations in system parameters due to uncertainties of parameters may result in system performance deterioration and create system internal stability problems. Uncertainties in structural modeling of structures are often considered to ensure that the control system is robust with respect to response errors. So the uncertain concept plays an important role in the analysis and design of the engineering structures. In this paper, the active control of the intelligent structures with the uncertainties is studied and a new method for analyzing the robustness of systems with the uncertainties is presented. Firstly, the system with uncertain parameters is considered as the perturbation of the system with deterministic parameters. Secondly, the feedback control law is designed on the basis of deterministic system. Thirdly, perturbation analysis and robustness analysis of intelligent structures with uncertainties are discussed when the feedback control law is applied to the original system and perturbed system. Combining the convex model of uncertainties with the finite element method, the analysis theory of the robustness of intelligent structures with the uncertainties can be developed. The description and computation of the robustness of intelligent structures with uncertain parameters is obtained. Finally, a numerical example of the application of the present method is given to show the validity of the method.

• International Journal of Control, Automation, and Systems
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• 제6권4호
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• pp.506-514
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• 2008

This paper presents an intelligent model; named as free model, approach for a closed-loop system identification using input and output data and its application to design a power system stabilizer (PSS). The free model concept is introduced as an alternative intelligent system technique to design a controller for such dynamic system, which is complex, difficult to know, or unknown, with input and output data only, and it does not require the detail knowledge of mathematical model for the system. In the free model, the data used has incremental forms using backward difference operators. The parameters of the free model can be obtained by simultaneous perturbation stochastic approximation (SPSA) method. A linear transformation is introduced to convert the free model into a linear model so that a conventional linear controller design method can be applied. In this paper, the feasibility of the proposed method is demonstrated in a one-machine infinite bus power system. The linear quadratic regulator (LQR) method is applied to the free model to design a PSS for the system, and compared with the conventional PSS. The proposed SPSA-based LQR controller is robust in different loading conditions and system failures such as the outage of a major transmission line or a three phase to ground fault which causes the change of the system structure.

• Nuclear Engineering and Technology
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• 제21권2호
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• pp.99-110
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• 1989

원자로 지논 농도의 최적 제어는 Linear Quadratic Regulator Problem이다. 지논 농도와 아이오다인 농도는 측정할 수 없기 때문에 최적 제어를 수행하기 위해서는 측정할 수 없는 상태 변수를 예측하는 것이 필요하다. 본 연구에서 사용된 예측방법은 Luenberger Observer를 기초로 했다. 원자로 상태 방정식은 빠른 상태 방정식(중성자 속, 핵연료 및 냉각재 온도)과 느린 상태 방정식(아이오다인, 지논)의 상호작용에 의해 Stiffness 문제가 발생되는데 이러한 시스템을 "Singularly Perturbed System"이라 한다. Stiffness문제를 해결하기 위해서 원 시스템을 느린 시스템과 빠른 시스템의 두 개의 모드로 나누는 Singular Perturbation Method를 사용한다. 예측기Observer를 이용한 원 시스템의 제어기는 느린 시스템과 빠른 시스템에 대한 분리된 예측기와 제어기의 설계에 의해 결정되어진다. 특히 원자로 상태 방정식에서는 빠른 모드는 빨리 사라지게 되므로 단지 느린 시스템에 대해서만 예측기를 설계하면 된다. 컴퓨터시뮬레이션을 통한 시험 결과는 원자로의 지논 진동은 Singular Perturbation Method와 예측기를 이용해서 거의 정확하게 효과적으로 짧은 시간내에 제어할 수 있음을 알았다.수 있음을 알았다.

• Kyungpook Mathematical Journal
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• 제60권3호
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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.

• 대한기계학회논문집A
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• 제22권4호
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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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• 제12권2호
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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.

• 한국음향학회지
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• 제31권1호
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• pp.11-18
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• 2012

본 논문은 경계가 주기적으로 변하는 주름관에 음파가 전파할 때 발생하는 차단주파수밴드 (stopband)를 이론 및 BEM으로 해석한 내용을 다루었다. 2-D 덕트를 고려하였으며 경계가 길이방향의 사인함수로 변하는 주름관에서 주름의 크기가 덕트 높이에 비해 충분히 작은 경우 다중 스케일 섭동법 (Multiple Scaling Perturbation Method)을 이용하여 해를 구하였다. 주파수가 복소수가 되는 조건에서 Bragg 공진과 Non-Bragg 공진에서 발생하는 차단주파수밴드의 형성조건을 구하였다. 2-D BEM 해석을 수행하여 주름관의 삽입손실 (Insertion Loss)을 계산하였으며 이론적으로 예측한 차단주파수밴드의 존재를 확인하였다.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 춘계학술대회논문집
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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.

• 한국통신학회논문지
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• 제22권8호
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• pp.1833-1841
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• 1997

집적광학에서 가장 기본적이고 필수적인 소자인 구형 유전체 도파로는 근사적인 해석방법에서부터 수치계산방법까지 여러가지 방법으로 연구되어왔다. 본 논문에서는 구형 유전체도파로의 해석을 위해 연속적인 섭동궤환방법을 이용하여 최적 등가도파로모델을 선택하고, 시뮬레이션을 통한 비교, 분석 결과, 섭동궤환방법을 이용해서 구한 전파상수가 다른 방법에 의해 얻어진 결과보다 더욱 정확한 값에 일치함으로써 최적의 근사치를 얻을 수 있음을 확인하였고, 또한 여기서 구한 전파 상수를 이용하여 여러 가지 집적광학 소자의 설계에 유용한 필드 특성을 표현하였다.

• 대한기계학회논문집A
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• 제26권4호
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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.