• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1995년도 Proceedings of the Korea Automation Control Conference, 10th (KACC); Seoul, Korea; 23-25 Oct. 1995
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• pp.10-13
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• 1995

This paper considers the linear-quadratic optimal regulator problem for nonstandard singularly perturbed systems making use of the recursive technique. We first derive a generalized Riccati differential equation by the Hamilton-Jacobi equation. In order to obtain the feedback gain, we must solve the generalized algebraic Riccati equation. Using the recursive technique, we show that the solution of the generalized algebraic Riccati equation converges with the rate of convergence of O(.epsilon.). The existence of a bounded solution of error term can be proved by the implicit function theorem. It is enough to show that the corresponding Jacobian matrix is nonsingular at .epsilon. = 0. As a result, the solution of optimal regulator problem for nonstandard singularly perturbed systems can be obtained with an accuracy of O(.epsilon.$^{k}$ ). The proposed technique represents a significant improvement since the existing method for the standard singularly perturbed systems can not be applied to the nonstandard singularly perturbed systems.

• 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.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2008년도 추계학술대회B
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• pp.2460-2464
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• 2008

The present paper suggests new method to know the effects of molecular diffusion and the helicity of microchannel flows on mixing in passive micromixers, which are essential components of a microfluidic chip. In this study, 'Helix Index' is newly defined as the magnitude of chaotic advection. Relationship between Helix Index and Mixing Index is analyzed numerically such as the wide range of Peclet and Reynolds numbers in three dimensional serpentine microchannel when using soluble solutions (water/glycerol). As a result, a simple algebraic equation is derived by this relationship based on a regression analysis. The algebraic equation is found to be able to accurately predict the mixing performance without solving the coupled, complex momentum and mass transfer equations.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제15권4호
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• pp.311-325
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• 2011

In this paper I propose that teaching students the most efficient method of problem solving may curtail students' creativity. Instead it is important to arm students with a variety of problem solving heuristics. It is the students' responsibility to decide which heuristic will solve the problem. The chosen heuristic is the one which is meaningful to the students.

• Transactions on Control, Automation and Systems Engineering
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• 제4권3호
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• pp.205-211
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• 2002

Unknown inputs observer(UIO) which is achieved by the coordinate transformation method has the differential of system outputs in the observer and the equation for unknown inputs estimation. Generally, the differential of system outputs in the observer can be eliminated by defining a new variable. But it brings about the partition of the observer into two subsystems and need of an additional differential of system outputs still remained to estimate the unknown inputs. Therefore, the block pulse function expansions and its differential operation which is a newly derived in this paper are presented to alleviate such problems from an algebraic form.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2001년도 제14회 신호처리 합동 학술대회 논문집
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• pp.107-110
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• 2001

In this paper, we propose a multiplication-free DFT kernel computation technique, whose input sequences are approximated into a ring of Algebraic Integers. This paper also gives computational examples for DFT and IDFT. And we proposes an architecture of the DFT using barrel shifts and adds. When the radix is greater than 4, the proposed method has a high Precision property without scaling errors due to twiddle factor multiplication. A possibility of higher radix system assumes that higher performance can be achievable for reducing the DFT stages in FFT.

• Journal of applied mathematics & informatics
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• 제8권2호
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• pp.651-658
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• 2001

The projection matrix plays an important role in the linear model theory. In this paper we derive an algebraic relationship between the projection matrices of submatrices of the design matrix. Using this relationship we can easily obtain the projection matrices of any submatrices of the design matrix. Also we show that every projection matrix can be obtained as a linear combination of Kronecker products of identity matrices and matrices with all elements equal to 1.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2002년도 ITC-CSCC -2
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• pp.920-923
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• 2002

In this paper, we propose Class Diagram With Constraints (CDWC) as an object oriented modeling technique which makes validation possible in software development. CDWC is a simple and basic model for the object oriented analysis, and has a reasonable strictness for software developers. CDWC consists of class diagrams and constraints (invariant and pre/post conditions), using UML and a subset of OCL.. We introduce a method of validation of CDWC using the verification technique of algebraic formal specification language CafeOBJ.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1992년도 추계학술대회 논문집
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• pp.349-353
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• 1992

The purpose of this paper is to develop methods for the dynamic analysis of multibody system that consist of interconnected rigid and deformable component. The equations of motion are derived by using the Lagrange's equation and finite element theory for the elastic mechanism systems. The type of equation of motion is the differential algebraic equation included kinematic nonlinear algebraic equation. The generalized coordinate partitioning method is used for solving this equation. To show the validity of this analysis solver, couple of models were canalized and those results were compared with the commercial package(ADAMS).

• 한국경영과학회지
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• 제20권2호
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• pp.139-158
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• 1995

A temporal database systems provides timing information and maintains history of data compared to the conventional database system. In this paper, we present a temporal relational database which use an interval-stamping method for instant-based events and for interval-based states. A set of temporal algebraic operators are developed on an instance of time and interval of time so that we can manipulate events and states at a same time. The set of operation is the basis for creating a relational algebra that is closed for temporal relations. And temporal SQL is also suggested as a temporal query relational language for our algebraic operations on temporal relations.