• The Transactions of the Korean Institute of Electrical Engineers A
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• v.54 no.2
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• pp.67-72
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• 2005

In conventional small signal stability analysis, system is assumed to be invariant and the state space equations are used to calculate the eigenvalues of state matrix. However, when a system contains switching elements such as FACTS devices, it becomes non-continuous system. In this case, a mathematically rigorous approach to system small signal stability analysis is by means of eigenvalue analysis of the system periodic transition matrix based on discrete system analysis method. In this paper, RCF(Resistive Companion Form) method is used to analyse small signal stability of a non-continuous system including switching elements. Applying the RCF method to the differential and integral equations of power system, generator, controllers and FACTS devices including switching elements should be modeled in the form of state transition equations. From this state transition matrix eigenvalues which are mapped to unit circle can be calculated.

• KIEE International Transactions on Power Engineering
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• v.5A no.4
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• pp.344-349
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• 2005

In conventional small signal stability analysis, the system is assumed to be invariant and the state space equations are used to calculate the eigenvalues of the state matrix. However, when a system contains switching elements such as FACTS equipments, it becomes a non-continuous system. In this case, a mathematically rigorous approach to system small signal stability analysis is performed by means of eigenvalue analysis of the system's periodic transition matrix based on the discrete system analysis method. In this paper, the RCF (Resistive Companion Form) method is used to analyze the small signal stability of a non-continuous system including switching elements. Applying the RCF method to the differential and integral equations of the power system, generator, controllers and FACTS equipments including switching devices should be modeled in the form of state transition equations. From this state transition matrix, eigenvalues that are mapped into unit circles can be computed precisely.

• Proceedings of the KIEE Conference
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• summer
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• pp.342-344
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• 2004

In conventional small signal stability analysis, system is assumed to be invariant and the state space equations are used to calculate the eigenvalues of state matrix. However, when a system contains switching elements such as FACTS devices, it becomes non-continuous system. In this case, a mathematically rigorous approach to system small signal stability analysis is by means of eigenvalue analysis of the system periodic transition matrix based on discrete system analysis method. In this research, RCF(Resistive Companion Form) method is used to analyse small signal stability of a non-continuous system including switching elements'. Applying the RCF method to the differential and integral equations of power system, generator, controllers and FACTS devices including switching elements should be modeled in the form of state transition matrix. From this state transition matrix eigenvalues which are mapped to unit circle can be calculated.

• Proceedings of the KIEE Conference
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• 1998.07c
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• pp.1027-1029
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• 1998

The method of building the system state matrix described here is the direct method which constructs elements of state matrix directly by the algebraic expressions from the machine data with time constants. From this method, it is reasonable to confirm the structure of state matrix and the relation of submatrices and elements efficiently. In this paper the interrelationship of submatrices of system matrix is investigated and a constitution of system matrix considering time constants.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.8
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• pp.1434-1439
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• 2008

Numerical methods for solving the state feedback control problem of linear time invariant system are presented in this paper. The methods are based on Haar wavelet approximation. The properties of Haar wavelet are first presented. The operational matrix of integration and its inverse matrix are then utilized to reduce the state feedback control problem to the solution of algebraic matrix equations. The proposed methods reduce the computation time remarkably. Finally a numerical example is illustrated to demonstrate the validity and applicability of the proposed methods.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.2
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• pp.608-616
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• 2018

If a general nonlinear system is linearized by the successive multiplication of the 1st and 2nd order systems, then there are four types of poles in this linearized system: the pole of the 1st order system and the equal poles, two distinct real poles, and complex conjugate pair of poles of the 2nd order system. Linear Quadratic (LQ) control is a method of designing a control law that minimizes the quadratic performance index. It has the advantage of ensuring the stability of the system and the pole placement of the root of the system by weighted matrix adjustment. LQ control by the weighted matrix can move the position of the pole of the system arbitrarily, but it is difficult to set the weighting matrix by the trial and error method. This problem can be solved using the characteristic equations of the Hamiltonian system, and if the control weighting matrix is a symmetric matrix of constants, it is possible to move several poles of the system to the desired closed loop poles by applying the control law repeatedly. The paper presents a method of calculating the state weighting matrix and the control law for moving the equal poles with Jordan blocks to two real poles using the characteristic equation of the Hamiltonian system. We express this characteristic equation with a state weighting matrix by means of a trigonometric function, and we derive the relation function (${\rho},\;{\theta}$) between the equal poles and the state weighting matrix under the condition that the two real poles are the roots of the characteristic equation. Then, we obtain the moving-range of the two real poles under the condition that the state weighting matrix becomes a positive semi-finite matrix. We calculate the state weighting matrix and the control law by substituting the two real roots selected in the moving-range into the relational function. As an example, we apply the proposed method to a simple example 3rd order system.

• Journal of the Korean Institute of Telematics and Electronics
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• v.22 no.3
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• pp.91-94
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• 1985

A method optimizing selection of a state weighting matrix is presented. The state weight-ing matrix is chosen so that the closed-loop system responses closely match to the ideal model responses. An algorithm is presented which determines a positive semidefinite state weighting matrix in the linear quadratic optimal control design problem and an numerical example is given to show the effect of the present algorithm.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.225-228
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• 1992

The purpose of this project is the presentation of new method for selection of a scalar control of linear time-periodic system. The approach has been proposed by Radziszewski and Zaleski [4] and utilizes the quadratic form of Lyapunov function. The system under consideration is assigned either in closed-loop state or in modal variables as in Calico, Wiesel [1]. The case of scalar control is considered, the gain matrix being assumed to be at worst periodic with the system period T, each element being represented by a Fourier series. As the optimal gain matrix we consider the matrix ensuring the minimum value of the larger real part of the two Poincare exponents of the system. The method, based on two-step optimization procedure, allows to find the approximate optimal gain matrix. At present state of art determination of the gain matrix for this case has been done by systematic numerical search procedure, at each step of which the Floquet solution must be found.

• Journal of the Korean Operations Research and Management Science Society
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• v.16 no.2
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• pp.128-147
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• 1991

We propose a dynamic incidence matrix (DIM) for reflecting states and time conditions of a timed Petri net (TPN) explicitly. Since a DIM consists of a conventional incidence matrix, two time-related vectors and two state-related vectors, we can get the advantages inherent in the conventional incidence matrix of describing a static structure of a system as well as another advantage of expressing time dependent state transitions. We introduce an algorithm providing the DIM with a state transition mechanism. Because the algorithm is, in fact, an algorithmic model for discrete event simulation of TPN models, we provide a theoretical basis of model transformation of a TPN model into a DEVS(Discrete Event system Specification) model. By executing the algorithm we can carry out performance analysis of computer communication protocols which are represented TPN models.

• Journal of Korean Society for Quality Management
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• v.20 no.1
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• pp.11-21
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• 1992

The Purpose of this paper contribute to design the multistate Markov process for the reliability of a system when the transition-rates of each unit depend on the current state of the system. The system transition-rate matrix has the form of the kronecker sum of transition rate matrices for the units, is analyzed and investigated. As a result, the system which has the state-dependent units is detaily analyzed and introduced by the approach of an algorithm for the system transition-rate matrix based on the kronecker algebra.