• Journal of IKEEE
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• v.13 no.1
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• pp.11-18
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• 2009

In this paper, the stability of second order uncertain systems with regulation of PID type controllers is analyzed by using Lyapunov second method for the first time in the time domain. The property of the stability of PID regulation servo systems is revealed in sense of Lyapunov, i.e., bounded stability due to the disturbances and uncertainties. By means of the results of this stability analysis, the maximum norm bound of the error from the output without variation of the uncertainties and disturbances is determined as a function of the gains of the PID control, which make it enable to analyze the effect resulted from the variations of the disturbances and uncertainties using this norm bound for given PID gains. Using the relationship of the error from the output without variation of the uncertainties and disturbances and the PID gain with maximum bounds of the disturbances and uncertainties, the robust gain design rule is suggested so that the error from the output without the variation of the disturbances and uncertainties can be guaranteed by the prescribed specifications as the advantages of this study. The usefulness of the proposed algorithm is verified through an illustrative example.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.540-543
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• 1997

In this paper, a precise trajectory tracking method for mobile robot using a vision system is presented. In solving the problem of precise trajectory tracking, a hierarchical control structure is used which is composed of the path planer, vision system, and dynamic controller. When designing the dynamic controller, non-ideal conditions such as parameter variation, frictional force, and external disturbance are considered. The proposed controller can learn bounded control input for repetitive or periodic dynamics compensation which provides robust and adaptive learning capability. Moreover, the usage of vision system makes mobile robot compensate the cumulative location error which exists when relative sensor like encoder is used to locate the position of mobile robot. The effectiveness of the proposed control scheme is shown through computer simulation.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.4
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• pp.753-761
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• 1998

The determination of sound pressure radiated from periodic plate structures is fundamental in the estimation of noise level in aircraft fuselages or ship hull structures. As a robust approach to this problem, here a very general and comprehensive analytical model is developed for predicting the sound radiated by a vibrating plate stiffened by periodically spaced orthogonal unsymmetrical beams subjected to a sinusoidally time varying point load. The plate is assumed to be infinite in extent, and the beams are considered to exert both line force and moment reactions on it. Using this theoretical model, the sound pressure levels on axis in a semi-infinited fluid (water) bounded by the plate were calculated using three numerical tools such as the Gauss-Jordan method, the LU decomposition method and the IMSL numberial package. Especially, the variation in the sound pressure levels and their modes were investigated according to the change in frequency, bay spacing and bay distance.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.737-748
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• 2012

The goal of this paper is to study the existence of non-trivial non-negative weak solution for the nonlinear elliptic equation: $$-div(h(x){\nabla}u)=f(x,u)\;in\;{\Omega}$$ with Dirichlet boundary condition in a bounded domain ${\Omega}{\subset}\mathbb{R}^N$, $N{\geq}3$, where $h(x){\in}L^1_{loc}({\Omega})$, $f(x,s)$ has asymptotically linear behavior. The solutions will be obtained in a subspace of the space $H^1_0({\Omega})$ and the proofs rely essentially on a variation of the mountain pass theorem in [12].

• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.91-109
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• 2007

In this paper, we derive a change of scale formula for conditional Wiener integrals, as integral transforms, of possibly unbounded functions over Wiener paths in abstract Wiener space. In fact, we derive the change of scale formula for the product of the functions in a Banach algebra which is equivalent to both the Fresnel class and the space of measures of bounded variation over a real separable Hilbert space, and the $L_p-type$cylinder functions over Wiener paths in abstract Wiener space. As an application of the result, we obtain a change of scale formula for the conditional analytic Fourier-Feynman transform of the product of the functions.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.93-107
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• 1995

In their paper [2,3], Cameron and Storvick introduced some classes $S"+m$ and of functionals on classical Wiener spaces $C_0[a,b]$. For such functionals, they showed that the analytic Feynman integral exists and they gave some formulas for this integral. Moreover they obtained that the functionals of the form $$ (1.1) F(x) = exp {\int^b_a{\theta(s,x(x))dx} $$ are in S" where they assumbed that the potential $\delta : [a,b] \times R \to C$ satisfies (i) for each $s \in [a,b], \theta(s,\cdot)$ is the Fourier-Stieltjes transform of $\sigma_s \in M(R)$, (ii) for each Borel subset E of $[a,b] \times R, \sigma_s (E^{(s)})$ is a Borel measurable function of s on [a,b], and (iii) the total variation $\Vert \sigma_s \Vert$ of $\sigma_s$ is bounded as a function of s.tion of s.

• Proceedings of the KIEE Conference
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• 2004.07d
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• pp.2212-2214
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• 2004

Robust stable analysis with the system bounded parameteric variation is very important among the various control theory. This study is to investigate the robust stable conditions using the quadratic form Lyapunov function in which the coefficient matrix is affined linear system. The quadratic stability using the quadratic form Lyapunov function is not investigated yet. The Lyapunov unction is robust stable not to be dependent by the variable parameters, which means that the Lyapunov function is conservative. We suggest the robust stable conditions in the Lyapunov function in which the variable parameters are dependent in order to reduce the conservativeness of quadratic stability.

• The Pure and Applied Mathematics
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• v.21 no.4
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• pp.271-279
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• 2014

Let $T_l$ be a transformation on the interval [-1, 1] defined by Chebyshev polynomial of degree $l(l{\geq}2)$, i.e., $T_l(cos{\theta})=cos(l{\theta})$. In this paper, we consider $T_l$ as a measure preserving transformation on [-1, 1] with an invariant measure $\frac{1}{\sqrt[\pi]{1-x^2}}dx$. We show that If f(x) is a nonconstant step function with finite k-discontinuity points with k < l-1, then it satisfies the Central Limit Theorem. We also give an explicit method how to check whether it satisfies the Central Limit Theorem or not in the cases of general step functions with finite discontinuity points.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.11 no.1
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• pp.52-60
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• 2002

The purpose of this research is to study the vibration and acoustic pressure radiation from a thin isotropic flat plate stiffened by a rectangular array of beams, and excited by a time harmonic point force. These constructions on aircraft and ship structures are often subjected to fiequency dependent pressure fluctuations and forces. Forces from the these excitations induce structural vibrations in a wide range of fiequencies, which may cause such things as acoustic fatigue and internal cabin noise in the aircraft. It is thus important that the response characteristics and vibration modes of such periodic structures be horn. From this theoretical model, the sound pressure levels(SPL) in a semi-infinite fluid(water) bounded by the plate with the variation in the locations of an external time harmonic point farce on the plate can be calculated efficiently using three numerical tools such as the Gauss-jordan method the LU decomposition method md the IMSL numerical package.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1998.03a
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• pp.214-220
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• 1998

The determination of sound pressure radiated from periodic plate structures is fundamental in the estimation of noise levels in aircraft fuselages and ship hull structures. As a robust approach to this problem, here a very general and comprehensive analytical model for prediction the sound radiated by a vibration plate stiffened by periodically spaced orthogonal symmetric beams subjected to a sinusoidally time varying point load is developed. The plate is assumed to be infinite in extent, and the beams are considered to exert both line force and moment reactions on it. Structural damping is included in both plate and beam materials. From this theoretical model, the sound pressure levels on axis in a semi-infinite fluid(water) bounded by the plate with the variation in the loactions of an external using three numerical tools such as the Gauss-Jordan method, the LU decomposition method and the IMSL numerical package.