• 전기학회논문지
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• 제62권3호
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• pp.407-413
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• 2013

This paper proposes anti-swing control of overhead crane system using sum of squares method. The dynamic equations of overhead crane include nonlinear terms, which are transformed into polynomials by using Taylor series expansion. Therefore the dynamic equation of overhead crane can be changed to the system of polynomial equation. On the basis of polynomial dynamics of crane system, we propose the Sum of Squares (SOS) conditions considering the input constraints. In addition, control gains are obtained by numerical tool which is called by SOSTOOL. The effectiveness of the proposed method is demonstrated by numerical simulation.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 춘계학술대회
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• pp.180-185
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• 2004

This paper investigates asimply supported orthotropic rectangular laminate with viscous interfaces subjected to bending. Additional mathematical difficulty is involved due to the presence of viscous interfaces because the behavior of the laminate depends on time. A step-by-step state-space approach is suggested, which is directly based on the threedimensional theory of elasticity. In particular, Taylor's expansion theorem is employed to model the variations of field variables with time. The proposed method is suitable for analyzing laminated plate of arbitrary thickness. Numerical calculations are performed and it is shown that the viscous interfaces have a significant fluence on the response.

• 동력기계공학회지
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• 제6권1호
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• pp.96-101
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• 2002

In this paper, we address the problem of controlling an end-effector to track and grab a moving target using the visual servoing technique. A visual servo mechanism based on the image-based servoing principle, is proposed by using visual feedback to control an end-effector without calibrated robot and camera models. Firstly, we consider the control problem as a nonlinear least squares optimization and update the joint angles through the Taylor Series Expansion. And to track a moving target in real time, the Jacobian estimation scheme(Dynamic Broyden's Method) is used to estimate the combined robot and image Jacobian. Using this algorithm, we can drive the objective function value to a neighborhood of zero. To show the effectiveness of the proposed algorithm, simulation results for a six degree of freedom robot are presented.

• Journal of Mechanical Science and Technology
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• 제20권6호
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• pp.759-769
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• 2006

This paper proposes a new method of discretization for nonlinear systems using a Taylor series expansion and the zero-order hold assumption. The method is applied to sampled-data representations of nonlinear systems with input time delays. The delayed input varies in time and its amplitude is bounded. The maximum time-delayed input is assumed to be two sampling periods. The mathematical expressions of the discretization method are presented and the ability of the algorithm is tested using several examples. A computer simulation is used to demonstrate that the proposed algorithm accurately discretizes nonlinear systems with variable time-delayed inputs.

• ETRI Journal
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• 제46권3호
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• pp.421-431
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• 2024

In this study, a direct position tracking method for non-circular (NC) signals using distributed passive arrays is proposed. First, we calculate the initial positions of sources using a direct position determination (DPD) approach; next, we transform the tracking into a compensation problem. The offsets of the adjacent time positions are calculated using a first-order Taylor expansion. The fusion calculation of the noise subspace is performed according to the NC characteristics. Because the proposed method uses the signal information from the previous iteration, it can realize automatic data associations. Compared with traditional DPD and two-step localization methods, our novel process has lower computational complexity and provides higher accuracy. Moreover, its performance is better than that of the traditional tracking methods. Numerous simulation results support the superiority of our proposed method.

• 대한수학회지
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• 제37권2호
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• pp.245-251
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• 2000

Assume that two boundaries of worm domains, which are parpametrizd by harmonic functions, are CR equivalent. Then we determine the Taylor expansion of CR equivalence mapping and get a relation of harmonic functions.

• 한국융합학회논문지
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• 제13권1호
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• pp.43-50
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• 2022

본 논문은 부가적인 잡음이 존재할 경우 모노펄스 알고리즘의 성능을 분석한 연구이다. 이전 연구에서는 변수가 4개일 때의 1차 테일러급수 전개와 2차 테일러급수 전개를 통한 진폭비교 모노펄스 알고리즘 성능 분석을 진행하였다. 4개의 잡음랜덤변수에서 2개의 잡음랜덤변수로 새롭게 정의하였으며, 2개의 랜덤변수와 관련된 수식의 복잡성이 4개의 랜덤변수와 관련된 수식의 복잡성보다 낮은 것을 보인다. 성능분석은 평균제곱오차(Mean Square Error : MSE)관점에서 몬테카를로(Mont-Carlo) 방법을 이용하여 분석하였다. 본 논문에서 제안한 방식은 기존 연구에서 제안한 방식보다 계산 복잡도 측면에서 더 효율적이다. 또한 본 연구에서 도출된 표현을 활용하여 추정각도 평균제곱오차의 해석적 표현을 구하는데 활용될 수 있다.

• 충청수학회지
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• 제37권1호
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• pp.27-40
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• 2024

In this paper, we consider the higher-order HartreeFock equations. The higher-order linear Schrödinger equation was introduced in [5] as the formal finite Taylor expansion of the pseudorelativistic linear Schrödinger equation. In [13], the authors established global-in-time Strichartz estimates for the linear higher-order equations which hold uniformly in the speed of light c ≥ 1 and as their applications they proved the convergence of higher-order Hartree-Fock equations to the corresponding pseudo-relativistic equation on arbitrary time interval as c goes to infinity when the Taylor expansion order is odd. To achieve this, they not only showed the existence of solutions in L² space but also proved that the solutions stay bounded uniformly in c. We address the remaining question on the convergence of higherorder Hartree-Fock equations when the Taylor expansion order is even. The distinguished feature from the odd case is that the group velocity of phase function would be vanishing when the size of frequency is comparable to c. Owing to this property, the kinetic energy of solutions is not coercive and only weaker Strichartz estimates compared to the odd case were obtained in [13]. Thus, we only manage to establish the existence of local solutions in H^s space for s > $\frac{1}{3}$ on a finite time interval [-T, T], however, the time interval does not depend on c and the solutions are bounded uniformly in c. In addition, we provide the convergence result of higher-order Hartree-Fock equations to the pseudo-relativistic equation with the same convergence rate as the odd case, which holds on [-T, T].

• Journal of Mechanical Science and Technology
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• 제18권8호
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• pp.1297-1305
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• 2004

In this paper, we propose a new scheme for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption. This scheme is applied to the sampled-data representation of a non-affine nonlinear system with constant input time-delay. The mathematical expressions of the discretization scheme are presented and the ability of the algorithm is tested for some of the examples. The proposed scheme provides a finite-dimensional representation for nonlinear systems with time-delay enabling existing controller design techniques to be applied to them. For all the case studies, various sampling rates and time-delay values are considered.

• Journal of Mechanical Science and Technology
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• 제18권7호
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• pp.1107-1120
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• 2004

This study proposes a new scheme for the sampled-data representation of nonlinear systems with time-delayed multi-input. The proposed scheme is based on the Taylor-series expansion and zero-order hold assumption. The mathematical structure of a new discretization scheme is explored. On the basis of this structure, the sampled-data representation of nonlinear systems including time-delay is derived. The new scheme is applied to nonlinear systems with two inputs and then the delayed multi-input general equation is derived. The resulting time-discretization provides a finite-dimensional representation of nonlinear control systems with time-delay enabling existing controller design techniques to be applied to them. In order to evaluate the tracking performance of the proposed scheme, an algorithm is tested for some of the examples including maneuvering of an automobile and a 2-DOF mechanical system.