• Journal of Institute of Control, Robotics and Systems
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• v.11 no.1
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• pp.1-8
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• 2005

A new discretization algorithm for nonlinear systems with delayed input is proposed. The algorithm is represented by Taylor series expansion and ZOH assumption. This method is applied to the sampled-data representation of a nonlinear system with the time-delay input. Additionally, the delay in input is time varying and its amplitude is bounded. The maximum time-delay in 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 for some of the examples. The computer simulation proves the proposed algorithm discretizes the nonlinear system with the variable time-delay input accurately.

• Journal of Mechanical Science and Technology
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• v.19 no.11
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• pp.1975-1987
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• 2005

An input time delay always exists in practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via digital computers. In this paper a new scheme for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption is proposed. The mathematical structure of the new discretization method is analyzed. On the basis of this structure the sampled-data representation of nonlinear systems with time-delayed multi-input is presented. The delayed multi-input general equation has been derived. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. Additionally, hybrid discretization schemes that result from a combination of the scaling and squaring technique (SST) with the Taylor series expansion are also proposed, especially under conditions of very low sampling rates. Practical issues associated with the selection of the method's parameters to meet CPU time and accuracy requirements, are examined as well. A performance of the proposed method is evaluated using a nonlinear system with time delay maneuvering an automobile.

• Proceedings of the KIEE Conference
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• 2005.05a
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• pp.125-127
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• 2005

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 sample-data representation of a nonlinear system with constant state tine-delay. The mathematical expressions of the discretization scheme are presented and the effect of the time-discretization method on key properties of nonlinear control system with state tine-delay, such as equilibrium properties and asymptotic ability, is examined. The proposed scheme provides a finite-dimensional representation for nonlinear systems with state time-delay enabling existing controller design techniques to be applied to then. The performance of the proposed discretization procedure is evaluated using a nonlinear system. For this nonlinear system, various sampling rates and time-delay values are considered.

• Journal of Power System Engineering
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• v.6 no.1
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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.

• International Journal of Naval Architecture and Ocean Engineering
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• v.13 no.1
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• pp.50-56
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• 2021

An accurate evaluation of three-dimensional (3D) Time-Domain Green Function (TDGF) in infinite water depth is essential for ship's hydrodynamic analysis. Various numerical algorithms based on the TDGF properties are considered, including the ascending series expansion at small time parameter, the asymptotic expansion at large time parameter and the Taylor series expansion combines with ordinary differential equation for the time domain analysis. An efficient method (referred as "Present Method") for a better accuracy evaluation of TDGF has been proposed. The numerical results generated from precise integration method and analytical solution of Shan et al. (2019) revealed that the "Present method" provides a better solution in the computational domain. The comparison of the heave hydrodynamic coefficients in solving the radiation problem of a hemisphere at zero speed between the "Present method" and the analytical solutions proposed by Hulme (1982) showed that the difference of result is small, less than 3%.

• Journal of Ocean Engineering and Technology
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• v.9 no.2
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• pp.53-60
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• 1995

A multi-leg spread mooring system for floating offshore structures is important, but the multi-leg static analysis is complicated due to the nonlinear behavior of each line and the effect of current which affects each line differently. The pretensioned position of the multi-leg mooring system obtained from the static equilibrium condition changes into a different position due to external loads and current. In this paper, the new position and the static tension at each line are caculated. The relation between the initial static equilibrium position and the new position due to the external loads is expressed in terms of the Taylor's series expansion. The Runge-Kutta $4^{th}$ method is employed in analyzing the 3-dimensional static cable nonlinear equations.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.49 no.2
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• pp.17-25
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• 2012

A general discretization method for input-driven nonlinear continuous time-delay systems is proposed, which can be applied to general order sampling hold assumptions. It is based on a combination of Taylor series expansion and the theories of sampling and hold. The mathematical structure of the new discretization scheme is introduced in detail. The performance of the proposed discretization procedure is evaluated by two degrees of systems. The results show that the proposed scheme is applicable to control systems.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.840-843
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• 2005

For an analysis of nonlinear dynamic behavior in carbon nanotube(CNT) an electrostatic force of CNT was investigated. The boundary condition in the CNT was assumed to clamped-clamped case at both ends. This type of CNT is widely used as micro and nano-sensors. For larger gaps in between sensor and electrode the van der Waals force can be ignored. The electrostatic force can be expressed as linear form using Taylor series. However, the first term of the series expansion was investigated here. The electrostatic force From this study we can conclude that for larger gaps the electrostatic force play an important role in determining the deflections as well as the pull-in voltage of simply supported switches.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.15 no.3
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• pp.8-16
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• 2006

This paper discusses design sensitivity analysis and its application to a structural dynamics modification. Eigenvalue derivatives are determined with respect to the element parameters, which include intrinsic property parameters such as Young's modulus, density of the material, diameter of a beam element, thickness of a plate element, and shape parameters. Derivatives of stiffness and mass matrices are directly calculated by derivatives of element matrices. The first and the second order derivatives of the eigenvalues are then mathematically derived from a dynamic equation of motion of FEM model. The calculation of the second order eigenvalue derivative requires the sensitivity of its corresponding eigenvector, which are developed by Nelson's direct approach. The modified eigenvalue of the structure is then evaluated by the Taylor series expansion with the first and the second derivatives of eigenvalue. Numerical examples for simple beam and plate are presented. First, eigenvalues of the structural system are numerically calculated. Second, the sensitivities of eigenvalues are then evaluated with respect to the element intrinsic parameters. The most effective parameter is determined by comparing sensitivities. Finally, we predict the modified eigenvalue by Taylor series expansion with the derivatives of eigenvalue for single parameter or multi parameters. The examples illustrate the effectiveness of the eigenvalue sensitivity analysis for the optimization of the structures.

• Communications for Statistical Applications and Methods
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• v.15 no.2
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• pp.147-159
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• 2008

We consider using ranked set sampling methods to draw inference about the three well-known measures of overlap, namely Matusita's measure $\rho$, Morisita's measure $\lambda$ and Weitzman's measure $\Delta$. Two exponential populations with different means are considered. Due to the difficulties of calculating the precision or the bias of the resulting estimators of overlap measures, because there are no closed-form exact formulas for their variances and their exact sampling distributions, Monte Carlo evaluations are used. Confidence intervals for those measures are also constructed via the bootstrap method and Taylor series approximation.