• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.61 no.1
• /
• pp.117-124
• /
• 2012

In this paper, we present some remarks on the correlations between s and w domains when a discrete-time transfer function is converted from z-plane by using the w-transform. With time response specifications, when a digital filter or controller is designed in z-plane, the w-transform is useful for the purpose if only the w-transformed system closely approximates to the continuous-time system. It will be shown that the approximation is accomplished only in the specific region depending on sampling time. Also, it is noted that such an approximation should be carefully dealt with for the case where a discrete-time reference transfer function is synthesized for the use of direct digital design.

• Honam Mathematical Journal
• /
• v.37 no.4
• /
• pp.487-504
• /
• 2015

For a smooth plane curve, the curvature can be characterized by the rate of change of the angle between the tangent vector and a fixed vector. In this article we prove that the curvature of a space curve can also be given by the rate of change of the locally defined angle between the tangent vector at a point and the nearby point. By using height functions, we introduce turning angle of a space curve and characterize the curvature by the rate of change of the turning angle. The main advantage of the turning angle is that it can be used to characterize the curvature of discrete curves. For this purpose, we introduce a discrete turning angle and a discrete curvature called visual curvature for space curves. We can show that the visual curvature is an approximation of curvature for smooth curves.

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.40 no.8
• /
• pp.774-781
• /
• 1991

This paper proposes an auto-tuning method of a discrete -PIC controllers which is based on the Ziegler and Nichols's PID Tuning Rule. This tunign rule is derived using the Pade's first order approximation and it prevents the performance degradation caused by the time-delay effect of zero order holder when the Ziegler-Nichols tuning rule is applied to a discrete PID controller. A simple and practical auto-tuning method is proposed through combining this discrete tuning rule with the relay control. The auto-tuning scheme is implemented on a microprocessor based system and is applied to a position control system to show the effectiveness of the discrete tuning rule.

• The Pure and Applied Mathematics
• /
• v.12 no.4 s.30
• /
• pp.275-287
• /
• 2005

Geometric invariants are basic tools for geometric processing and computer vision. In this paper, we give a linear approximation for the differentiation of the binormal vector field of a space curve by using the forward and backward differences of discrete binormal vectors. Two kind of discrete torsion, say, back-ward torsion $T_b$ and forward torsion $T_f$ can be defined by the dot product of the (backward and forward) discrete differentiation of binormal vectors that are linear approximations of torsion. Using Frenet formula and Taylor series expansion, we give error estimations for the discrete torsions. We also give numerical tests for a curve. Notably the average of $T_b$ and $T_f$ looks more stable in errors.

• Journal of the Korean Mathematical Society
• /
• v.59 no.3
• /
• pp.519-548
• /
• 2022

In this paper, a stabilized-penalized collocated finite volume (SPCFV) scheme is developed and studied for the stationary generalized Navier-Stokes equations with mixed Dirichlet-traction boundary conditions modelling an incompressible biological fluid flow. This method is based on the lowest order approximation (piecewise constants) for both velocity and pressure unknowns. The stabilization-penalization is performed by adding discrete pressure terms to the approximate formulation. These simultaneously involve discrete jump pressures through the interior volume-boundaries and discrete pressures of volumes on the domain boundary. Stability, existence and uniqueness of discrete solutions are established. Moreover, a convergence analysis of the nonlinear solver is also provided. Numerical results from model tests are performed to demonstrate the stability, optimal convergence in the usual L² and discrete H¹ norms as well as robustness of the proposed scheme with respect to the choice of the given traction vector.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
• /
• 2002.09a
• /
• pp.17.2-17
• /
• 2002

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.17 no.8
• /
• pp.1963-1970
• /
• 1993

A simple technique to decouple the modal equations of motion of a linear nonclassically damped system is to neglect the off-diagonal elements of the modal damping matrix. This is called the decoupling approximation. It has generally been conceived that smallness of off-diagonal elements relative to the diagonal ones would validate its use. In this study, the relationship between elements of the modal damping matrix and the error arising from the decoupling approximation is explored. It is shown that the enhanced diagonal dominance of the modal damping matrix need not diminish the error. In fact, the error may even increase. Moreover, the error is found to be strongly dependent on the exitation. Therefore, within the practical range of engineering applications, diagonal dominance of the modal damping matrix would not be sufficient to supress the effect of modal coupling.

• Interaction and multiscale mechanics
• /
• v.2 no.3
• /
• pp.295-319
• /
• 2009

In this work, we discuss a reproducing kernel collocation method (RKCM) for solving $2^{nd}$ order PDE based on strong formulation, where the reproducing kernel shape functions with compact support are used as approximation functions. The method based on strong form collocation avoids the domain integration, and leads to well-conditioned discrete system of equations. We investigate the convergence and the computational complexity for this proposed method. An important result obtained from the analysis is that the degree of basis in the reproducing kernel approximation has to be greater than one for the method to converge. Some numerical experiments are provided to validate the error analysis. The complexity of RKCM is also analyzed, and the complexity comparison with the weak formulation using reproducing kernel approximation is presented.

• Proceedings of the Korean Society of Broadcast Engineers Conference
• /
• 1996.06b
• /
• pp.61-66
• /
• 1996

In this paper, an efficient contour coding algorithm incorporating polygonal approximation and discrete sine transform is introduced. Contour information is inevitable in content based coding, and polygonal approximation method is widely used to compress the contour information. However polygonal approximation method is not suitable when fine contour is needed. We show that the error signal of polygonal approximation can be efficiently represented using DST, that is, the contour information can be represented accurately with polygons and DST coefficients. With this contour coding scheme, the required bits to represent a contour can be reduced by about 40-50% with virtually no degradation compared to the existing chain coding method.

• Journal of Korean Institute of Industrial Engineers
• /
• v.42 no.2
• /
• pp.86-95
• /
• 2016

We propose a new approach to the stochastic version of Lanchester model. Commonly used approach to stochastic Lanchester model is through the Markov-chain method. The Markov-chain approach, however, is not appropriate to high dimensional heterogeneous force case because of large computational cost. In this paper, we propose an approximation method of stochastic Lanchester model. By matching the first and the second moments, the distribution of each unit strength can be approximated with multivariate normal distribution. We evaluate an approximation of discrete Markov-chain model by measuring Kullback-Leibler divergence. We confirmed high accuracy of approximation method, and also the accuracy and low computational cost are maintained under high dimensional heterogeneous force case.