• 대한전기학회:학술대회논문집
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• 대한전기학회 1987년도 전기.전자공학 학술대회 논문집(I)
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• pp.195-197
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• 1987

A new method of model reduction, based on the differentiation of polynomials, is Introduced by Gutman(1982). Without the reciprocal transformation, and the differentiation of the numerator and denominator polynomials of the transfer function, used by Gutman, the lower-order system can be obtained by the permutation of the order of numerator and denominator and the number of differentiation.

• 한국정보통신학회논문지
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• 제5권7호
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• pp.1346-1353
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• 2001

본 논문에서는 2차원 분모분리형 디지털 필터의 선계에 대한 알고리즘을 제안한다. 제안된 알고리즘은 진폭 특성과 위상특성으로 주어진 2차원 디지털 필터의 주파수 영역 설계명세조건을 특이치 분해를 이용하여 1차원 디지털 필터의 설계명세조건으로 분해한다. 따라서, 2차원 디지털 필터 설계문제는 1차원 디지털 필터의 설계 문제로 귀착되며 이는 계산적으로 유효하며 수치적으로 안정한 설계법으로 고려되며 설계 예로부터 유효성을 확인한다.

• 대한수학회논문집
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• 제8권2호
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• pp.169-180
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• 1993

• Structural Engineering and Mechanics
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• 제75권3호
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• pp.311-325
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• 2020

In applying the spectral stochastic finite element methods to the frequency response analysis, the conventional methods are known to give unstable and inaccurate results near the natural frequencies. To address this issue, a new sensitivity based stabilized formulation for stochastic frequency response analysis is proposed in this paper. The main difference over the conventional spectral methods is that the polynomials of random variables are applied to both numerator and denominator in approximating the harmonic response solution. In order to reflect the resonance behavior of the structure, the denominator polynomials is constructed by utilizing the natural frequency sensitivity and the random mode superposition. The numerator is approximated by applying a polynomial chaos expansion, and its coefficients are obtained through the Galerkin or the spectral projection method. Through various numerical studies, it is seen that the proposed method improves accuracy, especially in the vicinities of structural natural frequencies compared to conventional spectral methods.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1986년도 한국자동제어학술회의논문집; 한국과학기술대학, 충남; 17-18 Oct. 1986
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• pp.119-122
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• 1986

An algorithm is proposed to find a stable rational function, which is frequently used in the linear system theory, by curve-fitting a given data. This problem is essentially a nonolinear optimization problem. In order to converge faster to the solution, the following method is used. First, the coefficients of the denominator polynomial are fixed and only the coefficients of the numerator polynomial are adjusted by its linear relationships. Then the coefficients of the numerator are fixed and the coefficients of the denominator polynomial are adjusted by nonlinear programming. This whole process is repeated until a convergent solution is found. The solution obtained by this method converges better than by other algorithms and its versatility is demonstrated by applying it to the design of a feedback control system and a low pass filter.

• 대한전기학회논문지
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• 제36권4호
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• pp.280-286
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• 1987

A new method is presented for obtaining redced-order model for time-invariant systems. This method does not require the calculation of the reciprocal transformation, the alpha table, the beta-table and the alpha-beta expansion which should be calculated in Routh approximation method, hence it is computationally very attractive better than Routh approximation method, furthemore the stability of the reduced-order model is guaranted if the original system is stable. This method starts with the continued fraction espansion of auxiliary denominator polynomial give for the denominator polynomial of the reduced-order model. The coefficients of the numerator polynomial are then obtained by equating moment of the original and the reduced-order medel.

