• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.6
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• pp.1114-1119
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• 2002

In this paper, the well-conditioned observer is designed to be insensitive to the ill-conditioning factors in transient and steady-state observer performance. A condition number based on 12-norm of the eigenvector matrix of the observer matrix has been proposed on a principal index in the observer performance. For the well-conditioned observer design, the non-normality measure and the observability condition of the observer matrix are utilized. The two constraints are specified into observer gain boundary region that guarantees a small condition number and a stable observer. The observer gain selected in this region guarantees a well-conditioned and observable property. In this study, this method is applied to the Luenberger observer and Kalman filters for small order systems. In designing Kalman filters, the ratio of the process noise covariance to the measurement noise covariance is a design parameter and its effect on the condition number is investigated.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2001.10a
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• pp.313-318
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• 2001

In this paper, the well-conditioned observer is designed to be insensitive to the ill-conditioning factors in transient and steady-state observer performance. A condition number based on $L_2-norm$ of the eigenvector matrix of the observer matrix has been proposed on a principal index in the observer performance. For the well-conditioned observer design, the non-normality measure and the observability condition of the observer matrix are utilized. The two constraints are specified into observer gain boundary region that guarantees a small condition number and a stable observer. The observer gain selected in this region guarantees a well-conditioned and observable property. In this study, this method is applied to the Luenberger observer and Kalman filters. In designing Kalman filters for small order systems, the ratio of the process noise covariance to the measurement noise covariance is a design parameter and its effect on the condition number is investigated.

• Proceedings of the KIEE Conference
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• 1987.11a
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• pp.133-136
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• 1987

This paper presents a new algorithm of optimal measurement system by using band matrix characteristic respectively for state estimation. A performance index of measurement system is established to reflect relation among measurement sets, probability of measurement failure and cost of individual meter installation. Selection ranking in the candidates of measurement sets is composed to guarantee the observability for any any single meter outage. Performance index sensitivity is introduced and recursive formula which based on the matrix inversion lemma used for selection. The proposed algorithm is composed of successive addition algorithm, successive elimination algorithm and combinatorial algorithm. The band matrix characteristic could save in memory requirements and calculate the performance index faster than earlier.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.461-468
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• 2004

Modal participation factor(MPF) is essential to analyze structural response under earthquake load. MPF of real structure differs from that of analytic mathematical model due to the error induced from analytical assumption and construction. In this study, a identification method is proposed to calculate the MPF of real structure based on H∞ optimal model reduction. The MPF is obtained from the relationship between observability, controllability matrix of realized from S.I. and typical 2-degree state space model. The proposed method is verified thorough examples.

• Proceedings of the KIEE Conference
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• 1995.11a
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• pp.523-526
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• 1995

This paper presents an improved algorithm of optimal measurement system design with a reliability evaluation method for a large power system. The proposed algorithm is developed to cosider the observability and to achieve highest accuracy of the state estimator as well with the limited investment cost. When the effect on these dummy bus measurements is considered in the proposed algorithm the other errors in the power system is also detected and then analyzed until to achieve the limited values. By taking advantage of the matrix sparsity and the optimal bus ordering the memory and the time are successfully reduced in the P/C's and workstation's model. The improved program is successfully tested for IEEK sample system and KEPCO system with PSS/E lineflow calculated data package.

• Journal of the Earthquake Engineering Society of Korea
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• v.9 no.1 s.41
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• pp.25-32
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• 2005

Seismic load is distributed to modes of a structure through the modal participation factor(MPF). The modal participation factor is essential to analyze structural response under earthquake load. MPF of a real structure differs from that of analytical mathematical model due to the error induced from analytical assumptions and during the construction. In this study, an identification method is proposed to calculate the 1st MPF of real structure based on $H^{\infty}$ optimal model reduction. The MPF is obtained from the relationship between observability and controllability matrices realized from system identification and those of a prototype 2-degree state space model. The proposed method is verified thorough numerical examples.

• Journal of KSNVE
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• v.4 no.1
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• pp.71-82
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• 1994

We propose a systematic method to select the master states, which are retained in the reduced model after the order reduction process. The proposed method is based on the fact that the range space of right eigenvector matrix is spanned by orthogonal base vectors, and tries to keep the orthogonality of the submatrix of the base vector matrix as much as possible during the reduction process. To quentify the skewness of that submatrix, we define "Absolute Singularity Factor(ASF)" based on its singular values. While the degree of observability is concerned with estimation error of state vector and up to n'th order derivatives, ASF is related only to the minimum state estimation error. We can use ASF to evaluate the estimation performance of specific partial measurements compared with the best case in which all the state variables are identified based on the full measurements. A heuristic procedure to find suboptimal master states with reduced computational burden is also proposed. proposed.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.3
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• pp.184-189
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• 2006

This paper deals with a fractional model reduction for T-S fuzzy systems with time varying delayed states. A contractive coprime factorization of time delayed T-S fuzzy systems is defined and obtained by solving linear matrix inequalities. Using generalized controllability and observability gramians of the contractive coprime factor, a balanced state space realization of the system is derived. The reduced model will be obtained by truncating states in the balanced realization and an upper bound of model approximation error is also presented. In order to demonstrate efficacy of the suggested method, a numerical example is performed.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.41 no.2
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• pp.29-36
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• 2004

This paper deals with a fractional model reduction for linear systems with time varying delayed states. A contractive coprime factorization of linear time delayed systems is defined and obtained by solving linear matrix inequalities. Using generalize controllability and observability gramians of tile contractive coprime factor, a balanced state space realization of the system is derived. The reduced model will be obtained by truncating states in the balanced realization and an upper bound of model approximation error is also presented. In order to demonstrate efficacy of the suggested method, a numerical example is illustrated.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.525-525
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• 2000

In this paper, we present recursive algorithms for state space model identification using subspace extraction via Schur complement. It is shown that an estimate of the extended observability matrix can be obtained by subspace extraction via Schur complement. A relationship between the least squares residual and the Schur complement matrix obtained from input-output data is shown, and the recursive algorithms for the subspace-based state-space model identification (4SID) methods are developed. We also proposed the above algorithm for an instrumental variable (IV) based 4SID method. Finally, a numerical example of the application of the algorithms is illustrated.