• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2260-2265
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• 2005

In this paper, an active vibration control of a tensioned elastic axially moving string is investigated. The dynamics of the translating string are described by a non-linear partial differential equation coupled with an ordinary differential equation. A time varying control in the form of right boundary transverse motions is proposed in stabilizing the transverse vibrations of the translating continuum. A control law based on Lyapunov's second method is derived. Exponential stability of the closed-loop system is verified. The effectiveness of the proposed controller is shown through simulations.

• Proceedings of the KIEE Conference
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• 2004.07d
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• pp.2438-2440
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• 2004

This study is concerned with development of 3-Dimensional simulator of a biped robot that has a prismatic balancing weight or a revolute balancing weight. The dynamic stability equation of a biped robot which have a prismatic balancing weight is conditional linear but a walking robot's stability equation with a revolute balancing weight is nonlinear. To get a stable gait of a biped robot, stabilization equations with ZMP (Zero Moment Point) are modeled as non-homogeneous second order differential equations for each balancing weight type. A trajectory of balancing weight can be directly calculated with the FDM (Finite Difference Method) solution of the linearized differential equation. In this paper, the 3-Dimensional graphic simulator is programmed to get and calculate the desired ZMP and the actual ZMP. Walking of 4 steps was simulated and verified. This balancing system will be applied to a biped humanoid robot, which consist Begs and upper body, at future work.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.9 no.1
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• pp.41-52
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• 1989

Numerical characteristics for the shallow water equation are analyzed with ADI, Hansen, Heaps, Richtmyer and MacCormack schemes. Stability, CPU time and accuracy are investigated for the linear model which has analytic solutions and circulation is simulated for the nonlinear model. The results show that ADI method has some defects in CPU time and accuracy for the computation of velocity. But ADI method simulates circulation well and has the largest stability region. Richtmyer scheme is the best among the other explicit schemes. Effective viscosity term is found to be essential for numerical experiments of the shallow water equation.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2002.10a
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• pp.440-445
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• 2002

The characteristic equation for regenerative chatter loop including a delay element replaced by a rational function is presented by a linear differential-difference equation, accounting for the dynamics of the AMB controllers, the uncut chip thickness equation and the cutting process as well as the rigid spindle dynamics itself. The chatter stability analysis of a rigid milling spindle suspended by 5-axes active magnetic bearings(AMBs) is also performed to investigate the influences of the damping and stiffness coefficients of AMBs on the chatter free cutting conditions, as they are allowed to vary within the stable region formed by the AMB control gains. Several cutting tests varying the derivative gains of the AMB were performed to investigate the regenerative chatter vibrations, and it was concluded that the theoretical analysis results are in good consistency with the test results.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.289-298
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• 2010

In this paper, we propose a second-order prediction/correction (SPC) domain decomposition method for solving one dimensional linear hyperbolic partial differential equation $u_{tt}+a(x,t)u_t+b(x,t)u=c(x,t)u_{xx}+{\int}(x,t)$. The method can be applied to variable coefficients problems and singular problems. Unconditional stability and error analysis of the method have been carried out. Numerical results support stability and efficiency of the method.

• Journal of the Korean Physical Society
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• v.73 no.12
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• pp.1800-1807
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• 2018

In this paper, we study the gravitational perturbation of traversable wormhole spacetime, especially the Morris-Thorne wormhole spacetime, by using the linearized theory of gravity. We restrict our interest to the first order term and ignore the higher order terms. We assume that the perturbation is axisymmetric. We also assume that the time dependence follows the Fourier decomposition and the angular dependence is expressed in terms of the Legendre functions. As a result, we derive the gravitational perturbation equation of traversable wormhole in terms of a single linear second-order differential equation. As a consequence, we could analyze the unstability of the spacetime with the effective potentials. Furthermore, we consider the interaction between the external gravitational perturbation and the exotic matter, constituting traversable wormholes and its effect on the stability of traversable wormholes.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.10
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• pp.47-55
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• 2003

In the development of positioning device for precision manufacturing and measuring, the friction from mechanical contact causes serious decrease of performance. In this study, we studied about variable reluctance type contact-free linear actuator to overcome drawbacks from friction. In the view of electromagnetics, we analyzed and derived theoretical magnetic force equation and designed structure for generating suspension and propulsion force simultaneously. In the view of dynamics, we derived equation of motion and identified the stability of the system. Finally, we verified the feasibility of the proposed system.

• Proceedings of the KIEE Conference
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• 1991.11a
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• pp.382-385
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• 1991

In order to stabilize linear time-invariant systems with the unknown system matrix, a piecewise constant linear state feedback control law including switching logic is developed. A number of feedback gain matrices are first precomputed by solving the Algebraic Riccati Equation with prescribed degree of stability, and then are switched over in a direction to increase degree of stability. Switching stops when a Lyapunov function shows the decreasing property, and hence switching times are finite.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.4
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• pp.272-280
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• 2023

We study the numerical analysis for the Cahn-Hilliard (CH) equation using the decoupled projection (DP) method. The CH equation is a fourth order nonlinear partial differential equation that is hard to solve. Therefore, various of numerical schemes have been proposed to solve the CH equation. To verify the relation of each existing scheme for the CH equation, we consider the DP method for linear convex splitting schemes. We present the numerical experiments to demonstrate our analysis. Throughout this study, it is expected to construct a novel numerical scheme using the relation with existing numerical schemes.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.4
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• pp.467-476
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• 2017

In this paper, we obtain the stability of the additive-quadratic functional equation f(x+y, z+w)+f(x+y, z-w) = 2f(x, z)+2f(x, w)+2f(y, z)+2f(y, w) and the bi-Jensen functional equation $$4f(\frac{x+y}{2},\;\frac{z+w}{2})=f(x,\;z)+f(x,\;w)+f(y,\;z)+f(y,\;w)$$ in 2-Banach spaces.