• Nonlinear Functional Analysis and Applications
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• 제26권2호
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• pp.225-236
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• 2021

In this paper, we determine position vector of a line of curvature of a regular surface which is relatively normal-slant helix, with respect to Darboux frame. Then, a vector differential equation is established by means Darboux formulas, in the case of the geodesic torsion is vanishes. In terms of solution, we determine the parametric representation of a line of curvature which is relatively normal-slant helix, with respect to standard frame in Euclidean 3-space. Thereafter, we apply this result to find the position vector of a line of curvature which is isophote curve.

• 전력전자학회논문지
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• 제27권2호
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• pp.118-125
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• 2022

With the aim to maximize the use of a given voltage source in the field of railway and electric vehicles, this study applies a technique for controlling the overmodulation region between the linear and the six-step regions. High linearity overmodulation techniques that do not use look-up table (LUT) to digital signal processor (DSP) using carrier based pulse width modulation (PWM) are proposed. Such technique requires the phase of the voltage vector at the point where the circular trajectory of the voltage command vector and hexagonal cross each other. Therefore, a method is proposed to obtain a phase of a voltage vector that is derived through an equation and applied to a carrier-based PWM. Validity of the proposed implementation method is confirmed through simulation and experiment.

• Journal of information and communication convergence engineering
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• 제9권5호
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• pp.500-504
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• 2011

In this paper, we propose an equivalent Wiener-Hopf equation. The proposed algorithm can obtain the weight vector of a TDL(tapped-delay-line) filter and the error simultaneously if the inputs are orthogonal to each other. The equivalent Wiener-Hopf equation was analyzed theoretically based on the MMSE(minimum mean square error) method. The results present that the proposed algorithm is equivalent to original Wiener-Hopf equation. The new algorithm was applied into the identification of an unknown system for evaluating the performance of the proposed method. We compared the Wiener-Hopf solution with the equivalent Wiener-Hopf solution. The simulation results were similar to those obtained in the theoretical analysis. In conclusion, our method can find the coefficient of the TDL (tapped-delay-line) filter where a lattice filter is used, and also when the process of Gram-Schmidt orthogonalization is used. Furthermore, a new cost function is suggested which may facilitate research in the adaptive signal processing area.

• 한국인터넷방송통신학회논문지
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• 제11권4호
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• pp.245-249
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• 2011

본 논문에서 등가의 Wiener-Hopf 공식을 제안한다. 제안된 알고리듬은 입력신호들이 직교하는 경우 TDL 필터의 가중치 벡터와 오차를 동시에 가질 수 있게 된다. 등가의 Wiener-Hopf 방정식은 최소 평균 자승 오차 방식에 근여 이론적으로 분석이 되었다. 제안된 알고리듬의 성능 결과는 원래 Wiener-Hopf 방정식의 성능과 동일함을 확인할 수 있다. 결론적으로 제안된 방식은 격자 필터가 적용되는 경우 TDL 필터 계수를 가지게 된다. 게다가 새로운 비용함수가 제안되어 더욱 우수한 적응신호처리 분야에서의 발전을 보일 것으로 기대된다.

• 전력전자학회:학술대회논문집
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• 전력전자학회 2000년도 전력전자학술대회 논문집
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• pp.207-210
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• 2000

In this paper a theoretical formulation of the direct control relating the action exerted by the inverter space vectors on the stator flux and the torque of Induction motor is analyzed. From the equation the scheme of the inverter switching is proposed and influence of the stator flux and the electromagnetic torque in each switching pattern is also analyzed.