• 제어로봇시스템학회논문지
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• 제10권3호
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• pp.205-215
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• 2004

The characteristic ratio assignment (CRA) method〔1〕 is new polynomial approach which allows to directly address the transient responses such as overshoot and speed of response time in time domain specifications. The method is based on the relationships between time response and characteristic ratios($\alpha_i$ ) and generalized time constant (T), which are defined in terms of coefficients of characteristic polynomial. However, even though the CRA can apply to developing a linear controller that meets good transient responses, there are still some fundamental questions to be explored. For the purpose of this, we have analyzed several sensitivities of a linear system with respect to the changes of coefficients itself and $\alpha_i$ of denominator polynomial. They are (i) the unnormalized root sensitivity : to determine how the poles change as $\alpha_i$ changes, and (ii) the function sensitivity to determine the sensitivity of step response to the change of o, and to analyze the sensitivity of frequency response as o, changes. As an other important result, it is shown that, under any fixed T and coefficient of the lowest order of s in denominator, the step response is dominantly affected merely by $\alpha_1, alpha_2 and alpha_3$ regardless of the order of denominator higher than 4. This means that the rest of the$\alpha_i$ s have little effect on the step response. These results provide some useful insight and background theory when we select $\alpha_i$ and T to compose a reference model, and in particular when we design a low order controllers such as PID controller.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제26권3호
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• pp.125-140
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• 2023

초등학교 수학에서 분수의 연산은 매우 중요하지만 학생들이 어려워하는 개념이다. 분수 연산의 기초가 되는 동분모 분수의 덧셈과 뺄셈에 대하여 현행 2015 개정 교육과정에 따른 국정 교과서 1종, 검정 교과서 10종을 분석하여 단원의 차시 흐름과 시각적 표현을 분석하였다. 분석결과, 각각의 교과서마다 나름의 순서와 차시 주제를 고민하여 단원을 구성하고 있었으며 비교적 충실하게 교육과정을 반영하였다. 또한, 각각의 교과서마다 사용하는 시각적 표현의 종류와 개수가 다르게 나타났으며 이는 분수의 연산 학습을 돕기 위하여 시각적 표현의 일관성 또는 다양성을 의도한 것으로 보인다. 각 교과서의 차시 구성 및 시각적 표현의 특성을 파악한다면 더욱 효과적으로 분수의 연산을 지도할 수 있을 것이다.

• Journal of Preventive Medicine and Public Health
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• 제38권2호
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• pp.147-153
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• 2005

Objectives: Studies on the geographical differences in mortality tend to use a census population, rather than a registration population, as the denominator of mortality rates in South Korea. However, an administratively determined registration population would be the logical denominator, as the geographical areas for death certificates (numerator) have been determined by the administratively registered residence of the deceased, rather than the actual residence at the time of death. The purpose of this study was to examine the differences in the total number of a district population, and the associated district-specific mortality indicators, when two different measures as a population denominator (census and registration) were used. Methods: Population denominators were obtained from census and registration population data, and the numbers of deaths (numerators) were calculated from raw death certificate data. Sex- and 5-year age-specific numbers for the populations and deaths were used to compute sex- and age-standardized mortality rates (by direct standardization methods) and standardized mortality ratios (by indirect standardization methods). Bland-Altman tests were used to compare district populations and district-specific mortality indicators according to the two different population denominators. Results : In 1995, 9 of 232 (3.9%) districts were not included in the 95% confidence interval (CI) of the population differences. A total of 8 (3.4%) among 234 districts had large differences between their census and registration populations in 2000, which exceeded the 95% CI of the population differences. Most districts (13 of 17) exceeding the 95% CI were rural. The results of the sex- and age-standardized mortality rates showed 15 (6.5%) and 16 (6.8%) districts in 1995 and 2000, respectively, were not included in the 95% CI of the differences in their rates. In addition, the differences in the standardized mortality ratios using the two different population denominators were significantly greater among 14 districts in 1995 and 11 districts in 2002 than the 95% CI. Geographical variations in the mortality indicators, using a registration population, were greater than when using a census population. Conclusion: The use of census population denominators may provide biased geographical mortality indicators. The geographical mortality rates when using registration population denominators are logical, but do not necessarily represent the exact mortality rate of a certain district. The removal of districts with large differences between their census and registration populations or associated mortality indicators should be considered to monitor geographical mortality rates in South Korea.

• 제어로봇시스템학회지
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• 제1권1호
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• pp.50-50
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• 1995

It has been pointed out in the literature that the Routh approximation method for order reduction has limitations in treating transfer functions with the denominator-numerator order difference not equal to one. The purpose of this paper is to present a new algorithm based on the Routh approximation method that can be applied to general rational transfer functions, yielding reduced models with arbitrary order.