• Journal of Mechanical Science and Technology
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• v.18 no.1
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• pp.122-131
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• 2004

A constraint equation-based control law design for large angle attitude maneuvers of flexible spacecraft is addressed in this paper The tip displacement of the flexible spacecraft model is prescribed in the form of a constraint equation. The controller design is attempted in the way that the constraint equation is satisfied throughout the maneuver. The constraint equation leads to a two-point boundary value problem which needs backward and forward solution techniques to satisfy terminal constraints. An observer-based tracking control law takes the constraint equation as the input to the dynamic observer. The observer state is used in conjunction with the state feedback control law to have the actual system follow the observer dynamics. The observer-based tracking control law eventually turns into a stabilized system with inherent nature of robustness and disturbance rejection in LQR type control laws.

• Transactions of the Korean Society of Automotive Engineers
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• v.5 no.1
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• pp.154-161
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• 1997

This paper presents the method to eliminate the constraint reaction in the Lagrange multiplier form equation of motion by using a generalized coordinate driveder from the velocity constraint equation. This method introduces a matrix method by considering the m dimensional space spanned by the rows of the constraint jacobian matrix. The orthogonal vectors defining the constraint manifold are projected to null vectors by the tangential vectors defined on the constraint manifold. Therefore the orthogonal projection matrix is defined by the tangential vectors. For correcting the generalized position coordinate, the optimization problem is formulated. And this correction process is analyzed by the quasi Newton method. Finally this method is verified through 3 dimensional vehicle model.

• Transactions of the Korean Society of Automotive Engineers
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• v.21 no.2
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• pp.122-130
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• 2013

Rail geometries such as cant, grade and curvature can be easily represented by means of a track coordinate system. In this analysis, in order to derive a dynamic and constraint equation of a wheelset, the track coordinate system is used as an intermediate stage. Dynamic and constraint equations of railway vehicle bodies except the wheelset are written in the Cartesian coordinate system as a conventional method. Therefore, whole dynamic equations of a railway vehicle are derived by combining wheelset dynamic equations and dynamic equations of railway vehicle bodies. Constraint equations and constraint Jacobians are newly derived for the track coordinate system. A process for numerical analysis is suggested for the derived dynamic and constraint equations of a railway vehicle. The proposed dynamic analysis of a railway vehicle is validated by comparison against results obtained from VI-RAIL analysis.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.1
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• pp.1-18
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• 2019

In contrast to the well-developed convex splitting schemes for gradient flows of two-component system, there were few efforts on applying the convex splitting idea to gradient flows of multi-component system, such as the vector-valued Cahn-Hilliard (vCH) equation. In the case of the vCH equation, one need to consider not only the convex splitting idea but also a specific method to manage the partition of unity constraint to design an unconditionally energy stable scheme. In this paper, we propose a constrained Convex Splitting (cCS) scheme for the vCH equation, which is based on a convex splitting of the energy functional for the vCH equation under the constraint. We show analytically that the cCS scheme is mass conserving and unconditionally uniquely solvable. And it satisfies the constraint at the next time level for any time step thus is unconditionally energy stable. Numerical experiments are presented demonstrating the accuracy, energy stability, and efficiency of the proposed cCS scheme.

• Transactions of the Korean Society of Pressure Vessels and Piping
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• v.15 no.1
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• pp.71-76
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• 2019

Actual stress distributions in the nozzle of a pressure vessel may not be in plane strain condition, implying that the crack-tip constraint condition may be relaxed in the nozzle. In this paper, a methodology for evaluating the fracture toughness of the ASME Code is presented considering the relaxation of the constraint effect in the nozzle of the reactor pressure vessel. The crack-tip constraint effect is quantified by the T-stress. The equation, which represent the relation between the fracture toughness in the lower constraint condition and the plane strain fracture toughness, is derived using the T-stress. This equation is similar to the method for evaluating the fracture toughness of the Master Curve for low constraint conditions. As a result of evaluating the fracture toughness considering the constraint effect in the reactor inlet, outlet and direct injection nozzles using the proposed equation, it was confirmed that the fracture toughness in the nozzles is higher than the plane strain fracture toughness. Applying the proposed evaluation methodology, it is possible to reflect the relaxation of the constraint effect in the nozzles of the reactor pressure vessel, therefore, the safe operation area on the pressure-temperature limit curve can be prevented from being excessively limited.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.04a
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• pp.661-665
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• 1996