• 전기학회논문지
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• 제67권10호
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• pp.1308-1316
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• 2018

Accurate tuning of parameter is very important in vector-controlled induction motor. Among the parameters of induction motor, detuning of rotor resistance used in controller design deteriorates drive performance. This paper presents a novel rotor resistance estimation strategy using slip angular velocity in vector-controlled induction motor drives. The slip angular velocity can be calculated by two methods. Firstly, it can be induced from the rotor voltage equation. Secondly, it can be induced from the difference between synchronous angular velocity and rotor angular velocity. The first method includes the rotor resistance, while the second method dose not include this parameter. From this fact, the rotor resistance can be identified by comparing the slip angular velocities in the two methods. In the tuned states of the rotor resistance, performances of flux estimator and speed drive are discussed. The simulation and experimental results are given to verify the validity of the proposed method in various situations.

• 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.

• Smart Structures and Systems
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• 제15권1호
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• pp.57-80
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• 2015

Extended Kalman Filter (EKF) has been widely used for structural identification and damage detection. However, conventional EKF approaches require that external excitations are measured. Also, in the conventional EKF, unknown structural parameters are included as an augmented vector in forming the extended state vector. Hence the sizes of extended state vector and state equation are quite large, which suffers from not only large computational effort but also convergence problem for the identification of a large number of unknown parameters. Moreover, such approaches are not suitable for intelligent structural damage detection due to the limited computational power and storage capacities of smart sensors. In this paper, a two-stage and two-step algorithm is proposed for the identification of structural damage as well as unknown external excitations. In stage-one, structural state vector and unknown structural parameters are recursively estimated in a two-step Kalman estimator approach. Then, the unknown external excitations are estimated sequentially by least-squares estimation in stage-two. Therefore, the number of unknown variables to be estimated in each step is reduced and the identification of structural system and unknown excitation are conducted sequentially, which simplify the identification problem and reduces computational efforts significantly. Both numerical simulation examples and lab experimental tests are used to validate the proposed algorithm for the identification of structural damage as well as unknown excitations for structural health monitoring.

• Journal of Mechanical Science and Technology
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• 제16권8호
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• pp.1072-1078
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• 2002

The constrained motion requires the determination of constraint force acting on unconstrained systems for satisfying given constraints. Most of the methods to decide the force depend on numerical approaches such that the Lagrange multiplier method, and the other methods need vector analysis or complicated intermediate process. In 1992, Udwadia and Kalaba presented the generalized inverse method to describe the constrained motion as well as to calculate the constraint force. The generalized inverse method has the advantages which do not require any linearization process for the control of nonlinear systems and can explicitly describe the motion of holonomically and/or nongolonomically constrained systems. In this paper, an explicit equation to describe the constrained motion is derived by minimizing the performance index, which is a function of constraint force vector, with respect to the constraint force. At this time, it is shown that the positive-definite weighting matrix in the performance index must be the inverse of mass matrix on the basis of the Gauss's principle and the derived differential equation coincides with the generalized inverse method. The effectiveness of this method is illustrated by means of two numerical applications.

• Korean Journal of Mathematics
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• 제19권1호
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• pp.77-85
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• 2011

In [7], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $${\sum_{i=1}^{n}}\left\|x_i-{\frac{1}{n}}{\sum_{j=1}^{n}}x_j \right\|^2={\sum_{i=1}^{n}}{\parallel}x_i{\parallel}^2-n\left\|{\frac{1}{n}}{\sum_{i=1}^{n}}x_i \right\|^2$$ holds for all $x_1$, ${\cdots}$, $x_n{\in}V$. Let V, W be real vector spaces. It is shown that if an even mapping $f:V{\rightarrow}W$ satisfies $$(0.1)\;{\sum_{i=1}^{2n}f}\(x_i-{\frac{1}{2n}}{\sum_{j=1}^{2n}}x_j\)={\sum_{i=1}^{2n}}f(x_i)-2nf\({\frac{1}{2n}}{\sum_{i=1}^{2n}}x_i\)$$ for all $x_1$, ${\cdots}$, $x_{2n}{\in}V$, then the even mapping $f:V{\rightarrow}W$ is quadratic. Furthermore, we prove the generalized Hyers-Ulam stability of the quadratic functional equation (0.1) in Banach spaces.