• International Journal of Control, Automation, and Systems
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• 제6권2호
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• pp.160-170
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• 2008

Temperature control of an enclosed thermal system which has many applications including Rapid Thermal Processing (RTP) of semiconductor wafers showed an input-constraint violation for nonlinear controllers due to inherent strong coupling between the elements [1]. In this paper, a constrained nonlinear optimal control design is developed, which accommodates input constraints using the linear algebraic equivalence of the nonlinear controllers, for the temperature control of an enclosed thermal process. First, it will be shown that design of nonlinear controllers is equivalent to solving a set of linear algebraic equations-the linear algebraic equivalence of nonlinear controllers (LAENC). Then an input-constrained nonlinear optimal controller is designed based on that LAENC using the constrained linear least squares method. Through numerical simulations, it is demonstrated that the proposed controller achieves the equivalent performances to the classical nonlinear controllers with less total energy consumption. Moreover, it generates the practical control solution, in other words, control solutions do not violate the input-constraints.

• 한국수학교육학회:학술대회논문집
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• 한국수학교육학회 2010년도 제44회 전국수학교육연구대회
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• pp.13-15
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• 2010

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제29권4호
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• pp.699-722
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• 2015

본 연구의 목적은 라그랑주의 방정식론을 바탕으로 한 방정식의 해법을 고등학교 1학년 수업에 적용하여 방정식의 해법과 관련한 근과 계수의 관계와 대칭성의 의의를 인식하게 하는 것이다. 대칭성은 라그랑주의 방정식론의 핵심 아이디어이며, 근과 계수의 관계는 그의 해법에 있어 중요한 수단이다. 학생들은 수업을 통해 근과 계수의 관계에 대한 학습 의의를 인식하였고, 대칭성의 아이디어를 이해하였으며, 새로운 해법에 흥미를 나타내었다. 이러한 연구는 학교수학에서 다루는 국소적인 방정식의 해법만이 아닌 교수학적 조직화에 의한 체계적인 방정식론에 대한 경험을 주며, 방정식의 해법과 관련한 지식들의 연결성을 이해하게 한다.

• 경영과학
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• 제12권2호
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• pp.63-75
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• 1995

The uncapacitated facility location problem considered here is to determine facility location sites, minimizing the total cost of establishing facilities and serving customer demand points which require primary and back-up services. To solve this problem effectively, we propose two things in this study. First, we propose an idea of Benders' decomposition approach as a solution method of the problem. Second, we implement the problem on GAMS. Using GAMS (general Algebraic Modeling System) can utilize an mixed-integer programming solver such as ZOOM/XMP and provide a completely general automated implementation with a proposed solution method.

• 한국정밀공학회지
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• 제12권5호
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• pp.57-68
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• 1995

A general procedure for the numerical solution of coupled, nonlinear, differential two-point boundary-value problems, solutions of which are crucial to the controller design, has been developed and demonstrated. A fixed-end-points, free-terminal-time, optimal-control problem, which is derived from Pontryagin's Maximum Principle, is solved by an extension of Davidenko's method, a differential form of Newton's method, for algebraic root finding. By a discretization process like finite differences, the differential equations are converted to a nonlinear algebraic system. Davidenko's method reconverts this into a pseudo-time-dependent set of implicitly coupled ODEs suitable for solution by modern, high-performance solvers. Another important advantage of Davidenko's method related to the time-optimal problem is that the terminal time can be computed by treating this unkown as an additional variable and sup- plying the Hamiltonian at the terminal time as an additional equation. Davidenko's method uas used to produce optimal trajectories of a single-degree-of-freedom problem. This numerical method provides switching times for open-loop control, minimized terminal time and optimal input torque sequences. This numerical technique could easily be adapted to the multi-point boundary-value problems.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1992년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 19-21 Oct. 1992
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• pp.680-685
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• 1992

Solar arrays and antennas of the satellite are usually stowed within the dimensions of the launch-vehicle fairing and deployed in the orbit. To solve such multibody dynamic problems, differential equations and algebraic equations are simultaneously solved, and special solution techniques are required. In this paper, Lagrange multipliers associated with the constraints are iteratively computed by monotonically reducing an appropriately defined constraint error vector, and the resulting equation of motion is solved by a well-established ODE technique. Defomable bodies as well as rigid bodies are treated, and applications to satellite solar arrays are explained.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1992년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 19-21 Oct. 1992
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• pp.742-746
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• 1992

This paper proposes a new linear robust state feedback controller for the linear discrete time systems which have uncertainties in the state and input matrices. The uncertainties need not satisfy the matching conditions, but only their bounds are needed to be known. The proposed controller is derived from the linear quadratic game problem, which solution is obtained via the modified algebraic Riccati equation. The controller guarantees the robust performance bound. The bound of the solution and the condition of the uncertainties, which can stabilize the uncertain system are explored.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2003년도 춘계 학술발표회 논문집
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• pp.25-30
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• 2003

We prove that the logarithm of the flow of stochastic differential equations is an element of the free Lie algebra generated by a finite set consisting of vector fields being coefficients of equations. As an application, we directly obtain a formula of the solution of stochastic differential equations given by Castell(1993) without appealing to an expansion for ordinary differential equations given by Strichartz (1987).

• Coupled systems mechanics
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• 제9권6호
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• pp.563-573
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• 2020

Dynamic responses of a laminated composite cantilever beam under a harmonic are investigated in this study. The governing equations of problem are derived by using the Lagrange procedure. The Timoshenko beam theory is considered and the Ritz method is implemented in the solution of the problem. The algebraic polynomials are used with the trivial functions for the Ritz method. In the solution of dynamic problem, the Newmark average acceleration method is used in the time history. In the numerical examples, the effects of load parameter, the fiber orientation angles and stacking sequence of laminas on the dynamic responses of the laminated beam are investigated.

• 대한기계학회논문집A
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• 제21권5호
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• pp.707-718
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• 1997

This paper presents an efficient numerical method for the computation of eigenpair derivatives for a real symmetric eigenvalue problem with distinct and multiple eigenvalues. The method has a very simple algorithm and gives an exact solution. Furthermore, it saves computer sotrage and CPU time. The algorithm preserves not only the symmetricity but also the band width of the matrices, allowing efficient computer storage and solution techniques. Results from the proposed method for calculating the eigenpair derivatives are compared with those from Rudisill and Chu's method and Nelson's method which is known efficient one in the case of distinct natural frequencies. As an example to demonstrate the efficiency of the proposed method in the case of distinct eigenvalues, a cantilever plate is considered. The design parameter of the cantilever plate is its thickness. For the eigenvalue problem with multiple natural frequencies, the adjacent eigenvectors are used in the algebraic equation as side conditions, lying adjacent to the multiplicity of multiple natural frequency distinct eigenvalues, which appear when design parameter varies. A cantilever beam is used to demonstrate the efficiency of the proposed method in the case of multiple natural frequencies. Results form the proposed method for calculating the eigenpair derivatives are compared with those from Dailey's method(an amendation of Ojalvo's work) which finds the exact eigenvector derivatives. The design parameter of the cantilever beam is its height. Data is presented showing the amount of CPU time used to compute the first ten eigenpair derivatives by each method. It is important to note that the numerical stability of the proposed method is proved.