• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2002년도 춘계학술대회 논문집
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• pp.253-258
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• 2002

This work is concerned with the estimation of output derivatives and their use for the design of robust controller for linear systems with systems uncertainties due to modeling errors and disturbance. It is assumed that a nominal transfer function model and quantitative bounds for system uncertainties are known The developed control schemes are shown to achieve regulation of the system output and ensures boundedness of the system states without imposing any structural conditions on system uncertainties and disturbances. Output derivative estimation is first conducted trough restructuring of the plant in a specific parameterization. They are utilized for constructing robust nonlinear high-gain feedback controller of a SMC(Sliding Mode Controller)Type. The performances of the developed controller are evaluated and shown to be effective and useful through simulation study.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1998년도 춘계학술대회논문집; 용평리조트 타워콘도, 21-22 May 1998
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• pp.407-412
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• 1998

In this work, a new time integration method is proposed using the generalized derivative concept to simulate the dynamic phenomena having sudden constraint occurring in dynamic contact/impact problems. By the adoption of the generalized derivative concept and jump assumption, discontinuity can be incorporated in time integration and as a result, the algorithm does not need any other special consideration of jumps in dynamic field variables due to sudden constraint like dynamic contact-release conditions. To observe the characteristics of the proposed time integration method, the stability and convergence analyses are carried out. In numerical tests, several dynamic contact/impact problems are analyzed by straightforward application of the proposed time integration method with the exterior penalty method.

• 대한수학회보
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• 제54권4호
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• pp.1141-1158
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• 2017

In this paper, we study the value distribution of the derivative of a Dirichlet L-function $L^{\prime}(s,{\chi})$ at the a-points ${\rho}_{a,{\chi}}={\beta}_{a,{\chi}}+i{\gamma}_{a,{\chi}}$ of $L^{\prime}(s,{\chi})$. We give an asymptotic formula for the sum $${\sum_{{\rho}_{a,{\chi}};0<{\gamma}_{a,{\chi}}{\leq}T}\;L^{\prime}({\rho}_{a,{\chi}},{\chi})X^{{\rho}_{a,{\chi}}}\;as\;T{\rightarrow}{\infty}$$, where X is a fixed positive number and ${\chi}$ is a primitive character mod q. This work continues the investigations of Fujii [4-6], $Garunk{\check{s}}tis$ & Steuding [8] and the authors [12].

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1997년도 춘계학술대회 논문집
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• pp.772-776
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• 1997

For a robot to perfom more versatile tasks, it is invitable for the robot's end-effector to come into contact with its environment. In thos case, to achieve better performance, it is necessary to properly control the contact force between the robot and the environment. In thos work, hybrid control theory is studied and is verified through experiment using a 3 DOF robot. In the experiment, two position/force controllers are used. Fist, proportional-integral-derivative controller is used as the controller for both position and force. Second, computed-torque method is used as the position controller, and proportional-integral-derivative controller is used as the force controller. For a proper modeling used in computed-torque method, the friction torque is measured by experiment, and compensation method is studied. The hybrid control method used in this experiment effectively control the contact force between the end-effector and the environment for various types of jobs.

• 대한전기학회논문지
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• 제45권2호
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• pp.273-282
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• 1996

This work is conceded with the estimation of output derivatives and their use for the design of robust controller for linear systems with system uncertainties due to modeling errors and disturbances. It is assumed that a nominal transfer function model and quantitative bounds for system uncertainties and known. The developed control schemes are shown to achieve regulation of the system output and ensures boundedness of the system states without imposing any structural conditions on system uncertainties and disturbances. Output derivative estimation is first conducted through restructuring of the plant in a specific parameterization. They are utilized for constructing robust nonlinear high-gain feedback controller of a SMC(Sliding Mode Control)type. The performances of the developed controller are evaluated and shown to be effective and useful through simulation study.

• Wind and Structures
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• 제28권6호
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• pp.347-354
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• 2019

This study provides an approximate analytical solution to the fractional vibration problem of thin plate governing anomalous motion of plate subjected to in-plane loads. The method of variable separable is employed to transform the fractional partial differential equations under consideration into a fractional ordinary differential equation in temporal variable and a bi-harmonic plate equation in spatial variable. The technique of conformable fractional derivative is utilized to solve the resulting fractional differential equation and the approach of finite sine integral transform method is used to solve the accompanying bi-harmonic plate equation. The deflection field which measures the transverse displacement of the plate is expressed in terms of product of Bessel and trigonometric functions via the temporal and spatial variables respectively. The obtained solution reduces to the solution of the free vibration problem of thin plate in literature. This work shows that conformable fractional derivative is an efficient mathematical tool for tracking analytical solution of fractional partial differential equation governing anomalous vibration of thin plates.

• Journal of Applied and Pure Mathematics
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• 제6권1_2호
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• pp.21-36
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• 2024

In this paper, we study the existence of solutions for hybrid fractional differential equations with p-Laplacian operator involving fractional Caputo derivative of arbitrary order. This work can be seen as an extension of earlier research conducted on hybrid differential equations. Notably, the extension encompasses both the fractional aspect and the inclusion of the p-Laplacian operator. We build our analysis on a hybrid fixed point theorem originally established by Dhage. In addition, an example is provided to demonstrate the effectiveness of the main results.

• East Asian mathematical journal
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• 제17권1호
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• pp.135-146
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• 2001

Several families of infinite series were summed recently by means of certain operators of fractional calculus(that is, calculus of derivatives and integrals of any real or complex order). In the present sequel to this recent work, it is shown that much more general classes of infinite sums can be evaluated without using fractional calculus. Some other related results are also considered.

• 대한수학회보
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• 제48권5호
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• pp.951-957
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• 2011

In 1996, Br$\ddot{u}$ck studied the relation between f and f' if an entire function f shares one value a CM with its first derivative f' and posed the famous Br$\ddot{u}$ck conjecture. In this work, we generalize the value a in the Br$\ddot{u}$ck conjecture to a small function ${\alpha}$. Meanwhile, we prove that the Br$\ddot{u}$ck conjecture holds for a class of meromorphic functions.

• Journal of the Korean Data and Information Science Society
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• 제18권1호
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• pp.11-16
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• 2007

Since the seminal work of Engle (1982), many researchers and practitioners have developed ARCH-type models to deal with volatility modelling, which, for instance, is crucial to perform the task of derivative pricing, measuring risk, and risk hedging. In this paper, we base the GARCH(1,1) model to analyze the KOSPI200 data, and perform the CUSUM test for detecting parameter changes in the GARCH model. It is shown that the data suffers from a parameter change.