• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.215-228
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• 2007

By using the variational calculus of fractional order, one derives a Hamilton-Jacobi equation and a Lagrangian variational approach to the optimal control of one-dimensional fractional dynamics with fractional cost function. It is shown that these two methods are equivalent, as a result of the Lagrange's characteristics method (a new approach) for solving non linear fractional partial differential equations. The key of this results is the fractional Taylor's series $f(x+h)=E_{\alpha}(h^{\alpha}D^{\alpha})f(x)$ where $E_{\alpha}(.)$ is the Mittag-Leffler function.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1987년도 한국자동제어학술회의논문집(한일합동학술편); 한국과학기술대학, 충남; 16-17 Oct. 1987
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• pp.932-938
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• 1987

The dynamic equations of robotic manipulators can be derived from either Newton-Euler equation or Lagrangian equation. Model parameters which appear in the resulting dynamic equation are the nonlinear functions of both the inertial parameters and the geometric parameters of robotic manipulators. The identification of the model parameters is important for advanced robot control. In the previous methods for the identification of the model parameters, the geometric parameters are required to be predetermined, or the robotic manipulators are required to follow some special motions. In this paper, we propose an approach to the identification of the model parameters, in which prior knowledge of the geometric parameters is not necessary. We show that the estimation equation for the model parameters can be formulated in an upper block triangular form. Utilizing the special structures, we obtain a simplified least-square estimation algorithm for the model parameter identification. To illustrate the practical use of our method, a 4DOF SCARA robot is examined.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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• pp.1082-1087
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• 2003

In this paper, we address the development of magnetic levitation positioning system. This planar magnetic levitator employs four permanent magnet liner motors. Each motor generates vertical force for suspension against gravity, as well as horizontal force for drive levitation object called a platen This stage can generate six degrees of freedom motion by the vertical and horizontal force. We derived the mechanical dynamics equation using lagrangian method and used coenergy to express an electromagnetic force. We proposed control algorithm for the position and posture control from its initial value to its desired value using sliding mode control. Some simulation result is provided to verify the effectiveness of the proposed control scheme.

• Journal of Advanced Marine Engineering and Technology
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• 제28권6호
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• pp.906-915
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• 2004

In this paper, we address the development of magnetic levitation positioning system. This planar magnetic levitator employs four permanent magnet liner motors. Each motor generates vertical force for suspension against gravity, as well as horizontal force for driving levitation object called a platen. This stage can generate six degrees of freedom motion by the vertical and horizontal force. We derived the mechanical dynamics equation using Lagrangian method and used coenergy to express an electromagnetic force. We proposed a control algorithm for the position and posture control from its initial value to its desired value using sliding mode control. Some simulation results are provided to verify the effectiveness of the proposed control scheme.

• 한국군사과학기술학회지
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• 제11권5호
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• pp.116-123
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• 2008

Hydrocodes are large computer programs that can be used to solve a wide variety of highly transient problems such as high-speed impact and explosion events. This paper describes the recent activity to develop a Multi-material hydrocode in Korea. The code consists of two stages; Lagrangian, and remap stages. Although a sophisticated contact algorithm has been developed for Lagrangian calculations, a relatively simple mechanics at the interfaces of materials are used in the multi-material Eulerian code. Volume of fluid interface reconstruction methods are used to resolve the interfaces between different materials. For the advection stage of the cell centered properties, one-dimensional hyperbolic equation is used. Test problems demonstrated here are the high-speed impact/penetration and explosion problems.

• 한국전산유체공학회지
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• 제12권4호
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• pp.14-19
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• 2007

We present a direct numerical simulation technique and some preliminary results of the capillary spreading of a droplet containing particles on the solid substrate. We used the level-set method with the continuous surface stress for description of droplet spreading with interfacial tension and employed the discontinuous Galerkin method for the stabilization of the interface advection equation. The distributed Lagrangian-multipliers method has been combined for the implicit treatment of rigid particles. We investigated the droplet spreading by the capillary force and discussed effects of the presence of particles on the spreading behavior. It has been observed that a particulate drop spreads less than the pure liquid drop. The amount of spread of a particulate drop has been found smaller than that of the liquid with effectively the same viscosity as the particulate drop.

