• Journal of Electrical Engineering and Technology
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• 제13권4호
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• pp.1705-1714
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• 2018

This paper develops a novel controller called iterative learning sliding mode (ILSM) to control linear and nonlinear fractional-order systems. This control applies a combination structures of continuous and discontinuous controller, conducts the system output to the desired output and achieve better control performance. This controller is designed in the way to be robust against the external disturbance. It also estimates unknown parameters of fractional-order systems. The proposed controller unlike the conventional iterative learning control for fractional systems does not need to apply direct control input to output of the system. It is shown that the controller perform well in partial and complete observable conditions. Simulation results demonstrate very good performance of the iterative learning sliding mode controller for achieving the desired control objective by increasing the number of iterations in the control loop.

• JSTS:Journal of Semiconductor Technology and Science
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• 제2권1호
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• pp.41-48
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• 2002

This paper presents a 18-mW, 2.5-㎓ fractional-N frequency synthesizer with l-bit $4^{th}$-order interpolative delta-sigma ($\Delta{\;}$\sum$)modulator to suppress fractional spurious tones while reducing in-band phase noise. A fractional-N frequency synthesizer with a quadruple prescaler has been designed and implemented in a $0.5-\mu\textrm{m}$ 15-GHz $f_t$ BiCMOS. Synthesizing 2.1 GHzwith less than 200 Hz resolution, it exhibits an in-band phase noise of less than -85 dBc/Hz at 1 KHz offset frequency with a reference spur of -85 dBc and no fractional spurs. The synthesizer also shows phase noise of -139 dBc/Hz at an offset frequency of 1.2 MHz from a 2.1GHz center frequency.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.357-374
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• 2019

In this paper, first we obtain some inequalities of Hadamard type for (h - m)-convex functions via Caputo k-fractional derivatives. Secondly, two integral identities including the (n + 1) and (n+ 2) order derivatives of a given function via Caputo k-fractional derivatives have been established. Using these identities estimations of Hadamard type integral inequalities for the Caputo k-fractional derivatives have been proved.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
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• pp.593-596
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• 1997

This paper is concerned with the properties of zeros of discrete-time systems which are composed of a hold, a continuous-time plant and a sampler in cascade. Here the signal reconstruction is based on the fractional order hold. In order to overcome the implementing problem of the fractional order hold, the piecewise constant reconstruction method by use of the zero order hold is introduced. The properties of the zeros are explored in the limiting cases when the sampling period tends to zero. The stability conditions of the zeros for sufficiently small sampling periods are also presented.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1157-1169
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• 2010

This paper presents the analytical solution of the fractional Fokker-Planck equation by Adomian decomposition method. By using initial conditions, the explicit solution of the equation has been presented in the closed form and then the numerical solution has been represented graphically. Two different approaches have been presented in order to show the application of the present technique. The present method performs extremely well in terms of efficiency and simplicity.

• 대한수학회지
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• 제57권3호
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• pp.721-745
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• 2020

In this paper we study fractional Sobolev spaces characterized by a norm based on eigenfunction expansions. The goal of this paper is twofold. The first one is to define fractional Sobolev spaces of order -1 ≤ s ≤ 2 equipped with a norm defined in terms of Neumann eigenfunction expansions. Due to the zero Neumann trace of Neumann eigenfunctions on a boundary, fractional Sobolev spaces of order 3/2 ≤ s ≤ 2 characterized by the norm are the spaces of functions with zero Neumann trace on a boundary. The spaces equipped with the norm are useful for studying cross-sectional traces of solutions to the Helmholtz equation in waveguides with a homogeneous Neumann boundary condition. The second one is to define fractional Sobolev spaces of order -1 ≤ s ≤ 1 for vector-valued functions in a simply-connected, bounded and smooth domain in ℝ². These spaces are defined by a norm based on series expansions in terms of eigenfunctions of the vector Laplacian with boundary conditions of zero tangential component or zero normal component. The spaces defined by the norm are important for analyzing cross-sectional traces of time-harmonic electromagnetic fields in perfectly conducting waveguides.

• 대한기계학회논문집
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• 제19권10호
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• pp.2667-2677
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• 1995

A new numerical algorithm using equal order linear finite element and fractional step method has been developed which is capable of analyzing unsteady fluid flow and heat transfer problems. Streamline Upwind Petrov-Galerkin (SUPG) method is used for the weighted residual formulation of the Navier-Stokes equations. It is shown that fractional step method, in which pressure term is splitted from the momentum equation, reduces computer memory and computing time. In addition, since pressure equation is derived without any approximation procedure unlike in the previously developed SIMPLE algorithm based FEM codes, the present numerical algorithm gives more accurate results than them. The present algorithm has been applied preferentially to the well known bench mark problems associated with steady flow and heat transfer, and proves to be more efficient and accurate.

• 대한수학회지
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• 제53권5호
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• pp.1019-1036
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• 2016

In this paper, we study the existence of solutions and $L^2$-regularity for fractional order retarded neutral functional differential equations in Hilbert spaces. We no longer require the compactness of structural operators to prove the existence of continuous solutions of the non-linear differential system, but instead we investigate the relation between the regularity of solutions of fractional order retarded neutral functional differential systems with unbounded principal operators and that of its corresponding linear system excluded by the nonlinear term. Finally, we give a simple example to which our main result can be applied.

• Structural Engineering and Mechanics
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• 제81권4호
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• pp.503-511
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• 2022

In this article, we have examined the effect of fractional order parameter in a two-dimensional orthotropic magneto-thermoelastic solid in generalized thermoelasticity without energy dissipation with fractional order heat transfer in the context of hall current, rotation and two-temperature due to normal force. Laplace and Fourier transform techniques are used to obtain the solution of the problem. The expressions for displacement components, stress components, current density components and conductive temperature are obtained in transformed domain and then in physical domain by using numerical inversion method. The effect of fractional parameter on all the components has been depicted through graphs. Some special cases are also discussed in the present investigation.

• 한국전자통신학회논문지
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• 제14권1호
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• pp.185-190
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• 2019

본 연구는 유리차수 미분의 수학적인 방법을 시스템의 응답을 제어하는 제어기에 적용하고자 한다. 일반적인 PID제어기의 라플라스 변환은 s의 정수지수를 갖게 된다. 유리차수의 미분은 라플라스 변환에서 s에 대한 유리수 지수를 갖게 된다. 따라서 이를 제어기로 구성하기 위해서는 유리수 지수에 대한 설계가 적절하지 않아 이산시간으로 변환하여 설계하는 방법을 제안한다. 이를 표준 2차 시스템에 적용하여 성능을 살펴보고, 산업현장에서 많이 사용되는 솔레노이드밸브에 적용한다. 외란 상태의 추정이 가능하도록 루엔버거 관측기를 설계하고 관측된 상태에 대하여 유리차수 제어기를 적용하여 균일하며 정밀한 제어성능을 얻을 수 있었다. 정상상태의 위치오차가 0.1 [%]이내이고, 기동시간이 약 0.3 [s]이내의 정밀하며 균일한 위치제어성능 가짐을 확인할 수 있었다.