• Advances in nano research
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• 제10권4호
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• pp.359-371
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• 2021

A tumor immune interaction is a main topic of interest in the last couple of decades because majority of human population suffered by tumor, formed by the abnormal growth of cells and is continuously interacted with the immune system. Because of its wide range of applications, many researchers have modeled this tumor immune interaction in the form of ordinary, delay and fractional order differential equations as the majority of biological models have a long range temporal memory. So in the present work, tumor immune interaction in fractional form provides an excellent tool for the description of memory and hereditary properties of inter and intra cells. So the interaction between effector-cells, tumor cells and interleukin-2 (IL-2) are modeled by using the definition of Caputo fractional order derivative that provides the system with long-time memory and gives extra degree of freedom. Moreover, in order to achieve more efficient computational results of fractional-order system, a discretization process is performed to obtain its discrete counterpart. Furthermore, existence and local stability of fixed points are investigated for discrete model. Moreover, it is proved that two types of bifurcations such as Neimark-Sacker and flip bifurcations are studied. Finally, numerical examples are presented to support our analytical results.

• Journal of Power Electronics
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• 제18권3호
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• pp.723-735
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• 2018

Linear proportional-integral (PI) controllers are an attractive choice for controlling the speed of induction machines because of their simplicity and ease of implementation. Fractional-order PI (FO-PI) controllers, however, perform better than PI controllers because of their nonlinear nature and the underlying iso-damping property of fractional-order operators. In this work, an FO-PI controller based on the proposed first-order plus dead-time induction motor model and integer-order (IO) controllers, such as Ziegler-Nichols PI, Cohen-Coon PI, and a PI controller tuned via trial-and-error method, is designed. Simulation and experimental investigation on an indirect field-oriented induction motor drive system proves that the proposed FO-PI controller has better speed tracking, lesser settling time, better disturbance rejection, and lower speed tracking error compared with linear IO-PI controllers. Our experimental study also validates that the FO-PI controller maximizes the torque per ampere output of the induction machine and can effectively control the motor at low speed, in field-weakening regions, and under detuned conditions.

• Journal of Electrical Engineering and Technology
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• 제10권4호
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• pp.1389-1399
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• 2015

This research suggests maximum power point tracking (MPPT) for the solar photovoltaic (PV) power scheme using a new constant voltage (CV) fractional order incremental conductance (FOINC) algorithm. The PV panel has low transformation efficiency and power output of PV panel depends on the change in weather conditions. Possible extracting power can be raised to a battery load utilizing a MPPT algorithm. Among all the MPPT strategies, the incremental conductance (INC) algorithm is mostly employed due to easy implementation, less fluctuations and faster tracking, which is not only has the merits of INC, fractional order can deliver a dynamic mathematical modelling to define non-linear physiognomies. CV-FOINC variation as dynamic variable is exploited to regulate the PV power toward the peak operating point. For a lesser scale photovoltaic conversion scheme, the suggested technique is validated by simulation with dissimilar operating conditions. Contributions are made in numerous aspects of the entire system, including new control algorithm design, system simulation, converter design, programming into simulation environment and experimental setup. The results confirm that the small tracking period and practicality in tracking of photovoltaic array.

• 전기전자학회논문지
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• 제3권1호
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• pp.39-49
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• 1999

This paper describes a 1 GHz, low-phase-noise CMOS fractional-N frequency synthesizer with an integrated LC VCO. The proposed frequency synthesizer, which uses a high-order delta-sigma modulator to suppress the fractional spurious tones at all multiples of the fractional frequency resolution offset, has 64 programmable frequency channels with frequency resolution of $f_ref/64$. The measured phase noise is as low as -110 dBc/Hz at a 200 KHz offset frequency from a carrier frequency of 980 MHz. The reference sideband spurs are -73.5 dBc. The prototype is implemented in a $0.5{\mu}m$ CMOS process with triple metal layers. The active chip area is about $4mm^2$ and the prototype consumes 43 mW, including the VCO buffer power consumption, from a 3.3 V supply voltage.