• 대한기계학회논문집
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• 제11권2호
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• pp.222-233
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• 1987

본 논문에서는 이와 관련하여 전형적인 중장비 구동체계를 대상으로 동적모델 을 유도하는 일련의 과정을 제시하고 구동체계의 효율적 제어를 위한 간략화된 모델을 유도하였다.

• Steel and Composite Structures
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• 제32권3호
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• pp.293-304
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• 2019

In the present paper, the element free Galerkin (EFG) method is developed for geometrically nonlinear analysis of deep beams considering small scale effect. To interpret the behavior of structure at the nano scale, the higher-order gradient elasticity nonlocal theory is taken into account. The radial point interpolation method with high order of continuity is used to construct the shape functions. The nonlinear equation of motion is derived using the principle of the minimization of total potential energy based on total Lagrangian approach. The Newmark method with the small time steps is used to solve the time dependent equations. At each time step, the iterative Newton-Raphson technique is applied to minimize the residential forces caused by the nonlinearity of the equations. The effects of nonlocal parameter and aspect ratio on stiffness and dynamic parameters are discussed by numerical examples. This paper furnishes a ground to develop the EFG method for large deformation analysis of structures considering small scale effects.

• 한국강구조학회 논문집
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• 제10권3호통권36호
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• pp.393-406
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• 1998

본 연구는 수평보강된 직교이방성판의 좌굴거동에 관한 것으로서 면내 선형분포하중을 받는 수평보강된 직교이방성판의 좌굴해석식을 Rayleigh-Ritz법을 사용하여 유도하였으며 보강재의 위치에 따른 좌굴응력의 상한치를 Lagrangian multiplier법을 사용하여 결정하였다. 판의 네 변은 단순지지되어 있다고 가정하였으며, 보강재는 보요소로 간주하였다. 유도된 식을 사용하여 보강재와 판의 폭비와 보강재의 위치를 변화시켜가며 좌굴해석을 수행한 결과 면내 선형분포하중을 받는 네 변이 단순지지된 수평보강된 직교이방성판의 효과적인 보강재의 설치 위치는 판의 좌굴응력의 상한치가 최대가 되는 위치임을 알 수 있었다.

• 한국대기환경학회지
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• 제22권1호
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• pp.73-84
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• 2006

Hazardous Air Pollutants (HAPs) are characterized by being relatively heavier and denser than that of ambient air due to the various reasons such as higher molecular weight, low temperature and other complicated chemical transformations (Witlox, 1994). In an effort to investigate transport and diffusion from instantaneous emission of heavy gas, Lagrangian Particle Dispersion Model (LPDM) coupled with the RAMS output was employed. Both deposition process and buoyancy term were added on the atmospheric diffusion equations of LPDM, and the locations and concentrations of dense gas particle released from instantaneous single point source (emitting initially for 10 minutes only) were analyzed. The result overall shows that adding deposition process and buoyancy terms on the diffusion equation of LPDM has very small but detectable effect on the vertical and horizontal distribution of Lagrangian particles that especially transported for a fairly long traveling time. Also the slumping of dense gas can be found to be ignored horizontally compared to the advection by the horizontal wind suggesting that it was essential to couple the Lagrangian particle dispersion model coupled with the RAMS model in order to explain the dispersion of HAPs more accurately. However, during the initial time of instantaneous emission, buoyancy term play an important role on the vertical locations of dense particles for near surface atmosphere and around source area, indicating the importance of densities of HAPs in the beginning stage or short duration for the risk assessment of HAPs or management of heavy vapors during the explosive accidents.