An inverse kinemetics problem of a reclaimer which digs and transports ironstones or coals in the raw yard is investigated. Because of the special features of the reclaimer of which scooping buckets are attached around the rotating drum at the end of boom, kinematic redundancy occurs in determining the joint varialbes For a given reclaiming point in space the forward kinematics yields 3 equations, however the number of involved variables in the equations are four. A plane equation approximating the surface near a reclaiming point is obtained by considering 8 adjacent points surrounding the reclaiming point. One extra equation to overcome redunduncyis further obtained from the condition that the normal vector at a reclaiming point is perpendicular to the plane. An approximate solution for a simplified problem is first discussed, Numerical solution for the oritinal nonlinear porblem with a constraint equation is also investigated. Finally a closed form solution which is not exact but sufficiently close enough is proposed by exploiting geometric constraint.

• Transactions on Control, Automation and Systems Engineering
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• v.4 no.3
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• pp.217-223
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• 2002

The paper presents a single constraint equation of the direct kinematic solution of 6-dof (Stewart-Gough) platforms. Many research works have presented a single polynomial of the direct kinematics for several 6-dof platforms. However, the formulation of the polynomial has potential problems such as complicated formulation procedures and discrimination of the actual solution from all roots. This results in heavy computational burden and time-consuming task. Thus, to overcome these problems, we use a new formulation approach, called the Tetrahedron Approach, to easily derive a single constraint equation, not a polynomial one, of the direct kinematics and use two well-known numerical iterative methods to find the solution of the single constraint equation. Their performance and characteristics are investigated through a series of simulation.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.40 no.2
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• pp.101-107
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• 2012

In this study, Constraint Force Equation Methodology (CFEM) is used to develop a multi-body dynamic analysis program with constraints. Seven constraint models are implemented to analyze constraint motions of multiple bodies. The augmented equations with the constraints are solved with the 4th order Runge-Kutta method for higher degree of accuracy. The analysis code is verified by comparing the analysis results of the motion of bodies with various constraints to published results.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.188-188
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• 2000

The most important problem in target tracking can be said to be modeling the tracking system correctly. Although the simple linear dynamic equation for this model has used until now, the satisfactory performance could not be obtained owing to uncertainties of the real systems in the case of designing the filters baged on the dynamic equations. In this paper, we propose the extended robust Kalman filter (ERKF) which can be applied to the real target tracking system with the parameter uncertainties. A nonlinear dynamic equation with parameter uncertainties is used to express the uncertain system model mathematically, and a measurement equation is represented by a nonlinear equation to show data from the radar in a Cartesian coordinate frame. To solve the robust nonlinear filtering problem, we derive the extended robust Kalman filter equation using the Krein space approach and sum quadratic constraint. We show the proposed filter has better performance than the existing extended Kalman filter (EKF) via 3-dimensional target tracking example.

• Nuclear Engineering and Technology
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• v.23 no.1
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• pp.30-40
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• 1991

For automatic power control of KMRR, a new method, Reactivity Constraint Method, is applied for time optimal control. This method limits the net reactivity to the amount that can be offset by instantaneous control rod action. The reactivity to be constrained for the constant reactor period should be obtained by the dynamic period equation. A new formulation of the dynamic period equation for 2-point kinetics model is presented. A methematical controller model was applied to the plant simulator, KMRSIM to test this control law. The performance test showed that reactivity constraint approach is also a reliable means for reactor power change control.