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공분산형 ARMA 고속 Transversal 필터에 관한 연구
이철희,장영수,Lee, Chul-Heui,Jang, Young-Soo 한국음향학회 1992 韓國音響學會誌 Vol.11 No.1
적응방식이나 실시간 처리에 적합한 온라인 ARMA 계수추정을 위하여 공분산형 ARMA 고속 transversal 필터 알고리즘을 제안하였다. 제안된 알고리즘은 ARMA 모델의 경우 상관함수 행렬의 이동불변 특성이 각 블록 별로 만족함을 이용하여 ELS(Extended Least Squares)를 공분산형의 경우에 대해 고속 시갱신 알고리즘으로 구현한 것으로서, 알고리즘의 유도에는 사영연산자를 이용한 기하학적 접근방식을 사용하였다. 제안된 알고리즘은 13N+37 MADPR의 연산량을 필요로 하며, AR부분과 MA부분의 차수를 달리할 수 있다. For effective on-line ARMA parameter estimation, a covariance type ARMA fast transversal filter (FTF) algorithm is presented. The proposed algorithm is a covariance type implementation of ELS(Extended Least Squares) estimator and it is a fast time update recursion which is based on the fact that the correlation matrix of ARMA model satisfies the shift invariance property in each sub-block. The geometric approach is used in the derivation of the proposed algorithm. It takes small computational burden of 13N+37 MADPR(Multiplication And Division Per Recursion). Also, AR and MA orders can be independetly and arbitrarily specified.
ARMA고속 transversal 필터의 수리적 안정성 개선
이철희(Chul-Heui Lee),남현도(Hyun-Do Nam) 대한전자공학회 1992 대한전자공학회 학술대회 Vol.1992 No.10
ARMA fast Transversal filter(FTF) algorithm solves the extended least squares estimation problems in a very efficient way. But, unfortunately, it exhibits a very unstable behavior, due to the accumulation of round-off errors. So, in this paper, two effective method to stabilize ARMA FTF algorithm is proposed. They are based on the analysis of the propagation of the numerical errors according to a first order linear model. The proposed methods mod fy the numerical properties of the variables responsible for the numerical instability, while preserving the theoretical form of the algorithm. The proposed algorithms still have the nice complexity properties of the original algorithm, but have a much more stable brhavior.
비선형 시스템 제어를 위한 퍼지 PID 제어기의 설계 및 해석
이철희(Lee Chul Heui),김성호(Kim Sung Ho) 강원대학교 산업기술연구소 2000 産業技術硏究 Vol.20 No.1
Although Fuzzy Logic Controller(FLC) adopted three terms as input gives better performance, FLC is in general composed of two-term control because of the difficulty in the construction of fuzzy rule base. In this paper, a three-term FLC which is similar to PID control but acts as a nonlinear controller is proposed. To reduce the complexity of the rule base design and to increase efficiency. a simplified fuzzy PID control is induced from a hybrid velocity/position type PID algorithm by sharing a common rule base for both fuzzy PI and fuzzy PD parts. It is simple in structure, easy in implementation, and fast in calculation. The phase plane technique is applied to obtain the rule base for fuzzy two-term control and the resultant rule base is Macvicar-Whelan type. And the membership function is a Gaussian function. The frequency response information is used in tuning of the membership functions. Also a tuning strategy for the scaling factors is proposed based on the relationship between PID gain and the scaling factors. Simulation results show better performance and the effectiveness of the proposed method.
금속-Trien 혼합착물의 양이온 교환수지상에서의 분리
박영규,이철희,이무강,Yung-Kyu Park,Chul- Heui Lee,Mu-Kang Lee 대한화학회 1980 대한화학회지 Vol.24 No.2
금속 Cd(II), Cu(II) 및 Pb(II)의 Trien-OH 계에서 ion강도 0.1, $25^{\circ}C{\pm}1$일때 혼합착물에 대한 안정도정수를 폴라그래프에 의해 구하였으며, 이들 혼합착물의 pH변화에 따른 분포상태를 컴퓨터로 계산하여 검토하였다. 또한 Cu(II)와 Cd(II)를 분리하기 위해 양ion 교환수지상에서의 조건분배계수이 이론식을 안정도정수를 이용하여 유도하였으며, pH변화에 따른 Cu(II)와 Cd(II)의 분리최적조건은 pH 9.0이상임을 알았다. EDTA를 가리움제로 하여 Cd(II)-Cu(II)-Trien-EDTA계에서 실험조건을 pH 11.0로 하고 Cu(II)를 Cd(II)로부터 분리한 결과는 만족할만 하였으며 이론치와 잘 일치하였다. The formation constants of the mixed-ligand complexes in the Cd(II), Cu(II) and Pb(II)-Trien-OH system were studied by polarograph. The formation constant $(log{\beta}_{ij})$ was determined at $25^{\circ}C$ in the ionic strength of 0.1. It was also confirmed that the mixed ligand complexes in this system were formed above pH 10.2, 10.5 and 9.0 for Cu(II), Cd(II) and Pb(II) by the calculation of the distribution for complexes at the various pH. Masking of Cd(II) by conversion to anionic EDTA-complexes has been used to separate Cu(II) from Cd(II) through passage of a combined Trien-EDTA solution on an cationic resin column. The optimal condition for the separation of Cu(II) from Cd(II) is confirmed at the pH range above 9.0, not only by considering the theoretical equation of the conditional-exchange-constant of metal on the cation exchange resin,but also by calculating the distribution of the mixed ligand complexes in the resin at the various pH with computer. By analyzing the synthetic sample of Cu(II) and Cd(II) with a EDTA masking at pH 9.5, it is found that the results of the experiment are satisfied with the theoretical value.