• 한국전자통신학회논문지
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• 제16권3호
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• pp.503-510
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• 2021

본 연구는 유리 차수 미분의 수학적인 방법을 시스템의 응답을 제어하는 제어기에 적용하고자 한다. 따라서 제어기로 구성하기 위해서는 유리수 지수에 대한 적분기를 이산시간으로 변환하여 설계한다. IP 제어기는 오차에 대한 적분제어기를 구성하고 비례제어기는 시스템 출력만 적용하는 구조이다. 유리 차수 적분기를 IP 제어기의 적분제어기에 활용함으로 제어기를 설계한다. 먼저 PI 제어기와 IP 제어기의 성능을 비교하고, 설계된 제어기를 전동기의 속도 제어에 적용한다. 그 결과 전동기의 출력상태인 속도가 균일하며 정밀한 제어 성능을 얻을 수 있었다. 정상상태의 속도오차가 0.1 [%] 이내 이고, 오버슈트가 없는 정밀하며 균일한 속도 제어 성능을 가짐을 확인할 수 있었다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제11권11호
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• pp.5377-5391
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• 2017

In this paper, we propose a new scheme to suppress the narrowband interference (NBI) in OFDM-based systems. The scheme utilizes code division multiple access (CDMA) and weighted-type fractional Fourier transform (WFRFT) domain preprocessing technologies. Through setting the WFRFT order, the scheme can switch into a single carrier (SC) or a multi-carrier (MC) frequency division multiple access block transmission system. The residual NBI can be eliminated to the maximum extent when the WFRFT order is selected properly. Final simulation results show that the proposed system can outperform MC and SC with CDMA and frequency domain preprocessing in terms of the narrowband interference suppression.

• International Journal of Computer Science & Network Security
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• 제21권12호
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• pp.223-227
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• 2021

A treatment based on the algebraic operations on fuzzy numbers is used to replace the fuzzy problem into an equivalent crisp one. The finite difference technique is used to replace the continuous boundary value problem (BVP) of arbitrary order 1<α≤2, with fuzzy boundary parameters into an equivalent crisp (algebraic or differential) system. Three numerical examples with different behaviors are considered to illustrate the treatment of the singular perturbed case with different fractional orders of the BVP (α=1.8, α=1.9) as well as the classical second order (α=2). The calculated fuzzy solutions are compared with the crisp solutions of the singular perturbed BVP using triangular membership function (r-cut representation in parametric form) for different values of the singular perturbed parameter (ε=0.8, ε=0.9, ε=1.0). Results are illustrated graphically for the different values of the included parameters.

• 대한수학회보
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• 제57권5호
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• pp.1269-1297
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• 2020

In this paper, we consider a two-species parabolic-parabolic-elliptic chemotaxis system with weak competition and a fractional diffusion of order s ∈ (0, 2). It is proved that for s > 2p₀, where p₀ is a nonnegative constant depending on the system's parameters, there admits a global classical solution. Apart from this, under the circumstance of small chemotactic strengths, we arrive at the global asymptotic stability of the coexistence steady state.

• Journal of applied mathematics & informatics
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• 제38권5_6호
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• pp.489-506
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• 2020

The spatial fractional diffusion equation can be discretized by employing the implicit finite difference scheme using the shifted Grünwald formula. The discretized linear system is obtained, whose the coefficient matrix has a diagonal-plus-Toeplitz structure. In order to solve the diagonal-plus-Toeplitz linear system, on the basis of circulant and skew-circulant splitting (CSCS splitting), we construct a new and efficient iterative method, called DSCS iterative methods, which have two parameters. Than we prove the convergence of DSCS methods. As a focus, we derive the simple and effective values of two optimal parameters under some restrictions. Some numerical experiments are carried out to illustrate the validity and accuracy of the new methods.

• 공업화학
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• 제5권4호
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• pp.731-736
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• 1994

DGEBA/MDA/MN계와 이 계에 촉매로서 hydroquinone(HQ)를 첨가한 계의 경화반응 속도론을 Fractional life법 및 Kissinger equation에 의해 연구함으로써 HQ가 경화반응 속도에 미치는 영향을 연구하였다. 경화반응 온도가 증가함에 따라 반응속도는 증가하였고, 반응차수는 약간의 변화가 있을 뿐 경화온도에 따른 경향성은 없었다. 촉매로 HQ를 첨가한 계가 첨가하지 않은 계보다 반응속도는 크게 증가하였고, 활성화 에너지는 13% 감소하였다. 이는 HQ의 히드록시기가 에폭사이드기, 아민기와 반응하여 전이상태를 형성함으로써 에폭사이드 고리를 쉽고 빠르게 개환시켜 주기 때문이다.